# prompt_examples

example_id: lp_01K7GX91ZHTK02Y0SMXM2RQAG5_01K7GX93W9ZN1ZFW9B5XD0PAJY_APPLICATION
skills: ["Creating $x$ and $y$ tables from equations"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg"]
subtopics: ["Substitution"]
subtopic_ids: ["subtopic_01GTC0BK1MFRXZVQHRAE8ZEA4E"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Detectives
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Creating Patterns to Solve Detective Mysteries","example1Header":"Situation\nDetectives use patterns and equations to solve mysteries. They track evidence trends by creating tables of $x$ and $y$ to find connections between clues.","example1Body":"Example\nDetectives use $y = 2x + 3$ to track evidence. For $x = 0, 1, 2$, $y = 3, 5, 7$, forming the table: $x = 0, 1, 2$ and $y = 3, 5, 7$. Patterns help connect clues.","example2Header":"","example2Body":""}


example_id: lp_01K7GX91ZHTK02Y0SMXM2RQAG5_01K7GX93W9ZN1ZFW9B6H79863F_THOUGHT_SPARKER
skills: ["Creating $x$ and $y$ tables from equations"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg"]
subtopics: ["Substitution"]
subtopic_ids: ["subtopic_01GTC0BK1MFRXZVQHRAE8ZEA4E"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Detectives
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A detective is tracking a suspect's car, and the distance it travels, $y$, in kilometres is given by the equation $y = 5x + 2$, where $x$ is the time in hours.","firstSentence":"How would you organise the values of $x$ and $y$ in a table to show the car's movement over time?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to start with simple values of $x$ like $0$, $1$, and $2$.","Discuss how substituting $x$ into the equation helps calculate $y$ values accurately.","Highlight the importance of patterns and relationships between $x$ and $y$ in the table."]}


example_id: lp_01K7GX91ZHTK02Y0SMXM2RQAG5_01K7GX93W9ZN1ZFW9B6PYV751S_EXIT_TICKET
skills: ["Creating $x$ and $y$ tables from equations"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg"]
subtopics: ["Substitution"]
subtopic_ids: ["subtopic_01GTC0BK1MFRXZVQHRAE8ZEA4E"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Detectives
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$2, 4, 6$","question":"A detective finds that $y = 2x$ represents the number of clues found based on hours worked. If $x = 1$, $2$, and $3$, what are the values of $y$?"},{"answer":"$2, 3, 5$","question":"A detective uses $y = x + 3$ to track patterns. If $x = -1$, $0$, and $2$, what are the corresponding $y$ values?"},{"answer":"$-8, -2, 10$","question":"The detective deciphers $y = 3x - 2$ as the equation for a case. What are the $y$ values if $x = -2$, $0$, and $4$?"}]}


example_id: lp_01K7GX91ZHTK02Y0SMXM2RQAG5_01K7GX93W9ZN1ZFW9B6BJ6H145_CONTEMPLATIVE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg"]
subtopics: ["Substitution"]
subtopic_ids: ["subtopic_01GTC0BK1MFRXZVQHRAE8ZEA4E"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Detectives
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have the equation $y = 3x + 2$. Choose $5$ values for $x$ and create an $x$ and $y$ table. How does changing $x$ affect $y$?","teacherTips":["Encourage students to pick both positive and negative values for $x$.","Discuss the relationship between $x$ and $y$ as $x$ increases or decreases.","Help students identify the pattern in the $x$ and $y$ table."],"difficulty":"mild"}


example_id: lp_01K7GX91ZHTK02Y0SMXM2RQAG5_01K7GX93W9ZN1ZFW9B5QXAWZ3F_WARM_UP_QUESTIONS_WITH_CONTEXT
skills: ["Creating $x$ and $y$ tables from equations"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg"]
subtopics: ["Substitution"]
subtopic_ids: ["subtopic_01GTC0BK1MFRXZVQHRAE8ZEA4E"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Detectives
class_year: 7
country: AU
period_number: 7
node_type: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"You're a detective analysing a coded message. You must decode it using patterns and equations.","questions":[{"answer":"$11$","question":"The code equation is $y = 2x + 3$. If $x = 4$, what is $y$?"},{"answer":"$16$","question":"The code equation is $y = 3x - 5$. If $x = 7$, what is $y$?"},{"answer":"$3, 5, 7$","question":"The code equation is $y = x + 2$. What are the $y$ values when $x = 1$, $x = 3$, and $x = 5$?"}]}


example_id: lp_01K7GX91ZHTK02Y0SMXM2RQAG5_01K7GX93W9ZN1ZFW9B620B5HA1_ACTIVITY
skills: ["Creating $x$ and $y$ tables from equations"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg"]
subtopics: ["Substitution"]
subtopic_ids: ["subtopic_01GTC0BK1MFRXZVQHRAE8ZEA4E"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Detectives
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Delivery Route Tracker\nYour team is tracking deliveries using equations to predict routes.","scenario":"Steps\n1. Write the equation $y = 2x + 3$ on your paper.\n2. Create a table for $x = 0, 1, 2, 3, 4$ and calculate $y$ values.\n3. Repeat for $y = 3x - 1$ and $y = x^2 + 1$.\n4. Compare tables with another team to check for accuracy.\n5. The team with the most correct tables wins!","steps":["Discussion\n• What patterns did you notice in the $y$ values?\n• How do different equations affect the $x$ and $y$ relationship?","Differentiation Opportunities\n• Support: Use simpler equations like $y = x + 2$ for practice.\n• Extend: Try equations with fractions, like $y = \\frac{1}{2}x + 3$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7H5P0CPAXME4AHT98430P80_01K7H5P2322RF9K6QZFV6CYVXG_APPLICATION
skill_ids: ["SQazVgRg9UC0CgKM16yb","7a7cDcySLeLKJ2KKDpCx","LIb6lFt6ul0tJ25WFo7H"]
subtopics: ["Area Calculations"]
subtopic_ids: ["subtopic_01GTC0BG0JV20CN5NWXWK5JSJ3"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Measuring Field Areas in Farming","example1Header":"Situation\nFarmers often measure triangular sections of fields to calculate areas for planting or irrigation planning. Knowing these areas helps them distribute seeds, water, and fertilisers efficiently, ensuring no resources are wasted.","example1Body":"Example\nA triangular field section has a base of $10$ m and a height of $8$ m. Using $\\text{Area} = \\frac{1}{2} \\times \\text{base} \\times \\text{height}$: $\\frac{1}{2} \\times 10 \\times 8 = 40$ m$^2$.","example2Header":"","example2Body":""}

skills:
["Calculating the area of a triangle","Applying the formula for area of a rectangle","Calculating the area of a parallelogram"]


example_id: lp_01K7H5P0CPAXME4AHT98430P80_01K7H5P2322RF9K6QZG9HAN0HM_THOUGHT_SPARKER
skill_ids: ["SQazVgRg9UC0CgKM16yb","7a7cDcySLeLKJ2KKDpCx","LIb6lFt6ul0tJ25WFo7H"]
subtopics: ["Area Calculations"]
subtopic_ids: ["subtopic_01GTC0BG0JV20CN5NWXWK5JSJ3"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A farmer divides their land into three sections: a rectangular wheat field measuring $80$ m by $50$ m, a triangular vegetable patch with a base of $30$ m and a height of $20$ m, and a parallelogram-shaped orchard with a base of $60$ m and a height of $25$ m.","firstSentence":"How would you calculate the total area of the farm from this information?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the formulas for the area of rectangles, parallelograms, and triangles before starting.","Encourage students to break the problem into smaller parts and calculate each section separately.","Ask students to explain their reasoning for using each formula to reinforce understanding."]}

skills:
["Calculating the area of a triangle","Applying the formula for area of a rectangle","Calculating the area of a parallelogram"]


example_id: lp_01K7H5P0CPAXME4AHT98430P80_01K7H5P2322RF9K6QZFY5PEX6M_ACTIVITY
skill_ids: ["SQazVgRg9UC0CgKM16yb","7a7cDcySLeLKJ2KKDpCx","LIb6lFt6ul0tJ25WFo7H"]
subtopics: ["Area Calculations"]
subtopic_ids: ["subtopic_01GTC0BG0JV20CN5NWXWK5JSJ3"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Park Design Challenge\nYour team is designing a new park with sections shaped like rectangles, parallelograms, and triangles.","scenario":"Steps\n1. Draw $3$ sections: a rectangle ($8$ m by $5$ m), a parallelogram (base $6$ m, height $4$ m), and a triangle (base $10$ m, height $6$ m).\n2. Use formulas to calculate the area of each section: rectangle ($l \\times w$), parallelogram ($b \\times h$), triangle ($\\frac{1}{2} \\times b \\times h$).\n3. Add up the areas of all sections to find the total park area.\n4. Compare your total area with other teams and discuss the designs.\n5. Check each other’s calculations for accuracy to earn points!","steps":["Discussion\n• Which section shape gave the largest area and why?\n• How would doubling the dimensions of each section affect the total area?","Differentiation Opportunities\n• Support: Provide step-by-step examples of area formulas before starting.\n• Extend: Design an extra section with a combination of shapes and calculate its area."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating the area of a triangle","Applying the formula for area of a rectangle","Calculating the area of a parallelogram"]


example_id: lp_01K7H5P0CPAXME4AHT98430P80_01K7H5P2322RF9K6QZG871BDHF_CONTEMPLATIVE_QUESTION
skill_ids: ["SQazVgRg9UC0CgKM16yb","7a7cDcySLeLKJ2KKDpCx","LIb6lFt6ul0tJ25WFo7H"]
subtopics: ["Area Calculations"]
subtopic_ids: ["subtopic_01GTC0BG0JV20CN5NWXWK5JSJ3"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a park with a total area of $200$ m$^2$. Use rectangles, triangles, and parallelograms. How will you arrange them?","teacherTips":["Encourage students to calculate and combine areas of all shapes.","Discuss how different shapes can fit together to meet the total area.","Prompt students to justify their shape choices and arrangements."],"difficulty":"mild"}


example_id: lp_01K7H5P0CPAXME4AHT98430P80_01K7H5P2322RF9K6QZGCY504MM_EXIT_TICKET
skill_ids: ["SQazVgRg9UC0CgKM16yb","7a7cDcySLeLKJ2KKDpCx","LIb6lFt6ul0tJ25WFo7H"]
subtopics: ["Area Calculations"]
subtopic_ids: ["subtopic_01GTC0BG0JV20CN5NWXWK5JSJ3"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$50$","question":"A farmer has a rectangular field that is $10$ m long and $5$ m wide. What is the area of the field?"},{"answer":"$84$","question":"A parallelogram-shaped barn roof has a base of $12$ m and a perpendicular height of $7$ m. What is its area?"},{"answer":"$60$","question":"A farmer’s triangular paddock has a base of $15$ m and a height of $8$ m. What is its area?"}]}


example_id: lp_01K7H5XVYBJJ6PNHC2K5FXQK8Z_01K7H5XXG3T99JZZPCQJ7YAXZY_APPLICATION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Calculating Volume in 3D Printing","example1Header":"Situation\n3D printing designers check object volume to save material and reduce waste. Knowing volume ensures the right amount of plastic is used for each print.","example1Body":"Example\nA designer prints a box with dimensions $10$ cm (length), $5$ cm (width), and $4$ cm (height). The volume is $10 \\times 5 \\times 4 = 200$ cm$^3$, ensuring $200$ cm$^3$ of material is used.","example2Header":"","example2Body":""}


example_id: lp_01K7H5XVYBJJ6PNHC2K5FXQK8Z_01K7H5XXG3T99JZZPCR7V8F7V3_THOUGHT_SPARKER
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A 3D printer creates a rectangular block with dimensions of $12$ cm in length, $8$ cm in width, and $5$ cm in height.","firstSentence":"How would you determine the volume of the block created by the 3D printer?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall the formula for the volume of a rectangular prism.","Discuss the importance of using consistent units when calculating volume.","Ask students to explain why multiplying the three dimensions gives the total volume."]}


example_id: lp_01K7H5XVYBJJ6PNHC2K5FXQK8Z_01K7H5XXG3T99JZZPCQNE4K6M4_ACTIVITY
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Box Packing Challenge\nYou are packers arranging boxes for shipment. Maximise the space used!","scenario":"Steps\n1. Each team draws $3$ rectangular prisms of different sizes on paper.\n2. Label each prism’s length, width, and height (e.g., $5$ cm, $3$ cm, $2$ cm).\n3. Calculate the volume of each prism using $V = \\text{length} \\times \\text{width} \\times \\text{height}$.\n4. Add the volumes to find the total space used by your boxes.\n5. Compare totals. The team using the most space efficiently wins!","steps":["Discussion\n• How does changing one dimension affect the prism's volume?\n• What strategies helped your team maximise the space?","Differentiation Opportunities\n• Support: Use whole numbers only for dimensions (e.g., $4$, $6$, $2$).\n• Extend: Include decimal dimensions (e.g., $4.5$ cm, $3.2$ cm)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7H5XVYBJJ6PNHC2K5FXQK8Z_01K7H5XXG3T99JZZPCREQR7VAX_EXIT_TICKET
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$60$ \\text{ cm}^3","question":"A 3D printer creates a box with dimensions $5$ cm, $4$ cm, and $3$ cm. What is the volume of the box?"},{"answer":"$70$ \\text{ cm}^3","question":"A 3D printer produces a rectangular prism with dimensions $7$ cm, $5$ cm, and $2$ cm. What is the volume of the prism in cm$^3$?"},{"answer":"$600$ \\text{ cm}^3","question":"A 3D-printed block has dimensions $12.5$ cm, $8$ cm, and $6$ cm. What is its volume?"}]}


example_id: lp_01K7H5XVYBJJ6PNHC2K5FXQK8Z_01K7H5XXG3T99JZZPCR551K835_CONTEMPLATIVE_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A box measures $8$ cm long, $5$ cm wide, and $10$ cm high. How could you design a new box with the same volume but different dimensions? Explain your reasoning.","teacherTips":["Guide students to use $V = l \\times w \\times h$ to preserve the volume.","Encourage testing different combinations of $l$, $w$, and $h$.","Discuss how changes in one dimension affect the others."],"difficulty":"mild"}


example_id: lp_01K7H63QDK7Y6NPKPSBTK1SRJ4_01K7H63S0A4KBEBT5Z96K516F0_APPLICATION
skill_ids: ["gHs3hX0Le4KyarJM3gg4","HmaPtBpD9GnOyg98qjjj","fNzMZxRMkJZom1e7kkXQ"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Darts
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"The Role of Pi in Darts Scoring","example1Header":"Situation\nDarts players use circular dartboards divided into numbered sections. Understanding circles helps players strategize and estimate their scoring zones.","example1Body":"Example\nA dartboard with $r = 10$ cm has an area $A = \\pi r^2 = 3.14 \\times 10^2 = 314$ cm$^2$. Understanding $\\pi$ helps players grasp circle geometry for better scoring.","example2Header":"","example2Body":""}

skills:
["Converting between diameter and radius","Understanding what pi represents","Finding the circumference of a circle"]


example_id: lp_01K7H63QDK7Y6NPKPSBTK1SRJ4_01K7H63S0B1SE78P2NMR1REEEC_THOUGHT_SPARKER
skill_ids: ["gHs3hX0Le4KyarJM3gg4","HmaPtBpD9GnOyg98qjjj","fNzMZxRMkJZom1e7kkXQ"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Darts
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A dartboard has a circular target area with a diameter of 45 cm.","firstSentence":"How could you calculate the circumference of the dartboard using this information?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the relationship between diameter, radius, and circumference before starting the discussion.","Encourage students to explain why pi ($\\pi$) is used in the formula for circumference.","Ask students to connect their calculations to real-world scenarios, like measuring around circular objects."]}

skills:
["Converting between diameter and radius","Understanding what pi represents","Finding the circumference of a circle"]


example_id: lp_01K7H63QDK7Y6NPKPSBTK1SRJ4_01K7H63S0B1SE78P2NMWFSMC92_EXIT_TICKET
skill_ids: ["gHs3hX0Le4KyarJM3gg4","HmaPtBpD9GnOyg98qjjj","fNzMZxRMkJZom1e7kkXQ"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Darts
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3.14$","question":"In darts, the value of $\\pi$ is used to calculate measurements of circular dartboards. What is the approximate value of $\\pi$ to two decimal places?"},{"answer":"$157$","question":"A circular dartboard has a radius of $25$ cm. What is its circumference in cm if $\\pi \\approx 3.14$?"},{"answer":"$15$","question":"A dartboard has a circumference of $94.2$ cm. Using $\\pi \\approx 3.14$, what is its radius in cm?"}]}

skills:
["Converting between diameter and radius","Understanding what pi represents","Finding the circumference of a circle"]


example_id: lp_01K7H63QDK7Y6NPKPSBTK1SRJ4_01K7H63S0B1SE78P2NMKF0A1H8_CONTEMPLATIVE_QUESTION
skill_ids: ["gHs3hX0Le4KyarJM3gg4","HmaPtBpD9GnOyg98qjjj","fNzMZxRMkJZom1e7kkXQ"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Darts
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have a circular garden with a radius of $3$ m. How would you calculate its circumference? What if the radius doubled? Explain how $\\pi$ is used.","teacherTips":["Encourage students to use $C = 2\\pi r$ for the circumference.","Discuss the relationship between radius, diameter, and circumference.","Explain $\\pi$ as the ratio of circumference to diameter."],"difficulty":"mild"}


example_id: lp_01K7H63QDK7Y6NPKPSBTK1SRJ4_01K7H63S0A4KBEBT5Z9AXBGABV_ACTIVITY
skill_ids: ["gHs3hX0Le4KyarJM3gg4","HmaPtBpD9GnOyg98qjjj","fNzMZxRMkJZom1e7kkXQ"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Darts
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Circular Path Challenge\nDesign circular walking paths for a park by calculating their dimensions.","scenario":"Steps\n1. Draw $3$ circles on paper with diameters $10$ cm, $15$ cm, and $20$ cm.\n2. Label the radius and diameter of each circle.\n3. Calculate the circumference of each circle using $C = \\pi d$ or $C = 2 \\pi r$.\n4. Compare circumferences and discuss which circle is best for a short walk.\n5. Teams with accurate calculations earn points!","steps":["Discussion\n• Why does doubling the radius double the circumference?\n• How does $\\pi$ help us measure circular paths in real life?","Differentiation Opportunities\n• Support: Provide $\\pi$ as $3.14$ and use simpler diameters like $5$ cm or $10$ cm.\n• Extend: Use $\\pi$ as $\\frac{22}{7}$ and calculate areas of the circles as well."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7H6ADPFY6AQVXYSXRHNRZV9_01K7H6AF88ADC7RT45FK7MCN03_CONTEMPLATIVE_QUESTION
skill_ids: ["01JZA0D2VC55B5NY58VTEACJ8Q","01JZA0BDPYEZJWNFCTNQ9QN0BV","bHjhBjEZPCgueX8D0BpR"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Circus
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A train track crosses two parallel roads. How could you identify co-interior, alternate, and corresponding angles? Draw and label possible examples.","teacherTips":["Prompt students to sketch a diagram with parallel lines and a transversal.","Encourage identification of each angle type using clear labels.","Discuss real-world examples like roads or railways to connect concepts."],"difficulty":"mild"}

skills:
["Understanding alternate angles in transversals","Understanding co-interior angles in transversals","Understanding corresponding angles in transversals"]


example_id: lp_01K7H6ADPFY6AQVXYSXRHNRZV9_01K7H6AF88ADC7RT45FWTX774X_EXIT_TICKET
skill_ids: ["01JZA0D2VC55B5NY58VTEACJ8Q","01JZA0BDPYEZJWNFCTNQ9QN0BV","bHjhBjEZPCgueX8D0BpR"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Circus
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$60^\\circ$","question":"In a circus tent, a rope crosses two parallel bars forming corresponding angles of $60^\\circ$ and $x$. What is the value of $x$?"},{"answer":"$50^\\circ$","question":"A tightrope in a circus crosses two parallel beams, forming an alternate angle of $x = 50^\\circ$. What is the measure of the other alternate angle?"},{"answer":"$70^\\circ$","question":"A circus tent pole crosses two parallel beams, forming co-interior angles of $x$ and $110^\\circ$. What is the value of $x$?"}]}

skills:
["Understanding alternate angles in transversals","Understanding co-interior angles in transversals","Understanding corresponding angles in transversals"]


example_id: lp_01K7H6ADPFY6AQVXYSXRHNRZV9_01K7H6AF88ADC7RT45F65KMQWP_ACTIVITY
skill_ids: ["01JZA0D2VC55B5NY58VTEACJ8Q","01JZA0BDPYEZJWNFCTNQ9QN0BV","bHjhBjEZPCgueX8D0BpR"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Circus
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Angle Detectives\nYou are city planners designing new intersections. Identify angle pairs to ensure smooth traffic flow.","scenario":"Steps\n1. Draw two parallel streets and a transversal road on paper using a ruler.\n2. Label all angles formed where the transversal crosses the streets.\n3. In teams, identify co-interior, alternate, and corresponding angles.\n4. Score $1$ point for each correctly identified angle pair.\n5. Team with the highest score presents their findings to the class.","steps":["Discussion\n• Why are co-interior angles supplementary?\n• What patterns do you notice in alternate angles?","Differentiation Opportunities\n• Support: Provide hints such as marking parallel lines and the transversal with different colours.\n• Extend: Design intersections with two transversals and identify all angle pairs."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding alternate angles in transversals","Understanding co-interior angles in transversals","Understanding corresponding angles in transversals"]


example_id: lp_01K7H6ADPFY6AQVXYSXRHNRZV9_01K7H6AF88ADC7RT45FTSP3NRB_THOUGHT_SPARKER
skill_ids: ["01JZA0D2VC55B5NY58VTEACJ8Q","01JZA0BDPYEZJWNFCTNQ9QN0BV","bHjhBjEZPCgueX8D0BpR"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Circus
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a circus, two parallel tightropes are connected by a diagonal rope, forming several angles where the ropes intersect.","firstSentence":"How can you identify which pairs of angles are corresponding, alternate, or co-interior?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Use a diagram of the tightropes and label the angles to help students visualise the relationships.","Discuss the definitions of corresponding, alternate, and co-interior angles before identifying them.","Encourage students to explain their reasoning for classifying each angle relationship."]}


example_id: lp_01K7H6ADPFY6AQVXYSXRHNRZV9_01K7H6AF88ADC7RT45F4CEH6VK_APPLICATION
skill_ids: ["01JZA0D2VC55B5NY58VTEACJ8Q","01JZA0BDPYEZJWNFCTNQ9QN0BV","bHjhBjEZPCgueX8D0BpR"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Circus
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Angle Safety in Circus Performances","example1Header":"Situation\nCircus engineers design safe rigging setups for acrobats. They ensure co-interior angles on crossing cables prevent tension imbalances.","example1Body":"Example\nWhen one cable is at $120^\\circ$ with a beam, the other must be $60^\\circ$ as $120^\\circ + 60^\\circ = 180^\\circ$. This keeps the rigging safe and balanced.","example2Header":"","example2Body":""}


example_id: lp_01K7H6M18GPGM90TMJFTARVEYM_01K7H6M3C9P4VJKXTPH1RTAQFB_APPLICATION
skill_ids: ["OlanqhQiPGOmPxEaJKsi","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Building Stable Treehouse Roofs","example1Header":"Situation\nTreehouse designers ensure roofs are stable by calculating angles. A triangle-shaped roof distributes weight evenly and requires precise angle measurements.","example1Body":"Example\nFor a roof triangle with angles $70^\\circ$ and $50^\\circ$, the missing angle is $180^\\circ - 70^\\circ - 50^\\circ = 60^\\circ$, ensuring a balanced design.","example2Header":"","example2Body":""}

skills:
["Calculating the angle sum of a quadrilateral","Understanding that angles in a triangle add up to $180$ degrees"]


example_id: lp_01K7H6M18GPGM90TMJFTARVEYM_01K7H6M3C9P4VJKXTPHJPWVFT4_THOUGHT_SPARKER
skill_ids: ["OlanqhQiPGOmPxEaJKsi","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A treehouse has a triangular roof where the angles add up to $180^\\circ$, and its walls form a quadrilateral where the angles sum to $360^\\circ$.","firstSentence":"How could you use these facts to check if the angles in the treehouse design are correct?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall and explain why triangles and quadrilaterals have specific angle sums.","Ask students to sketch or visualise the treehouse to connect geometry to real-world structures.","Support reasoning by discussing how incorrect angles could affect the stability of the design."]}

skills:
["Calculating the angle sum of a quadrilateral","Understanding that angles in a triangle add up to $180$ degrees"]


example_id: lp_01K7H6M18GPGM90TMJFTARVEYM_01K7H6M3C9P4VJKXTPHCYGN1HS_CONTEMPLATIVE_QUESTION
skill_ids: ["OlanqhQiPGOmPxEaJKsi","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a quadrilateral with two angles measuring $90^\\circ$ and one angle measuring $70^\\circ$. What could the fourth angle be? Explain how you know.","teacherTips":["Remind students that the angles in a quadrilateral add up to $360^\\circ$.","Encourage students to subtract the known angles from $360^\\circ$.","Discuss how different angle combinations create different quadrilateral shapes."],"difficulty":"mild"}

skills:
["Calculating the angle sum of a quadrilateral","Understanding that angles in a triangle add up to $180$ degrees"]


example_id: lp_01K7H6M18GPGM90TMJFTARVEYM_01K7H6M3C9P4VJKXTPH3ZZ8EVY_ACTIVITY
skill_ids: ["OlanqhQiPGOmPxEaJKsi","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Angle Challenge Relay\nYour team is solving a mystery! Use angle rules to unlock clues about triangles and quadrilaterals.","scenario":"Steps\n1. Draw a triangle with angles labeled $A$, $B$, and $C$.\n2. Measure or assign angles to $A$, $B$, and $C$. Verify $A + B + C = 180^\\circ$.\n3. Draw a quadrilateral and split it into $2$ triangles with a diagonal.\n4. Calculate the angle sum of the quadrilateral by adding the triangle sums.\n5. Compare answers with other teams to solve the mystery first!","steps":["Discussion\n• Why do the angles in a triangle always add to $180^\\circ$?\n• How does splitting a quadrilateral into triangles help find its angle sum?","Differentiation Opportunities\n• Support: Provide pre-drawn shapes for measuring and calculating.\n• Extend: Explore polygons with more than $4$ sides and calculate their angle sums."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7H6M18GPGM90TMJFTARVEYM_01K7H6M3C9P4VJKXTPHRMC72GB_EXIT_TICKET
skill_ids: ["OlanqhQiPGOmPxEaJKsi","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$40^\\circ$","question":"In a treehouse design, a triangular window has angles of $60^\\circ$ and $80^\\circ$. What is the measure of the third angle?"},{"answer":"$90^\\circ$","question":"The roof of a treehouse forms a quadrilateral with angles $90^\\circ$, $80^\\circ$, and $100^\\circ$. What is the measure of the fourth angle?"},{"answer":"$30^\\circ, 60^\\circ, 90^\\circ$","question":"A triangular frame in the treehouse has angles $x$, $2x$, and $3x$. What are the measures of the three angles?"}]}


example_id: lp_01K7H6VD94BYZ8YCXR2AMWZ38H_01K7H6VET3C0QA6W868VQ6WJ24_EXIT_TICKET
skills: ["Solving proportions in worded problems"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Camels
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$25$","question":"If $2$ camels drink $50$ litres of water in a day, how many litres does $1$ camel drink in a day?"},{"answer":"$4$","question":"If $4$ camels need $80$ kg of food in $5$ days, how much food does $1$ camel need for $1$ day?"},{"answer":"$12$","question":"If $5$ camels can carry $250$ kg of goods in total, how many camels are needed to carry $600$ kg of goods?"}]}


example_id: lp_01K7H6VD94BYZ8YCXR2AMWZ38H_01K7H6VET3C0QA6W86848YJ83X_ACTIVITY
skills: ["Solving proportions in worded problems"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Camels
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Recipe Ratio Challenge\nYour team is doubling or halving recipes to help a chef prepare the perfect meal.","scenario":"Steps\n1. Write down a simple recipe with $3$ ingredients (e.g., $2$ cups of flour, $3$ eggs, $1$ cup of sugar).\n2. The teacher gives a scale factor (e.g., double, half, or one-third the recipe).\n3. In teams, calculate the new amounts for each ingredient based on the scale.\n4. Write your new recipe and check your answers with another team.\n5. Earn $1$ point for every correct calculation. Most points win!","steps":["Discussion\n• How does changing the scale factor affect the recipe?\n• What strategies helped you solve the proportions quickly?","Differentiation Opportunities\n• Support: Use whole-number scale factors (e.g., double or triple the recipe).\n• Extend: Use fractional scale factors (e.g., one-third or one-quarter the recipe)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7H6VD94BYZ8YCXR2AMWZ38H_01K7H6VET3C0QA6W868FPV806P_CONTEMPLATIVE_QUESTION
skills: ["Solving proportions in worded problems"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Camels
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A recipe uses $3$ cups of flour for $4$ servings. How would you adjust the amounts for $10$ servings?","teacherTips":["Encourage students to scale both numbers proportionally.","Ask students to explain their reasoning when adjusting the quantities.","Discuss how proportions ensure the recipe stays consistent."],"difficulty":"mild"}


example_id: lp_01K7H6VD94BYZ8YCXR2AMWZ38H_01K7H6VET3C0QA6W867ZMT27K7_APPLICATION
skills: ["Solving proportions in worded problems"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Camels
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Water Ratios in Camel Care","example1Header":"Situation\nCamel caretakers in the outback manage water rations for camels. They calculate proportions to ensure each camel gets the right amount of water.","example1Body":"Example\nEach camel drinks $90 \\div 3 = 30$ litres. For $5$ camels, caretakers calculate $30 \\times 5 = 150$ litres of water to meet their needs.","example2Header":"","example2Body":""}


example_id: lp_01K7H6VD94BYZ8YCXR2AMWZ38H_01K7H6VET3C0QA6W868PNA9ET3_THOUGHT_SPARKER
skills: ["Solving proportions in worded problems"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Camels
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a camel caravan, the ratio of adult camels to baby camels is $5:2$, and there are $35$ camels in total.","firstSentence":"How many of the camels in the caravan are adults?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to write the ratio as parts and find the total number of parts.","Guide students to connect the total number of camels to the ratio parts using division and multiplication.","Discuss real-life examples of ratios to help students understand proportional relationships."]}


example_id: lp_01K7H73R49TXE526H71GS9HGSX_01K7H73SPYWT5K0F3DPJCVKPCD_EXIT_TICKET
skills: ["Classifying triangles","Naming polygons","Understanding polygons"]
skill_ids: ["ZxI5FLl2pSSXgiznQtoR","01JZA1FWX3HE8FH36E1HYVMFAC","01JZA1H8W39BK8XPFVJRKM4BH8"]
subtopics: ["Polygons"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89NQ96NW1"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Kites
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Quadrilateral","question":"If a kite has four sides, what type of polygon is it?"},{"answer":"Acute triangle","question":"If a kite's two rods form a triangle with angles $50^\\circ$ and $60^\\circ$, what type of triangle is it?"},{"answer":"Quadrilateral","question":"A kite has diagonals that divide it into two isosceles triangles. What is the name of the polygon formed by combining four such triangles?"}]}


example_id: lp_01K7H73R49TXE526H71GS9HGSX_01K7H73SPYWT5K0F3DPCTW9WTK_CONTEMPLATIVE_QUESTION
skills: ["Classifying triangles","Naming polygons","Understanding polygons"]
skill_ids: ["ZxI5FLl2pSSXgiznQtoR","01JZA1FWX3HE8FH36E1HYVMFAC","01JZA1H8W39BK8XPFVJRKM4BH8"]
subtopics: ["Polygons"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89NQ96NW1"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Kites
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a park using polygons. Name each polygon, classify any triangles, and explain your choices.","teacherTips":["Encourage students to use a mix of polygons like triangles, quadrilaterals, and hexagons.","Ask students to classify triangles by angles (acute, obtuse, right) and sides.","Discuss how the shapes' properties affect the design of the park."],"difficulty":"mild"}


example_id: lp_01K7H73R49TXE526H71GS9HGSX_01K7H73SPYWT5K0F3DNX0P0NN1_ACTIVITY
skills: ["Classifying triangles","Naming polygons","Understanding polygons"]
skill_ids: ["ZxI5FLl2pSSXgiznQtoR","01JZA1FWX3HE8FH36E1HYVMFAC","01JZA1H8W39BK8XPFVJRKM4BH8"]
subtopics: ["Polygons"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89NQ96NW1"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Kites
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Polygon Logo Challenge\nYour team is designing a logo for a sports team using polygons and triangles.","scenario":"Steps\n1. Draw at least $3$ polygons (e.g., a pentagon, hexagon, octagon) on paper.\n2. Add $3$ triangles, ensuring they are different types (e.g., scalene, right-angled).\n3. Label each shape with its name and classify all triangles.\n4. Explain your design to the class, focusing on the properties of the shapes.\n5. Vote on the most creative and accurate logo!","steps":["Discussion\n• How do the number of sides help in naming polygons?\n• Why is it important to classify triangles accurately?","Differentiation Opportunities\n• Support: Provide a list of polygons and triangle types to guide the design.\n• Extend: Incorporate irregular polygons and justify their inclusion in the logo."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7H73R49TXE526H71GS9HGSX_01K7H73SPYWT5K0F3DNRQTYPCC_APPLICATION
skills: ["Classifying triangles","Naming polygons","Understanding polygons"]
skill_ids: ["ZxI5FLl2pSSXgiznQtoR","01JZA1FWX3HE8FH36E1HYVMFAC","01JZA1H8W39BK8XPFVJRKM4BH8"]
subtopics: ["Polygons"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89NQ96NW1"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Kites
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Designing Kite Shapes with Triangles","example1Header":"Situation\nKite designers use triangles to plan stable and visually appealing kite shapes. Different triangle types affect the kite's flight and appearance.","example1Body":"Example\nKite designers classify triangles to balance shape. A $60^\\circ$, $60^\\circ$, $60^\\circ$ triangle is equilateral. A $90^\\circ$, $60^\\circ$, $30^\\circ$ triangle is scalene due to differing side lengths.","example2Header":"","example2Body":""}


example_id: lp_01K7H73R49TXE526H71GS9HGSX_01K7H73SPYWT5K0F3DPGY7N2R7_THOUGHT_SPARKER
skills: ["Classifying triangles","Naming polygons","Understanding polygons"]
skill_ids: ["ZxI5FLl2pSSXgiznQtoR","01JZA1FWX3HE8FH36E1HYVMFAC","01JZA1H8W39BK8XPFVJRKM4BH8"]
subtopics: ["Polygons"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89NQ96NW1"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Kites
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A kite has a diamond-like shape made of two triangles placed together, and the angles where the two triangles meet can vary.","firstSentence":"How could you identify and classify the triangles that make up the kite's shape?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to discuss different types of triangles (isosceles, scalene, equilateral).","Use diagrams of kites to help students visualise and label the triangles.","Discuss how angle measurements and side lengths help classify triangles."]}


example_id: lp_01K7HDMCGAKSW1CMC3QHPKRFCA_01K7HDMEJV4W3SG3XWZYJWKCEX_EXIT_TICKET
skill_ids: ["PDMK31LsJTBBdlsqNrVr","bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Spiderman
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$(-3, 2)$","question":"Spiderman sees his reflection across the $y$-axis while swinging from $(3, 2)$. Where is his reflected position?"},{"answer":"$(4, 3)$","question":"Spiderman places a tracker at $(4, -3)$. Where will the tracker appear if reflected across the $x$-axis?"},{"answer":"$(2, 4), (6, 8), (10, 12)$","question":"Spiderman enlarges a triangular web with vertices at $(1, 2)$, $(3, 4)$, and $(5, 6)$ by a scale factor of $2$. Where are the new vertices?"}]}

skills:
["Identifying reflections of shapes","Reflecting objects across the $x$-axis or the $y$-axis","Identifying dilated shapes"]


example_id: lp_01K7HDMCGAKSW1CMC3QHPKRFCA_01K7HDMEJV4W3SG3XWZRW8DZMV_CONTEMPLATIVE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Spiderman
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Draw a shape in one quadrant. Reflect it across the $x$-axis and then the $y$-axis. How does it change?","teacherTips":["Encourage students to note changes in coordinates after each reflection.","Discuss how reflections affect position but not size or shape.","Help students visualise symmetry across axes."],"difficulty":"mild"}

skills:
["Identifying reflections of shapes","Reflecting objects across the $x$-axis or the $y$-axis","Identifying dilated shapes"]


example_id: lp_01K7HDMCGAKSW1CMC3QHPKRFCA_01K7HDMEJV4W3SG3XWZB9MM6DT_ACTIVITY
skill_ids: ["PDMK31LsJTBBdlsqNrVr","bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Spiderman
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Shape Flip Challenge\nYou're a designer creating symmetrical patterns using reflections and dilations!","scenario":"Steps\n1. Draw a simple shape (e.g., triangle, square) on graph paper.\n2. Reflect your shape across the $x$-axis and label the new coordinates.\n3. Reflect the original shape across the $y$-axis and label coordinates.\n4. Dilate the original shape by a factor of $2$ and redraw it.\n5. Compare your transformed shapes and check for accuracy in teams.","steps":["Discussion\n• What patterns do you notice in the reflected coordinates?\n• How does dilation affect the size and angles of shapes?","Differentiation Opportunities\n• Support: Use smaller shapes and reflect only across one axis at a time.\n• Extend: Combine reflections and dilations in a single transformation sequence."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Identifying reflections of shapes","Reflecting objects across the $x$-axis or the $y$-axis","Identifying dilated shapes"]


example_id: lp_01K7HDMCGAKSW1CMC3QHPKRFCA_01K7HDMEJV4W3SG3XWZ7RBMPHH_APPLICATION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Spiderman
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Shape Reflections in Spiderman's Web Design","example1Header":"Situation\nSpiderman engineers his webs for precision and symmetry. When creating web patterns between buildings, he uses reflections to ensure balance and strength.","example1Body":"Example\nSpiderman's web triangle at $(2, 3)$, $(4, 7)$, $(6, 3)$ reflects over the $y$-axis, becoming $(-2, 3)$, $(-4, 7)$, $(-6, 3)$ for a symmetrical web.","example2Header":"","example2Body":""}


example_id: lp_01K7HDMCGAKSW1CMC3QHPKRFCA_01K7HDMEJV4W3SG3XWZW9HC28R_THOUGHT_SPARKER
skill_ids: ["PDMK31LsJTBBdlsqNrVr","bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Spiderman
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Spiderman swings through the city, leaving a web pattern shaped like a triangle. The vertices of the triangle are at $(3,2)$, $(-2,4)$, and $(1,-3)$.","firstSentence":"How could you identify the triangle's reflection across the $x$-axis?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to visualise the reflection using graph paper or digital tools.","Discuss how the $x$-coordinate and $y$-coordinate change during a reflection over the $x$-axis.","Ask students to verify their results by comparing distances from the axis before and after reflection."]}


example_id: lp_01K7HDZTA0VAR2E14X6AMD9CWR_01K7HDZW7N60HF8CS4GBM2Q37H_APPLICATION
skill_ids: ["01JZA3DBFRQ97FVS5Q7YSJ1KT5","01JZA3ENXAHF0GVQ3QNRJFJNE9","01JZA3EBMPZRDWSEMAERDXS41Z"]
subtopics: ["Classifying Shapes"]
subtopic_ids: ["subtopic_01GTC0BBR6D9ZYXAK2BFQ59WB4"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Flowers
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Identifying Trapeziums in Floral Garden Design","example1Header":"Situation\nLandscape designers use geometric shapes when planning flowerbeds. Trapeziums are great for unique patterns in gardens, blending symmetry and creativity.","example1Body":"Example\nA flowerbed with sides $8$ m, $5$ m, $8$ m, and $10$ m is a trapezium because only the two $8$ m sides are parallel, fulfilling the definition.","example2Header":"","example2Body":""}

skills:
["Describing relationships between quadrilaterals","Characterising a trapezium","Characterising a kite"]


example_id: lp_01K7HDZTA0VAR2E14X6AMD9CWR_01K7HDZW7N60HF8CS4H180P9Z6_THOUGHT_SPARKER
skill_ids: ["01JZA3DBFRQ97FVS5Q7YSJ1KT5","01JZA3ENXAHF0GVQ3QNRJFJNE9","01JZA3EBMPZRDWSEMAERDXS41Z"]
subtopics: ["Classifying Shapes"]
subtopic_ids: ["subtopic_01GTC0BBR6D9ZYXAK2BFQ59WB4"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Flowers
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a flower garden, one arrangement of flowers forms the shape of a kite, with two pairs of adjacent sides of equal length, while another forms a trapezium with one pair of parallel sides measuring 4 m and 6 m.","firstSentence":"Why can the kite and trapezium be classified as quadrilaterals based on their side lengths and angles?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall the definition of quadrilaterals and their subcategories.","Use diagrams of the flower arrangements to help students visualize the shapes.","Ask students to compare the side lengths and angles to justify the classifications."]}

skills:
["Describing relationships between quadrilaterals","Characterising a trapezium","Characterising a kite"]


example_id: lp_01K7HDZTA0VAR2E14X6AMD9CWR_01K7HDZW7N60HF8CS4GW6XE0WK_CONTEMPLATIVE_QUESTION
skill_ids: ["01JZA3DBFRQ97FVS5Q7YSJ1KT5","01JZA3ENXAHF0GVQ3QNRJFJNE9","01JZA3EBMPZRDWSEMAERDXS41Z"]
subtopics: ["Classifying Shapes"]
subtopic_ids: ["subtopic_01GTC0BBR6D9ZYXAK2BFQ59WB4"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Flowers
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a quadrilateral park. How can you use a kite or trapezium shape? Describe their properties.","teacherTips":["Ask students to explain why their chosen shape fits the park's purpose.","Encourage discussion on parallel sides or symmetry in their design.","Prompt connections between the shapes' properties and real-world uses."],"difficulty":"mild"}

skills:
["Describing relationships between quadrilaterals","Characterising a trapezium","Characterising a kite"]


example_id: lp_01K7HDZTA0VAR2E14X6AMD9CWR_01K7HDZW7N60HF8CS4H2FCVAF0_EXIT_TICKET
skill_ids: ["01JZA3DBFRQ97FVS5Q7YSJ1KT5","01JZA3ENXAHF0GVQ3QNRJFJNE9","01JZA3EBMPZRDWSEMAERDXS41Z"]
subtopics: ["Classifying Shapes"]
subtopic_ids: ["subtopic_01GTC0BBR6D9ZYXAK2BFQ59WB4"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Flowers
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$360^\\circ$","question":"A flower garden has a kite-shaped path with two pairs of equal adjacent sides. What is the sum of the interior angles?"},{"answer":"$80^\\circ$","question":"A flowerbed in the shape of a trapezium has one pair of parallel sides. If its angles are $80^\\circ$, $100^\\circ$, and $100^\\circ$, what is the fourth angle?"},{"answer":"Isosceles trapezium","question":"If a trapezium-shaped flower bed has parallel sides of $10$ m and $6$ m, and non-parallel sides of equal length, what type of trapezium is it?"}]}


example_id: lp_01K7HDZTA0VAR2E14X6AMD9CWR_01K7HDZW7N60HF8CS4GGPAF48P_ACTIVITY
skill_ids: ["01JZA3DBFRQ97FVS5Q7YSJ1KT5","01JZA3ENXAHF0GVQ3QNRJFJNE9","01JZA3EBMPZRDWSEMAERDXS41Z"]
subtopics: ["Classifying Shapes"]
subtopic_ids: ["subtopic_01GTC0BBR6D9ZYXAK2BFQ59WB4"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Flowers
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Quadrilateral Quest\nYour team is on a quest to identify and create kites and trapeziums correctly!","scenario":"Steps\n1. Draw $4$ quadrilaterals of your choice on paper using a ruler.\n2. Swap your drawings with another team to classify their shapes.\n3. Check if each shape is a kite or trapezium based on its properties.\n4. Score $1$ point for each correct classification and explain your reasoning.\n5. The team with the most points wins the quest!","steps":["Discussion\n• What makes a kite different from a trapezium?\n• Why are symmetry and parallel sides important in classification?","Differentiation Opportunities\n• Support: Provide examples of kites and trapeziums for reference during the activity.\n• Extend: Challenge teams to create irregular quadrilaterals that fit neither category."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HE6QQVP9JWB8KY2BJME84D_01K7HE6SPTV3192VAV9DKPF43X_ACTIVITY
skills: ["Calculating the mean","Finding the mode","Finding the median"]
skill_ids: ["koijWmj27uJSkzJwd8R5","FBdt1Ik4ATJRioMa3oIf","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Handball
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Basketball Stats Challenge\nYour team is analysing basketball scores to find the Most Valuable Player (MVP).","scenario":"Steps\n1. In a group, create $10$ fictional basketball scores (e.g., $12$, $15$, $20$).\n2. Organise the scores in ascending order on your paper.\n3. Find the mean, median, and mode of the scores.\n4. Discuss which measure best represents player performance.\n5. Share your group's MVP choice and reasoning with the class.","steps":["Discussion\n• Why might the mean not always represent player performance accurately?\n• How does the mode help identify trends in the scores?","Differentiation Opportunities\n• Support: Use $5$ scores instead of $10$ for simpler calculations.\n• Extend: Add $5$ more scores and compare how the measures change."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HE6QQVP9JWB8KY2BJME84D_01K7HE6SPTV3192VAV9REBZ1CY_CONTEMPLATIVE_QUESTION
skills: ["Calculating the mean","Finding the mode","Finding the median"]
skill_ids: ["koijWmj27uJSkzJwd8R5","FBdt1Ik4ATJRioMa3oIf","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Handball
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You recorded the ages of $10$ people in a park: $5, 12, 8, 12, 15, 8, 10, 12, 7, 8$. How would you find the mean, mode, and median? What do these tell you about the group?","teacherTips":["Guide students to add all values and divide by $10$ for the mean.","Encourage finding the most frequent value for the mode.","Explain ordering data to find the middle value for the median."],"difficulty":"mild"}


example_id: lp_01K7HE6QQVP9JWB8KY2BJME84D_01K7HE6SPTV3192VAVA1EHJCTJ_EXIT_TICKET
skills: ["Calculating the mean","Finding the mode","Finding the median"]
skill_ids: ["koijWmj27uJSkzJwd8R5","FBdt1Ik4ATJRioMa3oIf","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Handball
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$","question":"In a handball tournament, the number of goals scored by a player in 5 games is $3, 3, 5, 2, 3$. What is the mode?"},{"answer":"$8$","question":"The scores of a handball team in 5 games are $7, 12, 10, 6, 8$. What is the median score?"},{"answer":"$10$","question":"If a handball player scored $9, 7, 15, 11, 8$ goals in 5 matches, what is their mean score?"}]}


example_id: lp_01K7HE6QQVP9JWB8KY2BJME84D_01K7HE6SPTV3192VAV97V6YQ1F_APPLICATION
skills: ["Calculating the mean","Finding the mode","Finding the median"]
skill_ids: ["koijWmj27uJSkzJwd8R5","FBdt1Ik4ATJRioMa3oIf","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Handball
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Using Averages in Handball Performance","example1Header":"Situation\nHandball coaches track players' scoring performance. They calculate the mean goals per game to assess consistency and plan strategies.","example1Body":"Example\nA player scored $3$, $5$, $4$, $6$, and $2$ goals in $5$ games. The mean is calculated as $(3+5+4+6+2) \\div 5 = 20 \\div 5 = 4$ goals per game.","example2Header":"","example2Body":""}


example_id: lp_01K7HE6QQVP9JWB8KY2BJME84D_01K7HE6SPTV3192VAV9XB1AM3Z_THOUGHT_SPARKER
skills: ["Calculating the mean","Finding the mode","Finding the median"]
skill_ids: ["koijWmj27uJSkzJwd8R5","FBdt1Ik4ATJRioMa3oIf","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Handball
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a handball tournament, a player scored $5$, $8$, $8$, $10$, $6$, $5$, and $7$ goals over $7$ games.","firstSentence":"How could you use this data to identify the mode, median, and mean of their scores?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to describe each type of average before performing calculations.","Encourage visual organisation of the data, like sorting the scores in order.","Discuss why each type of average might be useful in understanding the player's performance."]}


example_id: lp_01K7HECY16ZF1FEZRV1XNDAT7E_01K7HECZJS3CD071P5RQ3MFNS5_THOUGHT_SPARKER
skill_ids: ["mW7LBBlIZ2ve3VXG49eB","8AeE3xcn5UYmYk1zdxmv","8SfCl3NwNnJpsH1MZDWJ"]
subtopics: ["Stem \u0026 Leaf Plots"]
subtopic_ids: ["subtopic_01GTC0BC5N4Y9ZNHQ0Q1PXZ9XB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A car dealership tracks the speeds of $20$ cars during a test drive and creates a stem-and-leaf plot to show the speeds in km/h. They also create a split stem-and-leaf plot to better display the data, where $40$–$44$ km/h and $45$–$49$ km/h are separated.","firstSentence":"How does splitting the stems make the data easier to interpret?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to compare a regular stem-and-leaf plot with a split one to see the difference.","Discuss how splitting stems can highlight clusters or gaps in the data.","Ask students to identify patterns or trends that might be hidden in an unsplit plot."]}

skills:
["Interpreting stem and leaf plots","Interpreting dot plots","Understanding split stem and leaf plots"]


example_id: lp_01K7HECY16ZF1FEZRV1XNDAT7E_01K7HECZJS3CD071P5QX2VW2NK_APPLICATION
skill_ids: ["mW7LBBlIZ2ve3VXG49eB","8AeE3xcn5UYmYk1zdxmv","8SfCl3NwNnJpsH1MZDWJ"]
subtopics: ["Stem \u0026 Leaf Plots"]
subtopic_ids: ["subtopic_01GTC0BC5N4Y9ZNHQ0Q1PXZ9XB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Understanding Car Preferences with Dot Plots","example1Header":"Situation\nCar sales analysts use dot plots to study customer preferences, like the number of cars sold in different colours or models. This helps them stock the most popular options.","example1Body":"Example\nA dot plot shows $8$ dots for red, $5$ for blue, and $7$ for black cars sold in a week. Total cars: $8 + 5 + 7 = 20$. Red is the most popular colour with $8$ cars.","example2Header":"","example2Body":""}

skills:
["Interpreting stem and leaf plots","Interpreting dot plots","Understanding split stem and leaf plots"]


example_id: lp_01K7HECY16ZF1FEZRV1XNDAT7E_01K7HECZJS3CD071P5R4KFXA44_ACTIVITY
skill_ids: ["mW7LBBlIZ2ve3VXG49eB","8AeE3xcn5UYmYk1zdxmv","8SfCl3NwNnJpsH1MZDWJ"]
subtopics: ["Stem \u0026 Leaf Plots"]
subtopic_ids: ["subtopic_01GTC0BC5N4Y9ZNHQ0Q1PXZ9XB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Data Detective Challenge\nYou're data detectives helping a sports team analyse their scores from a season!","scenario":"Steps\n1. Work in teams and copy this data set: $12, 15, 12, 18, 14, 15, 12, 18, 16$.\n2. Create a dot plot to represent the data set on a number line.\n3. Convert the data into a stem-and-leaf plot, showing tens and ones.\n4. Analyse both plots to find the most common score and range.\n5. Compare your findings with other teams to check accuracy.","steps":["Discussion\n• Which plot made it easier to find the most common score?\n• What does the range of scores tell you about the team's performance?","Differentiation Opportunities\n• Support: Provide a partially completed dot plot for students to fill in.\n• Extend: Ask students to calculate the mean and median of the data set."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Interpreting stem and leaf plots","Interpreting dot plots","Understanding split stem and leaf plots"]


example_id: lp_01K7HECY16ZF1FEZRV1XNDAT7E_01K7HECZJS3CD071P5RGZHM1RY_CONTEMPLATIVE_QUESTION
skill_ids: ["mW7LBBlIZ2ve3VXG49eB","8AeE3xcn5UYmYk1zdxmv","8SfCl3NwNnJpsH1MZDWJ"]
subtopics: ["Stem \u0026 Leaf Plots"]
subtopic_ids: ["subtopic_01GTC0BC5N4Y9ZNHQ0Q1PXZ9XB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a dot plot for your class's favourite sport. How would you describe the data's shape?","teacherTips":["Encourage students to collect data from classmates.","Discuss terms like 'symmetry' or 'clusters' in the dot plot.","Ask students to explain what the dot plot says about preferences."],"difficulty":"mild"}


example_id: lp_01K7HECY16ZF1FEZRV1XNDAT7E_01K7HECZJS3CD071P5RVGH8EJB_EXIT_TICKET
skill_ids: ["mW7LBBlIZ2ve3VXG49eB","8AeE3xcn5UYmYk1zdxmv","8SfCl3NwNnJpsH1MZDWJ"]
subtopics: ["Stem \u0026 Leaf Plots"]
subtopic_ids: ["subtopic_01GTC0BC5N4Y9ZNHQ0Q1PXZ9XB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$","question":"A dot plot shows the number of cars sold each day: $5$ dots on day $1$, $3$ dots on day $2$, and $4$ dots on day $3$. How many cars were sold on day $2$?"},{"answer":"$10\\,800$","question":"A stem and leaf plot shows car prices in thousands: Stem $10$ has leaves $1, 4, 8$. What is the highest car price?"},{"answer":"$9$","question":"A split stem and leaf plot for car speeds has stem $6$ with leaves $0, 3, 7$ and $6$ with leaves $8, 9$. What is the range of speeds?"}]}


example_id: lp_01K7HEZ1KE2Z561JCK39YYR399_01K7HEZ3HJA6YTVYPYR3N5H9SD_CONTEMPLATIVE_QUESTION
skill_ids: ["ALab4phdNMllkBAJt0tX","01JZH1GE4CYWBVDVXGD9W7D0D4","ySb9hd3IfMVaUIgTgFxy"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Ice Hockey
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You measure heights of plants daily for 2 weeks. How would you record this data? What graph best shows growth?","teacherTips":["Discuss why plant height is continuous data.","Suggest a frequency table for organising the data.","Explain why a line graph shows growth trends effectively."],"difficulty":"mild"}

skills:
["Identifying the most effective way to display data","Analysing and creating frequency tables with continuous data","Distinguishing between discrete and continuous data"]


example_id: lp_01K7HEZ1KE2Z561JCK39YYR399_01K7HEZ3HJA6YTVYPYQRNJ9GAQ_ACTIVITY
skill_ids: ["ALab4phdNMllkBAJt0tX","01JZH1GE4CYWBVDVXGD9W7D0D4","ySb9hd3IfMVaUIgTgFxy"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Ice Hockey
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Track Time Data Dive\nYou're timing classmates' $100$ m sprints and analysing the results!","scenario":"Steps\n1. In groups, each member runs $100$ m while others time them (to $0.1$ s).\n2. Record all times in a list, then group them into intervals (e.g., $12.0$-$12.5$ s).\n3. Create a frequency table showing the intervals and their frequencies.\n4. Analyse the table: What is the most common time range?\n5. Discuss if the data is continuous or discrete and explain why.","steps":["Discussion\n• Why is sprint time considered continuous data?\n• How does grouping data into intervals help in analysis?","Differentiation Opportunities\n• Support: Pre-define intervals for the frequency table (e.g., $12.0$-$12.5$ s).\n• Extend: Create a histogram using the frequency table to visualise the data."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Identifying the most effective way to display data","Analysing and creating frequency tables with continuous data","Distinguishing between discrete and continuous data"]


example_id: lp_01K7HEZ1KE2Z561JCK39YYR399_01K7HEZ3HJA6YTVYPYRDGHSP94_EXIT_TICKET
skill_ids: ["ALab4phdNMllkBAJt0tX","01JZH1GE4CYWBVDVXGD9W7D0D4","ySb9hd3IfMVaUIgTgFxy"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Ice Hockey
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Discrete","question":"In ice hockey, the number of goals scored by a team in a match is an example of what type of data: discrete or continuous?"},{"answer":"Histogram","question":"Which graph is most effective for showing the distribution of players' heights in an ice hockey team: a bar graph or a histogram?"},{"answer":"$2$","question":"An ice hockey player's skating speeds (in km/h) are recorded as $24.1$, $25.3$, $24.8$, $26.0$, and $25.1$. How many values fall in the interval $24.0-25.0$?"}]}

skills:
["Identifying the most effective way to display data","Analysing and creating frequency tables with continuous data","Distinguishing between discrete and continuous data"]


example_id: lp_01K7HEZ1KE2Z561JCK39YYR399_01K7HEZ3HJA6YTVYPYR7M9YRZM_THOUGHT_SPARKER
skill_ids: ["ALab4phdNMllkBAJt0tX","01JZH1GE4CYWBVDVXGD9W7D0D4","ySb9hd3IfMVaUIgTgFxy"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Ice Hockey
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The heights of players on an ice hockey team are measured in centimetres and recorded as follows: $165$, $170$, $172$, $175$, $175$, $180$, $182$, $185$, $188$, $190$.","firstSentence":"What type of graph would best display this data and why?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the difference between discrete and continuous data to clarify why height is continuous.","Encourage students to consider the strengths and weaknesses of different graphs (e.g., bar graphs, histograms, line graphs).","Use real-world examples to explain why certain graphs are more effective for continuous data."]}


example_id: lp_01K7HEZ1KE2Z561JCK39YYR399_01K7HEZ3HJA6YTVYPYQKQEK66T_APPLICATION
skill_ids: ["ALab4phdNMllkBAJt0tX","01JZH1GE4CYWBVDVXGD9W7D0D4","ySb9hd3IfMVaUIgTgFxy"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Ice Hockey
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Tracking Player Statistics in Ice Hockey","example1Header":"Situation\nIce hockey analysts classify player statistics into categories like goals scored (discrete) or ice time in minutes (continuous) for performance tracking.","example1Body":"Example\nAnalysts classify goals scored (e.g., $0$, $1$, $2$) as discrete since they are whole numbers. Ice time (e.g., $12.5$ or $15.3$ minutes) is continuous because it includes fractions.","example2Header":"","example2Body":""}


example_id: lp_01K7HF69WX2GSTGYWBGBKVXBPV_01K7HF6BX86XZ44SA5BABBFX45_CONTEMPLATIVE_QUESTION
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","ux8pYd1mCi62lCuhatJf","IWRYFhp62mlkdsnyBsUl"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Pickleball
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You toss a coin and roll a die. How would you represent the sample space using a tree diagram? What is the expected frequency of rolling a $4$ if you repeat this $30$ times?","teacherTips":["Encourage students to label all branches in the tree diagram clearly.","Explain that the sample space lists all combinations, e.g., Heads-$1$, Tails-$2$.","Guide them to calculate $\\frac{1}{6}$ of $30$ to find the expected frequency of rolling a $4$."],"difficulty":"mild"}

skills:
["Calculating the expected frequency of a result","Understanding what sample space represents","Representing sample space using a tree diagram"]


example_id: lp_01K7HF69WX2GSTGYWBGBKVXBPV_01K7HF6BX86XZ44SA5BM3XPR64_EXIT_TICKET
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","ux8pYd1mCi62lCuhatJf","IWRYFhp62mlkdsnyBsUl"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Pickleball
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"High-left, high-right, low-left, low-right","question":"In pickleball, if a player serves either a high or low serve, and the opponent returns either left or right, what does the sample space represent?"},{"answer":"$6$","question":"If a pickleball player serves either short or long and their opponent can return as a drop shot, a lob, or a drive, how many outcomes are there?"},{"answer":"$20$","question":"A pickleball player serves $50$ times. If their opponent returns $40\\%$ as a lob, how many lob returns should be expected?"}]}

skills:
["Calculating the expected frequency of a result","Understanding what sample space represents","Representing sample space using a tree diagram"]


example_id: lp_01K7HF69WX2GSTGYWBGBKVXBPV_01K7HF6BX86XZ44SA5AWEDDE07_ACTIVITY
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","ux8pYd1mCi62lCuhatJf","IWRYFhp62mlkdsnyBsUl"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Pickleball
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Probability Tree Challenge\nYour team is predicting outcomes of coin flips and dice rolls in a fun probability game!","scenario":"Steps\n1. Flip a coin and roll a die. Note the possible outcomes like $(H, 1)$, $(T, 2)$.\n2. Draw a tree diagram for all outcomes of flipping a coin and rolling a die.\n3. Count the total possible outcomes in your tree diagram.\n4. Choose an event (e.g., rolling $4$ or flipping heads) and calculate its probability.\n5. Use the probability to find the expected frequency for $30$ trials.","steps":["Discussion\n• How does the tree diagram help in listing all possible outcomes?\n• Why is expected frequency useful in predicting real-world events?","Differentiation Opportunities\n• Support: Use only a coin flip and a $4$-sided die to simplify the tree diagram.\n• Extend: Add a second coin flip and calculate probabilities with more outcomes."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating the expected frequency of a result","Understanding what sample space represents","Representing sample space using a tree diagram"]


example_id: lp_01K7HF69WX2GSTGYWBGBKVXBPV_01K7HF6BX86XZ44SA5BG9YK69G_THOUGHT_SPARKER
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","ux8pYd1mCi62lCuhatJf","IWRYFhp62mlkdsnyBsUl"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Pickleball
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a doubles pickleball match, each of the two players on Team A can either win or lose their game, and the same goes for the two players on Team B.","firstSentence":"How would you represent all the possible outcomes of these games using a tree diagram?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to start with one player's outcomes and build step by step.","Discuss what the complete sample space represents in terms of the match results.","Ask students how they could use the tree diagram to identify specific outcomes or calculate probabilities."]}


example_id: lp_01K7HF69WX2GSTGYWBGBKVXBPV_01K7HF6BX86XZ44SA5ATSVTZWM_APPLICATION
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","ux8pYd1mCi62lCuhatJf","IWRYFhp62mlkdsnyBsUl"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Pickleball
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Planning Pickleball Strategies with Probability","example1Header":"Situation\nPickleball coaches use probability to prepare game strategies. They consider all possible outcomes in a rally to decide the best game plan.","example1Body":"Example\nA sample space for a pickleball rally could be: opponent misses the serve, opponent returns but server wins, or opponent returns but server loses. This gives 3 clear outcomes.","example2Header":"","example2Body":""}


example_id: lp_01K7HFCTT4JXZXMAM4YN6Q86DX_01K7HFCWJETTEVXCM6MFFG11BR_APPLICATION
skill_ids: ["epyyn8wG9aa0qbIvsxmE","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Badminton
class_year: 7
country: AU
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Serving Strategy in Badminton Using Probability","example1Header":"Situation\nProfessional badminton players use probability to decide their serving strategies. They assess the likelihood of winning a point with different types of serves, improving their chances of success.","example1Body":"Example\nA player's high-serve probability is $6/10 = 0.6$. For low serves, it's $3/10 = 0.3$. High serves are more effective since $0.6 \u003e 0.3$.","example2Header":"","example2Body":""}

skills:
["Understanding that probabilities are represented as numbers between $0$ and $1$","Finding probability from experiments"]


example_id: lp_01K7HFCTT4JXZXMAM4YN6Q86DX_01K7HFCWJFZKSV1CGKHEC5JHAM_THOUGHT_SPARKER
skill_ids: ["epyyn8wG9aa0qbIvsxmE","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Badminton
class_year: 7
country: AU
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A badminton player serves $50$ times in practice, and $35$ of those serves land inside the service area.","firstSentence":"How could you use this data to estimate the probability of the player serving successfully?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the connection between experimental outcomes and probability as a fraction or decimal.","Encourage students to explain why the probability must be a number between $0$ and $1$.","Ask students to compare this estimate to what might happen in future games to explore variability."]}

skills:
["Understanding that probabilities are represented as numbers between $0$ and $1$","Finding probability from experiments"]


example_id: lp_01K7HFCTT4JXZXMAM4YN6Q86DX_01K7HFCWJFZKSV1CGKHASNCGZF_CONTEMPLATIVE_QUESTION
skill_ids: ["epyyn8wG9aa0qbIvsxmE","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Badminton
class_year: 7
country: AU
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip a coin $50$ times and record the outcomes. How would you calculate the probability of landing heads? What might happen if you repeat the experiment another $50$ times? Explain your reasoning.","teacherTips":["Encourage students to divide heads outcomes by total flips to find probability.","Discuss how results may vary with repeated experiments.","Highlight that probabilities are always between $0$ and $1$."],"difficulty":"mild"}

skills:
["Understanding that probabilities are represented as numbers between $0$ and $1$","Finding probability from experiments"]


example_id: lp_01K7HFCTT4JXZXMAM4YN6Q86DX_01K7HFCWJFZKSV1CGKHHKZ6SG4_EXIT_TICKET
skill_ids: ["epyyn8wG9aa0qbIvsxmE","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Badminton
class_year: 7
country: AU
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0$","question":"If the shuttlecock in badminton has no chance of landing outside the court, what is its probability of landing outside the court?"},{"answer":"$0.7$","question":"In $10$ badminton serves, a player hits $7$ successful serves. What is the experimental probability of a successful serve?"},{"answer":"$0.64$","question":"In $50$ badminton rallies, the shuttlecock lands on Player A's side $18$ times. What is the probability it does not land on Player A's side?"}]}


example_id: lp_01K7HFCTT4JXZXMAM4YN6Q86DX_01K7HFCWJETTEVXCM6MMPQKEBQ_ACTIVITY
skill_ids: ["epyyn8wG9aa0qbIvsxmE","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Badminton
class_year: 7
country: AU
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Probability Dice Challenge\nRoll dice, record outcomes, and calculate probabilities for a fun experiment!","scenario":"Steps\n1. In teams, roll a six-sided die $30$ times and record each outcome.\n2. Count how many times each number appears in your results.\n3. Calculate the experimental probability for each number (e.g., $P(3) = \\frac{\\text{frequency of } 3}{30}$).\n4. Compare your probabilities to the theoretical probability of $\\frac{1}{6}$.\n5. Discuss why your results might differ from the theoretical values.","steps":["Discussion\n• What does it mean if a probability is close to $0$ or $1$?\n• Why might experimental probabilities differ from theoretical ones?","Differentiation Opportunities\n• Support: Roll the die $15$ times instead of $30$ to simplify calculations.\n• Extend: Use two dice and calculate probabilities for sums (e.g., $P(7)$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HHERKGDFDX8GZ2QQQV29SZ_01K7HHET86X6Y5TSC49SHGTZRD_CONTEMPLATIVE_QUESTION
skill_ids: ["yU7IYhTRPNqzric6XAml","xk3vzmJzOkW3w4xL2Qvl","e6aOh6pP1sA7mcKMc0pI"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Recycling
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create three different expressions using the laws $a^m \\times a^n = a^{m+n}$, $a^m \\div a^n = a^{m-n}$, and $(a^m)^n = a^{m \\times n}$. Show how they simplify. How does $a^0 = 1$ apply if $m = n$?","teacherTips":["Encourage students to choose their own values for $a$, $m$, and $n$.","Discuss how $a^0 = 1$ is derived using $a^m \\div a^n = a^{m-n}$.","Check that students simplify each expression step-by-step."],"difficulty":"mild"}

skills:
["Understanding the index law $(a^m)^n = (a^n)^m = a^{m \\times n}$","Understanding the index laws $a^m \\times a^n = a^{m+n}$ and $a^m \\div a^n = a^{m-n}$","Understanding the index law $a^0 = 1$"]


example_id: lp_01K7HHERKGDFDX8GZ2QQQV29SZ_01K7HHET86X6Y5TSC49FSA7YCW_ACTIVITY
skill_ids: ["yU7IYhTRPNqzric6XAml","xk3vzmJzOkW3w4xL2Qvl","e6aOh6pP1sA7mcKMc0pI"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Recycling
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Index Law Showdown\nTeams compete to solve index law problems and earn points!","scenario":"Steps\n1. Each team writes $5$ index expressions (e.g., $2^3 \\times 2^2$) on paper.\n2. Swap expressions with another team and simplify them using index laws.\n3. Score $1$ point for each correct solution; incorrect answers score $0$.\n4. For $a^0$ expressions, explain why the answer is $1$ to earn an extra point.\n5. The team with the most points after $3$ rounds wins!","steps":["Discussion\n• Why does $a^0$ always equal $1$?\n• How do the index laws simplify large expressions?","Differentiation Opportunities\n• Support: Use smaller bases and positive indices only (e.g., $2^3 \\times 2^2$).\n• Extend: Include negative indices and fractions (e.g., $2^{-3} \\div 2^2$)."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding the index law $(a^m)^n = (a^n)^m = a^{m \\times n}$","Understanding the index laws $a^m \\times a^n = a^{m+n}$ and $a^m \\div a^n = a^{m-n}$","Understanding the index law $a^0 = 1$"]


example_id: lp_01K7HHERKGDFDX8GZ2QQQV29SZ_01K7HHET86X6Y5TSC4A1YDQ435_EXIT_TICKET
skill_ids: ["yU7IYhTRPNqzric6XAml","xk3vzmJzOkW3w4xL2Qvl","e6aOh6pP1sA7mcKMc0pI"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Recycling
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$1$","question":"A recycling plant processes $3^0$ tonnes of plastic in a day. How many tonnes is this?"},{"answer":"$256$","question":"A glass recycling machine processes $2^5$ bottles in the morning and $2^3$ bottles in the afternoon. How many bottles does it process in total?"},{"answer":"$4\\,096$","question":"A recycling plant compresses $2^4$ aluminium cans per hour for $3$ consecutive hours. How many cans are compressed in total?"}]}

skills:
["Understanding the index law $(a^m)^n = (a^n)^m = a^{m \\times n}$","Understanding the index laws $a^m \\times a^n = a^{m+n}$ and $a^m \\div a^n = a^{m-n}$","Understanding the index law $a^0 = 1$"]


example_id: lp_01K7HHERKGDFDX8GZ2QQQV29SZ_01K7HHET86X6Y5TSC49BXZ7JMP_APPLICATION
skill_ids: ["yU7IYhTRPNqzric6XAml","xk3vzmJzOkW3w4xL2Qvl","e6aOh6pP1sA7mcKMc0pI"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Recycling
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Recycling Facilities and the Zero Exponent Rule","example1Header":"Situation\nRecycling facility managers track large amounts of data, such as how much waste is collected daily. They use the index law $a^0 = 1$ to simplify calculations when working with data logs.","example1Body":"Example\nWhen managing recycling data, if $10^0$ bins of glass are recorded, $10^0 = 1$, meaning $1$ bin. This simplifies calculations involving data logs.","example2Header":"","example2Body":""}


example_id: lp_01K7HHERKGDFDX8GZ2QQQV29SZ_01K7HHET86X6Y5TSC49X15C6FZ_THOUGHT_SPARKER
skill_ids: ["yU7IYhTRPNqzric6XAml","xk3vzmJzOkW3w4xL2Qvl","e6aOh6pP1sA7mcKMc0pI"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Recycling
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A recycling plant compresses aluminium cans into cubes. Each compression stage reduces the total volume of the material by a factor of $2$, and after $3$ stages, the volume is written as $2^{-3}$ of the original.","firstSentence":"How could you use index laws to calculate the volume after $5$ stages of compression?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the meaning of negative indices and how they relate to fractions.","Encourage students to explain each step of their reasoning using the index laws.","Highlight the real-world application of exponential decay in recycling processes."]}


example_id: lp_01K7HH41N9YZWJYS3SH15W7XTY_01K7HH439YAED8ZP5DZ4C6314F_ACTIVITY
skills: ["Identifying irrational numbers"]
skill_ids: ["XHrGWcu54yB4u78LyNcJ"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Long Jump
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Rational or Irrational?\nYour team is a number detective squad! Classify numbers as rational or irrational to win points.","scenario":"Steps\n1. Each team writes $10$ numbers on paper (include fractions, decimals, and roots).\n2. Pass your list to another team for classification.\n3. Use calculators to check roots or decimals (e.g., $\\sqrt{2}$).\n4. Classify each number as rational or irrational and explain why.\n5. Earn $1$ point for each correct classification. The team with the most points wins!","steps":["Discussion\n• What clues help you identify irrational numbers?\n• Why can't irrational numbers be written as fractions?","Differentiation Opportunities\n• Support: Focus on simpler examples like $\\sqrt{4}$ and $\\sqrt{3}$.\n• Extend: Explore combinations like $2\\sqrt{3}$ or $\\pi + 1$ and classify them."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HH41N9YZWJYS3SH15W7XTY_01K7HH439YAED8ZP5DZGNFY45W_CONTEMPLATIVE_QUESTION
skills: ["Identifying irrational numbers"]
skill_ids: ["XHrGWcu54yB4u78LyNcJ"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Long Jump
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"How would you explain why $0.1010010001\\ldots$ is irrational? Can you create another example?","teacherTips":["Guide students to identify non-repeating, non-terminating decimals.","Encourage examples with clear non-repeating patterns.","Discuss why repeating decimals represent rational numbers."],"difficulty":"mild"}


example_id: lp_01K7HH41N9YZWJYS3SH15W7XTY_01K7HH439YAED8ZP5DZRZR722V_EXIT_TICKET
skills: ["Identifying irrational numbers"]
skill_ids: ["XHrGWcu54yB4u78LyNcJ"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Long Jump
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Irrational","question":"If an athlete's long jump distance is recorded as $6.7320508\\ldots$, is the number rational or irrational?"},{"answer":"Irrational","question":"A long jumper runs $3\\sqrt{2}$ m before jumping. Is $3\\sqrt{2}$ a rational or irrational number?"},{"answer":"Irrational","question":"During practice, a jumper's distance was $\\sqrt{50}$ m. If simplified, is $\\sqrt{50}$ a rational or irrational number?"}]}


example_id: lp_01K7HH41N9YZWJYS3SH15W7XTY_01K7HH439YAED8ZP5DZNEY2TAG_THOUGHT_SPARKER
skills: ["Identifying irrational numbers"]
skill_ids: ["XHrGWcu54yB4u78LyNcJ"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Long Jump
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a long jump competition, an athlete jumps $8.95$ m. Another athlete claims their jump distance is exactly the square root of $80$ m.","firstSentence":"Could the second athlete’s jump distance be exactly the square root of $80$ m, and why or why not?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the difference between rational and irrational numbers with real-world examples.","Encourage students to approximate the square root of $80$ to compare with the given distance.","Highlight how square roots of non-perfect squares are always irrational and connect this to the discussion."]}


example_id: lp_01K7HH41N9YZWJYS3SH15W7XTY_01K7HH439YAED8ZP5DYY39S0E3_APPLICATION
skills: ["Identifying irrational numbers"]
skill_ids: ["XHrGWcu54yB4u78LyNcJ"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Long Jump
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Irrational Numbers in Long Jump Measurements","example1Header":"Situation\nLong jump officials measure jumper distances with high precision. Distances sometimes have decimals that never end or repeat, showing irrational numbers.","example1Body":"Example\nLong jump officials measure $6.324555\\ldots$ m, derived from $\\sqrt{40}$. Since the decimal never ends or repeats, it is identified as an irrational number.","example2Header":"","example2Body":""}


example_id: lp_01K7HHNZRTRWXMXMKGVW5QE6HA_01K7HHP1JPAFZX3GP0PAY0W16X_CONTEMPLATIVE_QUESTION
skill_ids: ["Dbg371MrB5GkJ8t30hf6","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Hot Air Balloon
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You share $7$ pizzas equally among $12$ people. Will the decimal for each share terminate or recur? How do you know?","teacherTips":["Encourage students to divide $7$ by $12$ to explore the decimal form.","Discuss factors of $12$ to identify if the decimal will terminate.","Link recurring decimals to fractions and division processes."],"difficulty":"mild"}

skills:
["Defining terminating and non-terminating decimals","Identifying recurring fractions","Understanding and applying notation to recurring decimals"]


example_id: lp_01K7HHNZRTRWXMXMKGVW5QE6HA_01K7HHP1JPAFZX3GP0NYDCGXEV_ACTIVITY
skill_ids: ["Dbg371MrB5GkJ8t30hf6","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Hot Air Balloon
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Recurring Dice Challenge\nYou're rolling dice to create fractions and classify them as recurring or terminating decimals!","scenario":"Steps\n1. In pairs, roll two dice to create a fraction (e.g., $3/4$).\n2. Divide the fraction to find its decimal form.\n3. Classify the decimal as terminating or recurring.\n4. Record results and repeat for $10$ fractions.\n5. Discuss patterns in recurring and terminating decimals.","steps":["Discussion\n• What patterns do you notice in recurring decimals?\n• How do the denominator's factors affect the decimal type?","Differentiation Opportunities\n• Support: Stick to fractions with denominators of $2$, $4$, $5$, or $10$ for simplicity.\n• Extend: Explore fractions with larger denominators (e.g., $7$, $11$, $12$)."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Defining terminating and non-terminating decimals","Identifying recurring fractions","Understanding and applying notation to recurring decimals"]


example_id: lp_01K7HHNZRTRWXMXMKGVW5QE6HA_01K7HHP1JPAFZX3GP0PHC581SA_EXIT_TICKET
skill_ids: ["Dbg371MrB5GkJ8t30hf6","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Hot Air Balloon
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Terminating","question":"If a hot air balloon rises at a rate of $0.25$ m per second, is $0.25$ a terminating or non-terminating decimal?"},{"answer":"$0.\\overline{3}$","question":"If the height of a hot air balloon is measured as $0.333\\ldots$ km, write $0.333\\ldots$ using recurring decimal notation."},{"answer":"$0.\\overline{6}$","question":"A hot air balloon travels $2$ km in $3$ minutes. Express the distance per minute as a fraction and identify if it is recurring."}]}

skills:
["Defining terminating and non-terminating decimals","Identifying recurring fractions","Understanding and applying notation to recurring decimals"]


example_id: lp_01K7HHNZRTRWXMXMKGVW5QE6HA_01K7HHP1JPAFZX3GP0NSR95J7S_APPLICATION
skill_ids: ["Dbg371MrB5GkJ8t30hf6","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Hot Air Balloon
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Decimals in Hot Air Balloon Altitude Calculations","example1Header":"Situation\nHot air balloon pilots use decimals to calculate precise altitudes. Knowing whether a decimal ends or repeats helps when planning safe flight paths.","example1Body":"Example\nThe fraction $15 \\div 8 = 1.875$ is terminating, as $8$'s factors match $10$. $7 \\div 12 = 0.583\\overline{3}$ is non-terminating, as $12$ includes $3$, which doesn't divide into $10$.","example2Header":"","example2Body":""}


example_id: lp_01K7HHNZRTRWXMXMKGVW5QE6HA_01K7HHP1JPAFZX3GP0PDNQ5AHB_THOUGHT_SPARKER
skill_ids: ["Dbg371MrB5GkJ8t30hf6","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Hot Air Balloon
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A hot air balloon is measured at different heights during its flight. At one point, it is exactly $\\frac{7}{8}$ km above the ground, and later it rises to $\\frac{2}{3}$ km.","firstSentence":"How would you classify the decimal forms of these heights as either terminating or recurring?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to explain how they convert fractions to decimals.","Discuss the factors of the denominator to determine if the decimal terminates or recurs.","Use examples of other fractions to reinforce the patterns they observe."]}


example_id: lp_01K7HJ3SZ80SE4AA10REK2DCY9_01K7HJ3VJ7M5JDSBH11SRTS6PK_THOUGHT_SPARKER
skills: ["Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]
skill_ids: ["4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A helicopter pilot calculates the total fuel needed for a mission using $50 + 30 \\times 2 - 20$.","firstSentence":"Why is it important to follow the correct order of operations when calculating this?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify each operation and its priority according to BODMAS.","Ask students to calculate the expression step-by-step and compare results when the order changes.","Discuss real-world consequences of incorrect calculations, like running out of fuel mid-flight."]}


example_id: lp_01K7HJ3SZ80SE4AA10REK2DCY9_01K7HJ3VJ7M5JDSBH114EZQTQ7_APPLICATION
skills: ["Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]
skill_ids: ["4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Helicopter Fuel Calculations with BODMAS","example1Header":"Situation\nHelicopter pilots calculate fuel requirements for flights. They ensure enough fuel by factoring flight time, fuel efficiency, and distances using the order of operations.","example1Body":"Example\nA helicopter burns $5$ litres per minute on a $3$-leg flight with times $10$, $15$, $20$ and $10$ litres reserve. Using BODMAS: $5 \\times (10 + 15 + 20) + 10 = 235$ litres total.","example2Header":"","example2Body":""}


example_id: lp_01K7HJ3SZ80SE4AA10REK2DCY9_01K7HJ3VJ7M5JDSBH11MT4YZSA_CONTEMPLATIVE_QUESTION
skills: ["Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]
skill_ids: ["4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create your own number problem using all BODMAS operations. Solve it and explain the steps.","teacherTips":["Ensure students include brackets, orders, division, multiplication, addition, and subtraction.","Encourage students to solve step by step, following BODMAS rules.","Ask students to explain why they followed a specific order in their solution."],"difficulty":"mild"}


example_id: lp_01K7HJ3SZ80SE4AA10REK2DCY9_01K7HJ3VJ7M5JDSBH117KZYVRQ_ACTIVITY
skills: ["Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]
skill_ids: ["4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"BODMAS Expression Race\nTeams race to create and solve expressions using BODMAS rules correctly!","scenario":"Steps\n1. Each team creates $10$ cards: $6$ number cards and $4$ operation cards.\n2. Teams swap cards and build an expression using $4$ cards.\n3. Solve the expression using BODMAS rules and check the answer.\n4. Correct answers earn $1$ point; incorrect ones lose $1$ point.\n5. Play $5$ rounds. The team with the highest points wins!","steps":["Discussion\n• What happens if you ignore BODMAS in a multi-step problem?\n• Why is following BODMAS important when solving expressions?","Differentiation Opportunities\n• Support: Allow only two-step expressions (e.g., $5 + 3 \\times 2$).\n• Extend: Include brackets and exponents for more challenging expressions."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HJ3SZ80SE4AA10REK2DCY9_01K7HJ3VJ7M5JDSBH11VYN493Z_EXIT_TICKET
skills: ["Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]
skill_ids: ["4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$17$","question":"A helicopter flies $3 \\times 4 + 5$ km on its route. What is the total distance flown?"},{"answer":"$16$","question":"A helicopter travels $8 + (12 \\div 3) \\times 2$ km; calculate the total distance."},{"answer":"$5$","question":"A helicopter's mission requires solving $15 - [3 \\times (8 - 6) + 4]$ to calculate time in minutes. What is the result?"}]}


example_id: lp_01K7HJDQZ70GR8FBCCGDGB56QJ_01K7HJDSHB8FYFQJ2RQAC92Y80_ACTIVITY
skill_ids: ["BzCcZvkDQvKnDosjX5Os","OVEhnfNj7K2CXYmRsVr3","hD0esazlMhQ2l1nf0DmH"]
subtopics: ["Financial Maths Foundations"]
subtopic_ids: ["subtopic_01GTC0BC0TD90SMF8MHBTKGNG8"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Loan Interest Challenge\nYour team runs a bank offering loans. Calculate interest for clients to beat the competition!","scenario":"Steps\n1. Write loan terms: principal ($500$ to $2\\,000$), rate ($\\%$), and time (years).\n2. Swap terms with another team and calculate their loan's interest using $I = P \\times R \\times T$.\n3. Check each other’s calculations and resolve any discrepancies.\n4. Compare total interest earned. The team with the highest earns bonus points!","steps":["Discussion\n• How does increasing the rate or time affect the interest?\n• Why is it important to calculate interest accurately?","Differentiation Opportunities\n• Support: Use whole numbers for rates (e.g., $5\\%$, $10\\%$) and short time periods (e.g., $1$ year).\n• Extend: Introduce monthly compounding interest and calculate using $I = P \\times \\left(1 + \\frac{R}{n}\\right)^{nT} - P$."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving proportions in worded problems","Calculating simple interest","Defining and understanding simple interest"]


example_id: lp_01K7HJDQZ70GR8FBCCGDGB56QJ_01K7HJDSHB8FYFQJ2RQSZ4079H_EXIT_TICKET
skill_ids: ["BzCcZvkDQvKnDosjX5Os","OVEhnfNj7K2CXYmRsVr3","hD0esazlMhQ2l1nf0DmH"]
subtopics: ["Financial Maths Foundations"]
subtopic_ids: ["subtopic_01GTC0BC0TD90SMF8MHBTKGNG8"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$500$","question":"If a car loan of $10\\,000$ earns $5\\%$ simple interest per year, how much interest is earned in one year?"},{"answer":"$60$","question":"A car travels $280$ km using $40$ litres of fuel. How many litres are needed to travel $420$ km?"},{"answer":"$17\\,700$","question":"A $\\$15\\,000$ car loan is taken at $6\\%$ simple interest per annum. What is the total amount owed after $3$ years?"}]}

skills:
["Solving proportions in worded problems","Calculating simple interest","Defining and understanding simple interest"]


example_id: lp_01K7HJDQZ70GR8FBCCGDGB56QJ_01K7HJDSHB8FYFQJ2RQK85MY4J_CONTEMPLATIVE_QUESTION
skill_ids: ["BzCcZvkDQvKnDosjX5Os","OVEhnfNj7K2CXYmRsVr3","hD0esazlMhQ2l1nf0DmH"]
subtopics: ["Financial Maths Foundations"]
subtopic_ids: ["subtopic_01GTC0BC0TD90SMF8MHBTKGNG8"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You borrow $\\$500$ at $5\\%$ simple interest yearly. How could you calculate the total interest for $3$ years? How would the interest change if the rate was $10\\%$?","teacherTips":["Guide students to use $I = P \\times r \\times t$ for calculations.","Encourage comparison of interest for different rates.","Discuss the effect of time and rate on interest amounts."],"difficulty":"mild"}

skills:
["Solving proportions in worded problems","Calculating simple interest","Defining and understanding simple interest"]


example_id: lp_01K7HJDQZ70GR8FBCCGDGB56QJ_01K7HJDSHB8FYFQJ2RQ5KW7MT6_APPLICATION
skill_ids: ["BzCcZvkDQvKnDosjX5Os","OVEhnfNj7K2CXYmRsVr3","hD0esazlMhQ2l1nf0DmH"]
subtopics: ["Financial Maths Foundations"]
subtopic_ids: ["subtopic_01GTC0BC0TD90SMF8MHBTKGNG8"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Proportions in Car Fuel Efficiency","example1Header":"Situation\nAutomotive engineers calculate fuel efficiency to compare cars. They test how far a car travels on a set amount of fuel, often using proportions to find values.","example1Body":"Example\nAn engineer calculates fuel efficiency. If a car uses 12 litres for 180 km, they solve $12:180 = 8:x$. Solving, $x = 120$, so the car travels 120 km on 8 litres.","example2Header":"","example2Body":""}


example_id: lp_01K7HJDQZ70GR8FBCCGDGB56QJ_01K7HJDSHB8FYFQJ2RQQ7WK8W3_THOUGHT_SPARKER
skill_ids: ["BzCcZvkDQvKnDosjX5Os","OVEhnfNj7K2CXYmRsVr3","hD0esazlMhQ2l1nf0DmH"]
subtopics: ["Financial Maths Foundations"]
subtopic_ids: ["subtopic_01GTC0BC0TD90SMF8MHBTKGNG8"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"You are buying a car that costs $\\$20\\,000$ with a loan at a simple interest rate of $5\\%$ per year for $4$ years.","firstSentence":"How could you calculate the total amount you would pay for the car, including interest?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the difference between the principal and the interest when solving the problem.","Encourage students to identify the key elements in the simple interest formula: principal, rate, and time.","Ask students to explain why the interest increases linearly with time in this scenario."]}


example_id: lp_01K7HKMJAWW3FR6PNEBKFMJXV6_01K7HKMM71GP5D6JDPHTPX4PH9_THOUGHT_SPARKER
skills: ["Finding the intercepts of linear equations","Defining linear equations"]
skill_ids: ["EvPRaqLVITUf1OdmeTFL","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Superfoods
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The cost of buying blueberries and chia seeds together is given by the equation $y = 5x + 30$, where $x$ is the weight of blueberries in kilograms and $y$ is the total cost in dollars.","firstSentence":"How could you determine the intercepts of this equation to better understand the cost relationships?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the concept of intercepts in linear equations before starting the discussion.","Encourage students to interpret the meaning of the intercepts in the context of the problem.","Ask students to explore how changing the equation would affect the intercepts and the relationship between cost and weight."]}


example_id: lp_01K7HKMJAWW3FR6PNEBKFMJXV6_01K7HKMM71GP5D6JDPHAE9F5DZ_APPLICATION
skills: ["Finding the intercepts of linear equations","Defining linear equations"]
skill_ids: ["EvPRaqLVITUf1OdmeTFL","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Superfoods
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Tracking Nutrients in Superfood Farming","example1Header":"Situation\nSuperfood farmers track crop growth with linear equations. Knowing how nutrients affect yield helps them plan for better harvests.","example1Body":"Example\nFarmers use $y = 3x + 10$, where $x$ is fertiliser in kg and $y$ is yield in kg. For $x = 4$ kg of fertiliser: $y = 3(4) + 10 = 22$ kg yield.","example2Header":"","example2Body":""}


example_id: lp_01K7HKMJAWW3FR6PNEBKFMJXV6_01K7HKMM71GP5D6JDPHBTDPHRP_ACTIVITY
skills: ["Finding the intercepts of linear equations","Defining linear equations"]
skill_ids: ["EvPRaqLVITUf1OdmeTFL","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Superfoods
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Roadmap Intercept Game\nDesign roads on a map using linear equations, then find their intercepts.","scenario":"Steps\n1. Draw an $x$-$y$ grid on paper, labelling axes from $-10$ to $10$.\n2. Each team writes $3$ linear equations (e.g., $y = 2x + 3$).\n3. Swap equations with another team and plot them on your grid.\n4. Find the $x$- and $y$-intercepts of each road on the map.\n5. Earn $1$ point for each correct intercept found!","steps":["Discussion\n• How do you find the $x$- and $y$-intercepts from an equation?\n• What happens to the intercepts when the slope changes?","Differentiation Opportunities\n• Support: Use simpler equations like $y = x + 2$ or $y = -x$.\n• Extend: Create equations with fractions or larger slopes, like $y = \\frac{3}{2}x - 4$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HKMJAWW3FR6PNEBKFMJXV6_01K7HKMM71GP5D6JDPHQAXTJQD_CONTEMPLATIVE_QUESTION
skills: ["Finding the intercepts of linear equations","Defining linear equations"]
skill_ids: ["EvPRaqLVITUf1OdmeTFL","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Superfoods
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A line passes through $(-2, 0)$ and $(0, 4)$. What linear equation could represent this line? How would you find the $x$- and $y$-intercepts if given only the equation?","teacherTips":["Guide students to calculate slope using $(y_2 - y_1) / (x_2 - x_1)$.","Encourage using $y = mx + c$ to form the equation.","Explain how substituting $y=0$ gives the $x$-intercept and $x=0$ gives the $y$-intercept."],"difficulty":"mild"}


example_id: lp_01K7HKMJAWW3FR6PNEBKFMJXV6_01K7HKMM71GP5D6JDPJ119RJG7_EXIT_TICKET
skills: ["Finding the intercepts of linear equations","Defining linear equations"]
skill_ids: ["EvPRaqLVITUf1OdmeTFL","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Superfoods
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$10$","question":"A superfood store sells chia seeds by weight using the equation $y = 5x$, where $y$ is the cost in dollars and $x$ is the weight in kg. What is the cost of $2$ kg?"},{"answer":"$16$","question":"A superfood smoothie recipe is priced using the equation $y = 8x + 16$. What is the $y$-intercept of this equation?"},{"answer":"$4, -3$","question":"A superfood company's profit is modeled by $3x - 4y = 12$. What are the $x$-intercept and $y$-intercept?"}]}


example_id: lp_01K7HKX08Y9TKXVRWEDN7BS5EH_01K7HKX2B6HYTZN9V2167YJ5FD_CONTEMPLATIVE_QUESTION
skill_ids: ["sAGaGx5gJreM9HO5U3QN","UUonH9jgU4d89we8iMs1","bxr2hLcXtsj1Q1WgRVJz"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: High Jump
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A car travels at different speeds. Sketch graphs showing speed vs. time for $3$ trips: fast, slow, and stop-start. What do the steepness and flat parts mean? Represent inequalities for speeds in each trip.","teacherTips":["Discuss how steepness relates to speed changes.","Encourage students to compare graphs for each trip.","Guide students to write inequalities for speed ranges."],"difficulty":"mild"}

skills:
["Interpreting graph steepness","Comparing numbers using inequality symbols","Representing linear equations graphically"]


example_id: lp_01K7HKX08Y9TKXVRWEDN7BS5EH_01K7HKX2B6HYTZN9V21H3W7Q2H_EXIT_TICKET
skill_ids: ["sAGaGx5gJreM9HO5U3QN","UUonH9jgU4d89we8iMs1","bxr2hLcXtsj1Q1WgRVJz"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: High Jump
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$h \\geq 1.8$","question":"If a high jumper's height is $h$ and they must clear at least $1.8$ m, which inequality represents this requirement?"},{"answer":"$2$","question":"A high jumper's performance $h$ (in m) over time $t$ (in seconds) is given by $h = 0.5t + 1$. What is $h$ when $t = 2$?"},{"answer":"$0.75$","question":"If a graph shows the high jumper's height $h = 0.75t + 1.2$, what does the gradient $0.75$ represent in the context of high jump?"}]}

skills:
["Interpreting graph steepness","Comparing numbers using inequality symbols","Representing linear equations graphically"]


example_id: lp_01K7HKX08Y9TKXVRWEDN7BS5EH_01K7HKX2B6HYTZN9V20QQER31K_ACTIVITY
skill_ids: ["sAGaGx5gJreM9HO5U3QN","UUonH9jgU4d89we8iMs1","bxr2hLcXtsj1Q1WgRVJz"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: High Jump
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Ramp Design Challenge\nYou're designing ramps for a park. The ramps must be safe and meet specific slope requirements.","scenario":"Steps\n1. Draw a graph with $x$ (horizontal distance) and $y$ (height) axes.\n2. Choose a linear equation for your ramp (e.g., $y = 0.5x$).\n3. Plot your equation on the graph and label key points (e.g., $(0,0)$, $(2,1)$).\n4. Check if your ramp meets the safety rule $y \\leq 0.75x$.\n5. Discuss and adjust your equation to optimise the ramp design.","steps":["Discussion\n• What does the slope of your ramp tell you about its steepness?\n• How does changing the equation affect the ramp's safety?","Differentiation Opportunities\n• Support: Start with simpler equations (e.g., $y = 0.25x$) and plot fewer points.\n• Extend: Incorporate multiple constraints (e.g., $0.5x \\leq y \\leq 0.75x$) and optimise further."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Interpreting graph steepness","Comparing numbers using inequality symbols","Representing linear equations graphically"]


example_id: lp_01K7HKX08Y9TKXVRWEDN7BS5EH_01K7HKX2B6HYTZN9V20J80XTTT_APPLICATION
skill_ids: ["sAGaGx5gJreM9HO5U3QN","UUonH9jgU4d89we8iMs1","bxr2hLcXtsj1Q1WgRVJz"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: High Jump
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Graphing High Jump Progress","example1Header":"Situation\nHigh jump coaches track athletes’ progress by plotting their jump heights over time. These graphs help monitor improvements and set goals for competitions.","example1Body":"Example\nAn athlete's jump starts at 150 cm and increases by 5 cm weekly. Using $y = 5x + 150$, week 0 gives 150 cm, week 1 gives 155 cm, and week 2 gives 160 cm. Graphing these tracks progress.","example2Header":"","example2Body":""}


example_id: lp_01K7HKX08Y9TKXVRWEDN7BS5EH_01K7HKX2B6HYTZN9V21CRMSYC6_THOUGHT_SPARKER
skill_ids: ["sAGaGx5gJreM9HO5U3QN","UUonH9jgU4d89we8iMs1","bxr2hLcXtsj1Q1WgRVJz"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: High Jump
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A high jumper clears $1.8$ m on their first attempt, $2.0$ m on their second, and aims for $2.1$ m on their third attempt, where the bar height can be plotted on a graph over time.","firstSentence":"How could you use a graph to show whether the athlete clears the bar on each attempt?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to label the axes clearly when plotting the graph.","Discuss how inequalities represent whether the athlete's jump height is above or below the bar height.","Ask students to explain how the slope of a line could relate to the athlete's performance over time."]}


example_id: lp_01K7HM7VA44EFQFRRQ81MM32CV_01K7HM7WX26JNFJP4XGV8124WV_THOUGHT_SPARKER
skill_ids: ["xHEfrXq05P7v3mljb2tg","ucOI2emoDLtpi4N6h2AD","q545rOs61jTj5QPHtc74"]
subtopics: ["Composite Shapes"]
subtopic_ids: ["subtopic_01GTC0BRNJKF8Y0VNQ9KBXE8B8"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A farmer has a paddock shaped like a trapezium, where one parallel side is $120$ m and the other is $80$ m. The height between these sides is $50$ m, and the paddock also includes a small rectangular shed measuring $20$ m by $10$ m.","firstSentence":"How could you determine the total area of the paddock, including the shed?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to break the paddock into separate shapes for easier calculations.","Discuss the formula for the area of a trapezium and how it applies to this scenario.","Ask students to explain their reasoning for combining areas and verify their calculations."]}

skills:
["Finding the area of composite shapes","Finding the perimeter of polygons","Calculating the area of a trapezium"]


example_id: lp_01K7HM7VA44EFQFRRQ81MM32CV_01K7HM7WX26JNFJP4XG8D6EJ6S_APPLICATION
skill_ids: ["xHEfrXq05P7v3mljb2tg","ucOI2emoDLtpi4N6h2AD","q545rOs61jTj5QPHtc74"]
subtopics: ["Composite Shapes"]
subtopic_ids: ["subtopic_01GTC0BRNJKF8Y0VNQ9KBXE8B8"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Fencing Farmlands with Perimeter","example1Header":"Situation\nFarmers calculate the perimeter of fields to determine the amount of fencing required to protect crops from animals or secure grazing areas.","example1Body":"Example\nFor a 50 m by 30 m rectangular field, the perimeter is $2 \\times (50 + 30) = 160$ m. The farmer needs 160 m of fencing to surround the field.","example2Header":"","example2Body":""}

skills:
["Finding the area of composite shapes","Finding the perimeter of polygons","Calculating the area of a trapezium"]


example_id: lp_01K7HM7VA44EFQFRRQ81MM32CV_01K7HM7WX26JNFJP4XH0D9V7Z8_EXIT_TICKET
skill_ids: ["xHEfrXq05P7v3mljb2tg","ucOI2emoDLtpi4N6h2AD","q545rOs61jTj5QPHtc74"]
subtopics: ["Composite Shapes"]
subtopic_ids: ["subtopic_01GTC0BRNJKF8Y0VNQ9KBXE8B8"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$35$","question":"A farmer's storage shed has a trapezium-shaped roof with bases $8$ m and $6$ m, and height $5$ m. What is the area of the roof?"},{"answer":"$45$","question":"A farmer fences a triangular paddock with sides $10$ m, $15$ m, and $20$ m. What is the total length of the fence?"},{"answer":"$388.34$","question":"A farmer's land combines a rectangle of $20$ m by $15$ m and a semicircle with diameter $15$ m. What is the total area?"}]}

skills:
["Finding the area of composite shapes","Finding the perimeter of polygons","Calculating the area of a trapezium"]


example_id: lp_01K7HM7VA44EFQFRRQ81MM32CV_01K7HM7WX26JNFJP4XGQ3B0VZG_CONTEMPLATIVE_QUESTION
skill_ids: ["xHEfrXq05P7v3mljb2tg","ucOI2emoDLtpi4N6h2AD","q545rOs61jTj5QPHtc74"]
subtopics: ["Composite Shapes"]
subtopic_ids: ["subtopic_01GTC0BRNJKF8Y0VNQ9KBXE8B8"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design your own garden with a trapezium-shaped lawn and other polygons. Calculate the total area and perimeter of the garden. How could you rearrange shapes to maximise lawn space?","teacherTips":["Guide students to sketch their garden and label dimensions in metres.","Encourage breaking composite shapes into simpler parts for calculations.","Discuss how changing dimensions affects area and perimeter."],"difficulty":"mild"}


example_id: lp_01K7HM7VA44EFQFRRQ81MM32CV_01K7HM7WX26JNFJP4XGAK04S4R_ACTIVITY
skill_ids: ["xHEfrXq05P7v3mljb2tg","ucOI2emoDLtpi4N6h2AD","q545rOs61jTj5QPHtc74"]
subtopics: ["Composite Shapes"]
subtopic_ids: ["subtopic_01GTC0BRNJKF8Y0VNQ9KBXE8B8"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Farming
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Park Design Challenge\nDesign a park with paths, playgrounds, and gardens. Calculate areas and perimeters!","scenario":"Steps\n1. Draw a large composite shape for your park on paper, including at least one trapezium.\n2. Label all side lengths and dimensions on your drawing.\n3. Calculate the area of each section (e.g., trapezium, rectangle, triangle).\n4. Find the total area and perimeter of your park design.\n5. Share your design and calculations with your group for feedback.","steps":["Discussion\n• How did you decide the shapes and dimensions for your park?\n• Why is it useful to calculate both area and perimeter in real life?","Differentiation Opportunities\n• Support: Use simpler shapes (e.g., rectangles) and provide step-by-step guidance.\n• Extend: Include curved paths or irregular shapes and estimate their areas."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HN19WJ17YQDHW6A0DDASPH_01K7HN1BJREKQRZH5W679YTS7Y_EXIT_TICKET
skills: ["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Animation
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$","question":"An animation studio builds a rectangular screen with dimensions $5$ m, $3$ m, and $0.2$ m. What is the volume of the screen?"},{"answer":"$18$","question":"A box holding animation props has a base area of $12$ m$^2$ and height $1.5$ m. What is the volume of the box?"},{"answer":"$4.05$","question":"An animator builds a storage box with dimensions $2.5$ m, $1.8$ m, and $0.9$ m. What is its volume in cubic metrs?"}]}


example_id: lp_01K7HN19WJ17YQDHW6A0DDASPH_01K7HN1BJREKQRZH5W6050CRWX_CONTEMPLATIVE_QUESTION
skills: ["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Animation
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have a box with a base area of $15$ cm$^2$. How would you design it to hold a volume of $150$ cm$^3$? What heights could you choose?","teacherTips":["Discuss how $V=Ah$ relates base area and height to volume.","Encourage students to explore multiple height options.","Emphasize reasoning behind chosen heights and designs."],"difficulty":"mild"}


example_id: lp_01K7HN19WJ17YQDHW6A0DDASPH_01K7HN1BJREKQRZH5W5MJNM5X5_ACTIVITY
skills: ["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Animation
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Box Packing Challenge\nYou're designing shipping boxes for a company. Maximise the space used!","scenario":"Steps\n1. Draw three rectangular prisms with different dimensions on paper.\n2. Calculate the volume of each prism using $V=Ah$.\n3. Compare which prism holds the most space.\n4. Combine your prisms to maximise total volume in a $1\\,000$ cm$^3$ container.\n5. Share your strategy and final design with the class!","steps":["Discussion\n• How does changing one dimension affect the total volume?\n• What strategies helped you fit the prisms efficiently?","Differentiation Opportunities\n• Support: Use simpler dimensions like $5$ cm, $4$ cm, and $3$ cm for easier calculations.\n• Extend: Include irregular cross-sectional areas for advanced volume calculations."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HN19WJ17YQDHW6A0DDASPH_01K7HN1BJREKQRZH5W62MRVCDS_THOUGHT_SPARKER
skills: ["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Animation
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An animator is creating a 3D rectangular prism for a character's blocky arm. The prism has a base area of $120$ cm$^2$ and a total volume of $1\\,080$ cm$^3$.","firstSentence":"How could you determine the height of the prism using this information?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall the formula $V = Ah$ and identify the given values.","Discuss how dividing the volume by the base area gives the height.","Use visual aids like diagrams of prisms to help students connect the formula to the 3D shape."]}


example_id: lp_01K7HN19WJ17YQDHW6A0DDASPH_01K7HN1BJREKQRZH5W5JVD038Q_APPLICATION
skills: ["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Animation
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Calculating Volume in Animation Design","example1Header":"Situation\nAnimators create 3D models with realistic dimensions. They calculate volumes to ensure objects fit together and look proportional in scenes.","example1Body":"Example\nA 3D block with $8$ cm length, $5$ cm width, and $3$ cm height has a volume of $8 \\times 5 \\times 3 = 120$ cm$^3$. Animators use this to decide object proportions.","example2Header":"","example2Body":""}


example_id: lp_01K7HN96WHATPX96ZDDDTMCAF0_01K7HN98F4TTWZWENMZ66SPV8H_APPLICATION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Frisbee
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Measuring Frisbee Flight Paths","example1Header":"Situation\nProfessional frisbee players and coaches analyse the flight paths of frisbees. These paths often involve circular arcs, so knowing the circumference helps estimate distances thrown.","example1Body":"Example\nA frisbee with a diameter of $30$ cm has a circumference of $C = \\pi d = 30\\pi$ cm. Approximating $\\pi$ as $3.14$, $C \\approx 94.2$ cm. This helps players estimate the full flight path.","example2Header":"","example2Body":""}

skills:
["Calculating the area of a segment of a circle","Finding the circumference of a circle","Calculating the area of a circle"]


example_id: lp_01K7HN96WHATPX96ZDDDTMCAF0_01K7HN98F4TTWZWENMZR7X9XRG_THOUGHT_SPARKER
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Frisbee
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A Frisbee has a diameter of 30 cm, and players notice that its shape and size affect how far it can be thrown.","firstSentence":"How might the circumference of the Frisbee influence its ability to travel longer distances?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate the Frisbee's circumference to connect mathematics to the context.","Facilitate discussion on how a larger circumference might impact air resistance or spinning motion.","Guide students to consider other factors like the material or weight of the Frisbee while focusing on the mathematical reasoning."]}

skills:
["Calculating the area of a segment of a circle","Finding the circumference of a circle","Calculating the area of a circle"]


example_id: lp_01K7HN96WHATPX96ZDDDTMCAF0_01K7HN98F4TTWZWENMZANENTR3_ACTIVITY
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Frisbee
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Pizza Circle Challenge\nYour team is designing pizzas of different sizes. Calculate their areas and circumferences to plan toppings and crust sizes.","scenario":"Steps\n1. Each team draws three circles with radii $5$ cm, $7$ cm, and $10$ cm.\n2. Calculate the area of each circle using $A = \\pi r^2$.\n3. Find the circumference of each circle using $C = 2\\pi r$.\n4. Compare results and check calculations with another team.\n5. Earn $1$ point for each correct calculation. The team with the most points wins!","steps":["Discussion\n• How does doubling the radius affect the area and circumference?\n• Why is $\\pi$ important in these calculations?","Differentiation Opportunities\n• Support: Provide $\\pi \\approx 3.14$ and example calculations for practice.\n• Extend: Calculate areas and circumferences for radii with decimals (e.g., $6.5$ cm)."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating the area of a segment of a circle","Finding the circumference of a circle","Calculating the area of a circle"]


example_id: lp_01K7HN96WHATPX96ZDDDTMCAF0_01K7HN98F4TTWZWENMZMVRDEFG_CONTEMPLATIVE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Frisbee
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You’re designing a circular garden with a path. The garden's radius is 7 m, and the path takes up one quarter of the circle. How could you calculate the area of the path and its curved edge (circumference)?","teacherTips":["Guide students to calculate the total area, then find a quarter of it.","Help students apply the formula for circumference to find a quarter of it.","Encourage students to explain their steps and reasoning clearly."],"difficulty":"mild"}


example_id: lp_01K7HN96WHATPX96ZDDDTMCAF0_01K7HN98F4TTWZWENMZVXS6ZDX_EXIT_TICKET
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Frisbee
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$144\\pi$","question":"A frisbee has a radius of $12$ cm. What is the area of the frisbee?"},{"answer":"$20\\pi$","question":"If a frisbee has a diameter of $20$ cm, what is its circumference?"},{"answer":"$49\\pi$","question":"A frisbee has a radius of $14$ cm. If a $90^\\circ$ section of the frisbee is shaded, what is the area of the shaded segment?"}]}


example_id: lp_01K7HNHKN4Z2HQA083MSZ48VA1_01K7HNHNEJZHBHM8D7CFM0A26K_EXIT_TICKET
skill_ids: ["orJHUoGwCJf1DMY7qd7d","NrbZ2vpHTGqxEj4vOBwU","01JZH156SNES42695YNBF73M6P"]
subtopics: ["Time Applications"]
subtopic_ids: ["subtopic_01GTC0BP6GVE9CAQK5WPGB4FWY"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Basketball
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$90$","question":"A basketball game lasts $1$ hour $30$ minutes. How many minutes is that in total?"},{"answer":"$4:00$\\,PM","question":"If a basketball game starts at $7:00$ PM in Sydney (AEDT), what time does it start in Perth (AWST), $3$ hours behind Sydney?"},{"answer":"$11:00$\\,AM\\,\\text{(next day)}","question":"A basketball team travels from Brisbane (AEST) to New York (EST) for a game starting at $8:00$ PM EST. What time is it in Brisbane when the game starts?"}]}

skills:
["Understanding time zones","Converting between units of time","Calculating the time difference between time zones"]


example_id: lp_01K7HNHKN4Z2HQA083MSZ48VA1_01K7HNHNEJZHBHM8D7CBRVCA6E_CONTEMPLATIVE_QUESTION
skill_ids: ["orJHUoGwCJf1DMY7qd7d","NrbZ2vpHTGqxEj4vOBwU","01JZH156SNES42695YNBF73M6P"]
subtopics: ["Time Applications"]
subtopic_ids: ["subtopic_01GTC0BP6GVE9CAQK5WPGB4FWY"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Basketball
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are planning a call between Sydney and London. If it is 8:00 AM in Sydney, what time could it be in London? How might the time difference change during daylight saving, and how would you adjust your call time?","teacherTips":["Discuss how to calculate time differences using time zones.","Explain daylight saving time and its effect on time differences.","Encourage students to consider practical call times for both cities."],"difficulty":"mild"}

skills:
["Understanding time zones","Converting between units of time","Calculating the time difference between time zones"]


example_id: lp_01K7HNHKN4Z2HQA083MSZ48VA1_01K7HNHNEJZHBHM8D7BXEKYCCG_ACTIVITY
skill_ids: ["orJHUoGwCJf1DMY7qd7d","NrbZ2vpHTGqxEj4vOBwU","01JZH156SNES42695YNBF73M6P"]
subtopics: ["Time Applications"]
subtopic_ids: ["subtopic_01GTC0BP6GVE9CAQK5WPGB4FWY"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Basketball
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Global Meeting Planner\nYour team is tasked with planning a virtual meeting across 4 different time zones.","scenario":"Steps\n1. Draw a simple world map and mark 4 cities in different time zones.\n2. Write down each city's current time using a 24-hour format.\n3. Calculate time differences between the cities in hours and minutes.\n4. Convert all times to a single time zone to set a meeting time.\n5. Propose a meeting time that works for all cities and justify your choice.","steps":["Discussion\n• What challenges arise when scheduling across time zones?\n• How does converting to a single time zone simplify planning?","Differentiation Opportunities\n• Support: Provide a smaller range of time zones (e.g., 2 cities) to simplify calculations.\n• Extend: Add more cities and consider daylight saving time in your calculations."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding time zones","Converting between units of time","Calculating the time difference between time zones"]


example_id: lp_01K7HNHKN4Z2HQA083MSZ48VA1_01K7HNHNEJZHBHM8D7CCQJTWE9_THOUGHT_SPARKER
skill_ids: ["orJHUoGwCJf1DMY7qd7d","NrbZ2vpHTGqxEj4vOBwU","01JZH156SNES42695YNBF73M6P"]
subtopics: ["Time Applications"]
subtopic_ids: ["subtopic_01GTC0BP6GVE9CAQK5WPGB4FWY"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Basketball
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A basketball game in Los Angeles starts at 7:00 PM local time. The time difference between Los Angeles and Sydney is 18 hours.","firstSentence":"What time will the game start in Sydney?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to visualise time zones on a world map to understand the concept of time differences.","Discuss strategies for adding or subtracting hours across the international date line.","Ask students how daylight saving time might affect time zone calculations."]}


example_id: lp_01K7HNHKN4Z2HQA083MSZ48VA1_01K7HNHNEJZHBHM8D7BQZ581YD_APPLICATION
skill_ids: ["orJHUoGwCJf1DMY7qd7d","NrbZ2vpHTGqxEj4vOBwU","01JZH156SNES42695YNBF73M6P"]
subtopics: ["Time Applications"]
subtopic_ids: ["subtopic_01GTC0BP6GVE9CAQK5WPGB4FWY"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Basketball
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Game Timing in Basketball","example1Header":"Situation\nBasketball coaches and referees manage game timing. They track how long quarters last, timeouts take, and convert minutes to seconds for precision during games.","example1Body":"Example\nA $12$-minute quarter is $12 \\times 60 = 720$ seconds. A $1.5$-minute timeout is $1.5 \\times 60 = 90$ seconds. Coaches use these conversions during games to manage time effectively.","example2Header":"","example2Body":""}


example_id: lp_01K7HNTMKKN7BJM3QJ0X72PB4V_01K7HNTP6X7TSNGW5NHCRJ3Z5J_THOUGHT_SPARKER
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A helicopter flies $360$ km using $120$ litres of fuel.","firstSentence":"How could you calculate the amount of fuel the helicopter uses per kilometre?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to divide the total fuel by the total distance to find the unit rate.","Ask students to explain why the unit rate is useful for understanding and comparing fuel efficiency.","Discuss real-world applications of unit rates, such as planning trips or estimating costs."]}


example_id: lp_01K7HNTMKKN7BJM3QJ0X72PB4V_01K7HNTP6X7TSNGW5NGRNWRQW8_APPLICATION
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Calculating Helicopter Speeds Using Unit Rates","example1Header":"Situation\nHelicopter pilots calculate speeds to ensure safe and efficient flights. They use unit rates to adjust speed for emergencies or fuel efficiency.","example1Body":"Example\nA helicopter flying $240$ km in $2$ hours has a unit speed of $120$ km/hour, calculated as $240 \\div 2 = 120$ km/hour. Pilots use this to adjust their flight plans.","example2Header":"","example2Body":""}


example_id: lp_01K7HNTMKKN7BJM3QJ0X72PB4V_01K7HNTP6X7TSNGW5NGXPRYK1Y_ACTIVITY
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Data Plan Challenge\nYou're comparing mobile data plans to find the best value for money!","scenario":"Steps\n1. Each team creates three data plans with costs and data amounts (e.g., $\\$30$ for $10$ GB).\n2. Swap plans with another team and calculate the cost per GB for each plan.\n3. Rank the plans from most to least cost-effective based on your calculations.\n4. Present your rankings and justify your reasoning to the class.\n5. Teams earn $1$ point per correct ranking and explanation!","steps":["Discussion\n• Why is finding the cost per GB useful when comparing plans?\n• What happens to the unit rate if the data amount doubles but the cost stays the same?","Differentiation Opportunities\n• Support: Provide pre-made data plans with simple numbers (e.g., $\\$20$ for $5$ GB).\n• Extend: Include plans with fractional GB amounts (e.g., $7.5$ GB) for added complexity."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HNTMKKN7BJM3QJ0X72PB4V_01K7HNTP6X7TSNGW5NH9P7N44Q_CONTEMPLATIVE_QUESTION
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A car travels $360$ km using $24$ L of fuel. How would you find the distance it travels per litre? What would the distance be if the car used $18$ L of fuel?","teacherTips":["Guide students to calculate the unit rate: distance per litre.","Encourage using the unitary method to solve for $18$ L.","Discuss real-life applications of fuel efficiency rates."],"difficulty":"mild"}


example_id: lp_01K7HNTMKKN7BJM3QJ0X72PB4V_01K7HNTP6X7TSNGW5NHDMGMQVJ_EXIT_TICKET
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$150$","question":"A helicopter covers $450$ km in $3$ hours. What is its speed in km per hour?"},{"answer":"$150$","question":"The fuel consumption of a helicopter is $75$ litres for every $150$ km. How much fuel is needed for $300$ km?"},{"answer":"$24$","question":"A helicopter's flight time ratio is $3:5$ for training hours to operational hours. If it flies $40$ operational hours, how many training hours does it complete?"}]}


example_id: lp_01K7HP1TJBWZKJXD9P83NQ1K08_01K7HP1ZXX2QACSFCZBZQAT8Z4_APPLICATION
skill_ids: ["YODiHrgWgz8Rlcbfg3ba","YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Designing Roofs with Pythagoras' Theorem","example1Header":"Situation\nArchitects design triangular roofs with precise dimensions. They use Pythagoras' theorem to ensure angles and lengths fit perfectly for structural stability.","example1Body":"Example\nFor a roof with a height of $6$ m and base of $8$ m, architects calculate the diagonal using $c^2 = a^2 + b^2$: $6^2 + 8^2 = 100$, so $c = 10$ m.","example2Header":"","example2Body":""}

skills:
["Identifying Pythagorean triples","Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]


example_id: lp_01K7HP1TJBWZKJXD9P83NQ1K08_01K7HP1ZXX2QACSFCZCKH14ATT_THOUGHT_SPARKER
skill_ids: ["YODiHrgWgz8Rlcbfg3ba","YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An architect designs a triangular roof structure where two sides measure $9$ m and $12$ m, forming a right angle.","firstSentence":"How could you determine the length of the roof's longest side?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the Pythagorean theorem and its application to right-angled triangles before starting the discussion.","Encourage students to visualise or sketch the triangle to better understand the relationships between the sides.","Prompt students to explain their reasoning and the steps they would take to solve the problem using Pythagoras' theorem."]}

skills:
["Identifying Pythagorean triples","Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]


example_id: lp_01K7HP1TJBWZKJXD9P83NQ1K08_01K7HP1ZXX2QACSFCZCE1YDBK3_CONTEMPLATIVE_QUESTION
skill_ids: ["YODiHrgWgz8Rlcbfg3ba","YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A ladder is $10$ m long and leans against a wall, touching it $8$ m above the ground. How far is the base of the ladder from the wall? Could this form a Pythagorean triple? Explain.","teacherTips":["Encourage students to apply $a^2 + b^2 = c^2$ using given values.","Discuss the definition of Pythagorean triples and check if integers fit.","Prompt students to explain their reasoning for their solution."],"difficulty":"mild"}

skills:
["Identifying Pythagorean triples","Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]


example_id: lp_01K7HP1TJBWZKJXD9P83NQ1K08_01K7HP1ZXX2QACSFCZC3Q6ABTQ_ACTIVITY
skill_ids: ["YODiHrgWgz8Rlcbfg3ba","YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Ramp Design Challenge\nYour team is designing ramps for a building and must calculate their lengths using Pythagoras' theorem.","scenario":"Steps\n1. Draw a right triangle to represent a ramp with height $3$ m and base $4$ m.\n2. Use Pythagoras' theorem to calculate the ramp's length.\n3. Check if the triangle forms a Pythagorean triple.\n4. Repeat with a height of $5$ m and base $12$ m.\n5. Compare your answers with other teams for accuracy and speed.","steps":["Discussion\n• Why is it important to check for Pythagorean triples?\n• How does a longer ramp affect accessibility?","Differentiation Opportunities\n• Support: Use simpler dimensions, such as $3$ m and $4$ m, for all calculations.\n• Extend: Challenge students to create their own dimensions and verify if they form triples."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HP1TJBWZKJXD9P83NQ1K08_01K7HP1ZXX2QACSFCZCRMFTEAG_EXIT_TICKET
skill_ids: ["YODiHrgWgz8Rlcbfg3ba","YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"An architect uses a right-angled triangle with sides $6$ m, $8$ m, and $10$ m for a design. Is this a Pythagorean triple?"},{"answer":"$13$ m","question":"An architect designs a roof truss where the base is $12$ m and the height is $5$ m. What is the length of the diagonal support?"},{"answer":"$25$ m","question":"A triangular skylight has sides $7$ m and $24$ m enclosing a right angle. What is the length of the glass panel across the diagonal?"}]}


example_id: lp_01K7HPK8ZPXMXE7TZX7EWXSX0N_01K7HPKARDMTVXTZ5285YRPETH_APPLICATION
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Calculating Shooting Star Visibility Ratios","example1Header":"Situation\nAstronomers monitor shooting star activity during meteor showers. They calculate visibility in different locations to guide stargazers effectively.","example1Body":"Example\nIf $5$ shooting stars are visible in $10$ minutes, astronomers find stars per minute: $5 \\div 10 = 0.5$. Then, in $50$ minutes: $50 \\times 0.5 = 25$ stars.","example2Header":"","example2Body":""}

skills:
["Solving ratio problems with the unitary method","Solving proportions in worded problems","Solving proportions"]


example_id: lp_01K7HPK8ZPXMXE7TZX7EWXSX0N_01K7HPKARDMTVXTZ528R0TAK9S_THOUGHT_SPARKER
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"During a meteor shower, you count $120$ shooting stars in $30$ minutes, while your friend counts $200$ shooting stars in $50$ minutes.","firstSentence":"How would you compare the rate of shooting stars seen by you and your friend?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate the number of shooting stars seen per minute for each person.","Discuss how proportions can be used to compare rates in different units of time.","Prompt students to explain their reasoning and verify their calculations with examples."]}

skills:
["Solving ratio problems with the unitary method","Solving proportions in worded problems","Solving proportions"]


example_id: lp_01K7HPK8ZPXMXE7TZX7EWXSX0N_01K7HPKARDMTVXTZ528VJP4RWT_EXIT_TICKET
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$2$","question":"If $6$ shooting stars are spotted in $3$ hours, how many stars are spotted in $1$ hour?"},{"answer":"$36$","question":"A telescope captures $15$ stars every $5$ minutes. How many stars can it capture in $12$ minutes?"},{"answer":"$36$","question":"The brightness ratio of two shooting stars is $4:5$. If the brighter star has a brightness of $45$ lumens, what is the brightness of the dimmer star?"}]}

skills:
["Solving ratio problems with the unitary method","Solving proportions in worded problems","Solving proportions"]


example_id: lp_01K7HPK8ZPXMXE7TZX7EWXSX0N_01K7HPKARDMTVXTZ528MM68VHQ_CONTEMPLATIVE_QUESTION
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You and a friend share 60 chocolates in a ratio of $3:2$. How could you adjust the ratio to share them equally?","teacherTips":["Discuss how ratios represent parts shared between people.","Use the unitary method to calculate chocolates per part.","Explore how changing ratios affects the distribution."],"difficulty":"mild"}


example_id: lp_01K7HPK8ZPXMXE7TZX7EWXSX0N_01K7HPKARDMTVXTZ528A06EYFJ_ACTIVITY
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Recipe Ratio Challenge\nYour team is adjusting recipes for a big school event! Scale the ingredients to match different group sizes.","scenario":"Steps\n1. Write down a recipe with $5$ ingredients and their quantities (e.g., $3$ cups of flour).\n2. Your team is told how many times the recipe needs to be multiplied or divided (e.g., $4$ times).\n3. Use the unitary method to calculate the new quantities for all ingredients.\n4. Check your calculations with another team for accuracy.\n5. Score $1$ point for each correct adjustment. The team with the most points wins!","steps":["Discussion\n• Why is the unitary method useful for scaling recipes?\n• How would mistakes in proportions affect the recipe outcome?","Differentiation Opportunities\n• Support: Use simple quantities (e.g., $2$ cups, $3$ teaspoons) and whole-number multipliers.\n• Extend: Include fractions or decimals in ingredient quantities and multipliers."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HQ1FF985NK97HFNRFNBTVD_01K7HQ1H2D08Y64ZM0ABR396W6_APPLICATION
skill_ids: ["efVZBFKA3eLTuIVwRjqN","92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Verifying Triangle Similarity in Treehouse Design","example1Header":"Situation\nArchitects designing treehouses ensure structural safety by checking triangle similarity. This helps maintain proportions for stability and aesthetic design.","example1Body":"Example\nAn architect checks similarity for triangles with sides $3$ m, $4$ m, $5$ m and $6$ m, $8$ m, $10$ m. Using the SSS test: $3/6 = 1/2$, $4/8 = 1/2$, $5/10 = 1/2$. All ratios match, confirming similarity.","example2Header":"","example2Body":""}

skills:
["Proving triangle similarity using the AAA, SSS, SAS and RHS tests","Identifying congruent shapes","Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests"]


example_id: lp_01K7HQ1FF985NK97HFNRFNBTVD_01K7HQ1H2D08Y64ZM0AVRPAW56_THOUGHT_SPARKER
skill_ids: ["efVZBFKA3eLTuIVwRjqN","92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"You are designing a treehouse, and the triangular wooden supports for the walls must be identical for balance. The first triangle has sides measuring $3$ m, $4$ m, and $5$ m, while the second triangle has the same dimensions.","firstSentence":"How could you prove that these two triangles are congruent?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify which congruence test (SSS, SAS, AAS, or RHS) is applicable.","Discuss why congruent triangles are important for structural stability in real-world designs.","Provide diagrams or physical models to help students visualise and verify triangle congruence."]}

skills:
["Proving triangle similarity using the AAA, SSS, SAS and RHS tests","Identifying congruent shapes","Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests"]


example_id: lp_01K7HQ1FF985NK97HFNRFNBTVD_01K7HQ1H2D08Y64ZM0AY320MB1_EXIT_TICKET
skill_ids: ["efVZBFKA3eLTuIVwRjqN","92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"Two triangular windows in a treehouse have the same side lengths of $4$ m, $3$ m, and $5$ m. Are the triangles congruent?"},{"answer":"SSS","question":"A triangular roof of a treehouse has sides $6$ m, $8$ m, and $10$ m. Prove it is congruent to another triangle with the same sides."},{"answer":"AAA","question":"The angles of a triangular window in a treehouse are $40^\\circ$, $60^\\circ$, and $80^\\circ$. Prove its similarity to another triangle with the same angles."}]}

skills:
["Proving triangle similarity using the AAA, SSS, SAS and RHS tests","Identifying congruent shapes","Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests"]


example_id: lp_01K7HQ1FF985NK97HFNRFNBTVD_01K7HQ1H2D08Y64ZM0AQTE382J_CONTEMPLATIVE_QUESTION
skill_ids: ["efVZBFKA3eLTuIVwRjqN","92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a logo using at least 3 different types of triangles. How can you prove they are congruent or similar?","teacherTips":["Encourage students to use SSS, SAS, AAS, RHS, or AAA to prove congruence or similarity.","Discuss why congruence ensures identical shapes and similarity ensures proportional shapes.","Support students in identifying key sides and angles for their proofs."],"difficulty":"mild"}


example_id: lp_01K7HQ1FF985NK97HFNRFNBTVD_01K7HQ1H2D08Y64ZM0ACJZC4NH_ACTIVITY
skill_ids: ["efVZBFKA3eLTuIVwRjqN","92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Treehouse
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Triangle Congruence Race\nYour team must draw and test triangles to match given criteria. Prove congruence or similarity to score points!","scenario":"Steps\n1. In teams, draw $3$ triangles using rulers and protractors.\n2. Exchange triangles with another team for testing.\n3. Use SSS, SAS, AAS, RHS, or AAA to prove congruence or similarity.\n4. Score $2$ points for correct proofs and $1$ for identifying errors.\n5. The team with the highest score wins!","steps":["Discussion\n• Why is RHS only for right-angled triangles?\n• How does AAA show similarity but not congruence?","Differentiation Opportunities\n• Support: Provide written hints for using SSS, SAS, AAS, and RHS.\n• Extend: Challenge students to prove multiple properties for the same triangles."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7HQH7AH7WK9KQZ5AYTFW8ZC_01K7HQH8W89WNWKKZY9JCWJ8C2_CONTEMPLATIVE_QUESTION
skill_ids: ["m0na6OMpAVcpAdE0taHR","OlanqhQiPGOmPxEaJKsi"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Camping
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design your own quadrilateral. Explain how to confirm its angles add to $360^\\circ$. Use congruent triangles.","teacherTips":["Guide students to divide the quadrilateral into two triangles.","Encourage students to verify triangle congruency where needed.","Discuss how triangle angle sums relate to the quadrilateral's angles."],"difficulty":"mild"}

skills:
["Solving for unknown triangle elements using congruency","Calculating the angle sum of a quadrilateral"]


example_id: lp_01K7HQH7AH7WK9KQZ5AYTFW8ZC_01K7HQH8W89WNWKKZY9RGE2TMG_EXIT_TICKET
skill_ids: ["m0na6OMpAVcpAdE0taHR","OlanqhQiPGOmPxEaJKsi"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Camping
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$105^\\circ$","question":"A camping tent has a quadrilateral base with angles $90^\\circ$, $80^\\circ$, and $85^\\circ$. What is the measure of the fourth angle?"},{"answer":"$90^\\circ$","question":"Two tent covers form congruent triangles $\\triangle ABC$ and $\\triangle DEF$ where $\\angle A = 40^\\circ$ and $\\angle D = 50^\\circ$. What is $\\angle B$?"},{"answer":"$30^\\circ, 60^\\circ, 90^\\circ$","question":"A triangular camp flag has angles $x$, $2x$, and $3x$. What are the measures of each angle?"}]}

skills:
["Solving for unknown triangle elements using congruency","Calculating the angle sum of a quadrilateral"]


example_id: lp_01K7HQH7AH7WK9KQZ5AYTFW8ZC_01K7HQH8W89WNWKKZY93ZJMG3E_ACTIVITY
skill_ids: ["m0na6OMpAVcpAdE0taHR","OlanqhQiPGOmPxEaJKsi"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Camping
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Architectural Angle Quest\nYou are designing a unique window for a futuristic building! Ensure all shapes and angles fit perfectly.","scenario":"Steps\n1. In teams, draw a quadrilateral window with two diagonals.\n2. Calculate the angle sum of the quadrilateral to confirm it is $360^\\circ$.\n3. Divide the quadrilateral into two triangles using the diagonals.\n4. Prove the triangles are congruent using Side-Angle-Side or other rules.\n5. Present your design and explain your calculations.","steps":["Discussion\n• Why is the angle sum of a quadrilateral always $360^\\circ$?\n• How does congruency help ensure the design is accurate?","Differentiation Opportunities\n• Support: Provide hints on using protractors and basic congruency rules.\n• Extend: Challenge teams to design a hexagonal window and calculate its angle sum."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving for unknown triangle elements using congruency","Calculating the angle sum of a quadrilateral"]


example_id: lp_01K7HQH7AH7WK9KQZ5AYTFW8ZC_01K7HQH8W89WNWKKZY91MBD8SR_APPLICATION
skill_ids: ["m0na6OMpAVcpAdE0taHR","OlanqhQiPGOmPxEaJKsi"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Camping
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Determining Tent Poles for Stable Camping","example1Header":"Situation\nCampers use congruent triangles in tent designs to ensure stability. Matching pole lengths and angles create equal triangular sections, keeping tents secure.","example1Body":"Example\nA tent uses matching triangles for stability. One triangle has sides $6$ m, $8$ m, $10$ m. By congruence, the second triangle's missing side is $8$ m.","example2Header":"","example2Body":""}


example_id: lp_01K7HQH7AH7WK9KQZ5AYTFW8ZC_01K7HQH8W89WNWKKZY9NHYWNY7_THOUGHT_SPARKER
skill_ids: ["m0na6OMpAVcpAdE0taHR","OlanqhQiPGOmPxEaJKsi"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Camping
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"While setting up a camping tent, you notice one of its panels is a quadrilateral with three angles measuring $95^\\circ$, $85^\\circ$, and $90^\\circ$, and the other panel is a triangular flap with two angles measuring $50^\\circ$ and $60^\\circ$.","firstSentence":"How would you determine the missing angle in each of these panels?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the angle sum properties of triangles and quadrilaterals before starting the discussion.","Encourage students to explain their reasoning step by step for calculating unknown angles.","Discuss how congruency rules might apply if the tent panels were identical or symmetrical."]}


example_id: lp_01K7M9E1VESRDCAF2SJ41Q43RJ_01K7M9E3K7AZ00W74XKS915MD6_THOUGHT_SPARKER
skills: ["Calculating complementary probabilities"]
skill_ids: ["L1omaLcwFitXj3dblMO3"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Skateboarding
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A skateboarder has a $65\\%$ chance of successfully landing a kickflip during a competition.","firstSentence":"How would you determine the probability of the skateboarder not landing the kickflip?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to understand that complementary probabilities must add up to $100\\%$.","Encourage students to explain their reasoning in terms of 'success' and 'failure' outcomes.","Use real-world examples of probabilities to make the concept more relatable."]}


example_id: lp_01K7M9E1VESRDCAF2SJ41Q43RJ_01K7M9E3K7AZ00W74XK30K44CB_APPLICATION
skills: ["Calculating complementary probabilities"]
skill_ids: ["L1omaLcwFitXj3dblMO3"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Skateboarding
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Probability in Skateboarding Tricks","example1Header":"Situation\nSkateboarding event organisers predict successful tricks. They use probabilities to ensure fairness in judging and plan exciting show elements.","example1Body":"Example\nFor a trick with a $0.7$ probability of success, the chance of failure is $1 - 0.7 = 0.3$. This helps event planners assess performance risks.","example2Header":"","example2Body":""}


example_id: lp_01K7M9E1VESRDCAF2SJ41Q43RJ_01K7M9E3K7AZ00W74XK7F5JMJ2_ACTIVITY
skills: ["Calculating complementary probabilities"]
skill_ids: ["L1omaLcwFitXj3dblMO3"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Skateboarding
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Spin and Solve\nYour team designs a spinner and calculates probabilities to win points!","scenario":"Steps\n1. Draw a circle on paper and divide it into $4$ equal sections.\n2. Label each section with a colour or number.\n3. Spin your spinner and record the outcome $10$ times.\n4. Calculate the probability of landing on one section and its complement.\n5. Compare your calculations with results from your spins.","steps":["Discussion\n• Why do probabilities of an event and its complement add to $1$?\n• What happens if you change the number of sections on the spinner?","Differentiation Opportunities\n• Support: Use a spinner with only $2$ sections (e.g., red and blue).\n• Extend: Design a spinner with $6$ sections and calculate probabilities."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7M9E1VESRDCAF2SJ41Q43RJ_01K7M9E3K7AZ00W74XKKBESP53_CONTEMPLATIVE_QUESTION
skills: ["Calculating complementary probabilities"]
skill_ids: ["L1omaLcwFitXj3dblMO3"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Skateboarding
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"At a fair, the probability of winning a prize on a game is $0.3$. What could the probability of not winning be? Explain why.","teacherTips":["Guide students to use complementary probabilities.","Discuss why probabilities must add up to $1$.","Encourage students to justify the calculation clearly."],"difficulty":"mild"}


example_id: lp_01K7M9E1VESRDCAF2SJ41Q43RJ_01K7M9E3K7AZ00W74XKTY3D7K0_EXIT_TICKET
skills: ["Calculating complementary probabilities"]
skill_ids: ["L1omaLcwFitXj3dblMO3"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Skateboarding
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.2$","question":"If a skateboarder lands a trick with probability $0.8$, what is the probability of not landing the trick?"},{"answer":"$0.35$","question":"A skateboarder has a $65\\%$ chance to successfully perform a kickflip. What is the probability that they fail to perform it?"},{"answer":"$0.15$","question":"If a skateboarder has a $0.85$ probability of avoiding a fall, what is the probability they will fall on a given attempt?"}]}


example_id: lp_01K7MABZ1H8ED39KHBAVKVCBM7_01K7MAC0WH45SZV63A8K597FZX_THOUGHT_SPARKER
skill_ids: ["LEdzy5toa3hpfQFJXz0g","NlcP4a6JETto9xf03JFi","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Avengers
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The Avengers are planning a mission. The probability that Iron Man successfully disables a weapon is $0.6$, and the probability that Captain Marvel protects the base is $0.8$.","firstSentence":"How could you determine the probability that at least one of these events happens during the mission?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the meaning of 'at least one' in probability and how it relates to unions of events.","Use a Venn diagram to visually represent the events and their overlaps.","Encourage students to explore whether the events are dependent or independent and how this affects the calculations."]}

skills:
["Calculating conditional probabilities with Venn diagrams","Calculating the probability of the union or intersection of two events","Calculating the probability of combined events"]


example_id: lp_01K7MABZ1H8ED39KHBAVKVCBM7_01K7MAC0WH45SZV63A87GTPHDG_APPLICATION
skill_ids: ["LEdzy5toa3hpfQFJXz0g","NlcP4a6JETto9xf03JFi","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Avengers
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Probability in Avengers Missions","example1Header":"Situation\nAvengers strategists calculate probabilities to plan missions. They assess overlaps (intersection) or combinations (union) of potential obstacles, like enemy attacks or natural disasters.","example1Body":"Example\nIf the chance of an enemy attack is 0.6, a natural disaster is 0.4, and both is 0.2, the union (either happening) is $0.6 + 0.4 - 0.2 = 0.8$ or 80%.","example2Header":"","example2Body":""}

skills:
["Calculating conditional probabilities with Venn diagrams","Calculating the probability of the union or intersection of two events","Calculating the probability of combined events"]


example_id: lp_01K7MABZ1H8ED39KHBAVKVCBM7_01K7MAC0WH45SZV63A8B3D0V2P_ACTIVITY
skill_ids: ["LEdzy5toa3hpfQFJXz0g","NlcP4a6JETto9xf03JFi","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Avengers
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Venn Diagram Probability Game\nYour class is analysing survey results about favourite sports to calculate probabilities.","scenario":"Steps\n1. Draw a Venn diagram with two overlapping circles for soccer and basketball fans.\n2. Assign $15$ students to soccer only, $10$ to basketball only, and $5$ to both.\n3. Calculate the probability of a student liking either sport (union).\n4. Calculate the probability of a student liking only soccer or both sports.\n5. Compare results with another team and verify calculations.","steps":["Discussion\n• How does the overlap in the Venn diagram affect the probabilities?\n• What happens to probabilities if more students like both sports?","Differentiation Opportunities\n• Support: Use smaller numbers (e.g., $5$ for soccer, $3$ for basketball, $2$ for both).\n• Extend: Add a third sport and calculate probabilities with three sets."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating conditional probabilities with Venn diagrams","Calculating the probability of the union or intersection of two events","Calculating the probability of combined events"]


example_id: lp_01K7MABZ1H8ED39KHBAVKVCBM7_01K7MAC0WH45SZV63A8GHTENXP_CONTEMPLATIVE_QUESTION
skill_ids: ["LEdzy5toa3hpfQFJXz0g","NlcP4a6JETto9xf03JFi","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Avengers
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have a bag with $5$ red, $3$ blue, and $2$ green marbles. If you draw two marbles without replacement, how would you calculate the probability of drawing one red and one blue? What changes if you draw with replacement?","teacherTips":["Discuss how probabilities change with and without replacement.","Use Venn diagrams to analyse combined events of red and blue marbles.","Highlight how intersecting probabilities apply in combined events."],"difficulty":"mild"}


example_id: lp_01K7MABZ1H8ED39KHBAVKVCBM7_01K7MAC0WH45SZV63A8N9TBAAF_EXIT_TICKET
skill_ids: ["LEdzy5toa3hpfQFJXz0g","NlcP4a6JETto9xf03JFi","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Avengers
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$\\frac{1}{12}$","question":"Iron Man flips a coin and Thor rolls a fair $6$-sided die. What is the probability of getting heads and a $4$ on the die?"},{"answer":"$0.6$","question":"In an Avengers mission, $70\\%$ of heroes can fly, $50\\%$ have super strength, and $30\\%$ have both. What is the probability a hero can fly given they have super strength?"},{"answer":"$0.7$","question":"Black Widow calculates that $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \\cap B) = 0.2$. What is $P(A \\cup B)$?"}]}


example_id: lp_01K7MAJSYXXQHDRYKE6SFX1ART_01K7MAJVR8PF7HZ8NGYY3721D8_CONTEMPLATIVE_QUESTION
skills: ["Calculating the expected frequency of a result","Finding probability from experiments"]
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: The Northern Lights
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flipped a coin $50$ times and got $32$ heads. How would you calculate the experimental probability of heads and the expected frequency of heads in $200$ flips?","teacherTips":["Guide students to divide the number of heads by total flips for probability.","Help them use the probability to find the expected frequency: $200 \\times P$.","Encourage discussion on how results may vary in different experiments."],"difficulty":"mild"}


example_id: lp_01K7MAJSYXXQHDRYKE6SFX1ART_01K7MAJVR8PF7HZ8NGZ8E7XCZ0_EXIT_TICKET
skills: ["Calculating the expected frequency of a result","Finding probability from experiments"]
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: The Northern Lights
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.4$","question":"If the Northern Lights were visible $4$ nights out of $10$, what is the probability of seeing them on any given night?"},{"answer":"$5$","question":"If the probability of seeing the Northern Lights on a night is $0.25$, how many times would you expect to see them over $20$ nights?"},{"answer":"$10.5$","question":"If the probability of seeing the Northern Lights is $0.3$ and you plan a $15$-night trip, how often would you expect to not see them?"}]}


example_id: lp_01K7MAJSYXXQHDRYKE6SFX1ART_01K7MAJVR8PF7HZ8NGYECCFC0E_ACTIVITY
skills: ["Calculating the expected frequency of a result","Finding probability from experiments"]
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: The Northern Lights
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Dice Probability Challenge\nYou're testing dice fairness by finding probabilities and expected outcomes.","scenario":"Steps\n1. Each group rolls a dice $60$ times and records the results.\n2. Calculate the experimental probability for each outcome (e.g., rolling a $4$).\n3. Compare experimental probabilities to the theoretical probability of $\\frac{1}{6}$.\n4. Predict the expected frequency for $120$ rolls based on theoretical probabilities.\n5. Discuss how close experimental results are to predictions.","steps":["Discussion\n• Why might experimental probabilities differ from theoretical ones?\n• How would increasing rolls affect the experimental probability?","Differentiation Opportunities\n• Support: Roll the dice $30$ times instead and focus on one outcome (e.g., rolling a $6$).\n• Extend: Use two dice and calculate probabilities for combined outcomes (e.g., sum is $7$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7MAJSYXXQHDRYKE6SFX1ART_01K7MAJVR8PF7HZ8NGYCARWTKG_APPLICATION
skills: ["Calculating the expected frequency of a result","Finding probability from experiments"]
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: The Northern Lights
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Predicting Northern Lights Visibility","example1Header":"Situation\nAurora guides track Northern Lights sightings. They use experiments and probability to predict the best nights for tourists to witness this natural phenomenon.","example1Body":"Example\nAurora guides calculate visibility probability. If the Northern Lights were visible $15$ out of $20$ nights, the probability is $P = \\frac{15}{20} = 0.75$, which is $75\\%$.","example2Header":"","example2Body":""}


example_id: lp_01K7MAJSYXXQHDRYKE6SFX1ART_01K7MAJVR8PF7HZ8NGZ28H2V8N_THOUGHT_SPARKER
skills: ["Calculating the expected frequency of a result","Finding probability from experiments"]
skill_ids: ["yP1aS9kjBGzvSV7nDHN3","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: The Northern Lights
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A group of travellers in Norway has a $70\\%$ chance of seeing the Northern Lights on any given clear night during their $10$-night trip.","firstSentence":"How could you calculate the number of nights they are expected to see the Northern Lights?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to first identify the total number of trials and the probability of success for one trial.","Encourage students to connect their calculations to real-world expectations.","Discuss how probabilities can help in planning trips or setting realistic expectations for rare events."]}


example_id: lp_01K7N9AFK1WW282ZH5C1BYREZ2_01K7N9AH4K2PBNBY5706FH9RV7_EXIT_TICKET
skill_ids: ["OLTlbvQDtNHfBSsyagap","BvW1eTpDejIDS2lBA0X5"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Baseball
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Batting average","question":"In a baseball game, if a player hits $7$ times out of $20$ attempts, what is the term for the proportion of hits to attempts?"},{"answer":"$50$","question":"A baseball team recorded $10$ home runs, $15$ doubles, and $25$ singles in a game. What is the total frequency of hits?"},{"answer":"$50\\%$","question":"In a baseball season, a player had $8$ home runs, $12$ doubles, and $20$ singles. What percentage of the player's hits were singles?"}]}

skills:
["Analysing and creating frequency tables with categorical data","Understanding common terms in statistics"]


example_id: lp_01K7N9AFK1WW282ZH5C1BYREZ2_01K7N9AH4K2PBNBY5701R43JG2_CONTEMPLATIVE_QUESTION
skill_ids: ["OLTlbvQDtNHfBSsyagap","BvW1eTpDejIDS2lBA0X5"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Baseball
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A survey asks students their favourite fruit: apple, banana, or orange. Create a frequency table for $30$ responses. What patterns or trends can you identify? How might this data be useful for a school event?","teacherTips":["Encourage students to create realistic but varied data for $30$ responses.","Guide students to calculate totals and identify the most popular fruit.","Discuss how this data could inform decisions for a school event."],"difficulty":"mild"}

skills:
["Analysing and creating frequency tables with categorical data","Understanding common terms in statistics"]


example_id: lp_01K7N9AFK1WW282ZH5C1BYREZ2_01K7N9AH4K2PBNBY56ZNK4NYP7_ACTIVITY
skill_ids: ["OLTlbvQDtNHfBSsyagap","BvW1eTpDejIDS2lBA0X5"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Baseball
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Classroom Data Challenge\nYour team is tasked with collecting and organising class data to find trends.","scenario":"Steps\n1. In teams, choose a category (e.g., favourite sport, colour).\n2. Survey classmates and tally responses in a table.\n3. Create a frequency table with your data.\n4. Analyse your table for trends and share findings.\n5. Teams score points for clear, accurate tables!","steps":["Discussion\n• What did your frequency table reveal about the class?\n• Why is it useful to organise data this way?","Differentiation Opportunities\n• Support: Provide examples of frequency tables for guidance.\n• Extend: Create bar graphs from your frequency table data."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Analysing and creating frequency tables with categorical data","Understanding common terms in statistics"]


example_id: lp_01K7N9AFK1WW282ZH5C1BYREZ2_01K7N9AH4K2PBNBY5704HHHZCK_THOUGHT_SPARKER
skill_ids: ["OLTlbvQDtNHfBSsyagap","BvW1eTpDejIDS2lBA0X5"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Baseball
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a baseball game, a player's performance is recorded as $12$ hits, $8$ strikes, and $6$ outs.","firstSentence":"What patterns can you identify if this data is organised into a frequency table?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to group the data into clear categories for the table.","Discuss how frequency tables help reveal trends or patterns in data.","Ask students how they might use similar tables to compare performances across multiple players."]}


example_id: lp_01K7N9AFK1WW282ZH5C1BYREZ2_01K7N9AH4K2PBNBY56ZF6716XE_APPLICATION
skill_ids: ["OLTlbvQDtNHfBSsyagap","BvW1eTpDejIDS2lBA0X5"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Baseball
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Using Statistics in Baseball Performance","example1Header":"Situation\nBaseball coaches use statistics to evaluate players' performance. Terms like mean, median, and mode help analyze scores, hits, and pitching accuracy.","example1Body":"Example\nA player scores $15$, $20$, $10$, $20$, and $25$ in five games. Mean is $18$, median is $20$, and mode is $20$, helping the coach analyze consistency.","example2Header":"","example2Body":""}


example_id: lp_01K7N9G9MGZN0EJW7STCNT1G63_01K7N9GB9KAFYGR59TA47KZ84S_THOUGHT_SPARKER
skill_ids: ["A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26","8Tcl65LGb78533gvhcwn"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Skydiving
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A company wants to improve its skydiving services by surveying $100$ people, but they only ask those who have just completed a skydiving experience.","firstSentence":"How could you evaluate whether this sampling method provides fair and unbiased results?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss what makes a sample biased or unbiased in real-world scenarios.","Encourage students to suggest alternative methods for collecting more representative data.","Highlight why random sampling ensures everyone has an equal chance of being selected."]}

skills:
["Defining and recognising random samples","Identifying different sampling methods","Understanding the causes of sampling bias"]


example_id: lp_01K7N9G9MGZN0EJW7STCNT1G63_01K7N9GB9KAFYGR59T9FWFNN9A_APPLICATION
skill_ids: ["A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26","8Tcl65LGb78533gvhcwn"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Skydiving
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Avoiding Sampling Bias in Skydiving Safety Surveys","example1Header":"Situation\nSkydiving safety experts conduct surveys to understand how safe participants feel. If the survey only asks experienced skydivers, it may miss important views from beginners, leading to sampling bias.","example1Body":"Example\nA survey with $80$ professionals and $20$ beginners finds $90\\%$ of professionals ($72$) and $40\\%$ of beginners ($8$) rate skydiving as very safe. This leads to an $80\\%$ overall result, biased by the overrepresentation of professionals.","example2Header":"","example2Body":""}

skills:
["Defining and recognising random samples","Identifying different sampling methods","Understanding the causes of sampling bias"]


example_id: lp_01K7N9G9MGZN0EJW7STCNT1G63_01K7N9GB9KAFYGR59T9Y92TDX3_CONTEMPLATIVE_QUESTION
skill_ids: ["A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26","8Tcl65LGb78533gvhcwn"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Skydiving
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A school wants student opinions on a new canteen menu. How would you choose a random sample to avoid bias? What different sampling methods could you use? Justify your choices.","teacherTips":["Discuss how random sampling ensures fairness by giving each student an equal chance.","Explain how different sampling methods (e.g., stratified, cluster) might work in this context.","Encourage students to consider potential sources of bias in their methods."],"difficulty":"mild"}

skills:
["Defining and recognising random samples","Identifying different sampling methods","Understanding the causes of sampling bias"]


example_id: lp_01K7N9G9MGZN0EJW7STCNT1G63_01K7N9GB9KAFYGR59TA82HP3AA_EXIT_TICKET
skill_ids: ["A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26","8Tcl65LGb78533gvhcwn"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Skydiving
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"No","question":"A skydiving company asks every fifth customer to rate their experience; is this a random sample?"},{"answer":"Excluding intermediate and advanced students","question":"If a skydiving school only surveys beginner students about safety, what is a potential cause of bias?"},{"answer":"Stratified sampling","question":"A skydiving club divides customers by age groups and surveys $10$ people from each group; what sampling method is this?"}]}


example_id: lp_01K7N9G9MGZN0EJW7STCNT1G63_01K7N9GB9KAFYGR59T9J76G5RZ_ACTIVITY
skill_ids: ["A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26","8Tcl65LGb78533gvhcwn"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Skydiving
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Survey Sampling Showdown\nYour team is conducting a survey to find the most popular music genre in the class!","scenario":"Steps\n1. In teams, write $1$ survey question on your paper asking about music taste.\n2. Choose $3$ sampling methods: random, convenience, and biased sampling.\n3. Survey $5$ classmates using each method and record their responses.\n4. Compare the results and identify which method is most fair.\n5. Discuss how sampling bias affected the results.","steps":["Discussion\n• Why is random sampling considered fair?\n• How does sampling bias affect survey accuracy?","Differentiation Opportunities\n• Support: Use a smaller group of $3$ classmates to simplify the activity.\n• Extend: Analyse how sample size impacts the accuracy of your results."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7N9PW3VBQ40F88H1K7QZ97P_01K7N9PY97WP4QG3NT0FPFXD7K_THOUGHT_SPARKER
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","2ZVgCioON5G43gUiotqs","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A stem-and-leaf plot shows the speeds (in km/h) of $20$ cars passing through a school zone: $3 \\, | \\, 5 \\, 6 \\, 7$, $4 \\, | \\, 0 \\, 2 \\, 3 \\, 5 \\, 6$, $5 \\, | \\, 1 \\, 3 \\, 3 \\, 4$, $6 \\, | \\, 0 \\, 2 \\, 5 \\, 7$, $7 \\, | \\, 0 \\, 1$.","firstSentence":"What does the interquartile range tell us about how consistent the car speeds are?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to identify the median, Q1, and Q3 directly from the stem-and-leaf plot.","Discuss why the interquartile range is useful for understanding variability while ignoring outliers.","Encourage students to compare the IQR to the overall range for additional insights into data spread."]}

skills:
["Defining interquartile range","Calculating quartiles and IQR from a stem-and-leaf plot","Calculating range"]


example_id: lp_01K7N9PW3VBQ40F88H1K7QZ97P_01K7N9PY97WP4QG3NSZVGES7A3_APPLICATION
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","2ZVgCioON5G43gUiotqs","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Car Safety Data Analysis","example1Header":"Situation\nCar safety analysts evaluate crash-test data for various car models. They use measures like the interquartile range (IQR) to compare the spread of safety scores and identify consistent performers.","example1Body":"Example\nCrash-test scores are $55, 60, 62, 66, 70, 71, 73, 74, 78$. Median is $70$, quartiles are $61$ and $73.5$. IQR is $73.5 - 61 = 12.5$, showing score consistency.","example2Header":"","example2Body":""}

skills:
["Defining interquartile range","Calculating quartiles and IQR from a stem-and-leaf plot","Calculating range"]


example_id: lp_01K7N9PW3VBQ40F88H1K7QZ97P_01K7N9PY97WP4QG3NT0MQQ3Y8B_EXIT_TICKET
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","2ZVgCioON5G43gUiotqs","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$40$","question":"A car speed test records speeds of $40$, $50$, $60$, $70$, and $80$ km/h. What is the range of the speeds?"},{"answer":"$10$","question":"The stem-and-leaf plot shows car travel times: $1|3\\,5\\,6$, $2|0\\,2\\,4\\,6$, $3|1\\,4$. What is the interquartile range (IQR)?"},{"answer":"The interquartile range excludes outliers, showing the spread of the middle $50\\%$ of data.","question":"Why is the interquartile range a better measure of spread than the range when comparing car speeds?"}]}

skills:
["Defining interquartile range","Calculating quartiles and IQR from a stem-and-leaf plot","Calculating range"]


example_id: lp_01K7N9PW3VBQ40F88H1K7QZ97P_01K7N9PY97WP4QG3NSZZYVYN36_ACTIVITY
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","2ZVgCioON5G43gUiotqs","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Sports Stats Challenge\nYour team is analysing sports scores to find trends and variability.","scenario":"Steps\n1. Write $15$ scores (e.g., $12$, $19$, $23$) and create a stem-and-leaf plot.\n2. Identify the median, lower quartile (Q1), and upper quartile (Q3).\n3. Calculate the interquartile range (IQR) as $Q3 - Q1$.\n4. Find the range by subtracting the smallest score from the largest.\n5. Compare answers with other teams. Correct answers earn $1$ point!","steps":["Discussion\n• Why is the IQR more useful than the range for understanding data spread?\n• What happens to the IQR if we add an outlier to the data?","Differentiation Opportunities\n• Support: Use a smaller dataset (e.g., $8$ scores) to simplify calculations.\n• Extend: Add an outlier to your dataset and recalculate the IQR. Compare results."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7N9PW3VBQ40F88H1K7QZ97P_01K7N9PY97WP4QG3NT0B9D7154_CONTEMPLATIVE_QUESTION
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","2ZVgCioON5G43gUiotqs","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Cars
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A stem-and-leaf plot shows test scores. How could you calculate the range, quartiles, and IQR? Explain.","teacherTips":["Guide students to identify the smallest and largest scores for range.","Explain finding $Q_1$, $Q_3$, and median from the ordered data.","Discuss subtracting $Q_1$ from $Q_3$ to find the IQR."],"difficulty":"mild"}


example_id: lp_01K7N9WC4QZHFTB8GCAMYAP05K_01K7N9WDX0Z27JFYXRQCPFVG7N_EXIT_TICKET
skill_ids: ["mAJ9w8tH0ewNWof0AtWB","sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Positive","question":"The scatterplot shows the brightness of shooting stars and their visibility time; is the relationship positive, negative, or neither?"},{"answer":"Skewed right","question":"A graph of shooting star counts each night shows a long tail on the right. Is it skewed left, skewed right, or symmetric?"},{"answer":"Greater than","question":"If a dataset of star brightness is skewed right, will the mean be greater than, less than, or equal to the median?"}]}

skills:
["Describing scatterplots by direction, form, and strength","Understanding how skew affects the mean relative to the median","Understanding graph skewness"]


example_id: lp_01K7N9WC4QZHFTB8GCAMYAP05K_01K7N9WDX0Z27JFYXRQ4XHQ2BX_CONTEMPLATIVE_QUESTION
skill_ids: ["mAJ9w8tH0ewNWof0AtWB","sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Imagine you run a school survey on daily screen time. Create a scatterplot with your data. What direction, form, and strength could the pattern show? How might extreme values (skewness) affect the mean and median?","teacherTips":["Encourage students to describe scatterplot trends: positive, negative, or no direction.","Discuss how outliers or skewed data impact mean vs. median values.","Ask students to consider realistic data for screen time in their age group."],"difficulty":"mild"}

skills:
["Describing scatterplots by direction, form, and strength","Understanding how skew affects the mean relative to the median","Understanding graph skewness"]


example_id: lp_01K7N9WC4QZHFTB8GCAMYAP05K_01K7N9WDX0Z27JFYXRPQJ8M6XX_ACTIVITY
skill_ids: ["mAJ9w8tH0ewNWof0AtWB","sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Scatterplot Trends Challenge\nYour team is analysing scatterplots to uncover trends and patterns in data.","scenario":"Steps\n1. On graph paper, draw axes and plot $10$ random data points.\n2. Label and describe the scatterplot's direction, form, and strength.\n3. Discuss if the data is skewed positively, negatively, or not at all.\n4. Compare how skewness affects mean and median with your teammates.\n5. Present your findings and identify which team found the most unique pattern.","steps":["Discussion\n• How does skewness impact the mean compared to the median?\n• What patterns make scatterplots easy or hard to interpret?","Differentiation Opportunities\n• Support: Provide examples of scatterplot descriptions (e.g., positive, linear, weak).\n• Extend: Challenge students to create scatterplots with specific trends or skewness."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Describing scatterplots by direction, form, and strength","Understanding how skew affects the mean relative to the median","Understanding graph skewness"]


example_id: lp_01K7N9WC4QZHFTB8GCAMYAP05K_01K7N9WDX0Z27JFYXRPP892T87_APPLICATION
skill_ids: ["mAJ9w8tH0ewNWof0AtWB","sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Analysing Meteor Showers with Data","example1Header":"Situation\nAstronomers study meteor showers by charting how many meteors are seen per hour. They use graphs to see patterns and understand data skewness.","example1Body":"Example\nA graph of $5$, $7$, $10$, $12$, and $50$ meteors per hour is right-skewed. Most hours have few meteors, but $50$ creates a long right tail.","example2Header":"","example2Body":""}


example_id: lp_01K7N9WC4QZHFTB8GCAMYAP05K_01K7N9WDX0Z27JFYXRQ8YYEB22_THOUGHT_SPARKER
skill_ids: ["mAJ9w8tH0ewNWof0AtWB","sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Shooting Stars
class_year: 8
country: AU
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Astronomers watching shooting stars plot a scatterplot comparing the brightness of stars (on a scale from $1$ to $10$) and the number of shooting stars seen each hour.","firstSentence":"How might the skew of the data in this scatterplot affect the mean brightness compared to the median brightness?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to describe what skewness means in the context of the scatterplot data.","Encourage discussions on how extreme values in brightness might impact the mean versus the median.","Have students sketch examples of different skew directions and compare mean and median values for each case."]}


example_id: lp_01K7NB1VKDNCS9G5KKJ67B7YEC_01K7NB1XFCZNG11NHRD65MNDVE_THOUGHT_SPARKER
skill_ids: ["yU7IYhTRPNqzric6XAml","TzHcgDpDhsqhIVyZRFKF","xmkagkM1Gzb8c8k2x86l"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Pilots
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A pilot is studying the relationship between altitude and air pressure, represented by the expression $\\frac{(10^5)^2}{(10^2)^3} \\cdot 10^{-4}$. This expression models changes in pressure at different heights.","firstSentence":"How can you simplify this expression using index laws?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review each index law with examples before tackling the problem.","Encourage students to simplify step by step, focusing on one law at a time.","Ask students to explain why each index law is applied at each step to strengthen understanding."]}

skills:
["Understanding the index law $(a^m)^n = (a^n)^m = a^{m \\times n}$","Understanding the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{m}}$","Understanding the index laws $(ab)^n = a^n b^n$ and $(\\frac{a}{b})^m=\\frac{a^m}{b^m}$"]


example_id: lp_01K7NB1VKDNCS9G5KKJ67B7YEC_01K7NB1XFCZNG11NHRCGEP22PD_APPLICATION
skill_ids: ["yU7IYhTRPNqzric6XAml","TzHcgDpDhsqhIVyZRFKF","xmkagkM1Gzb8c8k2x86l"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Pilots
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Index Laws in Aviation Calculations","example1Header":"Situation\nPilots use index laws to calculate fuel efficiency and engine performance. These calculations help ensure safe and efficient flights.","example1Body":"Example\nTo calculate thrust: $(2 \\cdot 3)^2 = 2^2 \\cdot 3^2 = 36$. For fuel efficiency: $(\\frac{4}{2})^3 = \\frac{4^3}{2^3} = 8$. These ensure optimal engine performance.","example2Header":"","example2Body":""}

skills:
["Understanding the index law $(a^m)^n = (a^n)^m = a^{m \\times n}$","Understanding the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{m}}$","Understanding the index laws $(ab)^n = a^n b^n$ and $(\\frac{a}{b})^m=\\frac{a^m}{b^m}$"]


example_id: lp_01K7NB1VKDNCS9G5KKJ67B7YEC_01K7NB1XFCZNG11NHRD00CGPPB_CONTEMPLATIVE_QUESTION
skill_ids: ["yU7IYhTRPNqzric6XAml","TzHcgDpDhsqhIVyZRFKF","xmkagkM1Gzb8c8k2x86l"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Pilots
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A garden's area is $a^{\\frac{3}{2}}$ m$^2$. How could you rewrite and calculate its area using index laws?","teacherTips":["Encourage students to apply $a^{\\frac{m}{n}} = \\sqrt[n]{a^m}$ to simplify the expression.","Ask students to break down the process into smaller steps for clarity.","Discuss why understanding index laws simplifies complex expressions."],"difficulty":"mild"}

skills:
["Understanding the index law $(a^m)^n = (a^n)^m = a^{m \\times n}$","Understanding the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{m}}$","Understanding the index laws $(ab)^n = a^n b^n$ and $(\\frac{a}{b})^m=\\frac{a^m}{b^m}$"]


example_id: lp_01K7NB1VKDNCS9G5KKJ67B7YEC_01K7NB1XFCZNG11NHRCKSFJWWW_ACTIVITY
skill_ids: ["yU7IYhTRPNqzric6XAml","TzHcgDpDhsqhIVyZRFKF","xmkagkM1Gzb8c8k2x86l"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Pilots
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Exponent Challenge\nYour team is testing materials by calculating their properties using exponents.","scenario":"Steps\n1. In teams, write down $5$ expressions using $a^{\\frac{m}{n}}, (ab)^n$, or $(\\frac{a}{b})^m$.\n2. Swap expressions with another team to simplify.\n3. Solve each expression step by step, showing all workings.\n4. Earn $1$ point for each correct simplification.\n5. Team with the most points after $3$ rounds wins!","steps":["Discussion\n• Why does $a^{\\frac{1}{2}}$ represent a square root?\n• How does $(ab)^n$ differ from $(a^n)(b^n)$?","Differentiation Opportunities\n• Support: Focus on simpler cases like $a^{\\frac{1}{2}}$ and $a^{\\frac{1}{3}}$.\n• Extend: Include negative exponents or cases with $n \u003e 2$ in $a^{\\frac{m}{n}}$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NB1VKDNCS9G5KKJ67B7YEC_01K7NB1XFCZNG11NHRD9N68V6B_EXIT_TICKET
skill_ids: ["yU7IYhTRPNqzric6XAml","TzHcgDpDhsqhIVyZRFKF","xmkagkM1Gzb8c8k2x86l"]
subtopics: ["Index Laws"]
subtopic_ids: ["subtopic_01GTC0BCBD7SG25A0J4HF7GPRB"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Pilots
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$36$","question":"A pilot calculates fuel efficiency as $(2 \\cdot 3)^2$. Simplify using index laws."},{"answer":"$16$","question":"A pilot measures the altitude as $64^{\\frac{2}{3}}$ meters. Simplify using index laws."},{"answer":"$531\\,441$","question":"A pilot models an aircraft's speed as $((3^2)^3)^2$. Simplify using index laws."}]}


example_id: lp_01K7NHPMVMCHK73V28XWQN74RC_01K7NHPPFV1C7W1989XC239XG6_CONTEMPLATIVE_QUESTION
skill_ids: ["7qMtxkDwSGH35eFAlWnq","bHjBWVYvEE1qRqXagbQ9","KUMsu9PAaZRoWBoktpLo"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hot Air Balloon
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have a rectangle where the area is $64$ cm$^2$ and the length is $x+4$. How could you find $x$? What happens if the area was $-64$ cm$^2$? Explain your reasoning.","teacherTips":["Guide students to set up $x(x+4)=64$ and solve for $x$.","Discuss why $x(x+4)=-64$ has no real solutions.","Highlight connections to the difference of two squares if area changes."],"difficulty":"mild"}

skills:
["Solving quadratics without a $b$ term","Factorising using the difference of two squares","Identifying when quadratic equations have no real solutions"]


example_id: lp_01K7NHPMVMCHK73V28XWQN74RC_01K7NHPPFV1C7W1989XN4ARFGA_EXIT_TICKET
skill_ids: ["7qMtxkDwSGH35eFAlWnq","bHjBWVYvEE1qRqXagbQ9","KUMsu9PAaZRoWBoktpLo"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hot Air Balloon
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$x = 6, -6$","question":"If the height of a hot air balloon is modelled by $x^2 = 36$, what is the value of $x$?"},{"answer":"$x = 7, -7$","question":"If the area of a hot air balloon's shadow is modelled by $x^2 - 49 = 0$, what are the possible values of $x$?"},{"answer":"No real solutions","question":"If the vertical motion of a hot air balloon is modelled by $x^2 + 16 = 0$, does it have real solutions?"}]}

skills:
["Solving quadratics without a $b$ term","Factorising using the difference of two squares","Identifying when quadratic equations have no real solutions"]


example_id: lp_01K7NHPMVMCHK73V28XWQN74RC_01K7NHPPFV1C7W1989X51K9WEV_ACTIVITY
skill_ids: ["7qMtxkDwSGH35eFAlWnq","bHjBWVYvEE1qRqXagbQ9","KUMsu9PAaZRoWBoktpLo"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hot Air Balloon
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Escape the Quadratic Room!\nYou're trapped in a math escape room. Solve quadratic puzzles to unlock the doors!","scenario":"Steps\n1. Each team writes $3$ quadratic equations without a $b$ term (e.g., $x^2 = 16$).\n2. Swap equations with another team and solve them using factorisation.\n3. Check for solutions by substituting back into the equations.\n4. For each correct solution, your team earns $1$ key to unlock a 'door'.\n5. The team with the most keys after $5$ rounds escapes first!","steps":["Discussion\n• Why does $x^2 = -9$ have no real solutions?\n• How can you recognise a difference of two squares in an equation?","Differentiation Opportunities\n• Support: Provide examples like $x^2 = 25$ or $x^2 - 4 = 0$ to guide factorisation.\n• Extend: Create equations combining a difference of two squares and solving for $x$."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving quadratics without a $b$ term","Factorising using the difference of two squares","Identifying when quadratic equations have no real solutions"]


example_id: lp_01K7NHPMVMCHK73V28XWQN74RC_01K7NHPPFV1C7W1989X31XSTZK_APPLICATION
skill_ids: ["7qMtxkDwSGH35eFAlWnq","bHjBWVYvEE1qRqXagbQ9","KUMsu9PAaZRoWBoktpLo"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hot Air Balloon
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Height Calculations for Hot Air Balloons","example1Header":"Situation\nHot air balloon engineers calculate safe ascent paths. They often use algebra to find heights where paths cross obstacles like mountains and towers.","example1Body":"Example\nBalloon engineers solve $h^2 - 16 = 0$: factor $h^2 - 16 = (h + 4)(h - 4)$. Solve $h + 4 = 0$ or $h - 4 = 0$. Balloon height is $h = 4$ m.","example2Header":"","example2Body":""}


example_id: lp_01K7NHPMVMCHK73V28XWQN74RC_01K7NHPPFV1C7W1989XK9868VD_THOUGHT_SPARKER
skill_ids: ["7qMtxkDwSGH35eFAlWnq","bHjBWVYvEE1qRqXagbQ9","KUMsu9PAaZRoWBoktpLo"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hot Air Balloon
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The height of a hot air balloon is modelled by the quadratic equation $h^2 - 64 = 0$, where $h$ represents the height in metres.","firstSentence":"How could you determine whether this equation always gives a real height for the balloon?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the meaning of solutions in the context of the balloon's height.","Encourage students to explore the relationship between squaring and negative numbers.","Guide students through factorising $h^2 - 64$ as a difference of two squares."]}


example_id: lp_01K7NHZ4KCSMB5YKPFCH5DN9NP_01K7NHZ6BGSNB219R895G48S81_THOUGHT_SPARKER
skill_ids: ["xa8rofmVMqZ8hOkFtlEQ","Xp5WYIVvxQZjKmq1pC2y","gzt19fOHkyh3fjaYw1KP"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A zip line's height above the ground is modelled by the equation $2x^2 = 8x$, where $x$ represents the horizontal distance in metres from the starting point.","firstSentence":"How could you solve this equation to determine the horizontal distances where the zip line touches a specific height?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to recognise the absence of the $c$ term and discuss how it simplifies the equation.","Encourage students to try different methods, like factoring or grouping, to solve the equation.","Discuss the meaning of the solutions in the context of the zip line's height and position."]}

skills:
["Solving quadratic equations by grouping","Solving quadratic equations when there is no $c$ term","Factorising quadratic equations using the cross method"]


example_id: lp_01K7NHZ4KCSMB5YKPFCH5DN9NP_01K7NHZ6BGSNB219R88H3N5DMX_APPLICATION
skill_ids: ["xa8rofmVMqZ8hOkFtlEQ","Xp5WYIVvxQZjKmq1pC2y","gzt19fOHkyh3fjaYw1KP"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Engineering Safety in Zip Lining","example1Header":"Situation\nZip line engineers ensure cables are safe by studying forces. They calculate the best heights and slopes for thrilling yet secure rides.","example1Body":"Example\nFor $h^2 - 49h = 0$, engineers factor $h(h - 49) = 0$. Solving gives $h = 0$ or $h = 49$. The safe height difference is $49$ m.","example2Header":"","example2Body":""}

skills:
["Solving quadratic equations by grouping","Solving quadratic equations when there is no $c$ term","Factorising quadratic equations using the cross method"]


example_id: lp_01K7NHZ4KCSMB5YKPFCH5DN9NP_01K7NHZ6BGSNB219R88JB4FGPJ_ACTIVITY
skill_ids: ["xa8rofmVMqZ8hOkFtlEQ","Xp5WYIVvxQZjKmq1pC2y","gzt19fOHkyh3fjaYw1KP"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Quadratic Equation Race\nYour team is solving quadratic puzzles to unlock the next level in a math tournament!","scenario":"Steps\n1. Each group writes a quadratic equation with no $c$ term (e.g., $x^2 - 9x = 0$).\n2. Solve another group’s equation using factoring or grouping.\n3. Create a new quadratic equation for the next round (e.g., $x^2 + 5x + 6 = 0$).\n4. Solve this equation using the cross method and check with the group.\n5. Teams earn points for correct solutions. The first to $5$ points wins!","steps":["Discussion\n• How do you decide which method to use for solving?\n• Why is factoring effective for equations without a $c$ term?","Differentiation Opportunities\n• Support: Focus on equations with simpler coefficients and no cross products.\n• Extend: Create equations requiring grouping with larger coefficients or negatives."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving quadratic equations by grouping","Solving quadratic equations when there is no $c$ term","Factorising quadratic equations using the cross method"]


example_id: lp_01K7NHZ4KCSMB5YKPFCH5DN9NP_01K7NHZ6BGSNB219R890V7GY99_CONTEMPLATIVE_QUESTION
skill_ids: ["xa8rofmVMqZ8hOkFtlEQ","Xp5WYIVvxQZjKmq1pC2y","gzt19fOHkyh3fjaYw1KP"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A garden bed is shaped like a rectangle, and its area is $x^2 + 5x$. How could you use factoring to determine its possible dimensions? What are some other ways to solve for $x$ if more information is provided?","teacherTips":["Guide students to factor $x^2 + 5x$ as $x(x + 5)$, giving dimensions $x$ and $x + 5$.","Discuss solving using the cross method or grouping if additional terms exist.","Encourage exploration of scenarios where $x$ represents a length or width."],"difficulty":"mild"}


example_id: lp_01K7NHZ4KCSMB5YKPFCH5DN9NP_01K7NHZ6BGSNB219R89876V2CD_EXIT_TICKET
skill_ids: ["xa8rofmVMqZ8hOkFtlEQ","Xp5WYIVvxQZjKmq1pC2y","gzt19fOHkyh3fjaYw1KP"]
subtopics: ["Solving Quadratics"]
subtopic_ids: ["subtopic_01GTC0BHNGZ611Q49ZNNQHQ5JM"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$x = 0, x = 9$","question":"A zip line's height is modeled by $x^2 - 9x = 0$. What are the possible values for $x$?"},{"answer":"$x = -\\frac{3}{2}, x = -1$","question":"A zip line's travel time is modeled by $2x^2 + 7x + 3 = 0$. What are the solutions for $x$?"},{"answer":"$x = \\frac{2}{3}, x = -\\frac{5}{2}$","question":"The zip line's tension is modeled by $6x^2 + 11x - 10 = 0$. Solve for $x$ using grouping."}]}


example_id: lp_01K7NJ851Y27VK24PYDG14CVYD_01K7NJ87WSZ2711WJMFDGC1QM0_EXIT_TICKET
skill_ids: ["vInGFnruLrutFfS5l2zT","EvPRaqLVITUf1OdmeTFL","Gu8szS8MtqX4PUOmonKC"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: AFL
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$(2, 4), (5, 7)$","question":"In an AFL match analysis, a graph shows a line passing through the points $(2, 4)$ and $(5, 7)$. What are the coordinates of these points?"},{"answer":"$9$","question":"An AFL stadium entrance fee is modeled by $y = 3x + 9$. What is the $y$-intercept of the line?"},{"answer":"$2$","question":"An AFL coach plots a graph showing player speed improvement, with a line passing through $(1, 3)$ and $(4, 9)$. What is the gradient of the line?"}]}

skills:
["Calculating the gradient of a line","Finding the intercepts of linear equations","Reading coordinates from linear graphs"]


example_id: lp_01K7NJ851Y27VK24PYDG14CVYD_01K7NJ87WSZ2711WJMF3XQ7NKH_CONTEMPLATIVE_QUESTION
skill_ids: ["vInGFnruLrutFfS5l2zT","EvPRaqLVITUf1OdmeTFL","Gu8szS8MtqX4PUOmonKC"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: AFL
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A theme park designs a slide with a line equation $y = -2x + 8$. How can you find the $x$- and $y$-intercepts, read coordinates from the graph, and calculate its gradient? What does the gradient mean in this context?","teacherTips":["Substitute $y=0$ to find the $x$-intercept; $x=0$ for the $y$-intercept.","Use the formula $m=\\frac{\\text{rise}}{\\text{run}}$ to calculate the gradient.","Discuss how the gradient reflects the steepness of the slide."],"difficulty":"mild"}

skills:
["Calculating the gradient of a line","Finding the intercepts of linear equations","Reading coordinates from linear graphs"]


example_id: lp_01K7NJ851Y27VK24PYDG14CVYD_01K7NJ87WSZ2711WJMEQWASRXR_ACTIVITY
skill_ids: ["vInGFnruLrutFfS5l2zT","EvPRaqLVITUf1OdmeTFL","Gu8szS8MtqX4PUOmonKC"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: AFL
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Ramp Graph Design\nDesign a ramp by analysing its graph! Calculate intercepts, gradients, and coordinates.","scenario":"Steps\n1. Draw a graph with axes from $-10$ to $10$ using your paper.\n2. Pick two points for your ramp (e.g., $(-3, 2)$ and $(4, -1)$).\n3. Find the $x$- and $y$-intercepts of the line passing through these points.\n4. Calculate the gradient of your line using the formula $m = \\frac{y_2 - y_1}{x_2 - x_1}$.\n5. Present your ramp's graph and calculations to the class.","steps":["Discussion\n• How does the gradient affect the steepness of the ramp?\n• Why are intercepts important when designing real-world structures?","Differentiation Opportunities\n• Support: Provide pre-selected points for students to plot and analyse.\n• Extend: Have students write the equation of their line in slope-intercept form."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating the gradient of a line","Finding the intercepts of linear equations","Reading coordinates from linear graphs"]


example_id: lp_01K7NJ851Y27VK24PYDG14CVYD_01K7NJ87WSZ2711WJMEM17ZYA6_APPLICATION
skill_ids: ["vInGFnruLrutFfS5l2zT","EvPRaqLVITUf1OdmeTFL","Gu8szS8MtqX4PUOmonKC"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: AFL
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Tracking Player Performance in AFL","example1Header":"Situation\nAFL performance analysts use graphs to track players' running distances during games. They plot data on Cartesian planes to identify patterns and trends.","example1Body":"Example\nAn analyst reads the graph of a player's performance. At $(10, 5)$, the player ran $5$ km by the $10$th minute. At $(20, 11)$, the total distance is $11$ km by the $20$th minute.","example2Header":"","example2Body":""}


example_id: lp_01K7NJ851Y27VK24PYDG14CVYD_01K7NJ87WSZ2711WJMF7VBPMWV_THOUGHT_SPARKER
skill_ids: ["vInGFnruLrutFfS5l2zT","EvPRaqLVITUf1OdmeTFL","Gu8szS8MtqX4PUOmonKC"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: AFL
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An AFL player kicks the ball, and its trajectory can be modelled by the equation $y = -0.4x + 5$, where $x$ is the horizontal distance in metres, and $y$ is the height in metres.","firstSentence":"How could you determine the distance where the ball hits the ground?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to consider what happens to the height of the ball when it hits the ground.","Encourage students to solve for the x-intercept by substituting $y = 0$ into the equation.","Discuss the meaning of intercepts in real-world contexts to strengthen understanding."]}


example_id: lp_01K7NJHT9EZG5J6YHVVAP4TCM8_01K7NJHVWZJWWPW6EA8DKV4CYD_THOUGHT_SPARKER
skill_ids: ["oLWGbmMz5aPejLAh5pcj","jSTVpXXtucGUDyP2ODBd","kkSLJzGLs7xPkphZWmu0"]
subtopics: ["Parabola Graphs"]
subtopic_ids: ["subtopic_01GTC0BEF3TVHC9BZ64N4ZJ0GS"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Scuba Diving
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A scuba diver jumps off a platform, and their diving path follows the equation $y = -2(x - 3)^2 + 5$, where $x$ is the horizontal distance in metres and $y$ is the height in metres.","firstSentence":"What is the turning point of the diver’s path, and how can you tell from the equation?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the structure of the turning point form $y = a(x - h)^2 + k$ and how $h$ and $k$ determine the turning point.","Encourage students to explain their reasoning verbally or with diagrams, reinforcing understanding.","Discuss the significance of the turning point in the context of the diver's highest point during the jump."]}

skills:
["Matching a parabola’s graph to its equation in intercept form","Identifying the turning point of a parabola from its equation in turning point form","Finding the turning point of a parabola from its intercept form equation"]


example_id: lp_01K7NJHT9EZG5J6YHVVAP4TCM8_01K7NJHVWZJWWPW6EA7SSNB380_APPLICATION
skill_ids: ["oLWGbmMz5aPejLAh5pcj","jSTVpXXtucGUDyP2ODBd","kkSLJzGLs7xPkphZWmu0"]
subtopics: ["Parabola Graphs"]
subtopic_ids: ["subtopic_01GTC0BEF3TVHC9BZ64N4ZJ0GS"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Scuba Diving
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Calculating Safe Depths in Scuba Diving","example1Header":"Situation\nScuba diving instructors use physics to calculate safe diving depths. They rely on quadratic equations to predict pressure impacts at various depths, ensuring diver safety.","example1Body":"Example\nThe equation $p = -2(d - 20)^2 + 100$ has turning point $(h, k) = (20, 100)$. At $d = 20$ meters, pressure is maximal at $100$ atmospheres.","example2Header":"","example2Body":""}

skills:
["Matching a parabola’s graph to its equation in intercept form","Identifying the turning point of a parabola from its equation in turning point form","Finding the turning point of a parabola from its intercept form equation"]


example_id: lp_01K7NJHT9EZG5J6YHVVAP4TCM8_01K7NJHVWZJWWPW6EA8H364WEY_EXIT_TICKET
skill_ids: ["oLWGbmMz5aPejLAh5pcj","jSTVpXXtucGUDyP2ODBd","kkSLJzGLs7xPkphZWmu0"]
subtopics: ["Parabola Graphs"]
subtopic_ids: ["subtopic_01GTC0BEF3TVHC9BZ64N4ZJ0GS"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Scuba Diving
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$(1, 3)$","question":"A diver’s path underwater is modeled by $y = 2(x - 1)^2 + 3$. What is the turning point?"},{"answer":"$(-1, -27)$","question":"A scuba diver’s descent is modeled by $y = -3(x + 4)(x - 2)$. What is the turning point?"},{"answer":"$x$-intercepts: (1, 0), (-3, 0), turning point: (-1, -16)","question":"A diver’s trajectory is modeled by $y = 4(x-1)(x+3)$. Which graph matches this equation, and what are its key features?"}]}

skills:
["Matching a parabola’s graph to its equation in intercept form","Identifying the turning point of a parabola from its equation in turning point form","Finding the turning point of a parabola from its intercept form equation"]


example_id: lp_01K7NJHT9EZG5J6YHVVAP4TCM8_01K7NJHVWZJWWPW6EA808SCGJY_ACTIVITY
skill_ids: ["oLWGbmMz5aPejLAh5pcj","jSTVpXXtucGUDyP2ODBd","kkSLJzGLs7xPkphZWmu0"]
subtopics: ["Parabola Graphs"]
subtopic_ids: ["subtopic_01GTC0BEF3TVHC9BZ64N4ZJ0GS"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Scuba Diving
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Parabola Matching Game\nYou're a parabola detective! Match equations to graphs and find the turning points.","scenario":"Steps\n1. Each team writes an equation in turning point form, e.g., $y = 2(x-3)^2+4$.\n2. Plot the graph of your equation on graph paper, including the turning point.\n3. Swap equations anonymously with another team and plot their graph.\n4. Identify the turning point and match the graph to its equation.\n5. Check answers and discuss strategies. Points for correct matches!","steps":["Discussion\n• How does the turning point form make finding the vertex easier?\n• What challenges arise when matching graphs to equations?","Differentiation Opportunities\n• Support: Provide sample equations already in turning point form for practice.\n• Extend: Challenge teams with intercept form equations, e.g., $y = (x-2)(x+3)$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NJHT9EZG5J6YHVVAP4TCM8_01K7NJHVWZJWWPW6EA8BM2G69S_CONTEMPLATIVE_QUESTION
skill_ids: ["oLWGbmMz5aPejLAh5pcj","jSTVpXXtucGUDyP2ODBd","kkSLJzGLs7xPkphZWmu0"]
subtopics: ["Parabola Graphs"]
subtopic_ids: ["subtopic_01GTC0BEF3TVHC9BZ64N4ZJ0GS"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Scuba Diving
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A parabola has the equation $y = (x - 2)^2 + 3$. How would you find its turning point and match it to a graph? Can you create a different parabola equation with the same turning point?","teacherTips":["Guide students to recognise $(h, k)$ in $y = (x - h)^2 + k$ as the turning point.","Encourage students to sketch graphs for visual understanding.","Discuss how the same turning point can occur with different equations."],"difficulty":"mild"}


example_id: lp_01K7NJVQN26CDWTT1WJ3S03VE7_01K7NJVSBR45ET7CRFGVV3V39C_APPLICATION
skill_ids: ["sxKk73kTVhkschh3nS9S","UFrpaZO6fFzla0HbxpCp"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Long Jump
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Using Reflections in Long Jump Analysis","example1Header":"Situation\nLong jump coaches analyse athletes’ trajectories. They use graphs of jump paths and reflections to find symmetry and improve takeoff angles.","example1Body":"Example\nAn athlete’s jump path $f(x) = -x^2 + 6x$ reflects in the $y$-axis as $g(x) = -x^2 - 6x$. Coaches study $g(x)$ for improved trajectory symmetry.","example2Header":"","example2Body":""}

skills:
["Identifying and applying reflections in the $y$-axis to a graph or an equation","Identifying and applying reflections in the $x$-axis to a graph or an equation"]


example_id: lp_01K7NJVQN26CDWTT1WJ3S03VE7_01K7NJVSBR45ET7CRFHG039JQN_THOUGHT_SPARKER
skill_ids: ["sxKk73kTVhkschh3nS9S","UFrpaZO6fFzla0HbxpCp"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Long Jump
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a long jump competition, the trajectory of a jumper is modelled by the equation $y = -x^2 + 6x$, where $x$ represents the horizontal distance and $y$ the height. A coach suggests reflecting the graph over the $x$-axis to analyse a different scenario.","firstSentence":"Why might the coach choose to reflect the graph over the $x$-axis in this situation?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to describe how reflection over the $x$-axis changes the graph's shape and meaning in the context.","Encourage students to connect the reflection to real-world scenarios, such as observing patterns from a different perspective.","Use graphing technology to visually demonstrate the reflection and prompt students to explain the changes in coordinates."]}

skills:
["Identifying and applying reflections in the $y$-axis to a graph or an equation","Identifying and applying reflections in the $x$-axis to a graph or an equation"]


example_id: lp_01K7NJVQN26CDWTT1WJ3S03VE7_01K7NJVSBR45ET7CRFHKH4JKQ7_EXIT_TICKET
skill_ids: ["sxKk73kTVhkschh3nS9S","UFrpaZO6fFzla0HbxpCp"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Long Jump
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$g(x) = x^2 - 4$","question":"If a long jumper's path is modeled by $f(x) = -x^2 + 4$, what is the equation after reflecting it in the $x$-axis?"},{"answer":"$g(x) = 2x^2 + 3x$","question":"If a long jumper's path is modeled by $f(x) = 2x^2 - 3x$, what is the equation after reflecting it in the $y$-axis?"},{"answer":"$h(x) = x^3 - 2x$","question":"If a long jumper's trajectory is $f(x) = x^3 - 2x$, what is the equation after reflecting it in both the $x$-axis and $y$-axis?"}]}

skills:
["Identifying and applying reflections in the $y$-axis to a graph or an equation","Identifying and applying reflections in the $x$-axis to a graph or an equation"]


example_id: lp_01K7NJVQN26CDWTT1WJ3S03VE7_01K7NJVSBR45ET7CRFHDDCDPAN_CONTEMPLATIVE_QUESTION
skill_ids: ["sxKk73kTVhkschh3nS9S","UFrpaZO6fFzla0HbxpCp"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Long Jump
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A graph of $y = x^2$ is reflected in the $x$-axis and $y$-axis. How would you describe and compare these transformations?","teacherTips":["Reflection in the $x$-axis changes $y$ to $-y$, giving $y = -x^2$.","Reflection in the $y$-axis changes $x$ to $-x$, giving $y = (-x)^2$.","Encourage students to sketch and compare the graphs."],"difficulty":"mild"}


example_id: lp_01K7NJVQN26CDWTT1WJ3S03VE7_01K7NJVSBR45ET7CRFH11JWZHB_ACTIVITY
skill_ids: ["sxKk73kTVhkschh3nS9S","UFrpaZO6fFzla0HbxpCp"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Long Jump
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Mirror Graph Challenge\nYour team is designing mirror patterns for a funhouse using graph transformations!","scenario":"Steps\n1. Draw a shape (e.g., triangle or letter) on graph paper in the first quadrant.\n2. Reflect the shape across the $x$-axis and label the new coordinates.\n3. Reflect the original shape across the $y$-axis and label the new coordinates.\n4. Check symmetry by ensuring reflected points match the expected positions.\n5. Score $1$ point for each correct reflection. Play $3$ rounds!","steps":["Discussion\n• How does reflecting across the $x$-axis change the coordinates?\n• What patterns do you notice when reflecting across the $y$-axis?","Differentiation Opportunities\n• Support: Start with simpler shapes, like a single line segment.\n• Extend: Reflect shapes across both axes and write their equations."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NK2SCFE39BKHY9A1S1FJ8S_01K7NK2X3TSZ34JGY84XHSMJ2Q_APPLICATION
skill_ids: ["wKlSuE3JYwsCElcODMb5","kZijWEAoEuF4JxJAtgAc","RtGwVW4h5sm1ideXPCvM"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Gymnastics
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Perfecting Gymnastics Routines with Transformations","example1Header":"Situation\nGymnastics coaches use transformations to design routines. They ensure moves fit within the arena by adjusting timing, speeds, or positions.","example1Body":"Example\nA gymnast's move, $x(t) = t^2$, takes $4$ seconds. Stretching timing to $8$ seconds gives $x(t) = (\\frac{1}{2}t)^2$. Final position: $x(4) = 4$.","example2Header":"","example2Body":""}

skills:
["Identifying and applying vertical dilations to a graph or an equation","Identifying and applying translations to a graph or an equation","Identifying and applying horizontal dilations to a graph or an equation"]


example_id: lp_01K7NK2SCFE39BKHY9A1S1FJ8S_01K7NK2X3TSZ34JGY859N9874G_THOUGHT_SPARKER
skill_ids: ["wKlSuE3JYwsCElcODMb5","kZijWEAoEuF4JxJAtgAc","RtGwVW4h5sm1ideXPCvM"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Gymnastics
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A gymnast's jump can be modelled by the equation $y = -x^2 + 5$, where $x$ represents time in seconds and $y$ represents height in metres.","firstSentence":"What if the equation changes to $y = -2x^2 + 5$—how would this affect the graph of the gymnast's jump?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to describe the shape of the original parabola before discussing the transformation.","Encourage comparisons between the original graph and the transformed graph to identify changes.","Discuss the impact of the coefficient of $x^2$ on vertical dilation to strengthen understanding."]}

skills:
["Identifying and applying vertical dilations to a graph or an equation","Identifying and applying translations to a graph or an equation","Identifying and applying horizontal dilations to a graph or an equation"]


example_id: lp_01K7NK2SCFE39BKHY9A1S1FJ8S_01K7NK2X3TSZ34JGY855P0783V_CONTEMPLATIVE_QUESTION
skill_ids: ["wKlSuE3JYwsCElcODMb5","kZijWEAoEuF4JxJAtgAc","RtGwVW4h5sm1ideXPCvM"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Gymnastics
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create an equation for a graph $y=f(x)$ that is stretched horizontally, shifted up 3 units, and compressed vertically by a factor of $2$. Sketch and explain your reasoning.","teacherTips":["Discuss how horizontal dilations change $x$ in the function.","Explain how vertical dilations multiply the output values.","Link translations to shifts along the $x$ or $y$ axis."],"difficulty":"mild"}

skills:
["Identifying and applying vertical dilations to a graph or an equation","Identifying and applying translations to a graph or an equation","Identifying and applying horizontal dilations to a graph or an equation"]


example_id: lp_01K7NK2SCFE39BKHY9A1S1FJ8S_01K7NK2X3TSZ34JGY851295V6W_ACTIVITY
skill_ids: ["wKlSuE3JYwsCElcODMb5","kZijWEAoEuF4JxJAtgAc","RtGwVW4h5sm1ideXPCvM"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Gymnastics
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Graph Transformation Race\nTeams compete to correctly transform graphs using given equations and rules.","scenario":"Steps\n1. Draw a coordinate plane and graph $y = x^2$ as the starting graph.\n2. Each team gets a transformation (e.g., $y = 2x^2$ or $y = (x - 3)^2$).\n3. Apply the transformation and redraw the graph on the same plane.\n4. Write down the rule for the transformation (e.g., vertical stretch or translation).\n5. Score points for correct graphs and explanations. Most points wins!","steps":["Discussion\n• How do vertical and horizontal dilations differ visually?\n• Why does $y = (x - 3)^2$ move the graph to the right?","Differentiation Opportunities\n• Support: Focus only on vertical dilations and simple translations.\n• Extend: Combine multiple transformations, such as $y = 2(x + 1)^2 - 3$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NK2SCFE39BKHY9A1S1FJ8S_01K7NK2X3TSZ34JGY85FZMKMT5_EXIT_TICKET
skill_ids: ["wKlSuE3JYwsCElcODMb5","kZijWEAoEuF4JxJAtgAc","RtGwVW4h5sm1ideXPCvM"]
subtopics: ["Transformations of Functions"]
subtopic_ids: ["subtopic_01GTC0BPNQSQD59VWHQNKM5VNX"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Gymnastics
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$y = x^2 + 3$","question":"A gymnast's position on a trampoline is modeled by $y = x^2$. What happens to the graph if it is translated up by $3$ units?"},{"answer":"$y = 2x^2$","question":"If a gymnast's jump height is modeled by $y = x^2$, what is the new equation after a vertical dilation by a factor of $2$?"},{"answer":"$y = \\left(\\frac{x}{3} - 2\\right)^2$","question":"The gymnast's path is modeled by $y = (x - 2)^2$. What is the new equation after a horizontal dilation by a factor of $3$?"}]}


example_id: lp_01K7NK9HK56MJJ1GKFCDESBZRR_01K7NK9M6PWY93A6T38GR6WSAP_THOUGHT_SPARKER
skill_ids: ["EeHuflKuIhdmHFaC2gzP","y9P64ixgMvpUMYhzijkL","QHazjQhHKtp2487KJe3M"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Gardening
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"You are designing a garden pot that is in the shape of a cylinder with a cone-shaped lid. The cylindrical part of the pot has a radius of $8$ cm and a height of $15$ cm, while the conical lid has the same radius and a slant height of $10$ cm.","firstSentence":"How would you calculate the total surface area of the pot, including its lid?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify and calculate individual surface areas (cylinder and cone) before summing.","Discuss why the base of the cone is not included in the total surface area calculation.","Use real-life examples, like pots or containers, to connect the math to everyday objects."]}

skills:
["Calculating the total surface area of a cylinder","Calculating the total surface area of a prism","Calculating the total surface area of cones"]


example_id: lp_01K7NK9HK56MJJ1GKFCDESBZRR_01K7NK9M6PWY93A6T382KTVX00_APPLICATION
skill_ids: ["EeHuflKuIhdmHFaC2gzP","y9P64ixgMvpUMYhzijkL","QHazjQhHKtp2487KJe3M"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Gardening
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Calculating Surface Area for Garden Beds","example1Header":"Situation\nLandscape gardeners design raised garden beds to grow plants efficiently. They calculate surface area to know how much material is needed for the structure.","example1Body":"Example\nA garden bed with $2$ m length, $1$ m width, and $0.5$ m height has surface area $2 \\times (2 \\times 1 + 2 \\times 0.5 + 1 \\times 0.5) = 7$ m$^2$. This helps calculate material needed.","example2Header":"","example2Body":""}

skills:
["Calculating the total surface area of a cylinder","Calculating the total surface area of a prism","Calculating the total surface area of cones"]


example_id: lp_01K7NK9HK56MJJ1GKFCDESBZRR_01K7NK9M6PWY93A6T38DAY3DZS_CONTEMPLATIVE_QUESTION
skill_ids: ["EeHuflKuIhdmHFaC2gzP","y9P64ixgMvpUMYhzijkL","QHazjQhHKtp2487KJe3M"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Gardening
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a water tank with a cylindrical body and a cone-shaped top. How would you calculate the total surface area of your tank? Explain your method and choices.","teacherTips":["Guide students to calculate the surface area of both the cylinder and cone.","Encourage students to explore real-world dimensions for their design.","Discuss the importance of accuracy in calculating surface areas."],"difficulty":"mild"}

skills:
["Calculating the total surface area of a cylinder","Calculating the total surface area of a prism","Calculating the total surface area of cones"]


example_id: lp_01K7NK9HK56MJJ1GKFCDESBZRR_01K7NK9M6PWY93A6T385STG6PV_ACTIVITY
skill_ids: ["EeHuflKuIhdmHFaC2gzP","y9P64ixgMvpUMYhzijkL","QHazjQhHKtp2487KJe3M"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Gardening
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Gift Box Geometry\nYour team is designing custom gift boxes shaped as cylinders, cones, or prisms.","scenario":"Steps\n1. Choose a shape: cylinder, cone, or prism, and write its dimensions.\n2. Calculate the total surface area of your shape using the correct formula.\n3. Check calculations with a teammate and compare results.\n4. Draw a net of your shape to visualise its surface area.\n5. Present your design and explain how you calculated the surface area.","steps":["Discussion\n• Why do different shapes need different formulas for surface area?\n• How would doubling the dimensions affect the surface area?","Differentiation Opportunities\n• Support: Provide dimensions that result in whole numbers for easier calculations.\n• Extend: Design a composite shape by combining two shapes, then calculate its surface area."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NK9HK56MJJ1GKFCDESBZRR_01K7NK9M6PWY93A6T38Q665W57_EXIT_TICKET
skill_ids: ["EeHuflKuIhdmHFaC2gzP","y9P64ixgMvpUMYhzijkL","QHazjQhHKtp2487KJe3M"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Gardening
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$48\\pi$","question":"A garden water barrel has a radius of $3$ m and a height of $5$ m. What is its total surface area?"},{"answer":"$44\\pi$","question":"A cone-shaped garden sprinkler has a radius of $4$ m and a slant height of $7$ m. What is its total surface area?"},{"answer":"$108$","question":"A garden bed is a triangular prism with base area $6$ m$^2$, perimeter $12$ m, and length $8$ m. What is its total surface area?"}]}


example_id: lp_01K7NKHDM2Y4D0C2QZN07WZXRX_01K7NKHFHM57437E2DBM56RGR3_THOUGHT_SPARKER
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A 3D printer creates a cone with a base radius of $5$ cm and a height of $12$ cm, and a rectangular prism with dimensions $8$ cm by $6$ cm by $10$ cm.","firstSentence":"What would you need to calculate to determine the total volume of both objects?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the formulas for both the cone and rectangular prism before starting calculations.","Discuss the importance of correctly substituting values into the formulas for volume.","Ask students to explain their steps and reasoning to ensure understanding of how total volume is found."]}

skills:
["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism","Calculating the volume of cones"]


example_id: lp_01K7NKHDM2Y4D0C2QZN07WZXRX_01K7NKHFHM57437E2DB2G4P0ME_APPLICATION
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Calculating Material Usage in 3D Printing","example1Header":"Situation\n3D printing engineers calculate the volume of objects before printing. This ensures the printer uses the correct amount of material for the job.","example1Body":"Example\nA box with dimensions $10$ cm (length), $6$ cm (width), and $4$ cm (height) has a volume of $10 \\times 6 \\times 4 = 240$ cm$^3$. This helps engineers estimate material needs.","example2Header":"","example2Body":""}

skills:
["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism","Calculating the volume of cones"]


example_id: lp_01K7NKHDM2Y4D0C2QZN07WZXRX_01K7NKHFHM57437E2DBT6QFB22_EXIT_TICKET
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$400$","question":"A 3D printer creates a rectangular prism model with dimensions $10$ cm by $8$ cm by $5$ cm, what is its volume in cm$^3$?"},{"answer":"$300$","question":"A 3D printer creates a cylinder with a base area of $25$ cm$^2$ and a height of $12$ cm. What is the volume of the cylinder?"},{"answer":"$120\\pi$","question":"A cone printed by a 3D printer has a radius of $6$ cm and a height of $10$ cm. What is its volume in terms of $\\pi$?"}]}

skills:
["Solving for volume using $V=Ah$","Calculating the volume of a rectangular prism","Calculating the volume of cones"]


example_id: lp_01K7NKHDM2Y4D0C2QZN07WZXRX_01K7NKHFHM57437E2DB7K5K7MB_ACTIVITY
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Storage Space Showdown\nDesign storage containers to maximise space for a new warehouse.","scenario":"Steps\n1. Draw a cone (radius $3$ cm, height $10$ cm) and a rectangular prism ($4$ cm by $4$ cm by $10$ cm).\n2. Calculate the base area of each shape using $A = \\pi r^2$ for the cone and $A = l \\times w$ for the prism.\n3. Use $V = Ah$ to find the volume of each shape.\n4. Compare the volumes to decide which shape stores more efficiently.\n5. Discuss and justify your choice based on your calculations.","steps":["Discussion\n• Why does the cone have less volume than the prism with the same height?\n• How would doubling the dimensions affect the volume of each shape?","Differentiation Opportunities\n• Support: Use simpler dimensions (e.g., radius $2$ cm) and provide $A = \\pi r^2$ example calculations.\n• Extend: Add a cylinder (radius $3$ cm, height $10$ cm) and compare its volume to the cone and prism."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NKHDM2Y4D0C2QZN07WZXRX_01K7NKHFHM57437E2DBFZMZQP6_CONTEMPLATIVE_QUESTION
skill_ids: ["PAGdRpS75rtjcjOLRc0q","RHCO94iqkbeRFRSKAg8r","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a water tank. Would a cone-shaped tank or a rectangular prism tank hold more water if both have the same height and the same base area? Explain your reasoning and calculate example volumes.","teacherTips":["Remind students to use $V = Ah$ for both shapes.","Encourage students to compare volumes mathematically.","Discuss why the cone's volume is smaller despite equal base area and height."],"difficulty":"mild"}


example_id: lp_01K7NKQXG5VK17A0NDMY9SK5DF_01K7NKQZ7D15PSWTE9NTNYE5C7_CONTEMPLATIVE_QUESTION
skill_ids: ["bOmMN6kR4EL8dcQK0aj3","h5lEA3FMgxY8fXRqVKZt"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Stars
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You measure a distance as $0.003456$ km. How would you express it to $2$ significant figures and in scientific notation? Why might scientific notation be useful here?","teacherTips":["Discuss the importance of identifying significant figures in measurements.","Demonstrate steps to convert small numbers into scientific notation.","Connect scientific notation to real-world applications like science."],"difficulty":"mild"}

skills:
["Applying significant figure rules in rounding","Converting numbers to and from scientific notation"]


example_id: lp_01K7NKQXG5VK17A0NDMY9SK5DF_01K7NKQZ7D15PSWTE9P44ACGSM_EXIT_TICKET
skill_ids: ["bOmMN6kR4EL8dcQK0aj3","h5lEA3FMgxY8fXRqVKZt"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Stars
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$123$","question":"The brightness of a star is measured as $123.456$ lumens. Round this value to $3$ significant figures."},{"answer":"$4.3 \\times 10^6$","question":"A star is $4\\,300\\,000$ km away from Earth. Express this distance in scientific notation."},{"answer":"$9.877 \\times 10^{30}$","question":"The mass of a star is $9.8765 \\times 10^{30}$ kg. Round this value to $4$ significant figures."}]}

skills:
["Applying significant figure rules in rounding","Converting numbers to and from scientific notation"]


example_id: lp_01K7NKQXG5VK17A0NDMY9SK5DF_01K7NKQZ7CTR9E1SRYBNHJY9J6_ACTIVITY
skill_ids: ["bOmMN6kR4EL8dcQK0aj3","h5lEA3FMgxY8fXRqVKZt"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Stars
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Scientific Notation Showdown\nYou're part of a maths challenge! Convert and round numbers to score points for your team.","scenario":"Steps\n1. Each team writes $10$ large or small numbers on paper.\n2. Pass your numbers to another team to convert to scientific notation.\n3. Round each converted number to $3$ significant figures.\n4. Teams check each other's work; $1$ point per correct conversion and rounding.\n5. The team with the most points after $3$ rounds wins!","steps":["Discussion\n• Why is scientific notation useful for very large or small numbers?\n• How does rounding to significant figures simplify calculations?","Differentiation Opportunities\n• Support: Limit numbers to whole numbers or powers of $10$ for easier conversion.\n• Extend: Use numbers with decimals and require $4$ significant figures."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Applying significant figure rules in rounding","Converting numbers to and from scientific notation"]


example_id: lp_01K7NKQXG5VK17A0NDMY9SK5DF_01K7NKQZ7CTR9E1SRYBK9GVPW0_APPLICATION
skill_ids: ["bOmMN6kR4EL8dcQK0aj3","h5lEA3FMgxY8fXRqVKZt"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Stars
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Measuring the Brightness of Stars","example1Header":"Situation\nAstronomers measure star brightness using scientific notation. The light intensity from stars is tiny, so they write values as powers of ten for precision.","example1Body":"Example\nA star's light intensity of $0.000003$ watts per square metre is written as $3 \\times 10^{-6}$ in scientific notation. Converting back confirms the value.","example2Header":"","example2Body":""}


example_id: lp_01K7NKQXG5VK17A0NDMY9SK5DF_01K7NKQZ7D15PSWTE9NZAFJZYW_THOUGHT_SPARKER
skill_ids: ["bOmMN6kR4EL8dcQK0aj3","h5lEA3FMgxY8fXRqVKZt"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Stars
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A star in the Milky Way galaxy has a brightness of $3.7 \\times 10^{-9}$ lumens, while another star in a nearby galaxy is $0.0000000042$ lumens bright.","firstSentence":"How would you convert both brightness values into scientific notation to compare them easily?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the rules for writing numbers in scientific notation, including identifying the correct power of ten.","Discuss why scientific notation is useful for comparing extremely large or small values in astronomy.","Encourage students to explain their reasoning step-by-step to ensure clarity when applying significant figure rules."]}


example_id: lp_01K7NSX4PJ31PMNNK6ZGPNT0HC_01K7NSX69QEVQ6AK5XP90BWC88_CONTEMPLATIVE_QUESTION
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have a rectangular garden with one diagonal measuring $10$ m. One side is $6$ m. How could you find the other side length? If you scale the garden by a factor of $1.5$, what will the new side lengths and diagonal be?","teacherTips":["Guide students to use $a^2 + b^2 = c^2$ for the original dimensions.","Discuss how to apply the scale factor to all three dimensions.","Encourage checking their scaled dimensions using Pythagoras' theorem."],"difficulty":"mild"}

skills:
["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem","Solving for unknown sides using a scale factor"]


example_id: lp_01K7NSX4PJ31PMNNK6ZGPNT0HC_01K7NSX69QEVQ6AK5XNW1ZN3GV_ACTIVITY
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Ramp Design Challenge\nYour team designs ramps for a building. Use maths to ensure they are safe and functional.","scenario":"Steps\n1. Draw a right triangle with a base of $4$ m and height of $3$ m.\n2. Calculate the ramp's length using Pythagoras' theorem.\n3. Scale the triangle by a factor of $1.5$ and recalculate the ramp length.\n4. Compare ramp lengths and discuss which is more practical.\n5. Present your design with all calculations to the class!","steps":["Discussion\n• Why does the ramp length change with scale?\n• What other factors might affect the ramp design in real life?","Differentiation Opportunities\n• Support: Start with simpler dimensions like $3$ m base and $4$ m height.\n• Extend: Add a second ramp with a different scale factor and compare both."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem","Solving for unknown sides using a scale factor"]


example_id: lp_01K7NSX4PJ31PMNNK6ZGPNT0HC_01K7NSX69QEVQ6AK5XPNJMNHYG_EXIT_TICKET
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5$","question":"An architect designs a triangular window with sides $3$ m and $4$ m. What is the length of the hypotenuse?"},{"answer":"$2.5$","question":"A floor plan uses a scale factor of $1:100$. If a wall measures $2.5$ cm on the plan, what is its real-life length in metres?"},{"answer":"$5.45$","question":"A ramp is $6$ m long and $2.5$ m high. How far is the base of the ramp from the wall it leans on?"}]}

skills:
["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem","Solving for unknown sides using a scale factor"]


example_id: lp_01K7NSX4PJ31PMNNK6ZGPNT0HC_01K7NSX69QEVQ6AK5XPFHT6638_THOUGHT_SPARKER
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An architect designs a triangular roof where the longest side is $10$ m, and the other two sides are $6$ m and $8$ m. A scaled-down model of the roof is created with a scale factor of $0.25$.","firstSentence":"How could you determine the length of the longest side in the scaled-down model?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to first calculate the scale factor's effect on lengths.","Encourage the use of Pythagoras' theorem to confirm the triangle's properties before scaling.","Discuss how scale factors apply to all sides proportionally in similar triangles."]}


example_id: lp_01K7NSX4PJ31PMNNK6ZGPNT0HC_01K7NSX69QEVQ6AK5XNQXRJD8J_APPLICATION
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Using Scale Factors in Building Models","example1Header":"Situation\nArchitects use scale models to visualise buildings before construction. These models are scaled-down versions of actual structures, making them easier to study and present.","example1Body":"Example\nAn architect's model is $15$ cm tall with a scale factor of $1:100$. The building height is $15 \\times 100 = 1,500$ cm, or $15$ m, matching the correct scale.","example2Header":"","example2Body":""}


example_id: lp_01K7NT62DERXDH6B5Q4BH99TV4_01K7NT645FC7PY3RSPXZWS2XCX_APPLICATION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Flamingos
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Tracking Flamingo Population Changes","example1Header":"Situation\nConservationists monitor flamingo populations to track environmental health. They calculate percentage changes to see if populations grow or decline over time.","example1Body":"Example\nFlamingo numbers rise from $2\\,000$ to $2\\,400$. The increase is $400$, so the percentage change is $(400 \\div 2\\,000) \\times 100 = 20\\%$.","example2Header":"","example2Body":""}


example_id: lp_01K7NT62DERXDH6B5Q4BH99TV4_01K7NT645FC7PY3RSPYR5WBKR7_THOUGHT_SPARKER
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Flamingos
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A population of flamingos in a wildlife reserve increased from $1\\,200$ to $1\\,500$ over a year.","firstSentence":"What would the population be if it increased by another $30\\%$ the following year?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate the difference and percentage change step by step.","Discuss how to apply percentages to the original or new population.","Ask students to explain why finding $30\\%$ involves multiplying rather than adding."]}


example_id: lp_01K7NT62DERXDH6B5Q4BH99TV4_01K7NT645FC7PY3RSPYWX61SX4_EXIT_TICKET
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Flamingos
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$50\\%$","question":"A flamingo flock increases from $50$ to $75$ in population, what is the percentage increase?"},{"answer":"$4$ \\text{ kg}","question":"If a flamingo's weight decreases by $20\\%$ from $5$ kg, what is the new weight?"},{"answer":"$20\\%$","question":"A flamingo's habitat size decreases from $1\\,500$ m$^2$ to $1\\,200$ m$^2$. What is the percentage decrease?"}]}


example_id: lp_01K7NT62DERXDH6B5Q4BH99TV4_01K7NT645FC7PY3RSPY4244YE4_ACTIVITY
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Flamingos
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Shopping Discount Wars\nYour team must calculate discounts to find the best deals for a shopping spree!","scenario":"Steps\n1. Each team writes a list of $5$ items with prices (e.g., $\\$40$, $\\$75$).\n2. Assign a discount percentage to each item (e.g., $10\\%$, $20\\%$).\n3. Calculate the discounted price for all items on your list.\n4. Compare your savings with other teams' results.\n5. Team with the highest total savings wins!","steps":["Discussion\n• How does a higher discount percentage affect the savings?\n• Why might a smaller discount on an expensive item save more money?","Differentiation Opportunities\n• Support: Use simpler percentages like $10\\%$ and $20\\%$ to calculate.\n• Extend: Include price increases (e.g., tax) alongside discounts."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NT62DERXDH6B5Q4BH99TV4_01K7NT645FC7PY3RSPYH1ED0A8_CONTEMPLATIVE_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Flamingos
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A store increases the price of a $\\$50$ item by $20\\%$. Then, it decreases the new price by $10\\%$. What strategies could you use to calculate the final price? Could the order of changes affect the result?","teacherTips":["Encourage students to calculate the price after each percentage change.","Discuss why the order of percentage changes does not result in the same final price.","Ask students to explore how the initial dollar value influences the result."],"difficulty":"mild"}


example_id: lp_01K7NTE6E7JV7GEKGCNF6TW440_01K7NTE82JMEHCW7C8REWH3KT8_THOUGHT_SPARKER
skills: ["Solving ratio problems with the unitary method","Solving proportions in worded problems"]
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A helicopter travels $300$ km in $2$ hours, maintaining a constant speed throughout the journey.","firstSentence":"How would you calculate the distance it could travel in $5$ hours at the same speed?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to find the distance travelled in $1$ hour first using the unitary method.","Discuss how proportions can help solve similar problems with different time intervals.","Ask students to explain why maintaining a constant speed makes the ratio consistent."]}


example_id: lp_01K7NTE6E7JV7GEKGCNF6TW440_01K7NTE82JMEHCW7C8QTMC5WBG_APPLICATION
skills: ["Solving ratio problems with the unitary method","Solving proportions in worded problems"]
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Helicopter Fuel Planning with Ratios","example1Header":"Situation\nHelicopter pilots carefully calculate fuel usage for flights. They use ratios to ensure they carry enough fuel for distance and time while considering safety reserves.","example1Body":"Example\nA helicopter uses $30$ litres of fuel for $150$ km. The consumption per km is $0.2$ litres. For a $600$ km trip, $600 \\times 0.2 = 120$ litres are needed.","example2Header":"","example2Body":""}


example_id: lp_01K7NTE6E7JV7GEKGCNF6TW440_01K7NTE82JMEHCW7C8R9YK9SVS_CONTEMPLATIVE_QUESTION
skills: ["Solving ratio problems with the unitary method","Solving proportions in worded problems"]
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are mixing a drink with a ratio of $2:5$ (juice to water). How would you make $3$ litres of this drink?","teacherTips":["Use the unitary method to find the amount for $1$ part.","Scale up the ratio to match $3$ litres.","Check your total matches $3$ litres after calculations."],"difficulty":"mild"}


example_id: lp_01K7NTE6E7JV7GEKGCNF6TW440_01K7NTE82JMEHCW7C8QWX0TPHH_ACTIVITY
skills: ["Solving ratio problems with the unitary method","Solving proportions in worded problems"]
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Recipe Ratio Challenge\nYou're chefs scaling recipes for a school event. Adjust ingredients using ratios!","scenario":"Steps\n1. Write a recipe for $4$ people with $5$ ingredients (e.g., $2$ cups flour).\n2. Choose a new number of servings (e.g., $10$) and scale each ingredient.\n3. Solve proportions using the unitary method to adjust quantities.\n4. Compare your scaled recipe with another team’s for accuracy.\n5. Vote on the most creative and accurate recipe!","steps":["Discussion\n• How does the unitary method simplify scaling recipes?\n• What happens if you mix up the ratio when scaling?","Differentiation Opportunities\n• Support: Scale recipes for simpler ratios (e.g., $2:1$ or $3:1$).\n• Extend: Include fractional quantities (e.g., $1.5$ cups) in the recipe."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NTE6E7JV7GEKGCNF6TW440_01K7NTE82JMEHCW7C8RMA9X62P_EXIT_TICKET
skills: ["Solving ratio problems with the unitary method","Solving proportions in worded problems"]
skill_ids: ["pelss5UYj3L19Z5qsjMs","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Helicopters
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$120$","question":"A helicopter travels $60$ km in $30$ minutes. How far will it travel in $1$ hour, assuming the speed is constant?"},{"answer":"$250$","question":"The fuel-to-oil ratio for a helicopter is $50:1$. If $5$ L of oil is used, how much fuel is required?"},{"answer":"$750$","question":"A helicopter blade completes $150$ rotations in $12$ seconds. How many rotations will it complete in $1$ minute at the same rate?"}]}


example_id: lp_01K7NTN0ZNFSR4FKDVA3GHBSFH_01K7NTN2J6SYERDP4EDKNV6NS7_CONTEMPLATIVE_QUESTION
skills: ["Identifying a surd","Identifying irrational numbers","Identifying a radical"]
skill_ids: ["FOPsZf30hq9ztDRJ3RhL","XHrGWcu54yB4u78LyNcJ","asLHfoiSTUpnHOkBiDjq"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Treehouse
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a list of $5$ numbers, including at least one surd, one irrational number, and one radical. Explain how you identified each type of number in your list.","teacherTips":["Ensure students know surds, irrational numbers, and radicals are distinct concepts.","Explain a surd is an irrational square root, e.g., $\\sqrt{2}$.","Discuss how irrational numbers have non-repeating, non-terminating decimals."],"difficulty":"mild"}


example_id: lp_01K7NTN0ZNFSR4FKDVA3GHBSFH_01K7NTN2J6SYERDP4EDQAB9HS7_EXIT_TICKET
skills: ["Identifying a surd","Identifying irrational numbers","Identifying a radical"]
skill_ids: ["FOPsZf30hq9ztDRJ3RhL","XHrGWcu54yB4u78LyNcJ","asLHfoiSTUpnHOkBiDjq"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Treehouse
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"The length of a treehouse ladder is expressed as $\\sqrt{25}$. Is this a radical?"},{"answer":"Yes","question":"The wooden plank for a treehouse is cut to a length of $\\sqrt{18}$ m. Is $\\sqrt{18}$ a surd?"},{"answer":"Yes","question":"While designing a treehouse, the diagonal of the floor measures $\\sqrt{2}$ m. Is $\\sqrt{2}$ an irrational number?"}]}


example_id: lp_01K7NTN0ZNFSR4FKDVA3GHBSFH_01K7NTN2J6SYERDP4ED7NP0V6Q_ACTIVITY
skills: ["Identifying a surd","Identifying irrational numbers","Identifying a radical"]
skill_ids: ["FOPsZf30hq9ztDRJ3RhL","XHrGWcu54yB4u78LyNcJ","asLHfoiSTUpnHOkBiDjq"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Treehouse
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Number Sorting Challenge\nYour team is sorting numbers into surds, radicals, and irrational numbers to win points!","scenario":"Steps\n1. Write $15$ numbers on your paper, e.g., $2$, $\\sqrt{5}$, $\\pi$, $\\sqrt{9}$.\n2. In teams, classify each number as a surd, radical, or irrational.\n3. Check your classifications with another team for accuracy.\n4. Score $2$ points for each correct classification.\n5. Team with the highest score wins!","steps":["Discussion\n• Why is $\\sqrt{9}$ not a surd but $\\sqrt{5}$ is?\n• What makes a number irrational or not?","Differentiation Opportunities\n• Support: Provide examples of surds, radicals, and irrational numbers to guide classification.\n• Extend: Challenge students to create their own complex examples for classification."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NTN0ZNFSR4FKDVA3GHBSFH_01K7NTN2J6SYERDP4EDPAMTB2A_THOUGHT_SPARKER
skills: ["Identifying a surd","Identifying irrational numbers","Identifying a radical"]
skill_ids: ["FOPsZf30hq9ztDRJ3RhL","XHrGWcu54yB4u78LyNcJ","asLHfoiSTUpnHOkBiDjq"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Treehouse
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A treehouse is built on a square base with each side measuring $5$ m, and the diagonal of the square is calculated as $\\sqrt{50}$ m.","firstSentence":"Why do you think the diagonal is written as $\\sqrt{50}$ instead of a decimal?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to explore why $\\sqrt{50}$ is considered an exact value and how it relates to irrational numbers.","Encourage discussion about approximations versus exact representations in mathematics.","Use visual aids, such as a diagram of the square base, to help students connect the measurement to the Pythagorean theorem."]}


example_id: lp_01K7NTN0ZNFSR4FKDVA3GHBSFH_01K7NTN2J6SYERDP4ED5VXFGW9_APPLICATION
skills: ["Identifying a surd","Identifying irrational numbers","Identifying a radical"]
skill_ids: ["FOPsZf30hq9ztDRJ3RhL","XHrGWcu54yB4u78LyNcJ","asLHfoiSTUpnHOkBiDjq"]
subtopics: ["Surds \u0026 Radicals"]
subtopic_ids: ["subtopic_01GTC0BFR6W10HH6J0K5BY5DS1"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Treehouse
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Treehouse Stability with Radicals","example1Header":"Situation\nTreehouse builders ensure stability by calculating dimensions. Some lengths, like diagonal supports, involve square roots for accuracy.","example1Body":"Example\nTo find the diagonal of a triangular support with base $3$ m and height $4$ m, builders calculate $c = \\sqrt{3^2 + 4^2} = \\sqrt{25}$. This shows a radical before simplification.","example2Header":"","example2Body":""}


example_id: lp_01K7NTWKJVKTPZN7CT7BGW09QP_01K7NTWN5MMF7PABGBXR6BF1M4_APPLICATION
skill_ids: ["qTPzvnTNx4XiHQqpMART","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Paralympics
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Predicting Medal Wins in Paralympic Events","example1Header":"Situation\nParalympic statisticians predict medal outcomes by analysing probabilities of athletes winning multiple independent events. This helps teams strategise and allocate resources effectively.","example1Body":"Example\nAn athlete's gold probability in Event A is $0.7$, and in Event B is $0.6$. The combined probability is $0.7 \\times 0.6 = 0.42$, meaning a $42\\%$ chance of winning gold in both.","example2Header":"","example2Body":""}

skills:
["Calculating the probability of multiple independent events","Calculating the probability of combined events"]


example_id: lp_01K7NTWKJVKTPZN7CT7BGW09QP_01K7NTWN5MMF7PABGBYD0XN6Y3_THOUGHT_SPARKER
skill_ids: ["qTPzvnTNx4XiHQqpMART","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Paralympics
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a Paralympic event, the probability that an Australian athlete wins gold in wheelchair basketball is $0.6$, and the probability of winning gold in swimming is $0.75$.","firstSentence":"What is the probability of Australia winning gold in both events, assuming the outcomes are independent?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss what it means for events to be independent and how this affects probability calculations.","Encourage students to represent probabilities visually, such as with a tree diagram or table.","Have students explain why the product of probabilities is used for independent events."]}

skills:
["Calculating the probability of multiple independent events","Calculating the probability of combined events"]


example_id: lp_01K7NTWKJVKTPZN7CT7BGW09QP_01K7NTWN5MMF7PABGBYAHSQANM_CONTEMPLATIVE_QUESTION
skill_ids: ["qTPzvnTNx4XiHQqpMART","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Paralympics
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip a coin and roll a die at the same time. How would you calculate the probability of flipping heads and rolling a $4$? Explain your reasoning.","teacherTips":["Remind students that coin flips and die rolls are independent events.","Encourage students to find probabilities for each event separately.","Guide students to multiply independent probabilities for the combined event."],"difficulty":"mild"}

skills:
["Calculating the probability of multiple independent events","Calculating the probability of combined events"]


example_id: lp_01K7NTWKJVKTPZN7CT7BGW09QP_01K7NTWN5MMF7PABGBXW1K0G53_ACTIVITY
skill_ids: ["qTPzvnTNx4XiHQqpMART","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Paralympics
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Probability Battle\nTeams compete to predict and test probabilities using dice and coins.","scenario":"Steps\n1. Each team flips $2$ coins and rolls $1$ die $10$ times.\n2. Predict the probability of getting $2$ heads and a $4$ on the die.\n3. Record actual outcomes and compare with predictions.\n4. Calculate the experimental probability from your results.\n5. Discuss why theoretical and experimental probabilities differ.","steps":["Discussion\n• Why might experimental probabilities differ from theoretical ones?\n• How does adding events affect the overall probability?","Differentiation Opportunities\n• Support: Use only one coin and one die to simplify calculations.\n• Extend: Add a second die and calculate probabilities for combined outcomes."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NTWKJVKTPZN7CT7BGW09QP_01K7NTWN5MMF7PABGBYGX1P76E_EXIT_TICKET
skill_ids: ["qTPzvnTNx4XiHQqpMART","GE5sCMlhlaZ6mYjuN6NM"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Paralympics
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.3$","question":"At a Paralympics event, the probability of Australia winning a gold medal in swimming is $0.6$ and in athletics is $0.5$. What is the probability of winning both?"},{"answer":"$0.512$","question":"If the probability of an athlete hitting the bullseye in archery is $0.8$ each time, what is the probability of hitting it $3$ times in a row?"},{"answer":"$0.46$","question":"At a Paralympics game, the probability of winning in cycling is $0.7$, and the probability of winning in table tennis is $0.6$. If these are independent, what is the probability of winning only one?"}]}


example_id: lp_01K7NV3XCEVHQ0D6ASHJCT6K7X_01K7NV3Z40BQYZ6YB4VR5PMCKY_EXIT_TICKET
skill_ids: ["bfwhKwobovBxMDGzX5o2","NlcP4a6JETto9xf03JFi"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Filmmaking
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$8$","question":"A filmmaker records $10$ scenes, $4$ have action and $6$ have drama. If $2$ have both, how many scenes have action or drama?"},{"answer":"$0.8$","question":"If a film has $60\\%$ chance of success in cinemas and $50\\%$ in streaming, and $30\\%$ overlap, what's the probability of success in either?"},{"answer":"$0.2$","question":"A documentary has $40\\%$ chance of winning at one festival, $30\\%$ at another, and $20\\%$ overlap. What's the chance of winning at both?"}]}

skills:
["Understanding union and intersection","Calculating the probability of the union or intersection of two events"]


example_id: lp_01K7NV3XCEVHQ0D6ASHJCT6K7X_01K7NV3Z40BQYZ6YB4VJWFV7EG_CONTEMPLATIVE_QUESTION
skill_ids: ["bfwhKwobovBxMDGzX5o2","NlcP4a6JETto9xf03JFi"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Filmmaking
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You roll a $6$-sided die and spin a spinner with $4$ colours. How would you calculate: (a) the probability of rolling a $3$ or spinning red? (b) the probability of rolling a $3$ and spinning red?","teacherTips":["Explain the difference between union (or) and intersection (and).","Guide students to list possible outcomes for each event.","Encourage students to justify their probability calculations."],"difficulty":"mild"}

skills:
["Understanding union and intersection","Calculating the probability of the union or intersection of two events"]


example_id: lp_01K7NV3XCEVHQ0D6ASHJCT6K7X_01K7NV3Z40BQYZ6YB4VB5822Z2_ACTIVITY
skill_ids: ["bfwhKwobovBxMDGzX5o2","NlcP4a6JETto9xf03JFi"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Filmmaking
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Dice Probability Challenge\nRoll dice to explore unions and intersections of events!","scenario":"Steps\n1. In pairs, roll two dice $20$ times and record the outcomes.\n2. Define two events: $A$ (e.g., sum is $6$) and $B$ (e.g., one die shows $4$).\n3. Count outcomes in $A$, $B$, and $A \\cap B$ (intersection).\n4. Calculate probabilities for $A$, $B$, and $A \\cup B$ (union).\n5. Compare results and discuss patterns in probabilities.","steps":["Discussion\n• How does overlap between $A$ and $B$ affect $P(A \\cup B)$?\n• Why is $P(A \\cup B)$ greater than $P(A \\cap B)$?","Differentiation Opportunities\n• Support: Focus only on $A$ or $B$ initially, then introduce $A \\cap B$.\n• Extend: Add a third event (e.g., $C$: sum is even) and explore $A \\cup B \\cup C$."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding union and intersection","Calculating the probability of the union or intersection of two events"]


example_id: lp_01K7NV3XCEVHQ0D6ASHJCT6K7X_01K7NV3Z40BQYZ6YB4VMX6DRA2_THOUGHT_SPARKER
skill_ids: ["bfwhKwobovBxMDGzX5o2","NlcP4a6JETto9xf03JFi"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Filmmaking
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a film festival, $40\\%$ of the films are action, $30\\%$ are comedies, and $15\\%$ are both action and comedies.","firstSentence":"What is the probability of randomly choosing a film that is either an action film or a comedy?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to visually represent the problem using Venn diagrams.","Discuss the importance of subtracting the overlap when calculating union probabilities.","Ask students to explain their reasoning and explore alternative ways to verify their solutions."]}


example_id: lp_01K7NV3XCEVHQ0D6ASHJCT6K7X_01K7NV3Z40BQYZ6YB4V7T799ZJ_APPLICATION
skill_ids: ["bfwhKwobovBxMDGzX5o2","NlcP4a6JETto9xf03JFi"]
subtopics: ["Union \u0026 Intersection"]
subtopic_ids: ["subtopic_01GTC0BQGH0DKCB47KF6S02E59"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Filmmaking
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Planning Shots with Probability in Filmmaking","example1Header":"Situation\nFilm directors use probability to plan shots. They estimate how likely it is for good weather and quiet locations to align for outdoor scenes.","example1Body":"Example\nThe probability of good weather is $0.6$, and quiet locations $0.4$. With $P(A \\cap B)=0.2$, $P(A \\cup B)=0.6+0.4-0.2=0.8$, giving an $80\\%$ chance of favorable conditions.","example2Header":"","example2Body":""}


example_id: lp_01K7NVA5BEADTEVDZ6336RPWYE_01K7NVA7JED94X492XJXTBK0T4_EXIT_TICKET
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Fencing
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.8$","question":"In a fencing match, Alice scores hits in $8$ out of $10$ attempts. What is the probability of Alice scoring a hit?"},{"answer":"$0.1$","question":"If the theoretical probability of landing a scoring hit in fencing is $0.6$, but James scores in $70\\%$ of attempts, how do these compare?"},{"answer":"$0.06$","question":"In $50$ fencing attempts, the theoretical probability of success is $0.5$, but Sarah succeeds $28$ times. What is the difference in probabilities?"}]}

skills:
["Comparing theoretical and experimental probabilities","Finding probability from experiments","Comparing experimental results to expected outcomes"]


example_id: lp_01K7NVA5BEADTEVDZ6336RPWYE_01K7NVA7JED94X492XJNKJEJPV_CONTEMPLATIVE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Fencing
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip a coin $50$ times. How do the experimental probabilities compare to the theoretical probabilities? What could affect your results?","teacherTips":["Encourage students to calculate experimental probability as $\\frac{\\text{favourable outcomes}}{\\text{total trials}}$.","Discuss possible reasons for deviations, like bias in the coin or flipping technique.","Prompt students to consider how increasing trials might impact the results."],"difficulty":"mild"}

skills:
["Comparing theoretical and experimental probabilities","Finding probability from experiments","Comparing experimental results to expected outcomes"]


example_id: lp_01K7NVA5BEADTEVDZ6336RPWYE_01K7NVA7JED94X492XJEQPW0MW_ACTIVITY
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Fencing
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Dice Probability Challenge\nYour team is testing how often each number appears when rolling dice.","scenario":"Steps\n1. Each group rolls a die $30$ times and records the outcomes in a table.\n2. Calculate the experimental probability for each number (e.g., $1$, $2$, $3$).\n3. Compare your results to the theoretical probability of $\\frac{1}{6}$.\n4. Discuss why experimental probabilities may differ from theoretical ones.\n5. Combine class data to see if larger trials match theory better.","steps":["Discussion\n• Why might experimental and theoretical probabilities differ?\n• Does increasing trials make results closer to theory? Why?","Differentiation Opportunities\n• Support: Use fewer trials (e.g., $10$) and focus on one number's probability.\n• Extend: Roll two dice, calculate sums, and compare probabilities for each sum."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Comparing theoretical and experimental probabilities","Finding probability from experiments","Comparing experimental results to expected outcomes"]


example_id: lp_01K7NVA5BEADTEVDZ6336RPWYE_01K7NVA7JED94X492XJCKEHDJZ_APPLICATION
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Fencing
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Using Probability in Fencing Matches","example1Header":"Situation\nFencing coaches analyze match data to predict future outcomes. They track successful strikes in past matches to calculate probabilities and develop strategies for their fencers.","example1Body":"Example\nA fencer lands $45$ strikes in $60$ attempts. The probability of a successful strike is calculated as $P = \\frac{45}{60} = 0.75$, or $75\\%$. This helps the coach plan strategies based on performance.","example2Header":"","example2Body":""}


example_id: lp_01K7NVA5BEADTEVDZ6336RPWYE_01K7NVA7JED94X492XJPBCJ31H_THOUGHT_SPARKER
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Probability
topic_id: fc9c4c55-d558-542e-ae13-73e5e9da81d4
context: Fencing
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A fencer has a theoretical probability of $0.6$ of hitting the target during practice. In a recent session, they attempted $50$ hits and successfully hit the target $28$ times.","firstSentence":"How would you compare the experimental results to the theoretical probability of hitting the target?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to calculate the experimental probability before comparing it to the theoretical probability.","Encourage discussion about why the experimental results might differ from the theoretical probability.","Explore how increasing the number of attempts could impact the comparison between experimental and theoretical probabilities."]}


example_id: lp_01K7NVKDREBKEW13XDX2541GTC_01K7NVKFDA5QEHZ6VZHWD5PE94_APPLICATION
skill_ids: ["nx5Kj1XObFU4BaYjUGCD","xgWr4s3OW79uYfQ9tGCL","IGS71xKy75JFX29eDqDa"]
subtopics: ["Trigonometry Foundations"]
subtopic_ids: ["subtopic_01GTC0BHXSSGERHCP37RZ5Z7ZC"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Airplanes
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Trigonometry in Airplane Navigation","example1Header":"Situation\nPilots rely on trigonometry to navigate planes. They use triangles formed by the plane's path, altitude, and distance to calculate directions and ensure safe flights.","example1Body":"Example\nFor a $30^\\circ$ climb angle, the hypotenuse is the plane's path, the opposite side is the altitude, and the adjacent side is the horizontal ground distance. This naming helps pilots in navigation.","example2Header":"","example2Body":""}

skills:
["Finding angles using trigonometry","Identifying and naming the sides of a triangle relative to an angle","Finding side lengths using trigonometry"]


example_id: lp_01K7NVKDREBKEW13XDX2541GTC_01K7NVKFDA5QEHZ6VZJHMWASZR_THOUGHT_SPARKER
skill_ids: ["nx5Kj1XObFU4BaYjUGCD","xgWr4s3OW79uYfQ9tGCL","IGS71xKy75JFX29eDqDa"]
subtopics: ["Trigonometry Foundations"]
subtopic_ids: ["subtopic_01GTC0BHXSSGERHCP37RZ5Z7ZC"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Airplanes
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An airplane is flying at an angle of elevation of $30^\\circ$ from the ground observer's point of view, and the straight-line distance from the observer to the airplane is $500$ m.","firstSentence":"How would you determine the height of the airplane above the ground?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify and label the triangle's sides relative to the given angle.","Discuss which trigonometric ratio (sine, cosine, or tangent) is most appropriate to use.","Ask students to explain their reasoning for choosing a particular method or ratio."]}

skills:
["Finding angles using trigonometry","Identifying and naming the sides of a triangle relative to an angle","Finding side lengths using trigonometry"]


example_id: lp_01K7NVKDREBKEW13XDX2541GTC_01K7NVKFDA5QEHZ6VZJP967K8N_EXIT_TICKET
skill_ids: ["nx5Kj1XObFU4BaYjUGCD","xgWr4s3OW79uYfQ9tGCL","IGS71xKy75JFX29eDqDa"]
subtopics: ["Trigonometry Foundations"]
subtopic_ids: ["subtopic_01GTC0BHXSSGERHCP37RZ5Z7ZC"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Airplanes
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Opposite side","question":"On an airplane wing, if the angle $\\theta$ is $30^\\circ$, what is the side opposite $\\theta$ relative to the hypotenuse?"},{"answer":"$171.01$","question":"An airplane ascends at an angle of $20^\\circ$ with the runway, and the hypotenuse is $500$ m. What is the height it reaches?"},{"answer":"$36.87^\\circ$","question":"A pilot observes the runway at an angle of depression. If the adjacent side is $400$ m and the opposite side is $300$ m, what is the angle of depression?"}]}

skills:
["Finding angles using trigonometry","Identifying and naming the sides of a triangle relative to an angle","Finding side lengths using trigonometry"]


example_id: lp_01K7NVKDREBKEW13XDX2541GTC_01K7NVKFDA5QEHZ6VZJ3KK2N7T_ACTIVITY
skill_ids: ["nx5Kj1XObFU4BaYjUGCD","xgWr4s3OW79uYfQ9tGCL","IGS71xKy75JFX29eDqDa"]
subtopics: ["Trigonometry Foundations"]
subtopic_ids: ["subtopic_01GTC0BHXSSGERHCP37RZ5Z7ZC"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Airplanes
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Trigonometry Rescue Mission\nA hiker is stranded on a cliff! Calculate distances and angles to guide a rescue team.","scenario":"Steps\n1. Draw a right-angled triangle representing the cliff, the ground, and the rescue path.\n2. Label the sides as opposite, adjacent, and hypotenuse relative to a given angle.\n3. Use trigonometric ratios to calculate missing side lengths.\n4. Find the angle of elevation for the rescue path using inverse trigonometry.\n5. Check your solutions and compare strategies with your team.","steps":["Discussion\n• How do you decide which trigonometric ratio to use?\n• What happens if you choose the wrong side labels?","Differentiation Opportunities\n• Support: Provide a simplified triangle with one missing side length and one known angle.\n• Extend: Challenge students to solve a triangle with no angles provided, using inverse trigonometry."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NVKDREBKEW13XDX2541GTC_01K7NVKFDA5QEHZ6VZJEWYHG44_CONTEMPLATIVE_QUESTION
skill_ids: ["nx5Kj1XObFU4BaYjUGCD","xgWr4s3OW79uYfQ9tGCL","IGS71xKy75JFX29eDqDa"]
subtopics: ["Trigonometry Foundations"]
subtopic_ids: ["subtopic_01GTC0BHXSSGERHCP37RZ5Z7ZC"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Airplanes
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A ladder leans against a wall, forming a $65^\\circ$ angle with the ground. The ladder is $4$ m long. How would you find the height it reaches on the wall and how far its base is from the wall? Explain your strategy.","teacherTips":["Guide students to label sides as opposite, adjacent, and hypotenuse.","Encourage the use of $\\sin$, $\\cos$, and $\\tan$ appropriately.","Ask students to justify why they chose specific trigonometric ratios."],"difficulty":"mild"}


example_id: lp_01K7NVVWZG77AXP7DRC9G3C68H_01K7NVVZ443840XH3Q3MY01AXR_CONTEMPLATIVE_QUESTION
skills: ["Identifying dilated shapes"]
skill_ids: ["TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Halloween
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You see a triangle and its dilated version. How would you check if they are similar? What steps would you take to confirm this?","teacherTips":["Encourage students to compare corresponding angles and sides.","Discuss how proportionality is key in identifying dilated shapes.","Emphasise that angles remain unchanged during dilation."],"difficulty":"mild"}


example_id: lp_01K7NVVWZG77AXP7DRC9G3C68H_01K7NVVZ443840XH3Q3VW1J4ET_EXIT_TICKET
skills: ["Identifying dilated shapes"]
skill_ids: ["TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Halloween
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"A pumpkin decoration is enlarged by a factor of $2$. Does the enlarged pumpkin have the same shape as the original?"},{"answer":"Yes","question":"A witch's hat is resized by a scale factor of $0.5$. Are the angles of the resized hat the same as the original?"},{"answer":"$30$ \\text{ cm}","question":"A bat decoration is dilated with a scale factor of $3$. If the original wingspan is $10$ cm, what is the wingspan of the dilated bat?"}]}


example_id: lp_01K7NVVWZG77AXP7DRC9G3C68H_01K7NVVZ443840XH3Q3AHWN4W6_ACTIVITY
skills: ["Identifying dilated shapes"]
skill_ids: ["TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Halloween
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Shape Dilation Challenge\nYour team must resize shapes using scale factors and identify their properties.","scenario":"Steps\n1. Each team draws a triangle and a rectangle on graph paper.\n2. Choose a scale factor (e.g., $2$, $0.5$, $3$) and redraw each shape.\n3. Measure sides of original and dilated shapes to confirm proportionality.\n4. Compare results with another team to check accuracy.\n5. Score $1$ point for each correctly dilated shape!","steps":["Discussion\n• What stays the same in a dilated shape?\n• How does the scale factor affect the size of the shape?","Differentiation Opportunities\n• Support: Use only whole-number scale factors (e.g., $2$, $3$).\n• Extend: Experiment with fractional scale factors (e.g., $0.5$, $1.5$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NVVWZG77AXP7DRC9G3C68H_01K7NVVZ443840XH3Q36PC0MK3_APPLICATION
skills: ["Identifying dilated shapes"]
skill_ids: ["TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Halloween
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Halloween Decorations and Shape Transformations","example1Header":"Situation\nEvent planners for Halloween create decorations of different sizes. They make sure that when shapes are resized, their proportions remain correct to keep the designs consistent.","example1Body":"Example\nA spider web with sides $2$ cm, $4$ cm, and $5$ cm is resized to $6$ cm, $12$ cm, and $15$ cm. Since $6 \\div 2 = 3$, $12 \\div 4 = 3$, and $15 \\div 5 = 3$, the larger web is a correct dilation.","example2Header":"","example2Body":""}


example_id: lp_01K7NVVWZG77AXP7DRC9G3C68H_01K7NVVZ443840XH3Q3S523ASW_THOUGHT_SPARKER
skills: ["Identifying dilated shapes"]
skill_ids: ["TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Space
topic_id: 8f9c68ad-209e-50bd-a554-79e153693ae6
context: Halloween
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"For Halloween, a family creates pumpkin decorations in different sizes. The first pumpkin's face is carved on a triangle with sides $6$ cm, $8$ cm, and $10$ cm, and the second pumpkin's face is carved on a triangle with sides $12$ cm, $16$ cm, and $20$ cm.","firstSentence":"Are these triangles dilated versions of each other, and why?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the concept of dilation and how it affects side lengths.","Encourage students to compare the ratios of corresponding sides.","Use visual aids or drawings to help students identify patterns in the triangles."]}


example_id: lp_01K7NZ4CZEM2T0KAHF1W87KVJ4_01K7NZ4ERXD94ESBPMX6J6847E_APPLICATION
skills: ["Finding the mode","Calculating the mean","Finding the median"]
skill_ids: ["FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Card Games
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Finding the Mean in Card Game Scores","example1Header":"Situation\nProfessional card players track scores to analyse performance. Calculating the mean score helps understand overall performance across games played.","example1Body":"Example\nA card player scored $15$, $20$, $18$, $22$, and $25$ in five games. Adding these gives $100$. Dividing by $5$ gives the mean score: $20$.","example2Header":"","example2Body":""}


example_id: lp_01K7NZ4CZEM2T0KAHF1W87KVJ4_01K7NZ4ERXD94ESBPMXNMR6TE5_THOUGHT_SPARKER
skills: ["Finding the mode","Calculating the mean","Finding the median"]
skill_ids: ["FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Card Games
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"During a card game, a player scores the following points across $7$ rounds: $10$, $15$, $15$, $20$, $25$, $30$, and $40$.","firstSentence":"Which measure of central tendency—mean, median, or mode—do you think best represents the player's performance, and why?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate the mean, median, and mode before deciding which is most representative.","Discuss the strengths and weaknesses of each measure, especially in the context of outliers.","Facilitate a discussion about how context affects the choice of the most appropriate measure of central tendency."]}


example_id: lp_01K7NZ4CZEM2T0KAHF1W87KVJ4_01K7NZ4ERXD94ESBPMXQ1BHYCB_EXIT_TICKET
skills: ["Finding the mode","Calculating the mean","Finding the median"]
skill_ids: ["FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Card Games
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5$","question":"In a card game, the scores of $7$ players are $5, 7, 5, 9, 10, 5, 8$. What is the mode of their scores?"},{"answer":"$10$","question":"During a card game, the scores of $5$ players are $12, 8, 14, 10, 9$. What is the median score?"},{"answer":"$20$","question":"A card game has scores of $15, 20, 10, 25, 30, 20$. What is the mean score of the players?"}]}


example_id: lp_01K7NZ4CZEM2T0KAHF1W87KVJ4_01K7NZ4ERXD94ESBPMXB4ZGNM6_ACTIVITY
skills: ["Finding the mode","Calculating the mean","Finding the median"]
skill_ids: ["FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Card Games
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Sports Stats Challenge\nYour class is tracking scores in a basketball free-throw game to analyse the mean, median, and mode.","scenario":"Steps\n1. Each team takes $10$ basketball free-throw shots and records their scores.\n2. Write all $10$ scores in ascending order on your paper.\n3. Find the mode (most common score) from your team's data.\n4. Calculate the median by finding the middle score or averaging the two middle scores.\n5. Calculate the mean by adding all scores and dividing by $10$.","steps":["Discussion\n• What does the mean tell you about your team's performance?\n• How does the mode differ from the mean in representing the scores?","Differentiation Opportunities\n• Support: Provide a partially ordered list of scores to help with calculations.\n• Extend: Combine data from two teams and calculate the new mean, median, and mode."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7NZ4CZEM2T0KAHF1W87KVJ4_01K7NZ4ERXD94ESBPMXJ3J7Y91_CONTEMPLATIVE_QUESTION
skills: ["Finding the mode","Calculating the mean","Finding the median"]
skill_ids: ["FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Card Games
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your class surveys $10$ students on hours of TV watched weekly. Create data, find mean, median, mode.","teacherTips":["Guide students to create realistic data for hours watched.","Ensure students arrange data in order to find the median.","Discuss how mean, median, and mode describe data differently."],"difficulty":"mild"}


example_id: lp_01K7NZFM2GZKBTDVNC1F16FCKP_01K7NZFNM2BHXV3QC5NQD41VX5_EXIT_TICKET
skill_ids: ["33fD9GQeAaZUFpWBj8Zb","EynlqRpby7HISkWORU26","A2vaRoxM2u0gdY9tIxka"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Pangolins
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"If researchers randomly select $50$ pangolins from a population of $1\\,000$, is this a random sample?"},{"answer":"Stratified sampling","question":"If researchers divide the pangolin population by habitat type and sample $20$ pangolins from each habitat, what sampling method is this?"},{"answer":"Selection bias","question":"If researchers only sample pangolins near roads because they are easier to find, what type of sampling error does this introduce?"}]}

skills:
["Identifying different types of sampling errors","Identifying different sampling methods","Defining and recognising random samples"]


example_id: lp_01K7NZFM2GZKBTDVNC1F16FCKP_01K7NZFNM2BHXV3QC5N4ZSRE15_ACTIVITY
skill_ids: ["33fD9GQeAaZUFpWBj8Zb","EynlqRpby7HISkWORU26","A2vaRoxM2u0gdY9tIxka"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Pangolins
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Sampling Showdown\nYour team is tasked with finding out the class's favourite fruit using fair sampling!","scenario":"Steps\n1. List all classmates' names on a piece of paper (this is the population).\n2. Each team picks $10$ classmates using a random method (e.g., drawing names).\n3. Use a non-random method (e.g., choosing $10$ nearest students).\n4. Compare results from both methods and identify any sampling errors.\n5. Discuss which method gave more reliable results and why.","steps":["Discussion\n• Why is random sampling usually better than non-random methods?\n• What types of errors might occur even with random sampling?","Differentiation Opportunities\n• Support: Limit the sample size to $5$ students to simplify comparisons.\n• Extend: Test additional sampling methods, such as stratified sampling."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Identifying different types of sampling errors","Identifying different sampling methods","Defining and recognising random samples"]


example_id: lp_01K7NZFM2GZKBTDVNC1F16FCKP_01K7NZFNM2BHXV3QC5NHPEA409_CONTEMPLATIVE_QUESTION
skill_ids: ["33fD9GQeAaZUFpWBj8Zb","EynlqRpby7HISkWORU26","A2vaRoxM2u0gdY9tIxka"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Pangolins
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your school wants to survey students about lunch preferences. How would you ensure the sample is random, avoid sampling errors, and choose a fair sampling method?","teacherTips":["Explain why random sampling ensures fairness in surveys.","Discuss examples of potential sampling errors like bias or small sample size.","Encourage students to suggest and justify their sampling methods."],"difficulty":"mild"}

skills:
["Identifying different types of sampling errors","Identifying different sampling methods","Defining and recognising random samples"]


example_id: lp_01K7NZFM2GZKBTDVNC1F16FCKP_01K7NZFNM2BHXV3QC5MZVMNHXH_APPLICATION
skill_ids: ["33fD9GQeAaZUFpWBj8Zb","EynlqRpby7HISkWORU26","A2vaRoxM2u0gdY9tIxka"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Pangolins
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Sampling Methods in Pangolin Conservation","example1Header":"Situation\nWildlife researchers studying pangolins often cannot track every pangolin in a region. Instead, they use sampling methods to gather population data and understand their habitats.","example1Body":"Example\nResearchers use random sampling by selecting $100$ pangolins randomly from $1\\,000$. Alternatively, stratified sampling divides the forest into $10$ zones, sampling $10$ pangolins per zone for balanced data.","example2Header":"","example2Body":""}


example_id: lp_01K7NZFM2GZKBTDVNC1F16FCKP_01K7NZFNM2BHXV3QC5NJ00C94X_THOUGHT_SPARKER
skill_ids: ["33fD9GQeAaZUFpWBj8Zb","EynlqRpby7HISkWORU26","A2vaRoxM2u0gdY9tIxka"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Pangolins
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Researchers in Australia are studying pangolins and collect data from $50$ randomly selected forests, but they only visit forests with easy access by road.","firstSentence":"How might this sampling method affect the study's accuracy and reliability?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to think about how location affects the distribution of pangolins.","Discuss the difference between convenience sampling and true random sampling.","Ask students to suggest alternative sampling methods for better accuracy."]}


example_id: lp_01K7NZQ8PCPM4WX97D9AC9V5YN_01K7NZQAT0CNKZXPT0NBM8JS3F_ACTIVITY
skill_ids: ["01JZH2HS0MSSZ5GRQ3H2PW736X","b8ucObd21anVLda7sMsa","2ZVgCioON5G43gUiotqs"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Harry Potter
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Sports Stats Showdown\nYour team is analysing scores from two sports teams to find patterns and insights.","scenario":"Steps\n1. Draw a back-to-back stem-and-leaf plot for two teams' scores: Team A ($45, 48, 50, 52, 55, 60$) and Team B ($40, 42, 50, 53, 57, 62$).\n2. Label the diagram clearly with stems in the middle and leaves for each team on opposite sides.\n3. Calculate the quartiles (Q1, Q2, Q3) and interquartile range (IQR) for each team.\n4. Compare the spreads and medians to determine which team performed more consistently.\n5. Present your findings to the class, supporting your conclusions with data.","steps":["Discussion\n• How does the IQR help compare consistency between teams?\n• Why is the median a better measure than the mean for this data?","Differentiation Opportunities\n• Support: Provide a pre-drawn stem-and-leaf template for students to fill in.\n• Extend: Add a third dataset and compare all three teams' performances."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Interpreting back-to-back stem and leaf plots","Matching histograms to box plots","Calculating quartiles and IQR from a stem-and-leaf plot"]


example_id: lp_01K7NZQ8PCPM4WX97D9AC9V5YN_01K7NZQAT0CNKZXPT0NNM14VY9_CONTEMPLATIVE_QUESTION
skill_ids: ["01JZH2HS0MSSZ5GRQ3H2PW736X","b8ucObd21anVLda7sMsa","2ZVgCioON5G43gUiotqs"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Harry Potter
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a back-to-back stem-and-leaf plot for two classes' test scores. What are the quartiles, IQR, and how would you match a histogram to a box plot for this data?","teacherTips":["Guide students to organise data into stems and leaves clearly.","Explain how to calculate quartiles and IQR from the plot.","Discuss how features of the stem-and-leaf relate to histograms and box plots."],"difficulty":"mild"}

skills:
["Interpreting back-to-back stem and leaf plots","Matching histograms to box plots","Calculating quartiles and IQR from a stem-and-leaf plot"]


example_id: lp_01K7NZQ8PCPM4WX97D9AC9V5YN_01K7NZQAT0CNKZXPT0NVARHGQJ_EXIT_TICKET
skill_ids: ["01JZH2HS0MSSZ5GRQ3H2PW736X","b8ucObd21anVLda7sMsa","2ZVgCioON5G43gUiotqs"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Harry Potter
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Gryffindor","question":"The Gryffindor and Slytherin Quidditch teams recorded their practice times (minutes). Which team had the longer median time?"},{"answer":"$20$","question":"In a stem-and-leaf plot of Defense Against the Dark Arts test scores, if Q1 = 45 and Q3 = 65, what is the interquartile range?"},{"answer":"Left whisker longer","question":"A histogram of potion-making times at Hogwarts shows a skewed left shape. What feature would the box plot of this data reflect?"}]}

skills:
["Interpreting back-to-back stem and leaf plots","Matching histograms to box plots","Calculating quartiles and IQR from a stem-and-leaf plot"]


example_id: lp_01K7NZQ8PCPM4WX97D9AC9V5YN_01K7NZQAT0CNKZXPT0NA353TTD_APPLICATION
skill_ids: ["01JZH2HS0MSSZ5GRQ3H2PW736X","b8ucObd21anVLda7sMsa","2ZVgCioON5G43gUiotqs"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Harry Potter
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Comparing Spells with Data from Hogwarts","example1Header":"Situation\nAt Hogwarts, professors compare students' spell practice results. A back-to-back stem-and-leaf plot helps analyse proficiency between two houses (e.g., Gryffindor and Slytherin).","example1Body":"Example\nUsing the stem-and-leaf plot, Gryffindor's scores are 52, 54, 58, and Slytherin's are 51, 53, 57. The medians are 54 (Gryffindor) and 53 (Slytherin), showing small differences.","example2Header":"","example2Body":""}


example_id: lp_01K7NZQ8PCPM4WX97D9AC9V5YN_01K7NZQAT0CNKZXPT0NQ05FYTK_THOUGHT_SPARKER
skill_ids: ["01JZH2HS0MSSZ5GRQ3H2PW736X","b8ucObd21anVLda7sMsa","2ZVgCioON5G43gUiotqs"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Harry Potter
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Students from Gryffindor and Slytherin practiced casting a spell, and their times (in seconds) were recorded using a back-to-back stem-and-leaf plot.","firstSentence":"What conclusions can you draw about the differences in spell-casting times between the two houses?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify medians, quartiles, and IQR for each house.","Discuss how the spread of data relates to performance consistency.","Ask students to consider how the back-to-back stem-and-leaf plot visually compares the two distributions."]}


example_id: lp_01K7P009YVMWE42JX6STRJ2AN9_01K7P00BQTRT18PY4125KDQF6A_EXIT_TICKET
skill_ids: ["01JZH1GE4CYWBVDVXGD9W7D0D4","01JZH1GX69N3Q2JHMRP0YJR8N4"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Planets
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$","question":"A table shows the number of moons for $4$ planets: Mercury $0$, Venus $0$, Earth $1$, Mars $2$. What is the total number of moons?"},{"answer":"$5$","question":"A table shows planet diameters (in km): $10\\,000 \\leq d \u003c 20\\,000$: $2$, $20\\,000 \\leq d \u003c 30\\,000$: $3$. How many planets have $d \\geq 10\\,000$?"},{"answer":"$15$","question":"A table shows orbital periods (in days): $50 \\leq t \u003c 100$: $4$, $100 \\leq t \u003c 150$: $6$, $150 \\leq t \u003c 200$: $5$. What is the total?"}]}

skills:
["Analysing and creating frequency tables with continuous data","Analysing and creating frequency tables with discrete data"]


example_id: lp_01K7P009YVMWE42JX6STRJ2AN9_01K7P00BQTRT18PY411XER99Z5_CONTEMPLATIVE_QUESTION
skill_ids: ["01JZH1GE4CYWBVDVXGD9W7D0D4","01JZH1GX69N3Q2JHMRP0YJR8N4"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Planets
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Survey $30$ classmates on their weekly screen time in hours. Create a frequency table. How would you group the data into intervals to best represent it? Justify your choice.","teacherTips":["Guide students to choose logical intervals like $0-5$, $6-10$, etc.","Discuss how different interval choices impact data representation.","Encourage students to explain why their intervals are effective."],"difficulty":"mild"}

skills:
["Analysing and creating frequency tables with continuous data","Analysing and creating frequency tables with discrete data"]


example_id: lp_01K7P009YVMWE42JX6STRJ2AN9_01K7P00BQTRT18PY411M894VVV_ACTIVITY
skill_ids: ["01JZH1GE4CYWBVDVXGD9W7D0D4","01JZH1GX69N3Q2JHMRP0YJR8N4"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Planets
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Game Stats Frequency Fun\nYou're analysing player stats for a new video game to improve its design.","scenario":"Steps\n1. In teams, come up with $10$ player stats (e.g., scores, levels).\n2. Classify each stat as continuous or discrete on your paper.\n3. Create frequency tables for both continuous and discrete data.\n4. Compare your tables with another team for accuracy.\n5. Discuss improvements based on your analysis of the data.","steps":["Discussion\n• Why is it important to separate continuous and discrete data?\n• How could errors in the table affect the game's design?","Differentiation Opportunities\n• Support: Provide a list of example stats for students to classify.\n• Extend: Add a cumulative frequency column for continuous data."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Analysing and creating frequency tables with continuous data","Analysing and creating frequency tables with discrete data"]


example_id: lp_01K7P009YVMWE42JX6STRJ2AN9_01K7P00BQTRT18PY41204QP5MN_THOUGHT_SPARKER
skill_ids: ["01JZH1GE4CYWBVDVXGD9W7D0D4","01JZH1GX69N3Q2JHMRP0YJR8N4"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Planets
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The planets in our solar system vary greatly in size, with diameters ranging from $4\\,879$ km (Mercury) to $139\\,822$ km (Jupiter), and the number of moons they have ranges from $0$ (Venus) to $95$ (Saturn).","firstSentence":"What could you include in a frequency table to compare the planets?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the difference between continuous data (like diameters) and discrete data (like moon counts).","Encourage students to think about grouping continuous data into intervals for clarity in a frequency table.","Prompt students to consider how to visually represent both data types for comparison, such as using a dual table or separate graphs."]}


example_id: lp_01K7P009YVMWE42JX6STRJ2AN9_01K7P00BQTRT18PY411KQ21RJE_APPLICATION
skill_ids: ["01JZH1GE4CYWBVDVXGD9W7D0D4","01JZH1GX69N3Q2JHMRP0YJR8N4"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Planets
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Frequency Tables in Planetary Research","example1Header":"Situation\nAstronomers study planets by gathering data on their features like size and temperature. They use frequency tables to organize this data and identify patterns for further analysis.","example1Body":"Example\nAstronomers record planetary temperatures: $200$ K ($5$ planets), $250$ K ($4$), $300$ K ($3$), $350$ K ($3$), grouped into a frequency table for analysis.","example2Header":"","example2Body":""}


example_id: lp_01K7P080F15WZMYQHR15HPQ41N_01K7P082435KF01A4DXS3MB60G_APPLICATION
skills: ["Understanding how skew affects the mean relative to the median","Understanding graph skewness"]
skill_ids: ["sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Birdwatching
class_year: 9
country: AU
period_number: 9
node_type: APPLICATION
example_output_json:
{"title":"Using Graph Skewness in Bird Migration Data","example1Header":"Situation\nEcologists studying bird migration use graphs to track the number of birds passing through an area. They analyse skewness to identify peaks in migration patterns, helping them predict when the most birds will appear.","example1Body":"Example\nEcologists track bird counts: $30$, $40$, $50$, $70$, $250$. Mean: $88$, median: $50$. Since the mean is pulled higher by $250$, the graph is right-skewed, showing a few extreme high counts.","example2Header":"","example2Body":""}


example_id: lp_01K7P080F15WZMYQHR15HPQ41N_01K7P082435KF01A4DYDK5GMJ7_THOUGHT_SPARKER
skills: ["Understanding how skew affects the mean relative to the median","Understanding graph skewness"]
skill_ids: ["sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Birdwatching
class_year: 9
country: AU
period_number: 9
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A group of birdwatchers recorded the number of birds they spotted in an hour: $1$, $2$, $2$, $3$, $3$, $3$, $4$, $5$, $8$, $15$.","firstSentence":"How does the skew in this data affect the relationship between the mean and median?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the difference between left-skewed and right-skewed distributions before analysing the data.","Encourage students to calculate both the mean and median to confirm their observations.","Use visual aids like histograms or box plots to help students identify skewness and its effects on averages."]}


example_id: lp_01K7P080F15WZMYQHR15HPQ41N_01K7P082435KF01A4DXVPC4YW2_ACTIVITY
skills: ["Understanding how skew affects the mean relative to the median","Understanding graph skewness"]
skill_ids: ["sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Birdwatching
class_year: 9
country: AU
period_number: 9
node_type: ACTIVITY
example_output_json:
{"header":"Skewed Data Challenge\nYou're data analysts! Create and analyse skewed data sets to win the challenge.","scenario":"Steps\n1. Each group creates a data set of $10$ values between $1$ and $100$.\n2. Plot a histogram of your data set on graph paper.\n3. Calculate the mean and median for your data set.\n4. Adjust your values to make the data positively or negatively skewed.\n5. Compare mean and median for each skew and present your findings.","steps":["Discussion\n• How does skewness change the difference between mean and median?\n• Why is the median less affected by extreme values than the mean?","Differentiation Opportunities\n• Support: Provide pre-drawn histograms for students to fill in with data.\n• Extend: Challenge students to create a data set with zero skew (mean = median)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7P080F15WZMYQHR15HPQ41N_01K7P082435KF01A4DYAR0Y29M_CONTEMPLATIVE_QUESTION
skills: ["Understanding how skew affects the mean relative to the median","Understanding graph skewness"]
skill_ids: ["sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Birdwatching
class_year: 9
country: AU
period_number: 9
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You survey $20$ friends on daily screen time. Create data for left-skewed, right-skewed, or symmetric graphs. How does skewness affect the mean and median in each case?","teacherTips":["Guide students on examples of left-skewed, right-skewed, and symmetric data.","Discuss how outliers shift the mean more than the median.","Encourage students to compare the mean and median for each data set."],"difficulty":"mild"}


example_id: lp_01K7P080F15WZMYQHR15HPQ41N_01K7P082435KF01A4DYHHWQ8ZW_EXIT_TICKET
skills: ["Understanding how skew affects the mean relative to the median","Understanding graph skewness"]
skill_ids: ["sA00rXGfygMEiiBo5WQp","myAsMqBg8KkxJxXlr0Ad"]
subtopics: ["Data Relationships"]
subtopic_ids: ["subtopic_01GTC0BG25BBPQKNAVY7R2KVW8"]
topic: Statistics
topic_id: 1b2b7dba-4724-5c2e-955d-f538954483b7
context: Birdwatching
class_year: 9
country: AU
period_number: 9
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Positively skewed","question":"If a birdwatching group records bird sightings where most values are clustered to the left on a histogram, what type of skewness does the graph have?"},{"answer":"Mean","question":"During a birdwatching trip, the group finds bird counts per hour: $1$, $2$, $2$, $3$, $50$. Will the mean or median be greater?"},{"answer":"Mean \u003e Median","question":"A birdwatcher records bird calls in $7$ locations: $3$, $4$, $5$, $6$, $7$, $8$, $30$. How does the skew affect the mean and median?"}]}


example_id: lp_01K7R36FN9YXJPR8TA0GCM7A7Q_01K7R36H8CCX9MY9S36444XBQV_APPLICATION
skills: ["Expanding the square of a difference","Expanding two or more pairs of brackets"]
skill_ids: ["s9SGSEf4z5iNNiRTiyAC","SHHSEKBp7N6xXcw3iBAI"]
subtopics: ["Expansion"]
subtopic_ids: ["subtopic_01GTC0BRWH1K9ZBGXYWWNQ64JC"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Master Chef
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Recipe Scaling with Algebraic Expansion","example1Header":"Situation\nMaster chefs often create custom recipes for events. They use algebraic expansion when combining ingredient quantities to scale recipes accurately.","example1Body":"Example\nTo scale up a sauce recipe, chefs expand $(2x + 3)(x + 4)$. Expanding: $2x^2 + 8x + 3x + 12 = 2x^2 + 11x + 12$. This helps calculate ingredient amounts.","example2Header":"","example2Body":""}


example_id: lp_01K7R36FN9YXJPR8TA0GCM7A7Q_01K7R36H8CCX9MY9S36V7DRVYJ_THOUGHT_SPARKER
skills: ["Expanding the square of a difference","Expanding two or more pairs of brackets"]
skill_ids: ["s9SGSEf4z5iNNiRTiyAC","SHHSEKBp7N6xXcw3iBAI"]
subtopics: ["Expansion"]
subtopic_ids: ["subtopic_01GTC0BRWH1K9ZBGXYWWNQ64JC"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Master Chef
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a Master Chef competition, a contestant needs to prepare a sauce using $(x + 3)$ cups of tomato base and $(x - 2)$ cups of cream, then square the total to calculate the final mixture's volume.","firstSentence":"How would you simplify the expression for the volume of the mixture?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to expand the brackets step by step, showing all terms clearly.","Discuss the importance of combining like terms to simplify expressions.","Encourage students to verify their work by substituting values for $x$ to check consistency."]}


example_id: lp_01K7R36FN9YXJPR8TA0GCM7A7Q_01K7R36H8CCX9MY9S36QHKPAKS_CONTEMPLATIVE_QUESTION
skills: ["Expanding the square of a difference","Expanding two or more pairs of brackets"]
skill_ids: ["s9SGSEf4z5iNNiRTiyAC","SHHSEKBp7N6xXcw3iBAI"]
subtopics: ["Expansion"]
subtopic_ids: ["subtopic_01GTC0BRWH1K9ZBGXYWWNQ64JC"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Master Chef
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design your own two expressions with brackets, e.g., $(x+3)(x-2)$ or $(2a-5)^2$. Expand them and explain how you approached each step. What patterns do you notice?","teacherTips":["Encourage students to create expressions with two or more brackets.","Discuss patterns like combining like terms or simplifying squared terms.","Have students explain their reasoning for each step in expanding."],"difficulty":"mild"}


example_id: lp_01K7R36FN9YXJPR8TA0GCM7A7Q_01K7R36H8CCX9MY9S368593XQF_ACTIVITY
skills: ["Expanding the square of a difference","Expanding two or more pairs of brackets"]
skill_ids: ["s9SGSEf4z5iNNiRTiyAC","SHHSEKBp7N6xXcw3iBAI"]
subtopics: ["Expansion"]
subtopic_ids: ["subtopic_01GTC0BRWH1K9ZBGXYWWNQ64JC"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Master Chef
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Bracket Expansion Relay\nYour team is solving a puzzle by expanding algebraic expressions to unlock the next challenge.","scenario":"Steps\n1. Write $5$ expressions involving two brackets (e.g., $(x+3)(x-2)$).\n2. Write $3$ expressions involving squares of differences (e.g., $(x-4)^2$).\n3. In teams, take turns expanding these expressions accurately.\n4. Check each other's work and earn $2$ points for correct answers.\n5. The team with the highest score after $5$ rounds wins!","steps":["Discussion\n• What patterns do you notice when expanding $(a-b)^2$?\n• How does expanding $(x+3)(x-2)$ differ from $(x+3)^2$?","Differentiation Opportunities\n• Support: Focus on simpler brackets like $(x+1)(x+2)$ and $(x-3)^2$.\n• Extend: Expand more complex expressions like $(2x-5)(x+4)$ or $(3x-2)^2$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7R36FN9YXJPR8TA0GCM7A7Q_01K7R36H8CCX9MY9S36Y2W1F4S_EXIT_TICKET
skills: ["Expanding the square of a difference","Expanding two or more pairs of brackets"]
skill_ids: ["s9SGSEf4z5iNNiRTiyAC","SHHSEKBp7N6xXcw3iBAI"]
subtopics: ["Expansion"]
subtopic_ids: ["subtopic_01GTC0BRWH1K9ZBGXYWWNQ64JC"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Master Chef
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$x^2 - 6x + 9$","question":"A chef writes the expression $(x - 3)^2$ to calculate spice proportions. Expand it using brackets."},{"answer":"$x^2 - 3x - 10$","question":"The recipe involves the expression $(x + 2)(x - 5)$ for ingredient quantities. Expand the brackets."},{"answer":"$2x^3 + x^2 - 22x + 24$","question":"A dessert's cost is calculated with $(2x - 3)(x + 4)(x - 2)$. Expand it fully."}]}


example_id: lp_01K7R3NG78WZXEKWH5VJ7CXC3T_01K7R3NHQM1V27AZN57WMR5S2Q_APPLICATION
skill_ids: ["sYCva5Cd383yQ8r6hk9p","oeH4xPzMvOQwnIlVgKUw","5kcjJ4HejD0ZHsRNAHM1"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Fencing
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Designing Fencing Layouts with Linear Equations","example1Header":"Situation\nFencing contractors use linear equations to design straight fence sections. They match graphs of fences to equations to ensure proper alignment and land usage.","example1Body":"Example\nA fence graph passes $(0, 5)$ and $(4, 1)$. The slope is $m = -1$. Substituting into $y = mx + b$: $y = -x + 5$ matches the graph.","example2Header":"","example2Body":""}

skills:
["Forming inequalities from worded problems","Solving linear inequalities","Matching linear graphs to their equation in standard form"]


example_id: lp_01K7R3NG78WZXEKWH5VJ7CXC3T_01K7R3NHQM1V27AZN58GNT191A_THOUGHT_SPARKER
skill_ids: ["sYCva5Cd383yQ8r6hk9p","oeH4xPzMvOQwnIlVgKUw","5kcjJ4HejD0ZHsRNAHM1"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Fencing
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A fencing company charges $\\$25$ per metre for materials and a fixed $\\$200$ for installation, and you have a budget of $\\$1\\,000$.","firstSentence":"What inequality could represent the maximum length of fencing you can afford within your budget?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the difference between fixed costs and variable costs to clarify the linear relationship.","Encourage students to identify the components of the inequality (cost per metre, fixed cost, budget).","Ask students to graph the inequality to visually check their solution."]}

skills:
["Forming inequalities from worded problems","Solving linear inequalities","Matching linear graphs to their equation in standard form"]


example_id: lp_01K7R3NG78WZXEKWH5VJ7CXC3T_01K7R3NHQM1V27AZN58NBCSDJ4_EXIT_TICKET
skill_ids: ["sYCva5Cd383yQ8r6hk9p","oeH4xPzMvOQwnIlVgKUw","5kcjJ4HejD0ZHsRNAHM1"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Fencing
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$2$","question":"A fencing company charts costs with the equation $y = 2x + 100$. What is the slope of the graph?"},{"answer":"$400$","question":"The fencing company budgets $y \u003c 4x + 200$ for fencing material. If $x = 50$, what is the maximum $y$ value allowed?"},{"answer":"$22$","question":"A fencing contractor charges $\\$50$ per metre and $\\$100$ for installation. If the budget is at most $\\$1\\,200$, how many metres can they fence?"}]}

skills:
["Forming inequalities from worded problems","Solving linear inequalities","Matching linear graphs to their equation in standard form"]


example_id: lp_01K7R3NG78WZXEKWH5VJ7CXC3T_01K7R3NHQM1V27AZN58EHNE4F9_CONTEMPLATIVE_QUESTION
skill_ids: ["sYCva5Cd383yQ8r6hk9p","oeH4xPzMvOQwnIlVgKUw","5kcjJ4HejD0ZHsRNAHM1"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Fencing
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A company pays $\\$50$ per hour plus a $\\$20$ bonus. Write an inequality for $\\$300$ max pay. Graph it.","teacherTips":["Guide students to form $50x + 20 \\leq 300$ from the situation.","Discuss why $x$ must be a whole number for hours worked.","Show how to graph the inequality and interpret the solution range."],"difficulty":"mild"}


example_id: lp_01K7R3NG78WZXEKWH5VJ7CXC3T_01K7R3NHQM1V27AZN57Z64SX3Z_ACTIVITY
skill_ids: ["sYCva5Cd383yQ8r6hk9p","oeH4xPzMvOQwnIlVgKUw","5kcjJ4HejD0ZHsRNAHM1"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Fencing
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"City Budget Challenge\nYou are city planners balancing budgets and constraints for a new park.","scenario":"Steps\n1. Write three linear equations (e.g., $y = 2x + 3$, $y = -x + 5$, $2x + y = 7$).\n2. On graph paper, draw the graphs for these equations.\n3. Write three inequalities based on budget constraints (e.g., $y \\leq 2x + 3$).\n4. Shade the solution regions on the graphs and check which inequalities match.\n5. Earn points for each correct match and solution explanation.","steps":["Discussion\n• How does changing a graph's slope affect its inequality solutions?\n• Why is shading important when solving inequalities?","Differentiation Opportunities\n• Support: Use simpler equations like $y = x + 2$ and limit to one inequality.\n• Extend: Add a second inequality and find the intersection of the solution regions."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K7R3WEWDTA155MTNK91JQHPH_01K7R3WGCQ2FJKX86QZ6WQ6Y78_EXIT_TICKET
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Robotics
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$x = 1$","question":"A robot follows the equations $y = 2x + 1$ and $y = -x + 4$. What is the value of $x$ where these paths meet?"},{"answer":"$x = 2, y = 1$","question":"A robot's movement is modeled by $2x + y = 5$ and $x - y = 1$. What are the values of $x$ and $y$ where the paths intersect?"},{"answer":"$(4, 1)$","question":"A robot uses the equations $y = \\frac{1}{2}x - 1$ and $y = -\\frac{3}{2}x + 3$. What is the intersection point of these lines?"}]}

skills:
["Solving simultaneous equations containing two variables","Solving simultaneous equations of the form $y = mx + c$","Solving simultaneous equations graphically"]


example_id: lp_01K7R3WEWDTA155MTNK91JQHPH_01K7R3WGCQ2FJKX86QYQ3HPFFG_ACTIVITY
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Robotics
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Graph It to Solve It\nYour team must graph equations to find their intersection points and win the challenge!","scenario":"Steps\n1. Each team selects two equations of the form $y = mx + c$.\n2. On graph paper, draw the lines for both equations using a ruler.\n3. Find the point of intersection and label it clearly on the graph.\n4. Verify the solution by substituting the coordinates into both equations.\n5. Score $2$ points for each correct solution. First team to $10$ points wins!","steps":["Discussion\n• What does the intersection point represent in the equations?\n• What happens if the lines are parallel or overlap completely?","Differentiation Opportunities\n• Support: Provide equations with integer coefficients and solutions to simplify graphing.\n• Extend: Use equations with fractions or decimals for added complexity."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving simultaneous equations containing two variables","Solving simultaneous equations of the form $y = mx + c$","Solving simultaneous equations graphically"]


example_id: lp_01K7R3WEWDTA155MTNK91JQHPH_01K7R3WGCQ2FJKX86QYZTER5FE_CONTEMPLATIVE_QUESTION
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Robotics
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Two friends want to meet at the point where their paths cross. Friend A walks along $y = 2x + 1$, and Friend B walks along $y = -x + 4$. How would you graph these equations to find their meeting point? What does the solution mean in real life?","teacherTips":["Discuss how to graph $y = mx + c$ accurately.","Explain that the point of intersection satisfies both equations.","Connect the solution to real-life scenarios of meeting points."],"difficulty":"mild"}

skills:
["Solving simultaneous equations containing two variables","Solving simultaneous equations of the form $y = mx + c$","Solving simultaneous equations graphically"]


example_id: lp_01K7R3WEWDTA155MTNK91JQHPH_01K7R3WGCQ2FJKX86QYHK0JKFY_APPLICATION
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Robotics
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Path Planning in Robotics Using Linear Equations","example1Header":"Situation\nRobotics engineers program robots to navigate paths by calculating positions where the robot's path intersects obstacles or checkpoints.","example1Body":"Example\nFor two paths $y = 2x + 1$ and $y = -x + 4$, solving $2x + 1 = -x + 4$ gives $x = 1$. Substituting $x = 1$ into $y = 2x + 1$, $y = 3$. The paths intersect at $(1, 3)$.","example2Header":"","example2Body":""}


example_id: lp_01K7R3WEWDTA155MTNK91JQHPH_01K7R3WGCQ2FJKX86QZ2JXR8F7_THOUGHT_SPARKER
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Robotics
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Two robots are programmed to move along straight paths represented by the equations $y = 2x + 3$ and $y = -x + 6$.","firstSentence":"What does the intersection point of these two paths represent in the context of the robots' movements?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to graph the equations and locate the intersection visually.","Discuss what the coordinates of the intersection mean in terms of position and time.","Explore what it would mean if the lines did not intersect or were the same line."]}


example_id: lp_01K7R47K3MGDHMRVDGF5A319T8_01K7R47MR9GQV1CHCNK1X6T30E_THOUGHT_SPARKER
skill_ids: ["TCSMDxCtOwf0ntUUDOsh","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A zip line's height profile can be modelled by the equation $h(x) = x^2 - 6x + 8$, where $h(x)$ is the height in metres and $x$ is the horizontal distance in metres.","firstSentence":"How could you simplify this equation to better understand the key features of the zip line's height profile?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify which method (completing the square, factorising, or grouping) could make the equation easier to analyse.","Discuss the connection between the simplified form and the physical features of the zip line, such as its maximum or minimum height.","Provide visual aids like graphs to help students link the algebraic process to the real-world shape of the zip line."]}

skills:
["Understanding how to complete the square","Factorising by grouping in pairs","Factorising using the difference of two squares"]


example_id: lp_01K7R47K3MGDHMRVDGF5A319T8_01K7R47MR9GQV1CHCNJBR5FEQ3_APPLICATION
skill_ids: ["TCSMDxCtOwf0ntUUDOsh","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Factorisation in Zip Line Engineering","example1Header":"Situation\nZip line engineers design stable platforms and cables. They factorise equations to balance forces and ensure safety during rides.","example1Body":"Example\nA tension equation $2xy + 4x + 3y + 6$ is grouped as $(2xy + 4x) + (3y + 6)$. Factorising gives $2x(y + 2) + 3(y + 2)$, then $(2x + 3)(y + 2)$.","example2Header":"","example2Body":""}

skills:
["Understanding how to complete the square","Factorising by grouping in pairs","Factorising using the difference of two squares"]


example_id: lp_01K7R47K3MGDHMRVDGF5A319T8_01K7R47MR9GQV1CHCNJJ0J5ZHJ_ACTIVITY
skill_ids: ["TCSMDxCtOwf0ntUUDOsh","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Quadratic Rescue Mission\nYour team must rescue the lost keys by solving quadratic puzzles to unlock the vault!","scenario":"Steps\n1. Each team picks $3$ quadratic expressions (e.g., $x^2 - 16$, $x^2 + 6x + 9$).\n2. Solve each expression by completing the square or factorising.\n3. Check answers with another team to earn points for correct solutions.\n4. Each correct answer earns $1$ point; incorrect answers cost $1$ point.\n5. The team with the highest score after $5$ rounds wins!","steps":["Discussion\n• Why does completing the square help solve quadratics?\n• How does the difference of two squares simplify factorisation?","Differentiation Opportunities\n• Support: Provide expressions that are already simplified (e.g., $x^2 - 25$).\n• Extend: Include more complex expressions (e.g., $4x^2 - 36$ or $x^2 + 7x + 12$)."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding how to complete the square","Factorising by grouping in pairs","Factorising using the difference of two squares"]


example_id: lp_01K7R47K3MGDHMRVDGF5A319T8_01K7R47MR9GQV1CHCNK2AVCG1W_EXIT_TICKET
skill_ids: ["TCSMDxCtOwf0ntUUDOsh","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$(a-6)(a+6)$","question":"A zip lining platform has a square area, and its dimensions are represented as $a^2 - 36$. Factorise this expression."},{"answer":"$(x-4)^2 - 11$","question":"If the zip line length is represented as $x^2 - 8x + 5$, complete the square for the quadratic expression."},{"answer":"$(x-1)(y+2)$","question":"A zip line support structure's forces are modelled as $xy + 2x - y - 2$. Factorise this expression by grouping."}]}


example_id: lp_01K7R47K3MGDHMRVDGF5A319T8_01K7R47MR9GQV1CHCNJZBZ91TN_CONTEMPLATIVE_QUESTION
skill_ids: ["TCSMDxCtOwf0ntUUDOsh","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Zip Lining
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular garden has an area of $25x^2 - 16$. How could you determine its dimensions using factorisation?","teacherTips":["Encourage students to recognise $25x^2 - 16$ as a difference of squares.","Ask students to factorise it as $(5x + 4)(5x - 4)$.","Discuss how the factors represent the garden's dimensions."],"difficulty":"mild"}


example_id: lp_01K7R4F1RVPZF7F7Q74VYP9RPK_01K7R4F3NK3DN8ZQCE9E90R8E6_EXIT_TICKET
skill_ids: ["JcfAB2u5XHpO8EKJv5jd","uVGIp0DHBoD7dSGLqssh","vTgTgp0tMgxRpO342M38"]
subtopics: ["Exponential Equations"]
subtopic_ids: ["subtopic_01GTC0BK05N6EQJGBE0W1QP6D6"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Recycling
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$y = \\frac{1}{2}, 1, 2$","question":"If the amount of recycled paper is modeled by $y = 2^x$, what is the graph when $x = -1, 0, 1$?"},{"answer":"$5$","question":"If the volume of a recycled material is modeled by $x^3 = 125$, what is the value of $x$?"},{"answer":"$1$","question":"The recycling rate of a plant is modeled by $3^{4x} = 81$. Solve for $x$."}]}

skills:
["Matching a basic exponential equation to its graph","Solving equations containing odd and even exponents","Solving exponential equations by equating indices"]


example_id: lp_01K7R4F1RVPZF7F7Q74VYP9RPK_01K7R4F3NK3DN8ZQCE99Z4884G_CONTEMPLATIVE_QUESTION
skill_ids: ["JcfAB2u5XHpO8EKJv5jd","uVGIp0DHBoD7dSGLqssh","vTgTgp0tMgxRpO342M38"]
subtopics: ["Exponential Equations"]
subtopic_ids: ["subtopic_01GTC0BK05N6EQJGBE0W1QP6D6"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Recycling
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a scenario where $y = 2^x$ and $y = 2^{-x}$ describe real-world growth or decay. Sketch their graphs and explain differences in behaviour.","teacherTips":["Encourage students to link $y = 2^x$ to growth (e.g., population).","Link $y = 2^{-x}$ to decay (e.g., cooling temperature).","Discuss the symmetry of the graphs about the $y$-axis."],"difficulty":"mild"}

skills:
["Matching a basic exponential equation to its graph","Solving equations containing odd and even exponents","Solving exponential equations by equating indices"]


example_id: lp_01K7R4F1RVPZF7F7Q74VYP9RPK_01K7R4F3NK3DN8ZQCE8ZXC1E3S_ACTIVITY
skill_ids: ["JcfAB2u5XHpO8EKJv5jd","uVGIp0DHBoD7dSGLqssh","vTgTgp0tMgxRpO342M38"]
subtopics: ["Exponential Equations"]
subtopic_ids: ["subtopic_01GTC0BK05N6EQJGBE0W1QP6D6"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Recycling
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Exponential Growth Race\nYour team is predicting population growth using exponential equations and graphs.","scenario":"Steps\n1. Each team picks an equation, e.g., $y = 2^x$ or $y = 3^{x-1}$.\n2. Sketch the graph of your equation on graph paper.\n3. Exchange graphs with another team and identify their equation.\n4. Solve $2$ provided equations by equating indices, e.g., $2^{x+1} = 16$.\n5. Score $1$ point for correct graphs, $1$ for correctly matched equations!","steps":["Discussion\n• How does changing the base affect the graph's shape?\n• Why does equating indices work for solving exponential equations?","Differentiation Opportunities\n• Support: Provide simpler equations, e.g., $2^x = 8$, with hints like $8 = 2^3$.\n• Extend: Use equations with transformations, e.g., $y = 2^{x+1} + 3$, for graphing."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Matching a basic exponential equation to its graph","Solving equations containing odd and even exponents","Solving exponential equations by equating indices"]


example_id: lp_01K7R4F1RVPZF7F7Q74VYP9RPK_01K7R4F3NK3DN8ZQCE9B65CN26_THOUGHT_SPARKER
skill_ids: ["JcfAB2u5XHpO8EKJv5jd","uVGIp0DHBoD7dSGLqssh","vTgTgp0tMgxRpO342M38"]
subtopics: ["Exponential Equations"]
subtopic_ids: ["subtopic_01GTC0BK05N6EQJGBE0W1QP6D6"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Recycling
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A recycling plant processes waste such that the amount of waste decreases by $10\\%$ each day, starting with $1\\,000$ kg.","firstSentence":"How might the graph of this situation look over the first two weeks?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to describe key features of exponential decay graphs like asymptotes and initial values.","Ask students to discuss how the $10\\%$ daily reduction affects the shape of the graph.","Help students connect the equation form $y = 1\\,000 \\cdot (0.9)^x$ to the graph's behaviour."]}


example_id: lp_01K7R4F1RVPZF7F7Q74VYP9RPK_01K7R4F3NK3DN8ZQCE8WDP0S3F_APPLICATION
skill_ids: ["JcfAB2u5XHpO8EKJv5jd","uVGIp0DHBoD7dSGLqssh","vTgTgp0tMgxRpO342M38"]
subtopics: ["Exponential Equations"]
subtopic_ids: ["subtopic_01GTC0BK05N6EQJGBE0W1QP6D6"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Recycling
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Exponential Equations in Recycling Growth","example1Header":"Situation\nRecycling managers predict waste reduction rates over time. They use exponential equations to estimate future recycling levels and set goals.","example1Body":"Example\nRecycling grows by a factor of $3$ annually. Solving $3^x = 27$, $x = 3$. It takes $3$ years for recycling to triple its current level.","example2Header":"","example2Body":""}


example_id: lp_01K7R4T8RD78VDTH0DGRJ3JHAS_01K7R4TAH1G9Z5B6AGG3CVQ0Y4_THOUGHT_SPARKER
skill_ids: ["IIOhVnysHaXEt3EFFsUo","FFwIYdjWbi1am2niuyKs","4ijAYX5zyPx2pjVVnHz4"]
subtopics: ["Exponential Functions"]
subtopic_ids: ["subtopic_01GTC0BHNVB54F88NNTVKN4YHV"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Circus
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A new circus act gains popularity, and the audience size after $x$ weeks is modeled by the function $y = 100 \\cdot 2^x$, where $y$ represents the number of attendees.","firstSentence":"How would you determine the $y$-intercept of this function, and what does it represent in this context?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss what intercepts mean in terms of real-world scenarios like audience sizes.","Encourage students to substitute $x = 0$ into the function to find the $y$-intercept.","Explore how exponential growth affects audience numbers over time by comparing values for different $x$."]}

skills:
["Finding $x$ and $y$ intercepts of exponential functions","Identifying and understanding exponential functions","Finding the domain and range of an exponential function"]


example_id: lp_01K7R4T8RD78VDTH0DGRJ3JHAS_01K7R4TAH1G9Z5B6AGFFNJ0TB7_APPLICATION
skill_ids: ["IIOhVnysHaXEt3EFFsUo","FFwIYdjWbi1am2niuyKs","4ijAYX5zyPx2pjVVnHz4"]
subtopics: ["Exponential Functions"]
subtopic_ids: ["subtopic_01GTC0BHNVB54F88NNTVKN4YHV"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Circus
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Exponential Growth in Circus Audience Numbers","example1Header":"Situation\nCircus managers track audience growth. When a show gains popularity, ticket sales often grow exponentially as more people hear about it.","example1Body":"Example\nIf ticket sales start at $50$ and double daily, the total on day $3$ is $y = 50 \\cdot 2^3 = 400$. This exponential trend helps predict audience growth.","example2Header":"","example2Body":""}

skills:
["Finding $x$ and $y$ intercepts of exponential functions","Identifying and understanding exponential functions","Finding the domain and range of an exponential function"]


example_id: lp_01K7R4T8RD78VDTH0DGRJ3JHAS_01K7R4TAH1G9Z5B6AGFGDA2J9H_ACTIVITY
skill_ids: ["IIOhVnysHaXEt3EFFsUo","FFwIYdjWbi1am2niuyKs","4ijAYX5zyPx2pjVVnHz4"]
subtopics: ["Exponential Functions"]
subtopic_ids: ["subtopic_01GTC0BHNVB54F88NNTVKN4YHV"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Circus
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Graph the Growth\nYour team is modelling population growth of bacteria using exponential functions.","scenario":"Steps\n1. Write the function $y = 2^x$ on your paper.\n2. Find and calculate the $x$ and $y$ intercepts.\n3. Graph $y = 2^x$ for $x$ values from $-2$ to $3$.\n4. Identify the domain and range of your graph.\n5. Compare your results with another team and discuss any differences.","steps":["Discussion\n• Why is there no $x$-intercept for exponential functions like $y = 2^x$?\n• How does the range change if the function was $y = -2^x$?","Differentiation Opportunities\n• Support: Use a table of values to help graph the function.\n• Extend: Graph $y = 2^{x-1} + 3$ and find its domain, range, and intercepts."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Finding $x$ and $y$ intercepts of exponential functions","Identifying and understanding exponential functions","Finding the domain and range of an exponential function"]


example_id: lp_01K7R4T8RD78VDTH0DGRJ3JHAS_01K7R4TAH1G9Z5B6AGFXD9TMGV_CONTEMPLATIVE_QUESTION
skill_ids: ["IIOhVnysHaXEt3EFFsUo","FFwIYdjWbi1am2niuyKs","4ijAYX5zyPx2pjVVnHz4"]
subtopics: ["Exponential Functions"]
subtopic_ids: ["subtopic_01GTC0BHNVB54F88NNTVKN4YHV"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Circus
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design your own exponential function $y = ab^x$. Find its domain, range, $x$- and $y$-intercepts.","teacherTips":["Explain the domain is all real numbers for exponential functions.","Discuss how the range depends on the function's behaviour.","Show how to find $x$- and $y$-intercepts using substitution."],"difficulty":"mild"}


example_id: lp_01K7R4T8RD78VDTH0DGRJ3JHAS_01K7R4TAH1G9Z5B6AGG95RY2R2_EXIT_TICKET
skill_ids: ["IIOhVnysHaXEt3EFFsUo","FFwIYdjWbi1am2niuyKs","4ijAYX5zyPx2pjVVnHz4"]
subtopics: ["Exponential Functions"]
subtopic_ids: ["subtopic_01GTC0BHNVB54F88NNTVKN4YHV"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Circus
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"A circus performer balances on a pole that is $3^x$ metres high. Is $y = 3^x$ an exponential function?"},{"answer":"Domain: $(-\\infty, \\infty)$, Range: $(0, \\infty)$","question":"A spotlight at the circus follows $y = 2^x$. What are its domain and range?"},{"answer":"$y$-intercept: $5$, No $x$-intercept","question":"If a circus trapeze artist's height is described by $y = 5 \\cdot 2^x$, find the $y$-intercept and determine if there is an $x$-intercept."}]}


example_id: lp_01K7R5BC5HHA05ED085QGYBH4M_01K7R5BDXP6EVFHAQVP8XRXEER_APPLICATION
skill_ids: ["XEjvByxBIee7EdDR3OM6","z6guysqxmLLkTmWqGGjf"]
subtopics: ["Quadratic Applications"]
subtopic_ids: ["subtopic_01GTC0BKDBZ1AQ2NE4QE4YQPR5"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Sherlock Holmes
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Solving Crimes with Quadratics","example1Header":"Situation\nDetectives like Sherlock Holmes use logic and calculations to solve mysteries. Quadratic equations help determine distances or times in crime scene investigations.","example1Body":"Example\nA thief runs at 20 m/s for $t$ seconds. A detective runs at 25 m/s after 5 seconds. Setting distances equal: $20t = 25(t-5)$. Solving, $t = 25$ seconds.","example2Header":"","example2Body":""}

skills:
["Solving and graphing exponential growth and decay","Forming equations from quadratic worded problems"]


example_id: lp_01K7R5BC5HHA05ED085QGYBH4M_01K7R5BDXP6EVFHAQVPXT0ZKXS_THOUGHT_SPARKER
skill_ids: ["XEjvByxBIee7EdDR3OM6","z6guysqxmLLkTmWqGGjf"]
subtopics: ["Quadratic Applications"]
subtopic_ids: ["subtopic_01GTC0BKDBZ1AQ2NE4QE4YQPR5"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Sherlock Holmes
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a Sherlock Holmes case, a rare chemical decays by $15\\%$ every hour. It starts with $200$ grams, and Holmes needs to know how long it will take for the chemical to reach $50$ grams.","firstSentence":"How could you determine the time required for the chemical to decay to $50$ grams?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss how exponential decay is represented mathematically with equations.","Encourage students to think about how to isolate the time variable in the equation.","Explore how to graph the decay function and use it to verify the solution."]}

skills:
["Solving and graphing exponential growth and decay","Forming equations from quadratic worded problems"]


example_id: lp_01K7R5BC5HHA05ED085QGYBH4M_01K7R5BDXP6EVFHAQVPBEC1ZKN_ACTIVITY
skill_ids: ["XEjvByxBIee7EdDR3OM6","z6guysqxmLLkTmWqGGjf"]
subtopics: ["Quadratic Applications"]
subtopic_ids: ["subtopic_01GTC0BKDBZ1AQ2NE4QE4YQPR5"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Sherlock Holmes
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Exponential Growth Race\nYour team is tracking the population of a rare species to predict its growth or decline over time.","scenario":"Steps\n1. Write the equation $P(t) = P_0 \\times (1 + r)^t$ for growth or $P(t) = P_0 \\times (1 - r)^t$ for decay.\n2. Pick initial values: $P_0=100$, $r=0.05$ (growth) or $r=0.03$ (decay), and $t$ from $0$ to $10$.\n3. Calculate $P(t)$ for each $t$ and record your results in a table.\n4. Graph your values on graph paper and connect the points to see the curve.\n5. Compare graphs with other teams and discuss trends in growth and decay.","steps":["Discussion\n• How does the rate $r$ affect the steepness of the curve?\n• What happens to $P(t)$ as $t$ increases for growth versus decay?","Differentiation Opportunities\n• Support: Use smaller values for $t$ (e.g., $0$ to $5$) and simpler rates like $r=0.01$.\n• Extend: Try varying $P_0$ and $r$, or combine growth and decay in one scenario."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving and graphing exponential growth and decay","Forming equations from quadratic worded problems"]


example_id: lp_01K7R5BC5HHA05ED085QGYBH4M_01K7R5BDXP6EVFHAQVQ3ECD93T_EXIT_TICKET
skill_ids: ["XEjvByxBIee7EdDR3OM6","z6guysqxmLLkTmWqGGjf"]
subtopics: ["Quadratic Applications"]
subtopic_ids: ["subtopic_01GTC0BKDBZ1AQ2NE4QE4YQPR5"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Sherlock Holmes
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$16$","question":"Sherlock finds a rare chemical whose mass doubles every hour. If the initial mass is $2$ g, what is the mass after $3$ hours?"},{"answer":"$4$","question":"Sherlock observes a suspect's jump forms a parabola with $h = -x^2 + 4x$. What is the maximum height of the jump?"},{"answer":"$32.768$","question":"Dr. Watson notes a rare plant decays in mass by $20\\%$ daily. If the initial mass is $100$ g, what is the mass after $5$ days?"}]}


example_id: lp_01K7R5BC5HHA05ED085QGYBH4M_01K7R5BDXP6EVFHAQVPPC2FK59_CONTEMPLATIVE_QUESTION
skill_ids: ["XEjvByxBIee7EdDR3OM6","z6guysqxmLLkTmWqGGjf"]
subtopics: ["Quadratic Applications"]
subtopic_ids: ["subtopic_01GTC0BKDBZ1AQ2NE4QE4YQPR5"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Sherlock Holmes
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A bacteria culture starts with $50$ bacteria and doubles every hour. How would you graph and model its growth? What if the bacteria halved each hour instead? How does this change the equation and graph?","teacherTips":["Start with $N = 50 \\cdot 2^t$ for growth, where $t$ is time in hours.","Discuss how the base changes for halving, e.g., $N = 50 \\cdot (0.5)^t$.","Explore how exponential growth and decay differ visually on a graph."],"difficulty":"mild"}


example_id: lp_01K7R5Q8G9KND7Z2YMY8CNQ8DV_01K7R5QBXJGF96EA4V6PY01YX2_EXIT_TICKET
skill_ids: ["emvxQxWJZTYOXeonjFHH","Wx3taiTxaJT61aa5UDO2","p5lGOp1DXlDECwwmX7Va"]
subtopics: ["Matching Graphs \u0026 Equations"]
subtopic_ids: ["subtopic_01GTC0BMGBQYBN9TVK7TAGW2DF"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hockey
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"First and third quadrants","question":"A hockey stick is modeled by $y=\\frac{4}{x}$. Does its graph lie in the first and third quadrants or the second and fourth?"},{"answer":"$(3,6)$","question":"A hockey ball follows the path $y=-2(x-3)^2+6$. What are the coordinates of the ball's maximum height?"},{"answer":"Hyperbola","question":"A hockey puck's trajectory is modeled by $y=\\frac{1}{x+2}$. How is this equation classified and why?"}]}

skills:
["Classifying non-linear equations and their graphs","Matching a hyperbola of the form $y=\\frac{a}{x}$ with its graph","Matching the graph of a parabola with its equation in turning point form"]


example_id: lp_01K7R5Q8G9KND7Z2YMY8CNQ8DV_01K7R5QBXJGF96EA4V5YQ7YWW3_ACTIVITY
skill_ids: ["emvxQxWJZTYOXeonjFHH","Wx3taiTxaJT61aa5UDO2","p5lGOp1DXlDECwwmX7Va"]
subtopics: ["Matching Graphs \u0026 Equations"]
subtopic_ids: ["subtopic_01GTC0BMGBQYBN9TVK7TAGW2DF"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hockey
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Graph Match Challenge\nYour team is designing a roller coaster! Match equations to graph sections to create the track.","scenario":"Steps\n1. Draw two axes and sketch two hyperbolas and two parabolas on graph paper.\n2. Write equations like $y=\\frac{6}{x}$, $y=\\frac{-4}{x}$, $y=(x-2)^2+1$, $y=-(x+1)^2+3$.\n3. In teams, match each equation to the correct graph.\n4. Score $1$ point for each correct match and explain your reasoning.\n5. Team with the highest score after $4$ rounds wins!","steps":["Discussion\n• How do the signs of $a$ in $y=\\frac{a}{x}$ affect the graph's quadrants?\n• What changes in $y=(x-h)^2+k$ shift the vertex position?","Differentiation Opportunities\n• Support: Provide templates of graphs with key points labeled (e.g., vertex, asymptotes).\n• Extend: Ask teams to create and swap their own graphs and equations for extra rounds."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Classifying non-linear equations and their graphs","Matching a hyperbola of the form $y=\\frac{a}{x}$ with its graph","Matching the graph of a parabola with its equation in turning point form"]


example_id: lp_01K7R5Q8G9KND7Z2YMY8CNQ8DV_01K7R5QBXJGF96EA4V6BBPQY1F_CONTEMPLATIVE_QUESTION
skill_ids: ["emvxQxWJZTYOXeonjFHH","Wx3taiTxaJT61aa5UDO2","p5lGOp1DXlDECwwmX7Va"]
subtopics: ["Matching Graphs \u0026 Equations"]
subtopic_ids: ["subtopic_01GTC0BMGBQYBN9TVK7TAGW2DF"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hockey
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design two real-world scenarios where data follows $y = \\frac{a}{x}$ and $y = a(x-h)^2 + k$. Sketch graphs for both and explain why these equations fit.","teacherTips":["Discuss the shape of $y = \\frac{a}{x}$ (hyperbola) and $y = a(x-h)^2 + k$ (parabola).","Help students link equations to real-world examples, like speed-time or projectile motion.","Encourage students to explain why the shapes fit their scenarios."],"difficulty":"mild"}

skills:
["Classifying non-linear equations and their graphs","Matching a hyperbola of the form $y=\\frac{a}{x}$ with its graph","Matching the graph of a parabola with its equation in turning point form"]


example_id: lp_01K7R5Q8G9KND7Z2YMY8CNQ8DV_01K7R5QBXJGF96EA4V6FEHA3VZ_THOUGHT_SPARKER
skill_ids: ["emvxQxWJZTYOXeonjFHH","Wx3taiTxaJT61aa5UDO2","p5lGOp1DXlDECwwmX7Va"]
subtopics: ["Matching Graphs \u0026 Equations"]
subtopic_ids: ["subtopic_01GTC0BMGBQYBN9TVK7TAGW2DF"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hockey
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"During a hockey game, a player hits the ball, and its flight follows a parabolic path described by $y = -x^2 + 4x + 3$. Meanwhile, the relationship between the ball's height and its horizontal distance from the goalpost can also be modelled using $y = \\frac{6}{x}$.","firstSentence":"How could you classify these equations based on the type of graph they produce?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the differences between parabolas and hyperbolas, focusing on their shapes and equations.","Encourage students to sketch the graphs to visualise the relationships clearly.","Highlight the significance of the constants and coefficients in determining the graph's behaviour."]}


example_id: lp_01K7R5Q8G9KND7Z2YMY8CNQ8DV_01K7R5QBXJGF96EA4V5VE0CG7S_APPLICATION
skill_ids: ["emvxQxWJZTYOXeonjFHH","Wx3taiTxaJT61aa5UDO2","p5lGOp1DXlDECwwmX7Va"]
subtopics: ["Matching Graphs \u0026 Equations"]
subtopic_ids: ["subtopic_01GTC0BMGBQYBN9TVK7TAGW2DF"]
topic: Algebra
topic_id: 865f672b-bcea-5995-bdd3-8714ffa662ab
context: Hockey
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Hyperbolic Passes in Hockey Strategy","example1Header":"Situation\nIn hockey, players use precise passing angles to avoid defenders. The trajectory of a pass can resemble a hyperbola, ensuring it reaches a teammate safely.","example1Body":"Example\nThe path $y = \\frac{6}{x}$ gives $y = 3$ at $x = 2$, $y = 2$ at $x = 3$, and $y = -3$ at $x = -2$, forming a hyperbolic curve to guide passes.","example2Header":"","example2Body":""}


example_id: lp_01K7S94YRED4FWBJRZTNG6P7W9_01K7S950MK2EW614V04G8K676D_EXIT_TICKET
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DEY0MVT9EH3WG7G76NWVM2","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$500$","question":"A 3D printer creates a rectangular prism with a base area of $50$ cm$^2$ and a height of $10$ cm. What is its volume?"},{"answer":"$144$","question":"A 3D printer makes a pyramid with a square base of side $6$ cm and a height of $12$ cm. What is its volume?"},{"answer":"$175\\pi$","question":"A 3D printer makes a solid composed of a cylinder with radius $5$ cm, height $10$ cm, and a hemisphere on top. What is its total surface area?"}]}

skills:
["Solving for volume using $V=Ah$","Calculating the volume of pyramids","Calculating the total surface area of composite solids"]


example_id: lp_01K7S94YRED4FWBJRZTNG6P7W9_01K7S950MK2EW614V045PNJSK3_ACTIVITY
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DEY0MVT9EH3WG7G76NWVM2","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Design a Pyramid Fountain\nYour team is designing a pyramid-shaped fountain. Calculate its water capacity and material needs!","scenario":"Steps\n1. Draw a square-based pyramid with a base edge of $6$ m and height of $4$ m.\n2. Calculate the fountain's volume using $V = Ah$ where $A$ is the base area.\n3. Determine the total surface area, including the base and triangular sides.\n4. Adjust dimensions to maximise volume while keeping surface area under $150$ m$^2$.\n5. Compare designs with other teams to find the most efficient fountain!","steps":["Discussion\n• How does increasing the base edge affect volume and surface area?\n• Why might a larger surface area increase material costs?","Differentiation Opportunities\n• Support: Provide a template pyramid with labelled dimensions to simplify.\n• Extend: Add a cylindrical base and calculate the new composite solid's volume."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving for volume using $V=Ah$","Calculating the volume of pyramids","Calculating the total surface area of composite solids"]


example_id: lp_01K7S94YRED4FWBJRZTNG6P7W9_01K7S950MK2EW614V04C00M0XX_CONTEMPLATIVE_QUESTION
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DEY0MVT9EH3WG7G76NWVM2","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a storage box with a pyramid-shaped lid. How would you calculate its total surface area and volume?","teacherTips":["Ensure students calculate the base area for volume using $V=Ah$.","Guide students to find the surface area of each component separately.","Encourage students to explain how they combine areas and volumes."],"difficulty":"mild"}

skills:
["Solving for volume using $V=Ah$","Calculating the volume of pyramids","Calculating the total surface area of composite solids"]


example_id: lp_01K7S94YRED4FWBJRZTNG6P7W9_01K7S950MK2EW614V044AMF28W_APPLICATION
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DEY0MVT9EH3WG7G76NWVM2","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Surface Area in 3D Printing Prototypes","example1Header":"Situation\n3D printing specialists create composite prototypes with multiple shapes. Calculating surface area is critical to estimate material needed for smooth, accurate designs.","example1Body":"Example\nA cube with side $5$ cm and a hemisphere of radius $3$ cm have a total surface area of $150 + 18 \\pi \\approx 206.5$ cm$^2$, helping estimate material for 3D printing.","example2Header":"","example2Body":""}


example_id: lp_01K7S94YRED4FWBJRZTNG6P7W9_01K7S950MK2EW614V04EM17ZRX_THOUGHT_SPARKER
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DEY0MVT9EH3WG7G76NWVM2","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: 3D Printing
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A 3D printer is creating a trophy made up of two parts: a rectangular prism base with dimensions $10$ cm by $6$ cm by $4$ cm, and a square pyramid on top with a base side length of $6$ cm and a height of $8$ cm.","firstSentence":"How could you determine the total amount of material needed to print the entire trophy?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate the volume of each solid separately before combining them.","Discuss the importance of knowing surface area if additional material like coating is needed.","Guide students to consider the formula $V = Ah$ and check their understanding of base area calculations."]}


example_id: lp_01K7S9DVBPHQTF8R59E9M46R5M_01K7S9DX1RZXC9CR1JWS1CAA2F_THOUGHT_SPARKER
skill_ids: ["h5lEA3FMgxY8fXRqVKZt","bOmMN6kR4EL8dcQK0aj3","0iV3gdqJwxuYIndyinmo"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Snowboarding
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A professional snowboarder records their jump heights during training, ranging from $0.5$ m to $1\\,200$ m, with the data measured to $4$ significant figures.","firstSentence":"How could this range of jump heights be represented on a logarithmic scale to make it easier to interpret?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss why logarithmic scales are useful for representing wide-ranging data.","Highlight how to identify significant figures and why they are important in data accuracy.","Encourage students to convert data to scientific notation for easier handling of large numbers."]}

skills:
["Converting numbers to and from scientific notation","Applying significant figure rules in rounding","Using logarithmic scales for large data ranges"]


example_id: lp_01K7S9DVBPHQTF8R59E9M46R5M_01K7S9DX1RZXC9CR1JW4EVC6YE_APPLICATION
skill_ids: ["h5lEA3FMgxY8fXRqVKZt","bOmMN6kR4EL8dcQK0aj3","0iV3gdqJwxuYIndyinmo"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Snowboarding
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Scientific Notation in Snowboard Speed Calculations","example1Header":"Situation\nSnowboard designers test boards by measuring speed on slopes. Calculations involve large or small numbers like snow resistance and speed in scientific notation.","example1Body":"Example\nFor $57\\,000$ cm/s, the snowboard team converts to $5.7 \\times 10^4$ cm/s. Resistance $0.00032$ g/cm$^2$ is expressed as $3.2 \\times 10^{-4}$ g/cm$^2$, simplifying calculations.","example2Header":"","example2Body":""}

skills:
["Converting numbers to and from scientific notation","Applying significant figure rules in rounding","Using logarithmic scales for large data ranges"]


example_id: lp_01K7S9DVBPHQTF8R59E9M46R5M_01K7S9DX1RZXC9CR1JW6DM0JY8_ACTIVITY
skill_ids: ["h5lEA3FMgxY8fXRqVKZt","bOmMN6kR4EL8dcQK0aj3","0iV3gdqJwxuYIndyinmo"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Snowboarding
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Cosmic Distance Challenge\nYour team is calculating and comparing distances between planets and stars.","scenario":"Steps\n1. Write $5$ large or small distances (e.g., $384\\,400$ km or $0.00057$ km).\n2. Convert each distance to scientific notation.\n3. Round each number to $3$ significant figures.\n4. Compare your distances with another group’s results.\n5. Discuss which numbers are closest or furthest and why.","steps":["Discussion\n• Why is scientific notation useful for large or small numbers?\n• How do significant figures affect accuracy and clarity?","Differentiation Opportunities\n• Support: Start with smaller numbers under $1\\,000$ and round to $2$ significant figures.\n• Extend: Add an extra step: convert back to standard form and check for accuracy."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Converting numbers to and from scientific notation","Applying significant figure rules in rounding","Using logarithmic scales for large data ranges"]


example_id: lp_01K7S9DVBPHQTF8R59E9M46R5M_01K7S9DX1RZXC9CR1JWWR17WCY_EXIT_TICKET
skill_ids: ["h5lEA3FMgxY8fXRqVKZt","bOmMN6kR4EL8dcQK0aj3","0iV3gdqJwxuYIndyinmo"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Snowboarding
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$126$","question":"A snowboard is $125.678$ cm long. Round this length to $3$ significant figures."},{"answer":"$3.45 \\times 10^{-4}$","question":"A snowboarding competition recorded $0.000345$ seconds of delay. Write this time in scientific notation."},{"answer":"$2$","question":"A snowboarder experiences a force of $10^4$ N, while another experiences $10^2$ N. What is the difference in their forces on a logarithmic scale?"}]}


example_id: lp_01K7S9DVBPHQTF8R59E9M46R5M_01K7S9DX1RZXC9CR1JWM06WSND_CONTEMPLATIVE_QUESTION
skill_ids: ["h5lEA3FMgxY8fXRqVKZt","bOmMN6kR4EL8dcQK0aj3","0iV3gdqJwxuYIndyinmo"]
subtopics: ["Scientific Notation"]
subtopic_ids: ["subtopic_01GTC0BBXFASQYQRK6D7EJ9VH0"]
topic: Number
topic_id: 2e27e2d8-3ccf-5c16-90f6-d607e2c51d51
context: Snowboarding
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A telescope shows a galaxy's brightness as $2.5 \\times 10^{-8}$ lumens. How would you: (a) Convert this to standard form? (b) Round it to $2$ significant figures? (c) Place it on a logarithmic scale?","teacherTips":["Ensure students understand how to switch between standard and scientific notation.","Discuss why logarithmic scales are useful for very small or large values.","Review the rules for rounding to significant figures with examples."],"difficulty":"mild"}


example_id: lp_01K7S9MW8TN9SJF5VNVZWHFGD6_01K7S9MXV9BYPCA2PP7F94GBJG_EXIT_TICKET
skill_ids: ["zN8Lh6Nwxqqj4wf0sdpW","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: The Solar System
class_year: 10
country: AU
period_number: 10
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5\\,000$","question":"The distance between Earth and Mars is $3\\,000$ km, and the distance between Mars and Venus is $4\\,000$ km. What is the diagonal distance between Earth and Venus?"},{"answer":"$10$","question":"A spacecraft forms a right-angled triangular shape in space with a base of $6$ km and a height of $8$ km. What is the slant height of the spacecraft?"},{"answer":"$13$","question":"A satellite is at $(0, 0, 0)$ and another point in space is at $(3, 4, 12)$ km. What is the distance between the satellite and the point?"}]}

skills:
["Finding unknowns in 3D shapes using trigonometry and Pythagoras' theorem","Applying Pythagoras' theorem"]


example_id: lp_01K7S9MW8TN9SJF5VNVZWHFGD6_01K7S9MXV9BYPCA2PP73VM28B7_CONTEMPLATIVE_QUESTION
skill_ids: ["zN8Lh6Nwxqqj4wf0sdpW","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: The Solar System
class_year: 10
country: AU
period_number: 10
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A ladder leans against a wall, reaching $5$ m high with its base $3$ m from the wall. How would you calculate the ladder's length? If the wall is $6$ m tall, how far must the base move for the ladder to still reach the top?","teacherTips":["Start by using Pythagoras' theorem to find the ladder's length.","Apply trigonometry to determine the angle or distance as the base moves.","Encourage students to explain their reasoning and justify their steps."],"difficulty":"mild"}

skills:
["Finding unknowns in 3D shapes using trigonometry and Pythagoras' theorem","Applying Pythagoras' theorem"]


example_id: lp_01K7S9MW8TN9SJF5VNVZWHFGD6_01K7S9MXV9BYPCA2PP6MEZMWTD_ACTIVITY
skill_ids: ["zN8Lh6Nwxqqj4wf0sdpW","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: The Solar System
class_year: 10
country: AU
period_number: 10
node_type: ACTIVITY
example_output_json:
{"header":"Shortest Path Puzzle\nHelp design the shortest emergency escape route in a multi-story building!","scenario":"Steps\n1. Draw a 3D diagram of a building with dimensions (e.g., height $12$ m, base $9$ m by $15$ m).\n2. Mark two points: a starting point on the ground floor and an endpoint on the roof.\n3. Use Pythagoras' theorem to calculate the diagonal distance across the base.\n4. Apply trigonometry to find the shortest path from start to endpoint.\n5. Compare solutions and discuss the most efficient route.","steps":["Discussion\n• Why is the diagonal base essential for finding the shortest path?\n• How does trigonometry help in 3D problems?","Differentiation Opportunities\n• Support: Provide a simpler 2D version of the problem first (e.g., just the base).\n• Extend: Include additional obstacles and recalculate alternative routes."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Finding unknowns in 3D shapes using trigonometry and Pythagoras' theorem","Applying Pythagoras' theorem"]


example_id: lp_01K7S9MW8TN9SJF5VNVZWHFGD6_01K7S9MXV9BYPCA2PP6FMBFYHW_APPLICATION
skill_ids: ["zN8Lh6Nwxqqj4wf0sdpW","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: The Solar System
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Calculating Distances in Space Missions","example1Header":"Situation\nAstronomers and space scientists calculate vast distances in the solar system. They rely on geometric principles like Pythagoras' theorem to determine the shortest paths between objects.","example1Body":"Example\nA spacecraft $3,000$ km horizontally and $4,000$ km vertically from Earth forms a right triangle. Using Pythagoras' theorem: $c = \\sqrt{3,000^2 + 4,000^2} = 5,000$ km.","example2Header":"","example2Body":""}


example_id: lp_01K7S9MW8TN9SJF5VNVZWHFGD6_01K7S9MXV9BYPCA2PP783P6CAQ_THOUGHT_SPARKER
skill_ids: ["zN8Lh6Nwxqqj4wf0sdpW","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: The Solar System
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A spacecraft is travelling between Earth and Mars. At one point, Earth, Mars, and the spacecraft form a right triangle where the spacecraft is $30\\,000$ km from Mars and $24\\,000$ km from Earth.","firstSentence":"How would you determine the straight-line distance between Earth and Mars at that moment?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to visualise or sketch the right triangle to identify the hypotenuse and legs.","Discuss the importance of identifying right-angle relationships in real-world scenarios.","Prompt students to explain how Pythagoras' theorem applies to the given distances and why it works in this context."]}


example_id: lp_01K7S9WXHT5E0Q4PK2B6BAKXR7_01K7S9WZAQ2NPYMDMHQE77W973_THOUGHT_SPARKER
skill_ids: ["bpF2REtnGEySQ4U8l76R","7vmDhLdK32qFdOcSm51t","blHVvRXM2hNtWp4fUbww"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 10
country: AU
period_number: 10
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An architect designs a model of a building, where the height of the model is $30$ cm. The real building is scaled up by a factor of $50$ compared to the model.","firstSentence":"How would you calculate the height of the real building using this scale factor?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify and define the scale factor before attempting the calculation.","Discuss the concept of proportionality and how it applies to similar shapes in scaling.","Use visual aids or diagrams to help students visualise the relationship between the model and the real building."]}

skills:
["Solving for unknown sides using a scale factor","Applying similar triangles in $2$D problems","Calculating area and volume using a scale factor"]


example_id: lp_01K7S9WXHT5E0Q4PK2B6BAKXR7_01K7S9WZAQ2NPYMDMHPQ8VBM1D_APPLICATION
skill_ids: ["bpF2REtnGEySQ4U8l76R","7vmDhLdK32qFdOcSm51t","blHVvRXM2hNtWp4fUbww"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Measurement
topic_id: a366a9aa-182e-51ab-8525-26d7c1ad540e
context: Architecture
class_year: 10
country: AU
period_number: 10
node_type: APPLICATION
example_output_json:
{"title":"Scaling Building Models in Architecture","example1Header":"Situation\nArchitects use scale models to design buildings. These models represent real structures at a smaller size, helping clients visualise projects before construction.","example1Body":"Example\nAn architectural model has a height of $15$ cm with a $1:100$ scale. Architects calculate the real height as $15 \\times 100 = 1,500$ cm or $15$ m.","example2Header":"","example2Body":""}

skills:
["Solving for unknown sides using a scale factor","Applying similar triangles in $2$D problems","Calculating area and volume using a scale factor"]


