# prompt_examples

example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZP2R43E0K2SN0XKNXTE_CONTEMPLATIVE_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a box with a volume of $120$ cm$^3$. What are all possible sets of dimensions? Which is best for storing pencils?","teacherTips":["Possible dimensions: $10 \\times 3 \\times 4$, $6 \\times 5 \\times 4$, etc. Long, narrow shapes fit pencils best."],"difficulty":"spicy"}


example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZP2R43E0K2SMH323V4D_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the volume of a rectangular prism with a length of $4$ cm, a width of $3$ cm, and a height of $5$ cm?","answerOptions":["$60$ cm$^3$","$12$ cm$^3$","$20$ cm$^3$","$80$ cm$^3$"],"answer":"$60$ cm$^3$","difficulty":"mild"}


example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZP2R43E0K2SMKGZGE9Q_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular prism has a length of $5$ cm, a width of $3$ cm, and a height of $4$ cm. What is its volume?","answerOptions":["$60$ cm$^3$","$15$ cm$^3$","$12$ cm$^3$","$35$ cm$^3$"],"answer":"$60$ cm$^3$","difficulty":"mild"}


example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZP2R43E0K2SMSNKRD7N_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular prism has a length of $5$ cm, a width of $3$ cm, and a height of $4$ cm. What is its volume?","answerOptions":["$12$ cm$^3$","$20$ cm$^3$","$60$ cm$^3$","$100$ cm$^3$"],"answer":"$60$ cm$^3$","difficulty":"mild"}


example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZP2R43E0K2SMVMXETY8_CONTEMPLATIVE_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You are designing a fish tank. How would you calculate the volume if it is $60$ cm long, $30$ cm wide, and $40$ cm tall? Could you design another tank with the same volume but different dimensions?","teacherTips":["Use $V = 60 \\times 30 \\times 40 = 72\\,000$ cm$^3$. Different dimensions can achieve $72\\,000$ cm$^3$."],"difficulty":"hot"}


example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZ8SYENN61VDC0PC3X5H_SCAFFOLDED_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to calculate the volume of a rectangular prism. The formula is: Volume = length × width × height.","questions":[{"answer":"$60$ cm$^3$","question":"What is the volume of a rectangular prism with length $2$ cm, width $3$ cm, and height $4$ cm?"},{"answer":"$6$ cm$^3$","question":"What is the volume of a rectangular prism with length $5$ cm, width $4$ cm, and height $3$ cm?"},{"answer":"$12$ cm$^3$","question":"What is the volume of a rectangular prism with length $6$ cm, width $5$ cm, and height $2$ cm?"}],"difficulty":"enabling"}


example_id: lp_01K942VYDVK2V9YH0FZEQS6NEF_01K942VZ8SYENN61VDC83NPMXS_SCAFFOLDED_QUESTION
skills: ["Calculating the volume of a rectangular prism"]
skill_ids: ["RHCO94iqkbeRFRSKAg8r"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the concept of volume through challenging rectangular prism problems requiring critical thinking and reasoning.","questions":[{"answer":"Dimensions vary as long as their product equals $360$ cm$^3$.","question":"A rectangular prism has dimensions $3$ cm, $12$ cm, and $6$ cm. What is its volume?"},{"answer":"$216$ cm$^3$","question":"The volume of a rectangular prism is $450$ cm$^3$. Its width is $5$ cm, and its height is $10$ cm. What is its length?"},{"answer":"$9$ cm","question":"Several rectangular prisms have a volume of $360$ cm$^3$. Explain how their dimensions could vary and the relationships between those dimensions."}],"difficulty":"extension"}


example_id: lp_01K9432STZMJ3CT9JFG6DS45ZX_01K9432V3YS2Q7Y7KA9ECTEN5B_CONTEMPLATIVE_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a net for a box to hold $12$ cookies. How can you ensure it folds into a cube? Explain.","teacherTips":["Discuss how each face of the net must match the cube's dimensions.","Encourage trial and error by sketching and folding paper.","Relate the net to real-life items like packaging boxes."],"difficulty":"mild"}


example_id: lp_01K9432STZMJ3CT9JFG6DS45ZX_01K9432V3YS2Q7Y7KA9Q28HBV7_EXIT_TICKET
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 6
country: US
period_number: 6
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Cube","question":"Which Halloween decoration is represented by a net with $6$ equal squares: a pumpkin, a cube, or a cone?"},{"answer":"$6$ rectangles","question":"A Halloween candy box is shaped like a rectangular prism. Which net could represent it: $6$ rectangles or $6$ triangles?"},{"answer":"Cone","question":"A witch's hat is represented by a net with $1$ circle and $1$ triangle. Which $3$D shape does it form when folded?"}]}


example_id: lp_01K9432STZMJ3CT9JFG6DS45ZX_01K9432V3YS2Q7Y7KA93AF92HE_ACTIVITY
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 6
country: US
period_number: 6
node_type: ACTIVITY
example_output_json:
{"header":"Net-to-Shape Challenge\nYour team is designing a toy box prototype and must match nets to 3D shapes.","scenario":"Steps\n1. Draw and cut out a net of a cube, pyramid, and rectangular prism.\n2. Fold each net to form its corresponding 3D shape.\n3. Check if the folds align perfectly to create the shape.\n4. Discuss as a team which features of the net match the 3D shape.\n5. Present your shapes and explain the matching process to the class.","steps":["Discussion\n• What clues on the net help identify its 3D shape?\n• Why do some nets not fold into a 3D shape properly?","Differentiation Opportunities\n• Support: Provide a pre-drawn net for one shape to help with folding.\n• Extend: Design a net for a more complex shape, like a hexagonal prism."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K9432STZMJ3CT9JFG6DS45ZX_01K9432V3YS2Q7Y7KA8YRKBQTR_APPLICATION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 6
country: US
period_number: 6
node_type: APPLICATION
example_output_json:
{"title":"Designing Halloween Treat Boxes","example1Header":"Situation\nHalloween box designers create unique treat boxes for candies. They use nets to visualize how flat designs fold into 3D shapes like cubes or pyramids.","example1Body":"Example\nA net with $6$ equal squares folds into a cube. Each square forms one face: top, bottom, front, back, left, and right. Designers ensure the net fits perfectly.","example2Header":"","example2Body":""}


example_id: lp_01K9432STZMJ3CT9JFG6DS45ZX_01K9432V3YS2Q7Y7KA9J00FWEV_THOUGHT_SPARKER
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 6
country: US
period_number: 6
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"For Halloween, trick-or-treaters are using boxes shaped like cubes, triangular prisms, and rectangular prisms to collect candy.","firstSentence":"How could you figure out which net matches the shape of each box?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Provide physical models or pictures of nets and 3D shapes to support hands-on exploration.","Discuss how the number and shape of faces in a net relate to the 3D shape it forms.","Encourage students to explain their reasoning for matching a specific net to a shape."]}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JRX7HJ221TVNRR8RETW_CONTEMPLATIVE_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a net for a box to store your favorite toy. How would you ensure it folds into a cube? Explain.","teacherTips":["A cube's net has $6$ squares. Ensure edges align to make $3$D shape when folded."],"difficulty":"mild"}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JRX7HJ221TVNZHZRJAW_CONTEMPLATIVE_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"If you unfold a cube, what could its net look like? Draw at least 3 different possible nets and explain how each folds back into the cube.","teacherTips":["A cube's net has 6 squares. The arrangement must allow all edges to connect properly when folded."],"difficulty":"mild"}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JRX7HJ221TVPC65R1RM_MULTIPLE_CHOICE_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A net consists of $6$ identical squares. Which 3D shape can be formed by folding this net?","answerOptions":["A cube","A rectangular prism","A triangular prism","A pyramid"],"answer":"A cube","difficulty":"hot"}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JRX7HJ221TVPFCGWXQZ_MULTIPLE_CHOICE_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which 3D shape is formed by a net that has one rectangular base and four triangular faces?","answerOptions":["Triangular prism","Square pyramid","Rectangular pyramid","Cube"],"answer":"Rectangular pyramid","difficulty":"hot"}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JRX7HJ221TVP50J0NPV_MULTIPLE_CHOICE_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which 3D shape is formed by a net with $6$ equal square faces?","answerOptions":["A cube","A rectangular prism","A triangular prism","A pyramid"],"answer":"A cube","difficulty":"mild"}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JBBPKWP23XZDH07EQR1_SCAFFOLDED_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to match a net to its corresponding 3D shape. A net is a flat pattern that can fold into a 3D shape.","questions":[{"answer":"A net with $4$ triangles","question":"Which net can fold into a cube?"},{"answer":"A net with $6$ squares","question":"Which net can fold into a rectangular prism?"},{"answer":"A net with $4$ triangles","question":"A triangular pyramid has $4$ triangular faces. Describe the net that could fold into this shape."}],"difficulty":"enabling"}


example_id: lp_01K9433HFY3Y9ZYK29HDDXB81B_01K9433JBBPKWP23XZDN9W11DE_SCAFFOLDED_QUESTION
skills: ["Matching a net to its corresponding 3D shape"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore how nets create 3D shapes and identify relationships between faces, edges, and vertices.","questions":[{"answer":"Rearranging faces can create incomplete or misaligned shapes.","question":"A net has six congruent squares arranged so each square shares exactly one edge with another. Which 3D shape does the net form?"},{"answer":"Cube","question":"A net has two congruent triangles and three rectangles. The triangular faces share edges with the three rectangles. Which 3D shape is it?"},{"answer":"Triangular prism","question":"Explain how rearranging the faces in a net could change the resulting 3D shape. Provide examples and justify your reasoning."}],"difficulty":"extension"}


example_id: lp_01K943B50BM069HNSMQQH1TXHE_01K943B672T2TF655FD1FJ6C9W_ACTIVITY
skill_ids: ["y9P64ixgMvpUMYhzijkL","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Robotics
class_year: 6
country: US
period_number: 6
node_type: ACTIVITY
example_output_json:
{"header":"Surface Area Challenge\nYou're designing a gift box using prisms and composite shapes!","scenario":"Steps\n1. In groups, draw a composite solid made of a rectangular prism and a triangular prism.\n2. Label the dimensions of all sides (e.g., base, height, length).\n3. Calculate the surface area of each prism separately.\n4. Add the areas of all the faces to find the total surface area.\n5. Compare your surface area with other groups to check accuracy!","steps":["Discussion\n• Why do we add the areas of all faces to find the surface area?\n• How does changing one dimension affect the total surface area?","Differentiation Opportunities\n• Support: Provide dimensions for a single rectangular prism to simplify calculations.\n• Extend: Create a more complex solid by combining three prisms of different shapes."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating the total surface area of a prism","Calculating the total surface area of composite solids"]


example_id: lp_01K943B50BM069HNSMQQH1TXHE_01K943B672T2TF655FDPC87QRB_EXIT_TICKET
skill_ids: ["y9P64ixgMvpUMYhzijkL","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Robotics
class_year: 6
country: US
period_number: 6
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$208$","question":"A rectangular robot body has dimensions $4$ cm by $6$ cm by $8$ cm. What is its total surface area?"},{"answer":"$582.72$","question":"A robot has a cylindrical head with radius $3$ cm and height $5$ cm attached to a cube with side $6$ cm. What is the total surface area?"},{"answer":"$220.52$","question":"A robot arm is a prism with a rectangular base $4$ cm by $3$ cm and height $10$ cm, attached to a hemisphere of radius $3$ cm. Find the total surface area."}]}

skills:
["Calculating the total surface area of a prism","Calculating the total surface area of composite solids"]


example_id: lp_01K943B50BM069HNSMQQH1TXHE_01K943B672T2TF655FDHNHTWKZ_CONTEMPLATIVE_QUESTION
skill_ids: ["y9P64ixgMvpUMYhzijkL","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Robotics
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a gift box made of a rectangular prism with a triangular prism on top. How would you calculate the total surface area of the box? Can you create a different composite solid and calculate its surface area?","teacherTips":["Encourage students to break the composite solid into simpler shapes.","Remind them to calculate the area of each face and sum them up.","Discuss real-world uses of surface area, like packaging design."],"difficulty":"mild"}

skills:
["Calculating the total surface area of a prism","Calculating the total surface area of composite solids"]


example_id: lp_01K943B50BM069HNSMQQH1TXHE_01K943B672T2TF655FCY6S4N14_APPLICATION
skill_ids: ["y9P64ixgMvpUMYhzijkL","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Robotics
class_year: 6
country: US
period_number: 6
node_type: APPLICATION
example_output_json:
{"title":"Designing Robot Casings with Surface Area","example1Header":"Situation\nRobotics engineers design protective casings for robots. To ensure durability and cost efficiency, they calculate the surface area of the casing to determine the material needed.","example1Body":"Example\nA robot casing has dimensions $5$ cm, $3$ cm, and $4$ cm. Its surface area is $2 \\cdot (5 \\cdot 3 + 3 \\cdot 4 + 5 \\cdot 4) = 94$ cm$^2$. Engineers use this value to estimate material needed.","example2Header":"","example2Body":""}


example_id: lp_01K943B50BM069HNSMQQH1TXHE_01K943B672T2TF655FDMDEWGFR_THOUGHT_SPARKER
skill_ids: ["y9P64ixgMvpUMYhzijkL","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Robotics
class_year: 6
country: US
period_number: 6
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A robot arm is made up of three connected rectangular prisms: the base is $10$ cm by $8$ cm by $5$ cm, the middle section is $12$ cm by $6$ cm by $4$ cm, and the hand is $8$ cm by $4$ cm by $3$ cm.","firstSentence":"How could you figure out the total surface area of the robot arm?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to analyze each prism separately before combining their surface areas.","Discuss how to avoid double-counting shared faces between connected prisms.","Provide visual aids or 3D models to help students visualize the composite solid."]}


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C22VF4FN6EFSZBW6DNX9_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular box has a length of $4$ cm, width of $3$ cm, and height of $2$ cm. What is its total surface area?","answerOptions":["$24$ cm$^2$","$52$ cm$^2$","$48$ cm$^2$","$60$ cm$^2$"],"answer":"$52$ cm$^2$","difficulty":"mild"}

skills:
["Calculating the total surface area of composite solids","Calculating the total surface area of a prism"]


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C22VF4FN6EFSZDE8CW8X_CONTEMPLATIVE_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a new birdhouse by combining a cube, cylinder, and pyramid. How will you calculate the total surface area of your birdhouse? What measurements will you need, and how will the shapes connect?","teacherTips":["Find visible areas of each shape. Use $A = 6s^2$ for cube, $A = 2\\pi rh$ for cylinder, and $A = \\frac{1}{2}bh$ for pyramid."],"difficulty":"spicy"}

skills:
["Calculating the total surface area of composite solids","Calculating the total surface area of a prism"]


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C22VF4FN6EFSZA5ZBNF0_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular prism has a length of $4$ cm, a width of $3$ cm, and a height of $2$ cm. What is its total surface area?","answerOptions":["$24$ cm$^2$","$36$ cm$^2$","$52$ cm$^2$","$72$ cm$^2$"],"answer":"$52$ cm$^2$","difficulty":"mild"}

skills:
["Calculating the total surface area of composite solids","Calculating the total surface area of a prism"]


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C22VF4FN6EFSYP67SA1B_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular prism has a length of $8$ cm, width of $3$ cm, and height of $2$ cm. What is the total surface area?","answerOptions":["$48$ cm$^2$","$88$ cm$^2$","$84$ cm$^2$","$96$ cm$^2$"],"answer":"$88$ cm$^2$","difficulty":"mild"}


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C22VF4FN6EFSYRCJ9VM3_CONTEMPLATIVE_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You are designing a box to hold $12$ books. How would you calculate the total surface area of the box? What dimensions would you choose to minimize the material used?","teacherTips":["Use $2lw + 2lh + 2wh$ to find surface area. Smaller surface area saves material."],"difficulty":"hot"}


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C1K23HSFRSFXD3AXD5NC_SCAFFOLDED_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the total surface area of composite solids and prisms through advanced reasoning and calculations.","questions":[{"answer":"Answers should explain subtracting shared areas and summing separate surfaces.","question":"A rectangular prism has dimensions $4$ cm by $3$ cm by $2$ cm. What is its total surface area?"},{"answer":"$52$ cm$^2$","question":"A composite solid consists of two rectangular prisms: one with dimensions $5$ cm by $3$ cm by $2$ cm and another with dimensions $3$ cm by $2$ cm by $2$ cm. They are joined along a $3$ cm by $2$ cm face. What is the total surface area of the composite solid?"},{"answer":"$82$ cm$^2$","question":"A composite solid is made by attaching a triangular prism to the top of a rectangular prism. Describe a step-by-step method to calculate the total surface area of this solid, considering both shared and unshared surfaces."}],"difficulty":"extension"}


example_id: lp_01K943C0G730HR7XZVC4MJDCXA_01K943C1K23HSFRSFXCY3PPMR7_SCAFFOLDED_QUESTION
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","y9P64ixgMvpUMYhzijkL"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to calculate the surface area of a rectangular prism. Surface area is the total area of all the faces.","questions":[{"answer":"$94$ cm$^2$","question":"A rectangular prism has a length of $4$ cm and a width of $3$ cm. What is the area of one of its rectangular faces?"},{"answer":"$7$ cm$^2$","question":"The prism also has a height of $5$ cm. What is the area of the rectangular face with dimensions $5$ cm by $3$ cm?"},{"answer":"$12$ cm$^2$","question":"The rectangular prism has dimensions $4$ cm, $3$ cm, and $5$ cm. What is the total surface area?\nHint: A prism has $6$ faces."}],"difficulty":"enabling"}


example_id: lp_01K947FCTV1B5P4VRMDVNNPE9V_01K947FDTWA14JV9X5BMXRZDBZ_APPLICATION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Yoga
class_year: 6
country: US
period_number: 6
node_type: APPLICATION
example_output_json:
{"title":"Yoga Class Performance Analysis","example1Header":"Situation\nYoga instructors analyze student performance over sessions. They track flexibility improvement using side-by-side dot plots for comparison.","example1Body":"Example\nSession 1 has average flexibility of $16.6$, while Session 2 has $19.4$. Comparing side-by-side dot plots helps instructors see improvements over time.","example2Header":"","example2Body":""}

skills:
["Describing and comparing data distributions in side-by-side dot plots","Analysing and creating frequency tables with discrete data","Analysing and creating frequency tables with continuous data"]


example_id: lp_01K947FCTV1B5P4VRMDVNNPE9V_01K947FDTWA14JV9X5C6052PP4_THOUGHT_SPARKER
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Yoga
class_year: 6
country: US
period_number: 6
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A yoga studio tracks the number of students attending evening classes over two weeks, showing Week $1$ attendance as $6$, $8$, $5$, $7$, $10$, $9$, $6$ and Week $2$ attendance as $4$, $7$, $8$, $6$, $9$, $7$, $5$.","firstSentence":"How could you use dot plots to compare the attendance distributions between the two weeks?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify clusters, gaps, and ranges in the dot plots.","Discuss how dot plots visually highlight patterns and allow for easy comparisons.","Ask students to consider what the data might suggest about attendance trends."]}

skills:
["Describing and comparing data distributions in side-by-side dot plots","Analysing and creating frequency tables with discrete data","Analysing and creating frequency tables with continuous data"]


example_id: lp_01K947FCTV1B5P4VRMDVNNPE9V_01K947FDTWA14JV9X5BSK4NVCF_ACTIVITY
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Yoga
class_year: 6
country: US
period_number: 6
node_type: ACTIVITY
example_output_json:
{"header":"Dice Data Challenge\nYour team is collecting and comparing dice roll data to find patterns.","scenario":"Steps\n1. Each group rolls a die $30$ times and records the results.\n2. Create a frequency table for the results on your paper.\n3. Plot your data as a dot plot under the table.\n4. Compare your dot plot with another group’s plot.\n5. Discuss patterns or differences between the two plots.","steps":["Discussion\n• What patterns do you notice in the dot plots?\n• Why might the distributions look different between groups?","Differentiation Opportunities\n• Support: Roll the die $15$ times and use a pre-drawn table outline.\n• Extend: Roll two dice, record sums, and compare distributions of sums."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Describing and comparing data distributions in side-by-side dot plots","Analysing and creating frequency tables with discrete data","Analysing and creating frequency tables with continuous data"]


example_id: lp_01K947FCTV1B5P4VRMDVNNPE9V_01K947FDTWA14JV9X5C2YY11MN_CONTEMPLATIVE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Yoga
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a frequency table for the number of books classmates read in a month. Then, describe and compare the data using a dot plot. What patterns or trends do you notice?","teacherTips":["Encourage students to use realistic data for the frequency table.","Discuss how dot plots show data distribution clearly.","Ask students to compare clusters, gaps, or peaks in the dot plot."],"difficulty":"mild"}


example_id: lp_01K947FCTV1B5P4VRMDVNNPE9V_01K947FDTWA14JV9X5C9W2JQMN_EXIT_TICKET
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Yoga
class_year: 6
country: US
period_number: 6
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$13$","question":"A yoga class has $5$ students who did yoga $2$ times a week and $8$ students who did yoga $3$ times a week. How many students are there in total?"},{"answer":"Group B","question":"The dot plot shows $2$ groups' yoga session durations: Group A has a median of $45$ minutes, and Group B has a median of $50$ minutes. Which group has longer sessions?"},{"answer":"$15$","question":"A frequency table shows yoga durations grouped as $10$-$20$, $20$-$30$, $30$-$40$, with frequencies $3$, $5$, and $7$. What is the total number of sessions?"}]}


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H31RDXE6608D5RY3HE23_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If $10$ students chose basketball, $8$ chose soccer, and $12$ chose tennis, what is the total number of students surveyed?","answerOptions":["$28$","$30$","$32$","$34$"],"answer":"$30$","difficulty":"mild"}

skills:
["Analysing and creating frequency tables with discrete data","Analysing and creating frequency tables with continuous data","Describing and comparing data distributions in side-by-side dot plots"]


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H31RDXE6608D5XHG9GQH_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A survey recorded the number of books read by $20$ students: $3, 4, 3, 5, 2, 4, 3, 5, 2, 4, 4, 5, 3, 3, 2, 4, 5, 4, 3, 2$. What is the most frequent number of books read?","answerOptions":["$2$","$3$","$4$","$5$"],"answer":"$4$","difficulty":"spicy"}

skills:
["Analysing and creating frequency tables with discrete data","Analysing and creating frequency tables with continuous data","Describing and comparing data distributions in side-by-side dot plots"]


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H31SFFSHBM98TVPGG3WA_CONTEMPLATIVE_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A park tracks daily visitor counts over $30$ days. How would you group data into a frequency table? What choices would you make for intervals, and how could the table help predict future visitor trends?","teacherTips":["Group data into intervals, count visitors per group, and use trends to predict future counts."],"difficulty":"spicy"}

skills:
["Analysing and creating frequency tables with discrete data","Analysing and creating frequency tables with continuous data","Describing and comparing data distributions in side-by-side dot plots"]


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H31SFFSHBM98TV2ZJ912_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A frequency table shows students' test scores grouped into intervals. Which interval had the most students if the frequencies are $4$, $7$, $10$, and $6$?","answerOptions":["The first interval","The second interval","The third interval","The fourth interval"],"answer":"The third interval","difficulty":"hot"}


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H31RDXE6608D52GC8Y9X_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Two side-by-side dot plots show test scores. Group A has a range of $15$, and Group B has a range of $10$. Which group has more variability?","answerOptions":["Group A","Group B","Both groups have the same variability","Cannot be determined without more information"],"answer":"Group A","difficulty":"hot"}


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H31RDXE6608D585E14B5_CONTEMPLATIVE_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create two side-by-side dot plots showing test scores for two classes. How would you describe and compare their distributions? What does this tell you about the performance of each class?","teacherTips":["Compare distributions by range, center, and spread. Look for gaps, clusters, and overlaps in scores."],"difficulty":"spicy"}


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H2BMA9224M6FC8A3YVJA_SCAFFOLDED_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze and compare distributions using frequency tables and side-by-side dot plots for two groups of students' test scores.","questions":[{"answer":"Class A is consistent; Class B has varied performance.","question":"A frequency table shows the number of students scoring in intervals: $0-20$: $5$, $21-40$: $8$, $41-60$: $12$, $61-80$: $10$, $81-100$: $5$.\nHow many students are there in total?"},{"answer":"$40$","question":"Create a frequency table for these scores: $12, 18, 25, 37, 40, 45, 50, 63, 70, 72, 86, 90$, using intervals $0-20$, $21-40$, $41-60$, $61-80$, $81-100$."},{"answer":"Frequency table: $[2, 3, 2, 3, 2]$","question":"Two classes' test scores are shown as dot plots.\nClass A has scores clustered near $70$, while Class B has scores spread evenly from $40$ to $90$.\nExplain how their distributions differ and what this tells you about their performance."}],"difficulty":"extension"}


example_id: lp_01K947H1M9DFN26Q6175ZRHXBV_01K947H2BMA9224M6FC0XKWY1W_SCAFFOLDED_QUESTION
skill_ids: ["01JZH1GX69N3Q2JHMRP0YJR8N4","01JZH1GE4CYWBVDVXGD9W7D0D4","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Frequency Tables"]
subtopic_ids: ["subtopic_01GTC0BD5V2C0G5YQN22N39GB3"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to analyze data and create frequency tables. Frequency tables show how often a data value occurs.","questions":[{"answer":"10: 3, 11: 2, 12: 3, 13: 2","question":"A survey recorded the ages of $10$ people: $10, 12, 10, 11, 13, 12, 12, 11, 10, 13$.\nWhat is the frequency of the age $10$?"},{"answer":"$1$","question":"Using the same dataset: $10, 12, 10, 11, 13, 12, 12, 11, 10, 13$.\nWhich age occurs the most often?"},{"answer":"$2$","question":"Create a frequency table for the dataset: $10, 12, 10, 11, 13, 12, 12, 11, 10, 13$.\nList each age and its frequency."}],"difficulty":"enabling"}


example_id: lp_01K947Q5BHWM9427RZBHMCDFEG_01K947Q63VAJXXW5TPY0K6JE5J_APPLICATION
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Giraffes
class_year: 6
country: US
period_number: 6
node_type: APPLICATION
example_output_json:
{"title":"Tracking Giraffe Heights with Statistics","example1Header":"Situation\nWildlife researchers study giraffes' growth by analyzing their heights. By calculating the mean, they understand average height trends in different herds.","example1Body":"Example\nA researcher records giraffe heights: $4.5$ m, $5.3$ m, $4.8$ m, $5.1$ m, and $4.9$ m. Their mean height is $(4.5 + 5.3 + 4.8 + 5.1 + 4.9) \\div 5 = 4.92$ m.","example2Header":"","example2Body":""}


example_id: lp_01K947Q5BHWM9427RZBHMCDFEG_01K947Q63VAJXXW5TPYKW627T5_THOUGHT_SPARKER
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Giraffes
class_year: 6
country: US
period_number: 6
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A wildlife researcher measures the heights of $10$ giraffes in meters: $4.8$, $5.2$, $5.2$, $4.9$, $5.5$, $5.0$, $5.2$, $4.8$, $5.1$, $5.3$.","firstSentence":"How could you use this data to describe the average and most common height of these giraffes?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to calculate the mode, median, and mean separately before comparing results.","Encourage students to explain why different averages might be helpful for describing the data.","Discuss how outliers or repeating values can affect each type of calculation."]}


example_id: lp_01K947Q5BHWM9427RZBHMCDFEG_01K947Q63VAJXXW5TPY1N5PY9X_ACTIVITY
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Giraffes
class_year: 6
country: US
period_number: 6
node_type: ACTIVITY
example_output_json:
{"header":"Game Score Stats\nYour team analyzes game scores to find the mean, median, and mode to crown a winner!","scenario":"Steps\n1. Each team writes $10$ game scores between $1$ and $100$ on paper.\n2. Organize the scores in ascending order.\n3. Calculate the mean, median, and mode of the scores.\n4. Share your results and discuss patterns with the class.\n5. Compare results to decide the most consistent player!","steps":["Discussion\n• Why is the mean sometimes different from the median?\n• How does a repeated score affect the mode?","Differentiation Opportunities\n• Support: Use $5$ scores instead of $10$ to simplify calculations.\n• Extend: Add an outlier score and observe its effect on the mean."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K947Q5BHWM9427RZBHMCDFEG_01K947Q63VAJXXW5TPYCBCF47T_CONTEMPLATIVE_QUESTION
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Giraffes
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your class measured plant heights: $5$, $7$, $6$, $7$, $8$, $5$, $7$. How would you find the mean, median, and mode? What do these values tell you about the plant heights?","teacherTips":["Guide students to add all values and divide by $7$ for the mean.","Help students arrange the data to find the middle value for the median.","Explain the mode as the number appearing most often."],"difficulty":"mild"}


example_id: lp_01K947Q5BHWM9427RZBHMCDFEG_01K947Q63VAJXXW5TPYSV7G60E_EXIT_TICKET
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Giraffes
class_year: 6
country: US
period_number: 6
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$","question":"A group of giraffes eats $3$, $5$, $3$, $7$, and $3$ leaves each. What is the mode of the number of leaves eaten?"},{"answer":"$5.6$","question":"A zookeeper measures the neck lengths of $5$ giraffes as $5.2$ m, $5.8$ m, $6.0$ m, $5.4$ m, $5.6$ m. What is the median neck length?"},{"answer":"$5.1$","question":"The heights of $4$ giraffes are $4.8$ m, $5.2$ m, $5.0$ m, and $5.4$ m. What is the mean height?"}]}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QNGJCBN7J02C0J7YWNB2_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the mean of the numbers $4$, $6$, $8$, and $10$?","answerOptions":["$6$","$7$","$8$","$9$"],"answer":"$7$","difficulty":"mild"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QNGJCBN7J02C0PNZGNJB_CONTEMPLATIVE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your class collected data on how many books students read last month: $3, 7, 5, 4, 6$. How would you calculate the mean number of books read? Could the mean change if another student read $8$ books? Explain.","teacherTips":["To find the mean, add $3 + 7 + 5 + 4 + 6$ and divide by $5$. Adding $8$ changes the total and the mean."],"difficulty":"mild"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QNGJCBN7J02C2782080W_CONTEMPLATIVE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a data set of $9$ numbers where the median is $12$. How would adding another number change the median?","teacherTips":["The median is the middle value in an ordered set. Adding a number may shift or keep the median unchanged."],"difficulty":"spicy"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QNGJCBN7J02C25K8MTD1_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is the median of the dataset $12, 18, 15, 10, 22, 14, 19$?","answerOptions":["$14$","$15$","$18$","$19$"],"answer":"$15$","difficulty":"hot"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QNGJCBN7J02C1F16KPMX_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A dataset contains the numbers $3, 7, 7, 10, 12, 12, 12, 15$. If the number $12$ is removed, what will be the new mode?","answerOptions":["$7$","$10$","$12$","No mode"],"answer":"$7$","difficulty":"spicy"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QNGJCBN7J02C1CHHDBE5_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is the mode of the dataset $3, 7, 3, 7, 8, 9, 7, 3, 10, 7, 8$?","answerOptions":["$3$","$7$","$8$","$9$"],"answer":"$7$","difficulty":"hot"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QN0TX4D494QR56MP9A99_SCAFFOLDED_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn about mode, median, and mean. These are ways to describe data sets and find key information about them.","questions":[{"answer":"$5$","question":"What is the mode of this data set: $2, 3, 3, 4, 5$?\nThe mode is the number that appears most often."},{"answer":"$2$","question":"What is the median of this data set: $1, 3, 5, 7, 9$?\nThe median is the middle value when the numbers are in order."},{"answer":"$3$","question":"What is the mean of this data set: $2, 4, 6, 8$?\nTo find the mean, add all the numbers and divide by how many there are."}],"difficulty":"enabling"}


example_id: lp_01K947QM6XGA2PVCYGE1300G3T_01K947QN0TX4D494QR59BK3T81_SCAFFOLDED_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze and calculate the mode, median, and mean from increasingly complex data sets.","questions":[{"answer":"Mean: $10.33$, Median: $8.5$, Mode: $7$","question":"Find the mode of the data set: $4, 7, 9, 7, 11, 4, 7, 4, 9, 4$."},{"answer":"$4$","question":"Find the median of the data set: $12, 5, 8, 15, 7, 10, 5, 20$."},{"answer":"$9$","question":"A data set is $3, 7, 7, 10, 15, 20$. Explain how the mean, median, and mode compare and what this tells you about the data's distribution."}],"difficulty":"extension"}


example_id: lp_01K94805P76FEEG5B69ERGADT3_01K94806V1AXXEBAMGN11N0A0A_APPLICATION
skills: ["Interpreting dot plots","Interpreting histograms","Interpreting box plots"]
skill_ids: ["8AeE3xcn5UYmYk1zdxmv","01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Billiards
class_year: 6
country: US
period_number: 6
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Scores in Professional Billiards","example1Header":"Situation\nProfessional billiards players analyze their practice game data to improve. Scores are represented on dot plots to track performance trends over time.","example1Body":"Example\nA dot plot of scores ($7$, $7$, $8$, $9$, $9$, $10$) shows $2$ dots at $7$, $1$ dot at $8$, $2$ at $9$, and $1$ at $10$. The most frequent scores are $7$ and $9$.","example2Header":"","example2Body":""}


example_id: lp_01K94805P76FEEG5B69ERGADT3_01K94806V1AXXEBAMGNTHN6AH1_THOUGHT_SPARKER
skills: ["Interpreting dot plots","Interpreting histograms","Interpreting box plots"]
skill_ids: ["8AeE3xcn5UYmYk1zdxmv","01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Billiards
class_year: 6
country: US
period_number: 6
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a billiards tournament, the scores of $20$ players are recorded, and the data is displayed using a histogram, a dot plot, and a box plot.","firstSentence":"How would you decide which type of plot gives the most useful information about the players' scores?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to discuss the purpose of each plot type and how it represents data.","Ask students to compare features like range, clusters, and outliers across the different plots.","Guide students to think about what 'useful information' means based on the context of the scores."]}


example_id: lp_01K94805P76FEEG5B69ERGADT3_01K94806V1AXXEBAMGNKC5SDRQ_CONTEMPLATIVE_QUESTION
skills: ["Interpreting dot plots","Interpreting histograms","Interpreting box plots"]
skill_ids: ["8AeE3xcn5UYmYk1zdxmv","01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Billiards
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a histogram, dot plot, and box plot using data for daily hours of screen time over 7 days. How do the plots help you understand the data? Which plot is most useful and why?","teacherTips":["Encourage students to create realistic screen time data for 7 days.","Discuss features like spread, center, or outliers in each plot.","Ask students to compare the usefulness of the three plots."],"difficulty":"mild"}


example_id: lp_01K94805P76FEEG5B69ERGADT3_01K94806V1AXXEBAMGNZ8Z6YCC_EXIT_TICKET
skills: ["Interpreting dot plots","Interpreting histograms","Interpreting box plots"]
skill_ids: ["8AeE3xcn5UYmYk1zdxmv","01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Billiards
class_year: 6
country: US
period_number: 6
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5$","question":"In a dot plot showing the number of billiards games won, $5$ dots are above $3$. How many players won $3$ games?"},{"answer":"$6$","question":"A histogram shows the scores of billiards games. If the interval $20$ to $30$ has a height of $6$, how many games scored in this range?"},{"answer":"$20$","question":"A box plot shows billiard game scores with $Q_1 = 15$, median $= 25$, and $Q_3 = 35$. What is the interquartile range?"}]}


example_id: lp_01K94805P76FEEG5B69ERGADT3_01K94806V1AXXEBAMGN7WCHPD6_ACTIVITY
skills: ["Interpreting dot plots","Interpreting histograms","Interpreting box plots"]
skill_ids: ["8AeE3xcn5UYmYk1zdxmv","01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Billiards
class_year: 6
country: US
period_number: 6
node_type: ACTIVITY
example_output_json:
{"header":"Graph Guessing Challenge\nYour team creates a plot and challenges others to interpret it correctly!","scenario":"Steps\n1. In teams, choose a simple data set (e.g., student heights or pets per family).\n2. Create a histogram, dot plot, or box plot to display the data on paper.\n3. Swap plots with another team and interpret their data (e.g., median, range).\n4. Write down your interpretation and share it with the plot creators.\n5. Creators confirm or correct interpretations to score points!","steps":["Discussion\n• Which type of plot was easiest to interpret? Why?\n• What does a box plot show that a histogram does not?","Differentiation Opportunities\n• Support: Provide example data sets (e.g., test scores) and simpler plots to interpret.\n• Extend: Challenge teams to create and interpret more complex plots with multiple data sets."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E06973FZJM_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a histogram, what does the height of each bar represent?","answerOptions":["The total number of bars","The number of categories","The frequency of data in that range","The range of the data"],"answer":"The frequency of data in that range","difficulty":"mild"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E06ETMEG92_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A histogram shows students' test scores. If $15$ students scored between $60$-$70$, $20$ scored between $70$-$80$, and $25$ scored between $80$-$90$, what fraction of students scored $70$ or above?","answerOptions":["$\\frac{9}{10}$","$\\frac{3}{5}$","$\\frac{3}{4}$","$\\frac{5}{6}$"],"answer":"$\\frac{3}{4}$","difficulty":"spicy"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E05MBXSS07_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What does the length of the box in a box plot represent?","answerOptions":["The mean of the data","The range of the data","The interquartile range (IQR)","The total number of data points"],"answer":"The interquartile range (IQR)","difficulty":"mild"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E05QQ39QNB_CONTEMPLATIVE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A box plot shows test scores from $40$ students. How would you explain the spread and median of the data?","teacherTips":["The box shows the middle $50\\%$ of scores, the median divides it, and whiskers show the full range."],"difficulty":"mild"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E071MPHXQB_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a dot plot, what does each dot typically represent?","answerOptions":["A single data value","The total range of the data","The average of the data","The highest data value"],"answer":"A single data value","difficulty":"mild"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E079DSP7Q2_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A dot plot shows the number of pages read by students: $5$, $7$, $4$, $5$, $7$, $8$, $6$, $5$, $7$. What is the median number of pages read?","answerOptions":["$5$","$6$","$7$","$8$"],"answer":"$6$","difficulty":"spicy"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481HRMQ0FTD0E075S0VAP2_CONTEMPLATIVE_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"A dot plot shows the favorite fruits of $30$ students. How could you use the plot to decide which fruit to buy for a class party? Explain your reasoning.","teacherTips":["Choose the fruit with the most dots, as it represents the most popular choice among students."],"difficulty":"hot"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481H6GT11AEV9TH029QYKJ_SCAFFOLDED_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to interpret data from dot plots, histograms, and box plots. These plots show data in different ways.","questions":[{"answer":"The median","question":"In a dot plot, the column with the most dots represents:"},{"answer":"The most frequent value","question":"In a histogram, the height of each bar shows:"},{"answer":"The least frequent value","question":"In a box plot, what does the line inside the box represent?"}],"difficulty":"enabling"}


example_id: lp_01K9481GD0KHAP6FRGYCSJYAPQ_01K9481H6GT11AEV9TH3J810WZ_SCAFFOLDED_QUESTION
skills: ["Interpreting histograms","Interpreting box plots","Interpreting dot plots"]
skill_ids: ["01K5WQ4Y26FH7A28W1S8QQBTXR","Ffk4p77UQY4bqF1IASNA","8AeE3xcn5UYmYk1zdxmv"]
subtopics: ["Basic Data Representation"]
subtopic_ids: ["subtopic_01GTC0BM9E20VH2JVR921WSJHS"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore advanced concepts in interpreting histograms, dot plots, and box plots using abstract reasoning and data analysis.","questions":[{"answer":"Histogram shows mode; box plot shows median.","question":"A histogram shows scores grouped in intervals $0-10$, $11-20$, and $21-30$.\nThe $11-20$ interval has the highest frequency.\nWhat does this tell you about the data?"},{"answer":"Most data is within $11-20$.","question":"Two dot plots show $10$ data points each:\nSet A's dots are tightly grouped, while Set B's dots are spread widely.\nWhich set has greater variability?"},{"answer":"Set B","question":"When analyzing the same data set, a histogram shows a peak in the $11-20$ range, while a box plot shows a median at $15$.\nExplain how these graphs complement each other."}],"difficulty":"extension"}


example_id: lp_01K9487C07BVMV2T392PSPZ0RS_01K9487CSY708KWV24SH5WCJDC_CONTEMPLATIVE_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
context: Calligraphy
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You collect data on daily rainfall over 2 weeks. Create a histogram and box plot. What do they show?","teacherTips":["Guide students to group rainfall data into intervals for the histogram.","Help students calculate quartiles and the median for the box plot.","Encourage students to compare spread and center in both graphs."],"difficulty":"mild"}

skills:
["Describing and summarising numerical distributions in box plots","Interpreting histograms and summarising numerical distributions"]


example_id: lp_01K9487C07BVMV2T392PSPZ0RS_01K9487CSY708KWV24S5PV1F4J_ACTIVITY
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
context: Calligraphy
class_year: 6
country: US
period_number: 6
node_type: ACTIVITY
example_output_json:
{"header":"Data Detective Challenge\nYour team is analyzing survey results to find the most popular school activity!","scenario":"Steps\n1. List $10$ activities and survey $10$ classmates, recording their favorite activity.\n2. Create a histogram to show the frequency of each activity.\n3. Draw a box plot to summarize the number of votes per activity.\n4. Compare your results with another team to find patterns.\n5. Summarize which activity is most and least popular and why.","steps":["Discussion\n• What does the histogram reveal about activity preferences?\n• How does the box plot help summarize the data differently?","Differentiation Opportunities\n• Support: Use data from only $5$ activities and fewer classmates for simplicity.\n• Extend: Analyze data from two surveys and compare their distributions."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Describing and summarising numerical distributions in box plots","Interpreting histograms and summarising numerical distributions"]


example_id: lp_01K9487C07BVMV2T392PSPZ0RS_01K9487CSY708KWV24SRA9S74T_EXIT_TICKET
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
context: Calligraphy
class_year: 6
country: US
period_number: 6
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$8$","question":"A calligraphy club creates $30$ pieces, and the histogram shows $8$ pieces take $1$ hour. How many pieces take $1$ hour?"},{"answer":"$3$","question":"The calligraphy practice times are summarised in a box plot, with a median of $3$ hours. What does this median mean?"},{"answer":"$2$","question":"A box plot shows calligraphy times with quartiles at $2$, $4$, $6$, and $10$ hours. What is the interquartile range?"}]}

skills:
["Describing and summarising numerical distributions in box plots","Interpreting histograms and summarising numerical distributions"]


example_id: lp_01K9487C07BVMV2T392PSPZ0RS_01K9487CSY708KWV24SMGBKN8A_THOUGHT_SPARKER
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
context: Calligraphy
class_year: 6
country: US
period_number: 6
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A group of $50$ students tracked how many hours they practiced calligraphy in a month. They created a histogram to show the frequency of practice hours and a box plot to summarize the numerical distribution.","firstSentence":"How could you compare the histogram and the box plot to summarize the students' practice habits?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to observe the range, median, and any clusters or gaps in the data.","Encourage students to think about what each graph reveals about the distribution of practice hours.","Discuss how both graphs can be used together to provide a fuller picture of the data."]}


example_id: lp_01K9487C07BVMV2T392PSPZ0RS_01K9487CSY708KWV24S2YDGTV9_APPLICATION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
context: Calligraphy
class_year: 6
country: US
period_number: 6
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Pen Durability in Calligraphy","example1Header":"Situation\nCalligraphy artists test how long different pens last during use. They summarize the results using histograms to compare pen durability and find the best tools for their art.","example1Body":"Example\nThe histogram shows $5$ pens lasted $1$-$3$ hours, $10$ pens lasted $4$-$6$ hours, and $15$ pens lasted $7$-$9$ hours. Most pens last $7$-$9$ hours, as $15$ is the highest frequency.","example2Header":"","example2Body":""}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488BQX3ABFBM9S8JY2WXZ2_MULTIPLE_CHOICE_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a box plot, what does the line inside the box represent?","answerOptions":["Mean","Median","Range","Mode"],"answer":"Median","difficulty":"mild"}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488BQX3ABFBM9S8W7MGFT3_CONTEMPLATIVE_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a box plot for the test scores of two classes. How can you compare their medians, ranges, and IQRs? What might these differences tell you about the performance of each class?","teacherTips":["Compare medians for center, IQRs for spread, and ranges for variability. Discuss class score patterns."],"difficulty":"spicy"}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488BQX3ABFBM9S8RJXK0RP_MULTIPLE_CHOICE_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In a box plot, the vertical line inside the box represents which measure of central tendency?","answerOptions":["Mean","Median","Mode","Range"],"answer":"Median","difficulty":"hot"}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488BQX3ABFBM9S7TMG97PS_MULTIPLE_CHOICE_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In a histogram, the height of each bar represents which of the following?","answerOptions":["The total number of intervals","The frequency of data in the interval","The difference between intervals","The range of the data set"],"answer":"The frequency of data in the interval","difficulty":"hot"}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488BQX3ABFBM9S7YYZ3ACM_CONTEMPLATIVE_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a histogram comparing the heights of plants in two gardens. How would you summarize the differences in their distributions? What factors might explain the variations?","teacherTips":["Compare ranges, clusters, and outliers. Differences may be due to sunlight, soil, or water availability."],"difficulty":"spicy"}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488B7EZJ4YNX1K13TD26TZ_SCAFFOLDED_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to interpret histograms and understand numerical distributions.","questions":[{"answer":"Most data points are between $30$ and $40$","question":"In a histogram, what does the height of a bar represent?"},{"answer":"The frequency of data in that range","question":"If a histogram bar for $10-20$ shows $8$, what does this mean?"},{"answer":"The total data","question":"In a histogram, the bar for $30-40$ is taller than all others.\nWhat does this tell you about the data in this range?"}],"difficulty":"enabling"}


example_id: lp_01K94889JKM708X5SQCVXY2S6V_01K9488B7EZJ4YNX1K18WB4MQD_SCAFFOLDED_QUESTION
skill_ids: ["yQECa5oqeKBBPz3OVcNQ","MDssUZkETPdytJ8GSj41"]
subtopics: ["Histogram"]
subtopic_ids: ["subtopic_01GTC0BK1A1AW51786947FHS60"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 6
country: US
period_number: 6
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze and interpret distributions to make mathematical conclusions about histograms and box plots.","questions":[{"answer":"Answers vary; must compare shape and spread.","question":"A histogram shows $50$ students' test scores. $10$ students scored $40-50$, $15$ scored $50-60$, $20$ scored $60-70$, and $5$ scored $70-80$. What is the median score range?"},{"answer":"$60-70$","question":"A box plot shows a dataset with $Q_1 = 25$, $Q_2 = 50$, and $Q_3 = 75$. What is the interquartile range (IQR) of the data?"},{"answer":"$50$","question":"Compare a histogram showing scores concentrated between $60-80$ with a box plot where $Q_1 = 40$, $Q_2 = 60$, and $Q_3 = 80$. How do the shapes and spreads differ?"}],"difficulty":"extension"}


example_id: lp_01K949ZT3FFJFRZWZ4F5ZBZNDA_01K949ZTT7X8CAKNC722ZAS52Z_ACTIVITY
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Volleyball
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Lemonade Stand Challenge\nRun your lemonade stand! Find unit rates and adjust recipes to maximize profit.","scenario":"Steps\n1. Write the cost for ingredients (e.g., $\\$6$ for $12$ lemons, $\\$4$ for $8$ cups).\n2. Calculate the unit rate for each ingredient (e.g., cost per lemon or cup).\n3. Create a recipe for $1$ cup of lemonade using unit rates.\n4. Scale your recipe to serve $10$ cups and calculate the total cost.\n5. Price your lemonade per cup to make a profit and compare with others!","steps":["Discussion\n• How does finding unit rates help with pricing?\n• What challenges did you face when scaling the recipe?","Differentiation Opportunities\n• Support: Use only whole numbers for unit rates and recipe scaling.\n• Extend: Add a new ingredient and calculate its impact on cost and profit."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K949ZT3FFJFRZWZ4F5ZBZNDA_01K949ZTT7X8CAKNC72K0A5206_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: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Volleyball
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$4$","question":"A volleyball player serves $24$ balls in $6$ minutes. How many balls does the player serve per minute?"},{"answer":"$25$","question":"In a volleyball game, the ratio of successful serves to unsuccessful serves is $5:3$. If there are $40$ serves in total, how many were successful?"},{"answer":"$80$","question":"A volleyball team scores $48$ points in $12$ games. If they aim to maintain the same average, how many points must they score in $20$ games?"}]}


example_id: lp_01K949ZT3FFJFRZWZ4F5ZBZNDA_01K949ZTT7X8CAKNC72DSQDENF_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: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Volleyball
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You buy $8$ apples for $\\$12$. How would you find the cost of $1$ apple? What if you needed $15$ apples?","teacherTips":["Guide students to divide total cost by quantity for the unit rate.","Encourage students to multiply the unit rate by $15$ for the next step.","Discuss how unit rates simplify solving ratio problems."],"difficulty":"mild"}


example_id: lp_01K949ZT3FFJFRZWZ4F5ZBZNDA_01K949ZTT7X8CAKNC72FCP81JZ_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: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Volleyball
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a volleyball game, a player serves $24$ times and scores $72$ points.","firstSentence":"How would you determine the average points scored per serve?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to divide the total points by the number of serves to find the unit rate.","Ask students to explain why calculating the average points per serve might be useful in evaluating performance.","Discuss other contexts where unit rates are helpful, such as speed or cost per item."]}


example_id: lp_01K949ZT3FFJFRZWZ4F5ZBZNDA_01K949ZTT7X8CAKNC71VW4D354_APPLICATION
skills: ["Finding unit rates","Solving ratio problems with the unitary method"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","pelss5UYj3L19Z5qsjMs"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Volleyball
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Unit Rates in Volleyball Training","example1Header":"Situation\nVolleyball coaches track player performance during training. They calculate unit rates like hits per minute to improve efficiency and set personalized goals.","example1Body":"Example\nA player makes $48$ hits in $6$ minutes. The coach divides $48 \\div 6 = 8$ hits per minute. This helps track how consistent the player is during training.","example2Header":"","example2Body":""}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0D7HFNMENXGPH54YHVDN_MULTIPLE_CHOICE_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A factory produces $720$ units in $6$ hours. What is the unit production rate per hour?","answerOptions":["$100$ units/hour","$110$ units/hour","$120$ units/hour","$130$ units/hour"],"answer":"$120$ units/hour","difficulty":"hot"}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0D7HFNMENXGPH8TP7FR3_CONTEMPLATIVE_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are comparing two internet plans. Plan A costs $\\$45$ for $300$ GB, and Plan B costs $\\$60$ for $400$ GB. How would you calculate the unit rate for each plan? Which plan offers better value, and why?","teacherTips":["Plan A: $\\$45 \\div 300 = 0.15$ per GB. Plan B: $\\$60 \\div 400 = 0.15$ per GB. Both cost $\\$0.15$ per GB."],"difficulty":"spicy"}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0D7HFNMENXGPJ236DSGS_MULTIPLE_CHOICE_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Express the ratio $3$ feet to $36$ inches in its simplest form.","answerOptions":["$3:36$","$1:12$","$1:1$","$9:1$"],"answer":"$1:1$","difficulty":"mild"}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0D7HFNMENXGPJ47AKHH3_CONTEMPLATIVE_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"A recipe calls for $3$ cups of flour and $500$ mL of milk. How can you adjust the recipe so all parts of the ratio use the same unit? What unit would you choose, and why?","teacherTips":["Convert $3$ cups to $750$ mL (1 cup $=250$ mL), so the ratio becomes $750:500 = 3:2$ in mL."],"difficulty":"hot"}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0D7HFNMENXGPHW34KC70_MULTIPLE_CHOICE_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Convert the ratio $3$ kilograms to $500$ grams so that both parts are in grams.","answerOptions":["$3:500$","$3000:500$","$3000:5$","$6:500$"],"answer":"$3000:500$","difficulty":"mild"}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0CSMYC1C4998C374QRCF_SCAFFOLDED_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to find unit rates by converting all parts of a ratio to the same unit.","questions":[{"answer":"$0.4$","question":"A car travels $120$ miles in $2$ hours. How many miles does it travel per hour?"},{"answer":"$30$","question":"A cyclist travels $15$ miles in $30$ minutes. What is their speed in miles per hour?"},{"answer":"$40$","question":"A bakery uses $4\\,000$ grams of flour to bake $10$ cakes. How many kilograms of flour are used per cake? Show your work."}],"difficulty":"enabling"}


example_id: lp_01K94A0C0H5P9ZE28JH3KKRBRQ_01K94A0CSMYC1C4998C8JMSK7Z_SCAFFOLDED_QUESTION
skills: ["Finding unit rates","Converting all parts of a ratio to the same unit"]
skill_ids: ["01JZ9ZXQT3VJBKEJNNG84P08VJ","Q2wYvIZT7nG4SJ9uX1SR"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore unit rates and ratio conversions through challenging real-world scenarios.","questions":[{"answer":"Answers vary; must discuss unit scale and conversion impact.","question":"A car travels $240$ miles in $4$ hours. What is the car's speed in miles per hour?"},{"answer":"$60$ miles per hour","question":"An athlete runs $15$ kilometers in $1.5$ hours. What is the runner's speed in meters per second?"},{"answer":"$2.78$ meters per second","question":"Explain how changing the units of a ratio (e.g., from kilometers per hour to meters per second) affects the unit rate and why it is important to convert properly."}],"difficulty":"extension"}


example_id: lp_01K94D2WT1S1DN9E4S6GZVWE2R_01K94D2XQS1F27B4A9014AA5WV_APPLICATION
skills: ["Solving proportions in worded problems","Solving proportions"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Shooting Stars
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Proportions in Meteor Showers","example1Header":"Situation\nAstronomers calculate the number of meteors visible in certain time periods based on ratios. They predict how many shooting stars might be seen in an hour by observing smaller intervals.","example1Body":"Example\nIf $12$ meteors are seen in $15$ minutes, astronomers set up $12:15 = x:60$. Solving gives $15x = 720$, so $x = 48$. They expect $48$ meteors in $1$ hour.","example2Header":"","example2Body":""}


example_id: lp_01K94D2WT1S1DN9E4S6GZVWE2R_01K94D2XQS1F27B4A90JBE1Y6A_THOUGHT_SPARKER
skills: ["Solving proportions in worded problems","Solving proportions"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Shooting Stars
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a dark rural location, you can see $120$ shooting stars in one hour, while in a city, you can only see $30$ shooting stars in the same time.","firstSentence":"How could you use proportions to estimate how many shooting stars might be visible in a suburban area?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the relationship between the rural and city numbers first.","Guide students to set up a proportion to represent the situation for the suburban area.","Discuss how light pollution might affect the visibility of shooting stars to connect math to real-world reasoning."]}


example_id: lp_01K94D2WT1S1DN9E4S6GZVWE2R_01K94D2XQS1F27B4A90PWPZ7B7_EXIT_TICKET
skills: ["Solving proportions in worded problems","Solving proportions"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Shooting Stars
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$10$","question":"If $5$ shooting stars are seen in $10$ minutes, how many are seen in $20$ minutes?"},{"answer":"$27$","question":"During a meteor shower, $9$ shooting stars are seen in $12$ minutes. How many shooting stars are seen in $36$ minutes?"},{"answer":"$24$","question":"A telescope tracks $15$ shooting stars in $5$ hours. How many shooting stars does it track in $8$ hours?"}]}


example_id: lp_01K94D2WT1S1DN9E4S6GZVWE2R_01K94D2XQS1F27B4A90293MAH2_ACTIVITY
skills: ["Solving proportions in worded problems","Solving proportions"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Shooting Stars
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Recipe Scaling Challenge\nYour team is scaling recipes to serve more or fewer people at a party.","scenario":"Steps\n1. Write a recipe for 4 servings, including 4 ingredients (e.g., flour, sugar).\n2. Your team is assigned a new serving size (e.g., 10 servings).\n3. Use proportions to calculate the new ingredient amounts.\n4. Check your work with another team for accuracy.\n5. Score 1 point per correct recipe. The team with the most points wins!","steps":["Discussion\n• How do proportions help in scaling recipes?\n• What happens if you scale a recipe incorrectly?","Differentiation Opportunities\n• Support: Start with simpler serving sizes like doubling or halving the recipe.\n• Extend: Try scaling for non-whole numbers (e.g., 2.5 servings) or complex recipes."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94D2WT1S1DN9E4S6GZVWE2R_01K94D2XQS1F27B4A90DH7PDCW_CONTEMPLATIVE_QUESTION
skills: ["Solving proportions in worded problems","Solving proportions"]
skill_ids: ["BzCcZvkDQvKnDosjX5Os","01JZ9YZPMJ9TQM6VY6CJREWWM0"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Shooting Stars
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are mixing paint in the ratio $3:5$ (red to blue). If you need $40$ liters of paint, how many liters of each color would you use? What if you needed $60$ liters? Explain your method.","teacherTips":["Guide students to set up proportions like $3 + 5 = 8$ parts total.","Encourage students to scale the ratio to match the total amount needed.","Check students' reasoning when distributing total liters to both colors."],"difficulty":"mild"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH4GDWT22NHBS127YSX_MULTIPLE_CHOICE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If $3$ pencils cost $\\$6$, how much would $5$ pencils cost?","answerOptions":["$\\$8$","$10$","$12$","$15$"],"answer":"$10$","difficulty":"mild"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH4GDWT22NHBZ0HZYH1_MULTIPLE_CHOICE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A recipe requires 3 cups of flour for every 5 cups of sugar. If 18 cups of flour are used, how many cups of sugar are needed?","answerOptions":["$25$","$30$","$35$","$40$"],"answer":"$30$","difficulty":"spicy"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH4GDWT22NHBWD63PY2_MULTIPLE_CHOICE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"If $3$ pencils cost $\\$1.50$, how much will $8$ pencils cost?","answerOptions":["$\\$3.50$","$\\$4$","$\\$4.50$","$\\$5$"],"answer":"$\\$4$","difficulty":"hot"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH4GDWT22NHBN60NVK9_CONTEMPLATIVE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You mix red and blue paint in a ratio of $3:2$. If you use $15$ cups of red paint, how many cups of blue paint do you need? Could the ratio stay the same if you used $9$ cups of red paint instead? Explain.","teacherTips":["For $15$ cups red, blue is $10$ cups ($3:2 = 15:10$). $9$ cups red needs $6$ blue to keep $3:2$."],"difficulty":"mild"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH5WMKY1ME0B449B3HQ_MULTIPLE_CHOICE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If $3$ pencils cost $\\$6$, how much do $5$ pencils cost?","answerOptions":["$\\$8$","$10$","$12$","$15$"],"answer":"$10$","difficulty":"mild"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH5WMKY1ME0B89X2VB5_CONTEMPLATIVE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are designing a smoothie recipe. If $3$ cups of fruit mix make $5$ smoothies, how would you adjust the recipe to make $12$ smoothies? What if you only have $2$ cups of fruit mix? Explore different scenarios and justify your reasoning.","teacherTips":["Set up $\\dfrac{3}{5} = \\dfrac{x}{12}$ or $\\dfrac{3}{5} = \\dfrac{2}{y}$. Solve to find $x$ or $y$ respectively."],"difficulty":"spicy"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3HH5WMKY1ME0AYS1CCXH_MULTIPLE_CHOICE_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If $4$ pencils cost $\\$8$, how much do $6$ pencils cost?","answerOptions":["$\\$10$","$\\$12$","$\\$16$","$\\$18$"],"answer":"$\\$12$","difficulty":"mild"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3H2K84G7PR93P7ZRWKTZ_SCAFFOLDED_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Mastering proportions: Solve challenging real-world problems involving ratios and proportions.","questions":[{"answer":"Approximately $78$ gadgets","question":"A recipe requires $4$ cups of flour for every $6$ cups of sugar. If you use $10$ cups of sugar, how many cups of flour will you need?"},{"answer":"$6.67$ cups","question":"A car travels $\\frac{3}{4}$ of a mile in $5$ minutes. At the same rate, how far will it travel in $12$ minutes?"},{"answer":"$1.8$ miles","question":"A factory produces $50$ gadgets in $8$ hours. If the production rate increases by $25\\%$, how many gadgets will the factory produce in $10$ hours? Justify your answer."}],"difficulty":"extension"}


example_id: lp_01K94D3GAWKJXKBAK77TYH72AP_01K94D3H2K84G7PR93P238VZG5_SCAFFOLDED_QUESTION
skills: ["Solving proportions","Solving proportions in worded problems"]
skill_ids: ["01JZ9YZPMJ9TQM6VY6CJREWWM0","BzCcZvkDQvKnDosjX5Os"]
subtopics: ["Ratio Calculations"]
subtopic_ids: ["subtopic_01GTC0BM7JPKD3HGF0J54AC2DZ"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn to solve proportions by setting up equations from word problems.","questions":[{"answer":"$10$ gallons","question":"A recipe uses $2$ cups of sugar for $5$ cups of flour. How many cups of sugar are needed for $10$ cups of flour?"},{"answer":"$4$","question":"A bike travels $15$ miles in $3$ hours. How far will it travel in $6$ hours at the same speed?"},{"answer":"$5$","question":"A car uses $4$ gallons of fuel to travel $160$ miles. How many gallons are needed to travel $400$ miles at the same fuel efficiency?"}],"difficulty":"enabling"}


example_id: lp_01K94DHY3Y9W2WRARSB42W39BJ_01K94DHZ82WYEQJT2J9GFQAW8R_EXIT_TICKET
skills: ["Calculating the result of a percentage change","Calculating percentage change"]
skill_ids: ["clOYVMGxYpMCMjQIFe66","0KYfF7a6oIbrLZMfWTMM"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Camping
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$96$","question":"A tent costing $120$ dollars is on sale with a $20\\%$ discount. What is the new price of the tent after the discount?"},{"answer":"$30\\%$","question":"The price of a camping lantern increased from $50$ dollars to $65$ dollars. What is the percentage increase?"},{"answer":"$20\\%$","question":"During a camping sale, a backpack's price dropped from $80$ dollars to $64$ dollars. By what percentage did the price decrease?"}]}


example_id: lp_01K94DHY3Y9W2WRARSB42W39BJ_01K94DHZ82WYEQJT2J8TDTRCD3_ACTIVITY
skills: ["Calculating the result of a percentage change","Calculating percentage change"]
skill_ids: ["clOYVMGxYpMCMjQIFe66","0KYfF7a6oIbrLZMfWTMM"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Camping
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Popularity Contest Math\nYour class is hosting a popularity contest. Calculate how votes changed!","scenario":"Steps\n1. Each team picks 2 candidates and assigns them votes (e.g., $50$ and $80$).\n2. Set a scenario: Did votes increase or decrease? By what percentage?\n3. Calculate the new vote counts using the percentage changes.\n4. Share results and compare who gained or lost the most votes.\n5. The team with the most accurate calculations wins!","steps":["Discussion\n• Why does a $50\\%$ increase differ from a $50\\%$ decrease?\n• How does a smaller starting number affect percentage change?","Differentiation Opportunities\n• Support: Provide simpler percentages (e.g., $10\\%$, $25\\%$).\n• Extend: Ask students to calculate changes over multiple rounds."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94DHY3Y9W2WRARSB42W39BJ_01K94DHZ82WYEQJT2J99EVZYG4_CONTEMPLATIVE_QUESTION
skills: ["Calculating the result of a percentage change","Calculating percentage change"]
skill_ids: ["clOYVMGxYpMCMjQIFe66","0KYfF7a6oIbrLZMfWTMM"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Camping
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A store increases a $\\$50$ item by $20\\%$. How much does it cost now? What if it decreases by $20\\%$ instead? How do the results differ? Explain why.","teacherTips":["Guide students to calculate $20\\%$ of $\\$50$ using $\\frac{20}{100} \\times \\text{original price}$.","Discuss why a $20\\%$ increase and decrease don't cancel each other out.","Encourage students to explain how percentage change depends on the starting value."],"difficulty":"mild"}


example_id: lp_01K94DHY3Y9W2WRARSB42W39BJ_01K94DHZ82WYEQJT2J9FX2AV94_THOUGHT_SPARKER
skills: ["Calculating the result of a percentage change","Calculating percentage change"]
skill_ids: ["clOYVMGxYpMCMjQIFe66","0KYfF7a6oIbrLZMfWTMM"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Camping
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Last summer, a camping trip included 40 campers. This summer, the number of campers increased to 60.","firstSentence":"How would you calculate the percentage change in the number of campers from last summer to this summer?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the original and new values before calculating the change.","Discuss the formula for percentage change and its components to ensure clarity.","Ask students to explain their reasoning and compare different approaches to solving the problem."]}


example_id: lp_01K94DHY3Y9W2WRARSB42W39BJ_01K94DHZ82WYEQJT2J8RW576JR_APPLICATION
skills: ["Calculating the result of a percentage change","Calculating percentage change"]
skill_ids: ["clOYVMGxYpMCMjQIFe66","0KYfF7a6oIbrLZMfWTMM"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
context: Camping
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Percentage Change in Camping Supplies","example1Header":"Situation\nCamp organizers monitor how changes in supply prices, like tents and food, affect the overall budget for a camping trip.","example1Body":"Example\nA tent's price rises from $\\$100$ to $\\$120$. The change is $\\$20$, making the percentage increase $(\\$20 / \\$100) \\times 100 = 20\\%$.","example2Header":"","example2Body":""}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFY7GS8TDBJD66JNWQ2Y_CONTEMPLATIVE_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"A store increases the price of an item by $20\\%$ and then decreases it by $20\\%$. Is the final price the same as the original? Explain and calculate.","teacherTips":["No, the final price changes. A $20\\%$ increase then decrease gives $1.2x \\times 0.8 = 0.96x$."],"difficulty":"hot"}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFY7GS8TDBJD62G92HS6_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"The price of a book decreased from $\\$50$ to $\\$40$. What is the percentage decrease?","answerOptions":["$10\\%$","$20\\%$","$25\\%$","$30\\%$"],"answer":"$20\\%$","difficulty":"mild"}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFY7GS8TDBJD77DHS28R_CONTEMPLATIVE_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A store increases prices by $20\\%$. Later, they give a $20\\%$ discount. Will the final price match the original? Why?","teacherTips":["No, $20\\%$ of the increased price is larger than $20\\%$ of the original price. Final price is higher."],"difficulty":"spicy"}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFY7GS8TDBJD6XND7A2J_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If a shirt originally costs $\\$40$ and is on sale for $25\\%$ off, what is the sale price?","answerOptions":["$\\$10$","$\\$20$","$\\$30$","$\\$35$"],"answer":"$\\$30$","difficulty":"mild"}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFY7GS8TDBJD72S76BHY_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A shirt originally costs $\\$40$. It is now on sale with a $25\\%$ discount. What is the new price of the shirt?","answerOptions":["$\\$10$","$\\$30$","$\\$35$","$\\$25$"],"answer":"$\\$30$","difficulty":"mild"}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFFASHXAQS3185D24NKJ_SCAFFOLDED_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn how to calculate percentage change by applying simple steps to find increases or decreases.","questions":[{"answer":"$\\$230$","question":"A shirt costs $\\$50$. What is its price after a $10\\%$ increase?\nRemember: add $10\\%$ of $\\$50$ to the original price."},{"answer":"$\\$55$","question":"A bag costs $\\$80$. What is its price after a $20\\%$ decrease?\nRemember: subtract $20\\%$ of $\\$80$ from the original price."},{"answer":"$\\$$45","question":"A bicycle costs $\\$200$. What is its price after a $15\\%$ increase?\nHint: Find $15\\%$ of $\\$200$ and add it to the original price."}],"difficulty":"enabling"}


example_id: lp_01K94DJER2CY66DC09WWP2MDN6_01K94DJFFASHXAQS318A6X85WJ_SCAFFOLDED_QUESTION
skills: ["Calculating percentage change","Calculating the result of a percentage change"]
skill_ids: ["0KYfF7a6oIbrLZMfWTMM","clOYVMGxYpMCMjQIFe66"]
subtopics: ["Percentages"]
subtopic_ids: ["subtopic_01GTC0BBCXRVAGC30JSRECEQNE"]
topic: Ratios and Proportional Relationships
topic_id: 1c3afbe5-c014-4e91-8c72-2a7b5775d85c
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore percentage change through advanced applications in real-world scenarios.","questions":[{"answer":"The final price is higher by $2\\%$.","question":"A store increases the price of an item from $\\$120$ to $\\$150$. What is the percentage increase?"},{"answer":"$25\\%$","question":"A company reduces its workforce from $500$ employees to $400$. What is the percentage decrease?"},{"answer":"$20\\%$","question":"A product's price increases by $20\\%$ and then decreases by $15\\%$. Is the final price higher, lower, or the same as the original? Justify your answer."}],"difficulty":"extension"}


example_id: lp_01K94E99GQVPDKCRPMQA1C5MR5_01K94E9AGSYE234F2X09D5TACN_ACTIVITY
skill_ids: ["F4NYR2FDBTakhBy5R1rp","WD54OQwpSOVMTgAl9LoA"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Dolphins
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Temperature Tracker Race\nYour team is tracking temperatures in a city where it changes hourly—both rising and falling.","scenario":"Steps\n1. Draw a thermometer scale from $-20^\\circ$F to $20^\\circ$F on your paper.\n2. Each team rolls a dice to get a temperature change (e.g., $+3^\\circ$F or $-5^\\circ$F).\n3. Start at $0^\\circ$F and update the temperature after each roll.\n4. Track $10$ changes and calculate the final temperature.\n5. The team with the most accurate tracker wins!","steps":["Discussion\n• What happens when you add a negative number?\n• How can you check if your final temperature is correct?","Differentiation Opportunities\n• Support: Use smaller ranges like $-10^\\circ$F to $10^\\circ$F for simpler calculations.\n• Extend: Include multiplication or division with negatives for added challenge."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding negative and positive numbers","Basic addition and subtraction with negative numbers"]


example_id: lp_01K94E99GQVPDKCRPMQA1C5MR5_01K94E9AGSYE234F2X0M3PQG7E_CONTEMPLATIVE_QUESTION
skill_ids: ["F4NYR2FDBTakhBy5R1rp","WD54OQwpSOVMTgAl9LoA"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Dolphins
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A mountain's peak is at $+3\\,000$ ft, and its base is at $-500$ ft. What is the total height difference? How would the calculation change if the base was $-1\\,000$ ft?","teacherTips":["Guide students to subtract negative numbers correctly.","Encourage use of a number line to visualize changes.","Discuss how negative and positive values represent elevation."],"difficulty":"mild"}

skills:
["Understanding negative and positive numbers","Basic addition and subtraction with negative numbers"]


example_id: lp_01K94E99GQVPDKCRPMQA1C5MR5_01K94E9AGSYE234F2X0W8JMYTQ_EXIT_TICKET
skill_ids: ["F4NYR2FDBTakhBy5R1rp","WD54OQwpSOVMTgAl9LoA"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Dolphins
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$-5$","question":"A dolphin dives to $-10$ m below the ocean surface and then rises $5$ m. Where is the dolphin now?"},{"answer":"$-13$","question":"A dolphin dives $-15$ m, then rises $8$ m, and dives $-6$ m again. What is the dolphin's final depth?"},{"answer":"$-2$","question":"A dolphin swims from $-20$ m to $-5$ m, then dives $-12$ m and rises $15$ m. What is the dolphin's depth now?"}]}

skills:
["Understanding negative and positive numbers","Basic addition and subtraction with negative numbers"]


example_id: lp_01K94E99GQVPDKCRPMQA1C5MR5_01K94E9AGSYE234F2X0R7GMHCP_THOUGHT_SPARKER
skill_ids: ["F4NYR2FDBTakhBy5R1rp","WD54OQwpSOVMTgAl9LoA"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Dolphins
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Dolphins swim in ocean waters where the temperature can range from $15^\\circ$F to $-5^\\circ$F during the winter.","firstSentence":"How might dolphins adapt as the temperature shifts between these values?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to explore the difference between positive and negative temperatures.","Discuss how temperature changes could be represented on a number line.","Relate the discussion to real-world adaptations of marine animals to their environment."]}


example_id: lp_01K94E99GQVPDKCRPMQA1C5MR5_01K94E9AGSYE234F2X05T3BA8H_APPLICATION
skill_ids: ["F4NYR2FDBTakhBy5R1rp","WD54OQwpSOVMTgAl9LoA"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Dolphins
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Tracking Ocean Temperatures for Dolphins","example1Header":"Situation\nMarine biologists study dolphins' habitats by measuring ocean temperatures. They track positive and negative temperatures to understand climate effects on dolphins' food sources.","example1Body":"Example\nA biologist measures $-4^\\circ$F at night and $6^\\circ$F during the day. The temperature difference is $6 - (-4) = 6 + 4 = 10^\\circ$F, showing a $10^\\circ$F increase.","example2Header":"","example2Body":""}


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XWCJ8MX6W0MA0JG4CAN_CONTEMPLATIVE_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You are planning a hike with altitude changes of $-100$ m, $+250$ m, $-75$ m, and $+125$ m. How could you calculate your final altitude change? Could you rearrange the order to make the math easier?","teacherTips":["Add: $-100 + 250 - 75 + 125 = 200$ m. Rearrange as $(250 + 125) + (-100 - 75)$ for simplicity."],"difficulty":"hot"}

skills:
["Basic addition and subtraction with negative numbers","Understanding negative and positive numbers"]


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XWCJ8MX6W0M9YT6PV2Y_MULTIPLE_CHOICE_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $-3 + 7$?","answerOptions":["$10$","$-10$","$4$","$-4$"],"answer":"$4$","difficulty":"mild"}

skills:
["Basic addition and subtraction with negative numbers","Understanding negative and positive numbers"]


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XWCJ8MX6W0M9R8ZMTH5_MULTIPLE_CHOICE_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $-7 + 5$?","answerOptions":["$-12$","$2$","$-2$","$12$"],"answer":"$-2$","difficulty":"mild"}

skills:
["Basic addition and subtraction with negative numbers","Understanding negative and positive numbers"]


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XWCJ8MX6W0M8XVPWJBN_CONTEMPLATIVE_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are tracking temperatures for a week. Pick 3 days with positive and 3 with negative temperatures. How can you explain which day was warmest and which was coldest?","teacherTips":["On a number line, larger numbers are warmer. Compare positions to find warmest and coldest days."],"difficulty":"mild"}


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XWCJ8MX6W0M8W9HSMY3_MULTIPLE_CHOICE_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following is a negative number?","answerOptions":["$5$","$-3$","$0$","$7$"],"answer":"$-3$","difficulty":"mild"}


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XEQ6SYKRQVTZA148AMM_SCAFFOLDED_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the intricate relationships between positive and negative numbers using addition and subtraction.","questions":[{"answer":"Answers will vary, but must include reasoning about signs.","question":"What is the result of $(-7) + 15 - (-4)$?"},{"answer":"$12$","question":"Simplify $(-12) - [(-5) + (-3)] + 6$."},{"answer":"$2$","question":"Explain how to correctly evaluate the expression $(-6) - (-10) + (-8) - (+3)$, and why your method works for any combination of positive and negative numbers."}],"difficulty":"extension"}


example_id: lp_01K94E9WK7PZK453E57Y5PKKBR_01K94E9XEQ6SYKRQVTZ7A89VGC_SCAFFOLDED_QUESTION
skill_ids: ["WD54OQwpSOVMTgAl9LoA","F4NYR2FDBTakhBy5R1rp"]
subtopics: ["Negative Numbers"]
subtopic_ids: ["subtopic_01GTC0BQX9DWQBQQ3PGFVKJVDR"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to work with positive and negative numbers in addition and subtraction.","questions":[{"answer":"$0$","question":"What is $-2 + 5$?"},{"answer":"$7$","question":"What is $4 - (-3)$?\nHint: Subtracting a negative is the same as adding a positive."},{"answer":"$-7$","question":"What is $-5 + 8 - 3$?\nShow your steps."}],"difficulty":"enabling"}


example_id: lp_01K94EEJTHKCEX0TPJCVRKVM8P_01K94EEKP6ZS6P6C7A2HRJXPS9_THOUGHT_SPARKER
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: The Zoo
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"At a zoo, ticket prices changed during the winter. Adult tickets were reduced by $-3$ dollars, and child tickets increased by $2$ dollars per week for $5$ weeks.","firstSentence":"How could you determine the total change in ticket prices for adult and child tickets after $5$ weeks?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to explain the meaning of positive versus negative changes in the context of the problem.","Discuss strategies for multiplying and adding negative numbers, reinforcing the rules with examples.","Ask students to verify their calculations by breaking the problem into smaller steps and checking their reasoning."]}


example_id: lp_01K94EEJTHKCEX0TPJCVRKVM8P_01K94EEKP6ZS6P6C7A1QAKV36Z_APPLICATION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: The Zoo
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Tracking Animal Population Changes at the Zoo","example1Header":"Situation\nZookeepers track animal counts, including increases and decreases. Changes like births, relocations, and deaths often involve positive and negative numbers.","example1Body":"Example\nThe habitat starts with $100$ animals. If $2$ groups of $-5$ leave each week for $4$ weeks, the change is $2 \\cdot -5 \\cdot 4 = -40$. The new count is $100 + (-40) = 60$.","example2Header":"","example2Body":""}


example_id: lp_01K94EEJTHKCEX0TPJCVRKVM8P_01K94EEKP6ZS6P6C7A2CD8PKG9_CONTEMPLATIVE_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: The Zoo
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A temperature was $-15^\\circ$F. It increased by $5^\\circ$F each hour for $3$ hours, then dropped $4^\\circ$F each hour for $2$ hours. What is the final temperature? How can you calculate it?","teacherTips":["Encourage using multiplication for repeated changes like $5 \\times 3$ or $-4 \\times 2$.","Have students track steps to calculate the final temperature.","Discuss how adding and subtracting negatives affects results."],"difficulty":"mild"}


example_id: lp_01K94EEJTHKCEX0TPJCVRKVM8P_01K94EEKP6ZS6P6C7A2R6VV4K5_EXIT_TICKET
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: The Zoo
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$-12$","question":"A zookeeper feeds $-3$ pounds of food to $4$ different animals. What is the total weight of food fed?"},{"answer":"$300$","question":"A zoo's water filtration system uses $-50$ gallons per day for $-6$ days. How many gallons are filtered in total?"},{"answer":"$-12$","question":"A zookeeper divides $-144$ pounds of feed equally among $12$ animals. How much feed does each animal get?"}]}


example_id: lp_01K94EEJTHKCEX0TPJCVRKVM8P_01K94EEKP6ZS6P6C7A1YH2WC66_ACTIVITY
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: The Zoo
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Negative Number Showdown\nYou're managing a sports team—calculate scores (positive and negative) to win!","scenario":"Steps\n1. Each team starts with $10$ points. Write this on your paper.\n2. Draw random cards: positive or negative numbers between $-5$ and $5$.\n3. Multiply or divide the drawn number with your current score.\n4. Keep a running total of your score after each round.\n5. After $5$ rounds, the team with the highest score wins!","steps":["Discussion\n• Why does multiplying two negatives give a positive score?\n• How does dividing by a negative affect your score?","Differentiation Opportunities\n• Support: Use only positive numbers for division to simplify calculations.\n• Extend: Add a rule to include three-step operations (e.g., $(-4) \\times 3 \\div (-2)$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF6H23N93V34EEADQ1RE7_MULTIPLE_CHOICE_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $-5 \\times -3$?","answerOptions":["$-15$","$15$","$-8$","$8$"],"answer":"$15$","difficulty":"mild"}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF6H23N93V34EEF08ZT0Q_MULTIPLE_CHOICE_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $-6 \\times -3$?","answerOptions":["$-18$","$18$","$9$","$-9$"],"answer":"$18$","difficulty":"mild"}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF6H23N93V34EE4MKZQVY_CONTEMPLATIVE_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You owe $5$ dollars to each of $3$ friends. If you later pay back $2$ friends, how much do you owe now?","teacherTips":["Owing $5$ to $3$ friends is $-5 \\times 3 = -15$. Paying $2$ friends is $-5 \\times 2 = -10$. Debt left: $-5$."],"difficulty":"mild"}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF6H23N93V34EEGZFMZZK_MULTIPLE_CHOICE_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Calculate $-8 \\times \\left(-\\frac{3}{4}\\right) \\div \\left(-\\frac{2}{5}\\right) \\times \\left(-\\frac{5}{6}\\right)$.","answerOptions":["$4$","$-4$","$\\frac{15}{8}$","$-\\frac{15}{8}$"],"answer":"$4$","difficulty":"spicy"}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF6H23N93V34EE6MPQDY3_CONTEMPLATIVE_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You owe $5$ friends $-3$ dollars each. How would you calculate the total? What if you owe $3$ friends $-4$ dollars each?","teacherTips":["Multiplying debts: $5 \\times -3 = -15$ dollars. For $3 \\times -4$, total is $-12$ dollars."],"difficulty":"mild"}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF639MQZRZ9N4DW3ATVW1_SCAFFOLDED_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to multiply and divide with negative numbers. Remember: multiplying or dividing a negative and a positive gives a negative result.","questions":[{"answer":"$12$","question":"What is $-3 \\times 4$?\nHint: A negative times a positive gives a negative result."},{"answer":"$-12$","question":"What is $-20 \\div 5$?\nHint: A negative divided by a positive gives a negative result."},{"answer":"$12$","question":"What is $-6 \\times -2$?\nHint: A negative times a negative gives a positive result."}],"difficulty":"enabling"}


example_id: lp_01K94EF5DKYCCDQ53Y6ZMT8QDB_01K94EF639MQZRZ9N4E08KNSAT_SCAFFOLDED_QUESTION
skills: ["Multiplication and division with negative numbers"]
skill_ids: ["mcLSP0SK5ZfKru4CXw9d"]
subtopics: ["Division Advanced"]
subtopic_ids: ["subtopic_01GTC0BQ6AE9KXYPRC7RHN6TGM"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the complexities of multiplying and dividing with negative numbers through challenging scenarios.","questions":[{"answer":"Answers will vary; reasoning must include rules for signs and their justification.","question":"What is the result of $(-3) \\times (-4) \\times 2$?"},{"answer":"$24$","question":"Evaluate: $(-48) \\div (-6) \\times (-2)$."},{"answer":"$-16$","question":"Explain why multiplying two negative numbers gives a positive result, but dividing a negative number by a positive number gives a negative result."}],"difficulty":"extension"}


example_id: lp_01K94ENK2JV4Z5DW21W28T82QT_01K94ENM3Y5XXSV9S4HFQMGMD2_THOUGHT_SPARKER
skill_ids: ["UginYd135AAJocFrOoSj","N4zF9UZM8Y0Xux6SOQ6Z","2NGACKk6WzHaCjc0wgpf","oNGFLugARhUuMWJZQbC1"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Stars
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A star has a brightness of $3.45$ units. Another star's brightness is $\\frac{2}{3}$ of the first star's brightness, and a third star's brightness is $1.2$ times the second star's brightness.","firstSentence":"How could you calculate the total brightness of all three stars?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify operations required for each step before solving.","Discuss strategies for handling decimal and fractional calculations together.","Ask students to explain how they approached combining the results to find the total."]}

skills:
["Multiplying fractions","Decimal addition and subtraction","Multiplying and dividing decimals by powers of $10$","Addition and subtraction of fractions with different denominators"]


example_id: lp_01K94ENK2JV4Z5DW21W28T82QT_01K94ENM3Y5XXSV9S4GY727W10_APPLICATION
skill_ids: ["UginYd135AAJocFrOoSj","N4zF9UZM8Y0Xux6SOQ6Z","2NGACKk6WzHaCjc0wgpf","oNGFLugARhUuMWJZQbC1"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Stars
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Fraction Calculations in Star Brightness","example1Header":"Situation\nAstronomers compare star brightness using fractions. Since stars vary in light output, they add and subtract fractions to calculate total or difference in brightness accurately.","example1Body":"Example\nAstronomers add $2/3$ (Star A) and $3/4$ (Star B) brightness. With common denominator $12$: $8/12 + 9/12 = 17/12 = 1\\ 5/12$ times standard brightness.","example2Header":"","example2Body":""}

skills:
["Multiplying fractions","Decimal addition and subtraction","Multiplying and dividing decimals by powers of $10$","Addition and subtraction of fractions with different denominators"]


example_id: lp_01K94ENK2JV4Z5DW21W28T82QT_01K94ENM3Y5XXSV9S4HB382VP2_CONTEMPLATIVE_QUESTION
skill_ids: ["UginYd135AAJocFrOoSj","N4zF9UZM8Y0Xux6SOQ6Z","2NGACKk6WzHaCjc0wgpf","oNGFLugARhUuMWJZQbC1"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Stars
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are planning a bake sale with $12$ brownies. Each brownie costs $\\$1.25$. How would you calculate the total revenue if half are sold? What if you reduce the price by $10\\%$? Show your method using decimals or fractions.","teacherTips":["Encourage students to explore dividing decimals by $10$ to apply discounts.","Discuss adding fractions for multiple sales scenarios.","Support multiplying fractions to find half the brownies sold."],"difficulty":"mild"}

skills:
["Multiplying fractions","Decimal addition and subtraction","Multiplying and dividing decimals by powers of $10$","Addition and subtraction of fractions with different denominators"]


example_id: lp_01K94ENK2JV4Z5DW21W28T82QT_01K94ENM3Y5XXSV9S4H0ZVC38G_ACTIVITY
skill_ids: ["UginYd135AAJocFrOoSj","N4zF9UZM8Y0Xux6SOQ6Z","2NGACKk6WzHaCjc0wgpf","oNGFLugARhUuMWJZQbC1"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Stars
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Decimal Score Dash\nYou're scoring a sports game, and you need to use decimals to track points!","scenario":"Steps\n1. Draw a scorecard with $5$ rounds and $2$ teams on paper.\n2. Each round, write a decimal score for both teams (e.g., $12.5$, $7.3$).\n3. Add or subtract scores to find the total for each round.\n4. Multiply or divide scores by $10$, $100$, or $1\\,000$ when prompted.\n5. After $5$ rounds, the team with the highest total wins!","steps":["Discussion\n• What happens to a number when you divide by $10$?\n• How do decimals affect adding and subtracting scores?","Differentiation Opportunities\n• Support: Provide simpler scores with no more than $1$ decimal place.\n• Extend: Include multiplying/dividing by $0.1$ or $0.01$ for extra challenge."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94ENK2JV4Z5DW21W28T82QT_01K94ENM3Y5XXSV9S4HN050NT3_EXIT_TICKET
skill_ids: ["UginYd135AAJocFrOoSj","N4zF9UZM8Y0Xux6SOQ6Z","2NGACKk6WzHaCjc0wgpf","oNGFLugARhUuMWJZQbC1"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Stars
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$1.1$","question":"The brightness of a star increases from $2.5$ units to $3.6$ units. By how much has the brightness increased?"},{"answer":"$1\\frac{3}{20}$","question":"A star emits light in two phases: $\\frac{2}{5}$ of its energy in one phase and $\\frac{3}{4}$ in another phase. What is the total energy emitted?"},{"answer":"$\\frac{1}{3}$","question":"A distant star's energy output is halved, then $\\frac{2}{3}$ of the remaining energy reaches Earth. What fraction of the original energy reaches Earth?"}]}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GQAHVJNVN_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $\\frac{3}{4} \\div \\frac{1}{2}$?","answerOptions":["$\\frac{3}{2}$","$\\frac{3}{8}$","$\\frac{1}{2}$","$\\frac{7}{4}$"],"answer":"$\\frac{3}{2}$","difficulty":"mild"}

skills:
["Dividing fractions","Addition and subtraction of fractions with different denominators","Multiplying and dividing decimals by powers of $10$","Multiplying fractions"]


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GQH7ZKR7Y_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $\\frac{3}{4} \\div \\frac{1}{2}$?","answerOptions":["$\\frac{3}{8}$","$\\frac{3}{2}$","$\\frac{1}{2}$","$\\frac{5}{4}$"],"answer":"$\\frac{3}{2}$","difficulty":"mild"}

skills:
["Dividing fractions","Addition and subtraction of fractions with different denominators","Multiplying and dividing decimals by powers of $10$","Multiplying fractions"]


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GNWDBRTVJ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $\\frac{1}{4} + \\frac{1}{2}$?","answerOptions":["$\\frac{1}{6}$","$\\frac{3}{4}$","$\\frac{2}{3}$","$1$"],"answer":"$\\frac{3}{4}$","difficulty":"mild"}

skills:
["Dividing fractions","Addition and subtraction of fractions with different denominators","Multiplying and dividing decimals by powers of $10$","Multiplying fractions"]


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GNXZ49AN6_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is $\\frac{3}{4} + \\frac{2}{3}$ when expressed as a single fraction in simplest form?","answerOptions":["$\\frac{17}{12}$","$\\frac{5}{7}$","$\\frac{13}{12}$","$\\frac{6}{7}$"],"answer":"$\\frac{17}{12}$","difficulty":"hot"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GP2KHHN0T_CONTEMPLATIVE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are designing a new recipe that uses $\\frac{3}{4}$ cup of sugar and $\\frac{2}{3}$ cup of honey. If you want to triple the recipe and share it with a friend who can only make half of it, how would you calculate the total sugar and honey needed?","teacherTips":["Find $\\frac{3}{4} \\times 3$, $\\frac{2}{3} \\times 3$, and their sum. Halve for the friend’s portion."],"difficulty":"spicy"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GRBADR1GW_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $4.56 \\times 10$?","answerOptions":["$45.6$","$4.56$","$456$","$0.456$"],"answer":"$45.6$","difficulty":"mild"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GR844G1HN_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $4.5 \\times 10$?","answerOptions":["$4.50$","$45$","$450$","$0.45$"],"answer":"$45$","difficulty":"mild"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GPMZ2TY9J_MULTIPLE_CHOICE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is $\\frac{2}{3} \\times \\frac{3}{4}$?","answerOptions":["$\\frac{1}{2}$","$\\frac{3}{7}$","$\\frac{1}{3}$","$\\frac{1}{4}$"],"answer":"$\\frac{1}{2}$","difficulty":"mild"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FX0FMMRG20K6GPPCFRCHF_CONTEMPLATIVE_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a recipe for $12$ people if the original recipe serves $4$. Include at least $3$ ingredients with fractional amounts. How would you adjust each ingredient to serve $12$ people?","teacherTips":["Multiply each ingredient by $3$: e.g., $\\frac{1}{2} \\times 3 = \\frac{3}{2}$. Simplify fractions if needed."],"difficulty":"spicy"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FWYRB0Z8WQT83360XTC6Z_SCAFFOLDED_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore complex fraction operations and decimal manipulation through advanced reasoning and problem-solving.","questions":[{"answer":"$\\frac{-23}{24}$","question":"Simplify: $\\frac{3}{4} \\times \\frac{8}{9} \\times \\frac{27}{16}$."},{"answer":"$\\frac{9}{8}$","question":"Evaluate: $\\frac{5}{6} \\div \\frac{2}{3} \\times 10$."},{"answer":"$12.5$","question":"Explain and evaluate: $\\frac{7}{8} + \\frac{5}{12} - \\frac{3}{4} \\div \\frac{1}{3}$. Justify each step in your solution."}],"difficulty":"extension"}


example_id: lp_01K94FWXMJ2E8H9JVJDZM93RBP_01K94FWYRAJHSDER5CG48JMBVJ_SCAFFOLDED_QUESTION
skill_ids: ["avN9feq7XZ3YmoBZDWnh","oNGFLugARhUuMWJZQbC1","2NGACKk6WzHaCjc0wgpf","UginYd135AAJocFrOoSj"]
subtopics: ["Fraction Calculations"]
subtopic_ids: ["subtopic_01GTC0BBKNS34DMDFY8WM9Q525"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will multiply decimals by powers of $10$. Multiplying by a power of $10$ moves the decimal point to the right.","questions":[{"answer":"Three places","question":"What is $0.5 \\times 10$?\nRemember: the decimal point moves one place to the right when multiplying by $10$."},{"answer":"$0.05$","question":"What is $0.5 \\times 100$?\nHint: The decimal point moves two places to the right when multiplying by $100$."},{"answer":"$5$","question":"If you multiply $0.5$ by $1\\,000$, how many places to the right does the decimal point move?\nHint: Count the zeros in $1\\,000$."}],"difficulty":"enabling"}


example_id: lp_01K94G4BAPRH8V9BXZQ57GJA1F_01K94G4CNN4HY40GBZ56V74EGR_APPLICATION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Hot Air Balloon
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Balancing Weight in Hot Air Balloons","example1Header":"Situation\nHot air balloon pilots calculate weight distribution to ensure safe flight. They simplify terms for accurate weight management of passengers and equipment.","example1Body":"Example\nThe basket weighs $50$ kg, three tanks weigh $60$ kg, and passengers weigh $60x$ kg. Simplifying: $50 + 60 + 60x = 110 + 60x$. The total is $110 + 60x$ kg.","example2Header":"","example2Body":""}


example_id: lp_01K94G4BAPRH8V9BXZQ57GJA1F_01K94G4CNN4HY40GBZ5T9HWFDH_THOUGHT_SPARKER
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Hot Air Balloon
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A hot air balloon can lift $3x$ kilograms of cargo and $5y$ kilograms of passengers, but the balloon itself weighs $2x + 3y$ kilograms.","firstSentence":"How would you simplify an expression that represents the total weight being lifted by the balloon?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify and group like terms clearly before simplifying.","Discuss the meaning of coefficients and variables in the context of weight and lifting capacity.","Ask students to explain each step of their simplification process to ensure understanding."]}


example_id: lp_01K94G4BAPRH8V9BXZQ57GJA1F_01K94G4CNN4HY40GBZ5NNWCQTY_CONTEMPLATIVE_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Hot Air Balloon
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create an expression with at least 4 terms, multiply two terms, and simplify by combining like terms. What strategies did you use?","teacherTips":["Encourage students to choose terms with clear like terms for simplification.","Ask students to explain their reasoning for grouping terms.","Guide students to check their multiplication and simplification steps."],"difficulty":"mild"}


example_id: lp_01K94G4BAPRH8V9BXZQ57GJA1F_01K94G4CNN4HY40GBZ5Y0G6SGM_EXIT_TICKET
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Hot Air Balloon
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5y$","question":"A hot air balloon ascends $3y + 2y$ meters in total; what is the simplified expression for the total ascent?"},{"answer":"$6xy$","question":"If a hot air balloon's lift is given by $2x$ and its speed is $3y$, what is the product of lift and speed?"},{"answer":"$6x + 8y$","question":"The hot air balloon covers $4x + 3y + 2x + 5y$ meters in flight; what is the simplified expression for the total distance?"}]}


example_id: lp_01K94G4BAPRH8V9BXZQ57GJA1F_01K94G4CNN4HY40GBZ5AVM8Y89_ACTIVITY
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Hot Air Balloon
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Algebra Expression Relay\nYour team is solving algebra puzzles in a relay race to earn points!","scenario":"Steps\n1. Each team writes $5$ algebraic terms (e.g., $3x$, $-2y$, $4a$) on paper.\n2. Pass your terms to another team to create a multiplication expression.\n3. Simplify the expression by multiplying terms and combining like terms.\n4. Check answers with the other team for accuracy.\n5. Correct answers earn $2$ points; incorrect answers lose $1$ point. Repeat!","steps":["Discussion\n• Why do we only combine like terms when simplifying?\n• How does multiplying coefficients affect the variables?","Differentiation Opportunities\n• Support: Use simpler terms (e.g., $2x$, $3y$) and skip negative coefficients.\n• Extend: Create expressions with three terms (e.g., $2x \\cdot 3y \\cdot -4z$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G58HHHVWEYKYRD4VGAAHS_MULTIPLE_CHOICE_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Simplify $4x + 7y - 2x + 5y$.","answerOptions":["$6x + 12y$","$2x + 12y$","$6x + 2y$","$2x + 2y$"],"answer":"$2x + 12y$","difficulty":"hot"}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G58HHHVWEYKYRD5864XVJ_CONTEMPLATIVE_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a math puzzle where simplifying like terms leads to $2x + 3y - 4x + 7y$. What steps would you take to simplify? Can you design a similar puzzle with a different outcome?","teacherTips":["Combine $x$ terms: $2x - 4x = -2x$. Combine $y$ terms: $3y + 7y = 10y$. Simplified: $-2x + 10y$."],"difficulty":"spicy"}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G58HHHVWEYKYRDSR76HPH_CONTEMPLATIVE_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create an expression by multiplying three algebraic terms. How could you simplify it? What changes if one term is negative?","teacherTips":["Multiply coefficients and combine variables: $(2x)(-3y)(4z) = -24xyz$. Negative flips the sign."],"difficulty":"spicy"}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G58HHHVWEYKYRDNTK5YPE_MULTIPLE_CHOICE_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Simplify $3x^2 \\cdot 4x^3$.","answerOptions":["$7x^5$","$12x^6$","$12x^5$","$7x^6$"],"answer":"$12x^5$","difficulty":"hot"}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G58HHHVWEYKYRDJXNTWE1_MULTIPLE_CHOICE_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Simplify $3x \\times 4y$.","answerOptions":["$12xy$","$7xy$","$12x^2y$","$7x^2y$"],"answer":"$12xy$","difficulty":"mild"}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G583056WQ7VWEVDD6H7GK_SCAFFOLDED_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn to multiply and simplify algebraic terms. Algebraic terms with the same variables can be combined or simplified.","questions":[{"answer":"$24x^2y$","question":"What is $3x \\times 2x$?\nRemember: Multiply the numbers first, then the variables."},{"answer":"$5x^2$","question":"What is $4 \\times 5y$?\nRemember: Multiply the constant and the coefficient of $y$."},{"answer":"$6x^2$","question":"Simplify $2x \\times 3y \\times 4x$.\nRemember: Multiply the numbers first, then combine the variables."}],"difficulty":"enabling"}


example_id: lp_01K94G57AHWVHKMH51Y1YF14N3_01K94G583056WQ7VWEVHMSXH8Y_SCAFFOLDED_QUESTION
skills: ["Simplifying like terms","Multiplying algebraic terms"]
skill_ids: ["QuYvh7M85CWRn2sJhYk2","4ynb4jPCghcw5yB2rqQC"]
subtopics: ["Simplifying"]
subtopic_ids: ["subtopic_01GTC0BKQRRQ55JSNQQ8ZMBD22"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the complexities of multiplying and simplifying algebraic terms to uncover hidden patterns.","questions":[{"answer":"$2x^3 + x^2 - 2x$","question":"Simplify the expression $3x^2 \\cdot 4x^3$."},{"answer":"$12x^5$","question":"Simplify $-2x^3 \\cdot 5x \\cdot (-3x^2)$."},{"answer":"$30x^6$","question":"Simplify the expression $2x(x^2 + 3x - 4) - x(5x - 6)$ and explain each step in your process."}],"difficulty":"extension"}


example_id: lp_01K94GBASJPKR8CXGSG2WVWWT3_01K94GBBT01YNPXDTQNBD0PJ9M_THOUGHT_SPARKER
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Rugby
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a rugby game, a team scores $5x + 3$ points where $x$ represents the number of tries they make, and another team scores $5x + 3 = 23$ points.","firstSentence":"How would you explain the difference between $5x + 3$ and $5x + 3 = 23$ in this situation?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to identify what $x$ represents in the context of the game.","Encourage students to compare how an expression and an equation convey different kinds of information.","Discuss why equations can be solved while expressions cannot, using real-world examples from the rugby scenario."]}


example_id: lp_01K94GBASJPKR8CXGSG2WVWWT3_01K94GBBT01YNPXDTQMWRK965Q_APPLICATION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Rugby
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Algebra in Rugby Scoring","example1Header":"Situation\nRugby coaches use algebra to analyze team scoring patterns. They compare equations and expressions to track points and predict future performance.","example1Body":"Example\nA coach sees $x + 3 = 10$ and solves $x = 7$ to find $7$ points scored in one half. The expression $x + 3$ alone shows a pattern but does not give a total.","example2Header":"","example2Body":""}


example_id: lp_01K94GBASJPKR8CXGSG2WVWWT3_01K94GBBT01YNPXDTQNFSRW28X_EXIT_TICKET
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Rugby
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Equation","question":"A rugby team writes $3x + 2 = 11$ on their strategy board. Is this an equation or an expression?"},{"answer":"Expression","question":"A rugby coach uses $5x + 3$ to calculate points scored for $x$ tries. Is this an equation or an expression?"},{"answer":"$2x + 5 = 15$","question":"If a rugby player sees $2x + 5 = 15$ and $4x + 7$, which one can be solved for $x$?"}]}


example_id: lp_01K94GBASJPKR8CXGSG2WVWWT3_01K94GBBT01YNPXDTQN73T2AKY_CONTEMPLATIVE_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Rugby
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create an expression and an equation about the number of apples you have. Explain the difference.","teacherTips":["Expressions describe quantities without using an equals sign.","Equations compare two expressions with an equals sign.","Encourage students to use real-life examples, like counting apples."],"difficulty":"mild"}


example_id: lp_01K94GBASJPKR8CXGSG2WVWWT3_01K94GBBT01YNPXDTQMYHYP9CC_ACTIVITY
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Rugby
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Equation vs. Expression\nSort and classify math statements as equations or expressions in a fun group challenge.","scenario":"Steps\n1. Each team writes $10$ math statements (e.g., $3x + 2$, $5x = 20$).\n2. Mix all statements and swap with another team.\n3. Sort the statements into 'equation' or 'expression' piles.\n4. Check the sorting by discussing whether each has an equals sign.\n5. Score $1$ point for each correct classification. Most points win!","steps":["Discussion\n• How does the equals sign change a math statement?\n• Why can't expressions be solved like equations?","Differentiation Opportunities\n• Support: Provide examples of equations and expressions to guide sorting.\n• Extend: Add more complex examples, like $x^2 + 3x$ or $2x + 5 = 15$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCF0XH74RTV45SMYKDYXQ_MULTIPLE_CHOICE_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Which of the following is an equation and not an expression?","answerOptions":["$3x + 5$","$2y - 7 = 9$","$4a + 6b$","$7x^2 - 2$"],"answer":"$2y - 7 = 9$","difficulty":"spicy"}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCF0XH74RTV45SN6FKCJK_CONTEMPLATIVE_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You have $2x + 5 = 15$ and $3x + 2$. How could you compare these? What makes one solvable and the other not?","teacherTips":["Equations have an equals sign to balance both sides. Expressions lack this, so they cannot be solved."],"difficulty":"spicy"}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCF0XH74RTV45SDRDJR9X_MULTIPLE_CHOICE_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of the following is an equation?","answerOptions":["$4x - 7 = 13$","$5y + 2$","$6 + 3z$","$8m - 4$"],"answer":"$4x - 7 = 13$","difficulty":"hot"}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCF0XH74RTV45SF03TQS5_CONTEMPLATIVE_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"How would you explain the difference between $2x + 5$ and $2x + 5 = 15$? Create examples to show your reasoning.","teacherTips":["An expression like $2x + 5$ shows a calculation, while $2x + 5 = 15$ lets us find $x$."],"difficulty":"hot"}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCF0XH74RTV45SBGR69TY_MULTIPLE_CHOICE_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following is an equation?","answerOptions":["$3x + 2$","$5y - 7 = 13$","$4a - 1$","$2b + 6$"],"answer":"$5y - 7 = 13$","difficulty":"mild"}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCEKASG2SDXK3373ZG8B3_SCAFFOLDED_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to compare equations and expressions. Equations have equal signs, while expressions do not.","questions":[{"answer":"$5x + 3 = 18$ is an equation; $5x + 3$ is an expression.","question":"Which of the following is an equation?"},{"answer":"$2x + 5$","question":"Which of the following is an expression?"},{"answer":"$3x + 4 = 10$","question":"Explain why $5x + 3 = 18$ is an equation and $5x + 3$ is an expression."}],"difficulty":"enabling"}


example_id: lp_01K94GCDVX1DNJW6D4SSW6QW2Q_01K94GCEKASG2SDXK339K7S7M1_SCAFFOLDED_QUESTION
skills: ["Comparing equations and expressions"]
skill_ids: ["9lyO2I1ZDQDqta4L3wUF"]
subtopics: ["Understanding Terms"]
subtopic_ids: ["subtopic_01GTC0BH3PETPWYDVVXE1Q2RPE"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore deeper understanding by comparing equations and expressions with abstract reasoning.","questions":[{"answer":"Equations impose conditions; expressions evaluate values.","question":"What is the key difference between an equation and an expression?"},{"answer":"An equation has an equals sign, an expression does not.","question":"Compare $2x + 4$ and $2x + 4 = 10$. Are they equivalent? Explain your reasoning."},{"answer":"No, they are not equivalent.","question":"Why can an equation like $x^2 = 9$ have multiple solutions, while an expression like $x^2 - 9$ cannot? Explain in detail."}],"difficulty":"extension"}


example_id: lp_01K94GQKX70TK10A72AE1FXTP4_01K94GQMWMS22ZPVWZTJ7MWW0V_EXIT_TICKET
skill_ids: ["yXHIEJebSK69tH40B15K","PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Formula One
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$13$","question":"An F1 engineer measures $3 + 2 \\times 5$. What is the result using BODMAS?"},{"answer":"$3$","question":"A Formula 1 car covers $\\left(8 + 4\\right) \\div 2 - 3$ laps in a simulation. How many laps are covered?"},{"answer":"$19$","question":"An F1 team calculates $\\left(2^3 + 4\\right) \\times 2 - 5$. What is the result?"}]}

skills:
["Applying BODMAS to number problems\t","Applying BODMAS to number problems with exponents","Defining the order of operations using BODMAS"]


example_id: lp_01K94GQKX70TK10A72AE1FXTP4_01K94GQMWMS22ZPVWZT7P48AY3_CONTEMPLATIVE_QUESTION
skill_ids: ["yXHIEJebSK69tH40B15K","PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Formula One
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create your own equation with at least 4 operations, including exponents. How would you solve it using BODMAS?","teacherTips":["Remind students to solve brackets or parentheses first.","Encourage them to include exponents in their equation.","Ensure they follow the BODMAS order for all operations."],"difficulty":"mild"}

skills:
["Applying BODMAS to number problems\t","Applying BODMAS to number problems with exponents","Defining the order of operations using BODMAS"]


example_id: lp_01K94GQKX70TK10A72AE1FXTP4_01K94GQMWMS22ZPVWZSW9K4DFR_ACTIVITY
skill_ids: ["yXHIEJebSK69tH40B15K","PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Formula One
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"BODMAS Problem Relay\nTeams compete to solve BODMAS problems the fastest and earn points!","scenario":"Steps\n1. In your team, write $3$ BODMAS problems with exponents on paper.\n2. Swap problems with another team and solve them.\n3. Check each other's solutions and explain any mistakes.\n4. Score $2$ points for correct solutions and lose $1$ point for errors.\n5. Repeat for $3$ rounds. The team with the most points wins!","steps":["Discussion\n• Why is it important to follow BODMAS rules?\n• How do exponents affect the order of solving problems?","Differentiation Opportunities\n• Support: Use simpler problems, avoiding exponents and focusing on basic BODMAS.\n• Extend: Include brackets and more complex exponents in your problems."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Applying BODMAS to number problems\t","Applying BODMAS to number problems with exponents","Defining the order of operations using BODMAS"]


example_id: lp_01K94GQKX70TK10A72AE1FXTP4_01K94GQMWMS22ZPVWZST5T14WT_APPLICATION
skill_ids: ["yXHIEJebSK69tH40B15K","PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Formula One
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Pit Stop Strategy in Formula One","example1Header":"Situation\nFormula One engineers use order of operations to calculate fuel, tire wear, and timing for pit stops to ensure the fastest race strategy.","example1Body":"Example\nTo calculate total race time: $60 \\cdot 90 + 2 \\cdot 25 = 5,450$ seconds. Using BODMAS ensures correct order: $5,400 + 50 = 5,450$ seconds, or $90$ minutes and $50$ seconds.","example2Header":"","example2Body":""}


example_id: lp_01K94GQKX70TK10A72AE1FXTP4_01K94GQMWMS22ZPVWZTD87RJH1_THOUGHT_SPARKER
skill_ids: ["yXHIEJebSK69tH40B15K","PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Formula One
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a Formula One race, a car completes three laps with times of $2^3$ seconds, $4 \\times 5$ seconds, and $50 - 15$ seconds.","firstSentence":"What order should you calculate these times to find the total time for all three laps?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the BODMAS rule before beginning the discussion.","Encourage students to explain why each step in the order of operations matters.","Ask students to compare their answers and discuss any differences in their approaches."]}


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRCN3R87EDAYZ2X8FFYWQ_CONTEMPLATIVE_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"Design a puzzle where the solution to $3^2 + (4 \\times 2) - 5$ equals $15$. How could you alter it to give a different result?","teacherTips":["Use BODMAS: $3^2 = 9$, then $4 \\times 2 = 8$, add $9 + 8 = 17$, subtract $5$: $17 - 5 = 15$."],"difficulty":"hot"}

skills:
["Applying BODMAS to number problems with exponents","Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRCN3R87EDAYZ19KWG6RF_CONTEMPLATIVE_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You are designing a puzzle where players must solve $3 \\times (5 + 2) - 4$. How could you change the order of operations using brackets to create a different answer? Explain your reasoning.","teacherTips":["Changing brackets changes the order: $(3 \\times 5) + (2 - 4)$ gives $13$, not $17$."],"difficulty":"hot"}

skills:
["Applying BODMAS to number problems with exponents","Defining the order of operations using BODMAS","Applying BODMAS to number problems\t"]


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRCN3R87EDAYZ12EB0CG7_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What does the B stand for in BODMAS?","answerOptions":["Brackets","Base","Balance","Binary"],"answer":"Brackets","difficulty":"mild"}


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRCN3R87EDAYZ20HD8WN7_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the result of $6 + 3 \\times 2$ using the BODMAS rule?","answerOptions":["$18$","$12$","$24$","$12$"],"answer":"$12$","difficulty":"mild"}


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRCN3R87EDAYZ266BZSRF_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is the value of $5 + 3 \\times (12 - 7) - 4$?","answerOptions":["$16$","$20$","$22$","$24$"],"answer":"$16$","difficulty":"hot"}


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRC5XVNG0TP14VBXEKH00_SCAFFOLDED_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn how to use BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) to solve math problems.","questions":[{"answer":"$14$","question":"What is the correct result of $(3 + 2) \\times 4$?\nRemember, calculate inside the brackets first."},{"answer":"$20$","question":"What is the correct result of $2^3 + 6$?\nRemember, calculate the exponent first."},{"answer":"$14$","question":"What is the result of $(2^2 + 3) \\times 2$?\nApply BODMAS: solve the brackets, then multiply."}],"difficulty":"enabling"}


example_id: lp_01K94GRBFHZDMS7MQRYSWEHF3M_01K94GRC5XVNG0TP14VJS6E0MC_SCAFFOLDED_QUESTION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
subtopics: ["Order of Operations"]
subtopic_ids: ["subtopic_01GTC0BQ7GCK8Y71ZXPZ3HQER9"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Master advanced BODMAS with problems involving exponents, parentheses, and multiple operations","questions":[{"answer":"BODMAS ensures the correct calculation hierarchy.","question":"Evaluate $3^2 + (4 \\times 2) - 5$."},{"answer":"$12$","question":"Simplify $[(2^3 - 4) \\times 2] + 9$."},{"answer":"$17$","question":"Explain why $3 \\times (4 + 5^2) - 6$ gives a different result if BODMAS is not followed.\nShow calculations for both cases to support your explanation."}],"difficulty":"extension"}


example_id: lp_01K94H1DS6W1VRN63A11CBF3SZ_01K94H1ETG6BTHC03BR445W77V_THOUGHT_SPARKER
skill_ids: ["oeH4xPzMvOQwnIlVgKUw","NIHuoS0uMJHAosuMw07S","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Astronauts
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An astronaut's oxygen tank has a capacity of $8$ hours, but they use $x$ hours of oxygen during a spacewalk. The backup tank adds $2x + 4$ hours of oxygen, and the total capacity must equal $20$ hours.","firstSentence":"How could you determine the value of $x$ that balances the oxygen supply?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to set up the equation $x + (2x + 4) = 20$ before solving.","Discuss strategies for isolating $x$ and balancing equations step by step.","Highlight the importance of checking the solution by substituting $x$ back into the original equation."]}

skills:
["Solving linear inequalities","Making a variable the subject of an equation","Solving equations with unknowns on both sides"]


example_id: lp_01K94H1DS6W1VRN63A11CBF3SZ_01K94H1ETG6BTHC03BQ90QCZ8F_APPLICATION
skill_ids: ["oeH4xPzMvOQwnIlVgKUw","NIHuoS0uMJHAosuMw07S","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Astronauts
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Balancing Oxygen Levels for Astronauts","example1Header":"Situation\nAstronauts rely on precisely calculated oxygen levels in space. Engineers use equations to determine how much oxygen each crew member needs for a mission.","example1Body":"Example\nEngineers solve $2x + 5 = 25$ to find oxygen per astronaut. Subtract $5$: $2x = 20$. Divide by $2$: $x = 10$. Each astronaut needs $10$ units.","example2Header":"","example2Body":""}

skills:
["Solving linear inequalities","Making a variable the subject of an equation","Solving equations with unknowns on both sides"]


example_id: lp_01K94H1DS6W1VRN63A11CBF3SZ_01K94H1ETG6BTHC03BQEF24G7M_ACTIVITY
skill_ids: ["oeH4xPzMvOQwnIlVgKUw","NIHuoS0uMJHAosuMw07S","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Astronauts
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Equation Showdown\nYour team is competing in a math debate. Solve equations and inequalities to win!","scenario":"Steps\n1. Each team writes $5$ equations or inequalities with unknowns on both sides.\n2. Swap your equations with another team and solve their problems.\n3. Check each other's solutions for accuracy and discuss mistakes.\n4. Score $1$ point for each correct solution and lose $1$ point for errors.\n5. Team with the highest score after $5$ rounds wins!","steps":["Discussion\n• What strategies help solve equations faster?\n• How does solving inequalities differ from solving equations?","Differentiation Opportunities\n• Support: Focus only on equations with one operation on each side.\n• Extend: Create equations or inequalities with fractions or multiple variables."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Solving linear inequalities","Making a variable the subject of an equation","Solving equations with unknowns on both sides"]


example_id: lp_01K94H1DS6W1VRN63A11CBF3SZ_01K94H1ETG6BTHC03BQY6DHCQG_CONTEMPLATIVE_QUESTION
skill_ids: ["oeH4xPzMvOQwnIlVgKUw","NIHuoS0uMJHAosuMw07S","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Astronauts
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have $2x + 5 = 3x - 7$. How would you solve for $x$, then check your solution? Could $x$ also satisfy $3x - 7 \u003e 10$?","teacherTips":["Encourage students to isolate $x$ by simplifying both sides.","Remind students to verify their solution by substitution.","Discuss checking if the solution works for the inequality."],"difficulty":"mild"}


example_id: lp_01K94H1DS6W1VRN63A11CBF3SZ_01K94H1ETG6BTHC03BR7XRZP2H_EXIT_TICKET
skill_ids: ["oeH4xPzMvOQwnIlVgKUw","NIHuoS0uMJHAosuMw07S","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Astronauts
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$x = 5$","question":"An astronaut's oxygen supply satisfies $3x + 2 = 2x + 7$. Solve for $x$."},{"answer":"$t = \\frac{d - 20}{5}$","question":"The time $t$ for an astronaut's mission is given by $d = 5t + 20$. Rearrange to make $t$ the subject."},{"answer":"$x \\leq 2$","question":"An astronaut's food rations satisfy $4x - 3 \\leq 9 - 2x$. Solve the inequality for $x$."}]}


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4QFD20X81Z9MBQ7HP148_CONTEMPLATIVE_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You know $2x + 3y = 12$. How would you make $x$ the subject? Then, how would you make $y$ the subject?","teacherTips":["For $x$: $x = \\frac{12 - 3y}{2}$. For $y$: $y = \\frac{12 - 2x}{3}$."],"difficulty":"spicy"}

skills:
["Making a variable the subject of an equation","Solving linear inequalities","Solving equations with unknowns on both sides"]


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4QFD20X81Z9MBMJMT3R1_MULTIPLE_CHOICE_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Make $x$ the subject of the equation $2x + 4 = 10$.","answerOptions":["$x = 6$","$x = 3$","$x = 2$","$x = 4$"],"answer":"$x = 3$","difficulty":"mild"}

skills:
["Making a variable the subject of an equation","Solving linear inequalities","Solving equations with unknowns on both sides"]


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4QFD20X81Z9MCXYJD2W6_MULTIPLE_CHOICE_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the solution to the inequality $3x + 2 \u003e 8$?","answerOptions":["$x \u003e 2$","$x \u003e 3$","$x \u003c 2$","$x \u003c 3$"],"answer":"$x \u003e 2$","difficulty":"mild"}

skills:
["Making a variable the subject of an equation","Solving linear inequalities","Solving equations with unknowns on both sides"]


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4QFD20X81Z9MD4KG3SAC_CONTEMPLATIVE_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a story where you need to solve $3x + 5 \u003e 20$ to make a decision. What could $x$ represent, and how would you solve and check your solution?","teacherTips":["Solve: $3x \u003e 15$, so $x \u003e 5$. Check by substituting $x \u003e 5$ into $3x + 5 \u003e 20$."],"difficulty":"spicy"}


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4QFD20X81Z9MC9EJYG91_MULTIPLE_CHOICE_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Solve for $x$: $4(x + 3) = 2x + 18 + x$.","answerOptions":["$x = 2$","$x = 3$","$x = 4$","$x = 5$"],"answer":"$x = 2$","difficulty":"spicy"}


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4QFD20X81Z9MC7FCGAG1_MULTIPLE_CHOICE_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Solve for $x$: $3x + 5 = 2x + 10$.","answerOptions":["$x = 5$","$x = -5$","$x = 10$","$x = 0$"],"answer":"$x = 5$","difficulty":"hot"}


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4PYYMAHN4V8H28E08K3G_SCAFFOLDED_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to solve equations with unknowns on both sides and make a variable the subject of the equation.","questions":[{"answer":"$z = 3$","question":"Solve for $x$: $2x + 3 = x + 5$."},{"answer":"$x = 2$","question":"Solve for $y$: $3y - 4 = 7 + 2y$."},{"answer":"$x = 3$","question":"Solve for $z$: $5z + 10 = 3z + 16$."}],"difficulty":"enabling"}


example_id: lp_01K94H4NRSNFF9GZH6NCK2TXC3_01K94H4PYYMAHN4V8H2ANVZMM1_SCAFFOLDED_QUESTION
skill_ids: ["NIHuoS0uMJHAosuMw07S","oeH4xPzMvOQwnIlVgKUw","44KM5HiZbMmfJmI9HmfG"]
subtopics: ["Solving Multi-Step Equations"]
subtopic_ids: ["subtopic_01GTC0BD74GH53GP279RBNDW4D"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Challenge yourself with solving equations, rearranging variables, and analyzing inequalities in advanced scenarios.","questions":[{"answer":"Solution: $x \\leq 9$. Verification includes boundary tests.","question":"Solve for $x$: $2x - \\frac{1}{3} = \\frac{5}{6} + x$."},{"answer":"$\\frac{7}{6}$","question":"Rearrange the equation $y^2 + 3x = 7$ to make $x$ the subject."},{"answer":"$x = \\frac{7 - y^2}{3}$","question":"Solve the inequality $3x - 4 \\leq 2x + 5$, and explain how you could verify the solution set on a number line."}],"difficulty":"extension"}


example_id: lp_01K94JR1RNCQ5RJ00MQGYKN69J_01K94JR2SS6M0EZP1RKW6G6PXB_APPLICATION
skill_ids: ["efVZBFKA3eLTuIVwRjqN","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Street Art
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Scaling Patterns in Street Art","example1Header":"Situation\nStreet artists often create large murals from small designs. They scale up their sketches, keeping proportions accurate to ensure the artwork looks the same on a bigger wall.","example1Body":"Example\nThe artist's small sketch has angles $40^\\circ$, $60^\\circ$, and $80^\\circ$. The mural's triangle has the same angles, proving similarity using the AAA test to keep proportions accurate.","example2Header":"","example2Body":""}

skills:
["Proving triangle similarity using the AAA, SSS, SAS and RHS tests","Solving for unknown sides using a scale factor"]


example_id: lp_01K94JR1RNCQ5RJ00MQGYKN69J_01K94JR2SS6M0EZP1RMJ7MSP78_THOUGHT_SPARKER
skill_ids: ["efVZBFKA3eLTuIVwRjqN","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Street Art
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A street artist is painting a mural with a triangular pattern. One triangle in the design has side lengths of $3$ ft, $4$ ft, and $5$ ft, and a second triangle is scaled up by a factor of $2.5$.","firstSentence":"How would you determine if the two triangles are similar?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall similarity tests like SSS and AAA.","Discuss the role of scale factors in proving similarity.","Have students calculate and compare side ratios to reinforce their reasoning."]}

skills:
["Proving triangle similarity using the AAA, SSS, SAS and RHS tests","Solving for unknown sides using a scale factor"]


example_id: lp_01K94JR1RNCQ5RJ00MQGYKN69J_01K94JR2SS6M0EZP1RMNK8B2N3_EXIT_TICKET
skill_ids: ["efVZBFKA3eLTuIVwRjqN","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Street Art
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$2$","question":"A street art mural scaled up by a factor of $3$ has a side of $6$ m. What was the original side length in meters?"},{"answer":"Yes","question":"Two triangles in a street art sketch have angles $50^\\circ$, $70^\\circ$, and $60^\\circ$ each. Are they similar by the AAA test?"},{"answer":"Yes","question":"Two triangles in a mural have sides $6$ m, $8$ m, $10$ m and $3$ m, $4$ m, $5$ m. Are they similar by the SSS test?"}]}

skills:
["Proving triangle similarity using the AAA, SSS, SAS and RHS tests","Solving for unknown sides using a scale factor"]


example_id: lp_01K94JR1RNCQ5RJ00MQGYKN69J_01K94JR2SS6M0EZP1RM2B6YFX0_ACTIVITY
skill_ids: ["efVZBFKA3eLTuIVwRjqN","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Street Art
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Mini-Golf Triangle Design\nYour team is designing mini-golf obstacles using similar triangles. Prove which triangles fit!","scenario":"Steps\n1. Each team draws $3$ triangles of different sizes on paper using a ruler.\n2. Exchange triangles with another team and identify corresponding sides and angles.\n3. Use AAA, SSS, SAS, or RHS tests to prove if the triangles are similar.\n4. If triangles are similar, use a scale factor to calculate unknown side lengths.\n5. Score $1$ point for each correct similarity proof and $1$ for correct side calculations!","steps":["Discussion\n• Which similarity test was easiest to use, and why?\n• How does using a scale factor help in real-world problems?","Differentiation Opportunities\n• Support: Focus only on the AAA test and compare angles between triangles.\n• Extend: Challenge students to create non-similar triangles and explain their differences."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94JR1RNCQ5RJ00MQGYKN69J_01K94JR2SS6M0EZP1RMEMB8827_CONTEMPLATIVE_QUESTION
skill_ids: ["efVZBFKA3eLTuIVwRjqN","bpF2REtnGEySQ4U8l76R"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Street Art
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You want to build a model of a triangular park. The park has sides $30$ m, $40$ m, and $50$ m. How would you use a scale factor to create a similar triangle model? Explain how you can prove the triangles are similar.","teacherTips":["Guide students to choose a scale factor, e.g., $1:10$, to shrink the dimensions.","Encourage students to calculate the scaled dimensions for all sides.","Remind students to use SSS similarity to prove the triangles are similar."],"difficulty":"mild"}


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JS06R7GGEAR06JENTK1AN_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangle is scaled by a factor of $2$. If the original width is $3$ cm, what is the new width?","answerOptions":["$6$ cm","$4$ cm","$5$ cm","$8$ cm"],"answer":"$6$ cm","difficulty":"mild"}

skills:
["Solving for unknown sides using a scale factor","Proving triangle similarity using the AAA, SSS, SAS and RHS tests"]


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JS06R7GGEAR06JJH0G0K7_CONTEMPLATIVE_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You design a model city where the tallest building is 120 m. If the model uses a scale factor of $1:500$, how would you calculate the height of the building in the model? Could you apply the same scale to a park 1 km long? Explain your reasoning.","teacherTips":["Model height is $120 \\div 500 = 0.24$ m. Scale factor applies equally to 1 km: $1\\,000 \\div 500 = 2$ m."],"difficulty":"spicy"}

skills:
["Solving for unknown sides using a scale factor","Proving triangle similarity using the AAA, SSS, SAS and RHS tests"]


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JS06R7GGEAR06JHNXFN0M_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Two similar triangles have a scale factor of $3:5$. If a side of the smaller triangle is $12$ cm, what is the corresponding side length of the larger triangle?","answerOptions":["$20$ cm","$15$ cm","$18$ cm","$30$ cm"],"answer":"$20$ cm","difficulty":"hot"}

skills:
["Solving for unknown sides using a scale factor","Proving triangle similarity using the AAA, SSS, SAS and RHS tests"]


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JS06R7GGEAR06HM97RY52_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which similarity rule applies if two triangles have all three pairs of corresponding angles equal?","answerOptions":["AAA","SSS","SAS","RHS"],"answer":"AAA","difficulty":"mild"}


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JS06R7GGEAR06HTW503MG_CONTEMPLATIVE_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"Design three different triangles that are similar to a given triangle with angles $50^\\circ$, $60^\\circ$, and $70^\\circ$. Use AAA, SSS, and SAS to prove their similarity. How are the side lengths related?","teacherTips":["AAA proves similarity by angle equality. SSS and SAS show side ratios are proportional in similar triangles."],"difficulty":"hot"}


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JRZQHVVXSE83ADW79APSP_SCAFFOLDED_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Use scale factors and similarity tests to solve unknown sides and prove triangle similarity.","questions":[{"answer":"AAA test; sides are proportional because similarity preserves shape.","question":"Two similar triangles have corresponding sides $6$ cm and $9$ cm. If the smaller triangle's other side is $10$ cm, what is the length of the larger triangle's corresponding side?"},{"answer":"$15$ cm","question":"Two triangles have sides $4$, $6$, $8$ and $6$, $9$, $12$. Are the triangles similar? If yes, state the similarity test used."},{"answer":"Yes, SSS test","question":"Two triangles have angles $A = 40^\\circ$, $B = 60^\\circ$, and $C = 80^\\circ$, and $P = 40^\\circ$, $Q = 60^\\circ$, and $R = 80^\\circ$. Prove that the triangles are similar using a similarity test, and explain why the lengths of corresponding sides must be proportional."}],"difficulty":"extension"}


example_id: lp_01K94JRYR5E0N30BP1K3BTS8WT_01K94JRZQHVVXSE83ADPGB878R_SCAFFOLDED_QUESTION
skill_ids: ["bpF2REtnGEySQ4U8l76R","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to use scale factors to find unknown side lengths and prove triangle similarity using similarity tests.","questions":[{"answer":"$15$ cm","question":"If two triangles have all corresponding angles equal, which similarity test proves they are similar?"},{"answer":"AAA","question":"Triangle A has sides $3$, $6$, and $9$. Triangle B has sides $6$, $12$, and $18$. Which similarity test proves they are similar?"},{"answer":"SSS","question":"Triangle A has a side of $5$ cm. Triangle B is similar to Triangle A with a scale factor of $3$. What is the length of the corresponding side in Triangle B?"}],"difficulty":"enabling"}


example_id: lp_01K94JYE0K4RVSYF3B4CV5X55A_01K94JYF11ZFPF1E47688BZRH6_ACTIVITY
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Architecture
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Triangle Angle Challenge\nYour team must prove that triangle angles always add up to $180^\\circ$!","scenario":"Steps\n1. Draw any triangle on paper and label its vertices (e.g., $A$, $B$, $C$).\n2. Measure each angle with a protractor and record the values.\n3. Add the three angles together to check if they equal $180^\\circ$.\n4. Repeat with two more triangles of different shapes and sizes.\n5. Compare your results with other teams and discuss any differences.","steps":["Discussion\n• Why do the angles in every triangle always add up to $180^\\circ$?\n• What might cause errors in your measurements or calculations?","Differentiation Opportunities\n• Support: Provide pre-drawn triangles for students to measure and verify.\n• Extend: Challenge students to create triangles with specific angle requirements (e.g., one angle is $90^\\circ$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94JYE0K4RVSYF3B4CV5X55A_01K94JYF11ZFPF1E476PKR85X4_CONTEMPLATIVE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Architecture
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a triangle where one angle is $50^\\circ$ and another is $70^\\circ$. What could the third angle be? How do you know your answer is correct?","teacherTips":["Remind students that angles in a triangle add up to $180^\\circ$.","Encourage students to explain their reasoning clearly.","Discuss how changing one angle affects the others."],"difficulty":"mild"}


example_id: lp_01K94JYE0K4RVSYF3B4CV5X55A_01K94JYF11ZFPF1E476X63V010_EXIT_TICKET
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Architecture
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$60^\\circ$","question":"An architect designs a triangular window with angles $50^\\circ$ and $70^\\circ$. What is the measure of the third angle?"},{"answer":"$75^\\circ$","question":"In a triangular roof design, one angle measures $40^\\circ$ and another measures $65^\\circ$. What is the measure of the third angle?"},{"answer":"$30^\\circ, 60^\\circ, 90^\\circ$","question":"An architect designs a triangular arch with angles $x$, $2x$, and $3x$. What is the measure of each angle?"}]}


example_id: lp_01K94JYE0K4RVSYF3B4CV5X55A_01K94JYF11ZFPF1E476R7SWQP1_THOUGHT_SPARKER
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Architecture
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"An architect is designing a triangular roof truss with one angle measuring $65^\\circ$ and another angle measuring $50^\\circ$.","firstSentence":"How could you determine the measure of the third angle in the triangle?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Explain that the sum of angles in any triangle is always $180^\\circ$, and ask students to confirm this with examples.","Encourage students to share their reasoning and calculations step by step.","Use diagrams or physical models of triangles to help students visualize the angles."]}


example_id: lp_01K94JYE0K4RVSYF3B4CV5X55A_01K94JYF11ZFPF1E4763K4EFWV_APPLICATION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Architecture
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Triangle Angles in Architecture","example1Header":"Situation\nArchitects design triangular roof frames for strength and stability. They use precise angle measurements to ensure structural balance.","example1Body":"Example\nAn architect has a triangular frame with angles $70^\\circ$ and $50^\\circ$. To find the third angle: $70^\\circ + 50^\\circ = 120^\\circ$, then $180^\\circ - 120^\\circ = 60^\\circ$.","example2Header":"","example2Body":""}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZF3QX877PZYRMEB4YMBJ_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A triangle has angles of $50^\\circ$ and $60^\\circ$. What is the measure of the third angle?","answerOptions":["$70^\\circ$","$80^\\circ$","$90^\\circ$","$100^\\circ$"],"answer":"$70^\\circ$","difficulty":"mild"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZF3QX877PZYRMQ0WEG47_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A triangle has angles $3x$, $5x - 10$, and $x + 20$. What is the value of $x$?","answerOptions":["$16$","$18$","$20$","$22$"],"answer":"$20$","difficulty":"spicy"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZF3QX877PZYRM76APTAW_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A triangle has angles measuring $50^\\circ$ and $60^\\circ$. What is the measure of the third angle?","answerOptions":["$70^\\circ$","$80^\\circ$","$90^\\circ$","$100^\\circ$"],"answer":"$70^\\circ$","difficulty":"mild"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZF3QX877PZYRMY8B5W1D_CONTEMPLATIVE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a triangle where one angle is twice another, and the third angle is $10^\\circ$ more than the smallest. What are the angles? How many different triangles can you create with these rules?","teacherTips":["Let $x$ be the smallest angle. Solve $x + 2x + (x + 10) = 180$ to find $x = 42.5^\\circ$."],"difficulty":"spicy"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZF3QX877PZYRMKNMV5V9_CONTEMPLATIVE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a triangular garden. Choose any two angles, calculate the third, and explain how you know your triangle works.","teacherTips":["Subtract the sum of two angles from $180^\\circ$ to find the third angle and verify the total is $180^\\circ$."],"difficulty":"mild"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZF3QX877PZYRMBM8B1A6_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A triangle has two angles measuring $50^\\circ$ and $60^\\circ$. What is the measure of the third angle?","answerOptions":["$70^\\circ$","$80^\\circ$","$90^\\circ$","$100^\\circ$"],"answer":"$70^\\circ$","difficulty":"mild"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZEPG796JAHK18913AN4C_SCAFFOLDED_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore how angles in a triangle sum to $180^\\circ$ through algebra and reasoning.","questions":[{"answer":"The sum of the angles in the triangle is $180^\\circ$ due to alternate interior angles and parallel line properties.","question":"A triangle has angles $x$, $3x$, and $5x$.\nWhat is the value of $x$?"},{"answer":"$20$","question":"One angle of a triangle is $40^\\circ$.\nThe second angle is twice the third angle.\nWhat are the measures of the second and third angles?"},{"answer":"Second: $93.33^\\circ$, Third: $46.67^\\circ$","question":"A triangle is inscribed in a parallelogram.\nProve that the sum of the angles in the triangle is $180^\\circ$, using properties of parallel lines."}],"difficulty":"extension"}


example_id: lp_01K94JZDVQ1PA25CN8JKE39VGQ_01K94JZEPG796JAHK1863VG4H0_SCAFFOLDED_QUESTION
skills: ["Understanding that angles in a triangle add up to $180$ degrees"]
skill_ids: ["Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn that the angles in a triangle always add up to $180^\\circ$. This is true for all types of triangles.","questions":[{"answer":"$60^\\circ$","question":"A triangle has angles measuring $60^\\circ$, $60^\\circ$, and $60^\\circ$. Do the angles add up to $180^\\circ$?"},{"answer":"Yes","question":"Can the angles $90^\\circ$, $60^\\circ$, and $50^\\circ$ form a triangle?"},{"answer":"No","question":"A triangle has two angles measuring $70^\\circ$ and $50^\\circ$. What is the measure of the third angle?"}],"difficulty":"enabling"}


example_id: lp_01K94K6QSHCM3GVMV68ZW6EHV7_01K94K6RQFJ6N354HMYRJ45NAR_THOUGHT_SPARKER
skills: ["Matching a net to its corresponding 3D shape","Classifying $3$D shapes"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6","1EiT0AQznGy2pjvTSth2"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Circus
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"At the circus, you see a clown juggling props shaped like a sphere, a cone, and a cube. Nearby, there are unfolded nets that could form these $3$D shapes when assembled.","firstSentence":"How would you match each net to its correct $3$D shape?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Provide physical models or images of $3$D shapes and their nets to help students visualize.","Encourage students to explain their reasoning for each match, focusing on the faces and edges of the shapes.","Discuss how different $3$D shapes have unique nets, emphasizing the connection between the net and the shape's geometry."]}


example_id: lp_01K94K6QSHCM3GVMV68ZW6EHV7_01K94K6RQFJ6N354HMY8577Q3Z_APPLICATION
skills: ["Matching a net to its corresponding 3D shape","Classifying $3$D shapes"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6","1EiT0AQznGy2pjvTSth2"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Circus
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Circus Tent Design and 3D Shapes","example1Header":"Situation\nCircus architects design tents using nets of 3D shapes. They match nets to shapes like cones, cylinders, and pyramids to create unique structures that are easy to assemble.","example1Body":"Example\nA net with a circle and a triangle forms a cone, which is used for a cone-shaped tent. Architects ensure the net matches the 3D shape to assemble the tent correctly.","example2Header":"","example2Body":""}


example_id: lp_01K94K6QSHCM3GVMV68ZW6EHV7_01K94K6RQFJ6N354HMYA17NTQM_ACTIVITY
skills: ["Matching a net to its corresponding 3D shape","Classifying $3$D shapes"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6","1EiT0AQznGy2pjvTSth2"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Circus
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Shape \u0026 Net Match Race\nWork in teams to match $3$D shapes with their unfolded nets before time runs out!","scenario":"Steps\n1. Each team draws $5$ $3$D shapes (e.g., cube, pyramid, cylinder).\n2. Draw the net for each shape on a separate sheet of paper.\n3. Mix up all the nets and shapes for the other team to solve.\n4. Match each $3$D shape to its correct net in $5$ minutes.\n5. The team with the most correct matches wins!","steps":["Discussion\n• What clues helped you match the nets to the shapes?\n• Why do some shapes have more complex nets than others?","Differentiation Opportunities\n• Support: Provide pre-drawn shapes and nets for students to match.\n• Extend: Challenge teams to design nets for more complex $3$D shapes."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94K6QSHCM3GVMV68ZW6EHV7_01K94K6RQFJ6N354HMYWATAP9E_EXIT_TICKET
skills: ["Matching a net to its corresponding 3D shape","Classifying $3$D shapes"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6","1EiT0AQznGy2pjvTSth2"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Circus
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Sphere","question":"A performer uses a large, round object like a ball at the circus. What $3$D shape is the ball?"},{"answer":"A circle and a sector","question":"If a circus tent is shaped like a cone, which net could it match: a circle and a sector, or six squares?"},{"answer":"Rectangle array","question":"A juggler uses a $3$D shape with $6$ rectangular faces. What net could be used for this shape: a rectangle array or triangles?"}]}


example_id: lp_01K94K6QSHCM3GVMV68ZW6EHV7_01K94K6RQFJ6N354HMYKBWCMVA_CONTEMPLATIVE_QUESTION
skills: ["Matching a net to its corresponding 3D shape","Classifying $3$D shapes"]
skill_ids: ["ZSgrCFBqWzVhvtNm9zG6","1EiT0AQznGy2pjvTSth2"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Circus
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Imagine you need to design a box for a gift. Draw a net for your box and describe its 3D shape. How would its faces, edges, and corners relate to the net you drew?","teacherTips":["Discuss how each face of the net matches a face of the 3D shape.","Encourage students to count edges and corners on both net and shape.","Help students visualize folding the net into the 3D shape."],"difficulty":"mild"}


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7QMQJGMSQ4ZK544BF7SP_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"If a cube is sliced parallel to its base, what shape is the cross-section?","answerOptions":["A triangle","A rectangle","A hexagon","A circle"],"answer":"A rectangle","difficulty":"hot"}

skills:
["Describing cross-sections parallel to the base of $3$D solids","Classifying $3$D shapes","Matching a net to its corresponding 3D shape"]


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7QMQJGMSQ4ZK589JRW81_CONTEMPLATIVE_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Imagine slicing a cone, a cylinder, and a sphere parallel to their bases. What shapes could you see? How would the shapes change if the slices were at different heights?","teacherTips":["A cone shows smaller circles higher up, a cylinder shows equal circles, and a sphere shows varying circles."],"difficulty":"spicy"}

skills:
["Describing cross-sections parallel to the base of $3$D solids","Classifying $3$D shapes","Matching a net to its corresponding 3D shape"]


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7QMRBMPSTA7Q2SZYR36Y_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which $3$D shape has $6$ faces, all of which are rectangles?","answerOptions":["Cube","Rectangular prism","Triangular prism","Cylinder"],"answer":"Rectangular prism","difficulty":"mild"}

skills:
["Describing cross-sections parallel to the base of $3$D solids","Classifying $3$D shapes","Matching a net to its corresponding 3D shape"]


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7QMRBMPSTA7Q2WVGWMFR_CONTEMPLATIVE_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You have a box of $3$D shapes. How could you classify these shapes into groups? What rules or properties would you use to decide?","teacherTips":["Classify by properties: number of faces, types of faces (e.g., squares, circles), and vertices."],"difficulty":"hot"}


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7QMRBMPSTA7Q2B37S9FN_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A net consists of one square and four triangles. Which 3D shape does it form when folded?","answerOptions":["A cube","A rectangular prism","A triangular pyramid","A square pyramid"],"answer":"A square pyramid","difficulty":"hot"}


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7QMRBMPSTA7Q25A584S3_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A net consists of $6$ equal squares. Which 3D shape does it form when folded?","answerOptions":["A cube","A rectangular prism","A triangular prism","A pyramid"],"answer":"A cube","difficulty":"mild"}


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7Q4ZN0EJWRMA180V1QV7_SCAFFOLDED_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore cross-sections of $3$D solids and match $3$D shapes to their nets in challenging ways.","questions":[{"answer":"Square-based pyramid","question":"What shape is the cross-section when a plane cuts a square-based pyramid parallel to its base?"},{"answer":"Square","question":"A $3$D shape has circular cross-sections parallel to its base and triangular cross-sections perpendicular to its base. What is the shape?"},{"answer":"Cone","question":"A net consists of one square and four triangles. Explain how this net folds into a $3$D shape and name the shape."}],"difficulty":"extension"}


example_id: lp_01K94K7P54JN2YXV770TT5BFG3_01K94K7Q4ZN0EJWRMA15FZA13D_SCAFFOLDED_QUESTION
skill_ids: ["01K3581BJ02ZPXBM4YPJYDQ7XJ","1EiT0AQznGy2pjvTSth2","ZSgrCFBqWzVhvtNm9zG6"]
subtopics: ["Identifying 3D Shapes"]
subtopic_ids: ["subtopic_01H25WKW315GW2GF7MCT6QQWMD"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn about $3$D shapes and their cross-sections. A cross-section is the shape you see when you slice through a solid.","questions":[{"answer":"Cylinder","question":"What is the shape of the base of a cylinder?"},{"answer":"Rectangle","question":"If you slice a cylinder parallel to its base, what shape is the cross-section?"},{"answer":"Triangle","question":"A net has two circles and one rectangle.\nWhat $3$D shape does this net create?\nHint: Think about the shape of the base and sides."}],"difficulty":"enabling"}


example_id: lp_01K94KG89CXS40F6S9ZEKEE0E3_01K94KG9AWH85A0TC4EQTTYJ9K_EXIT_TICKET
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Eclipses
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$100\\pi$","question":"If the Moon's shadow during a solar eclipse has a radius of $10$ km, what is the area of the shadow?"},{"answer":"$12\\,000\\pi$","question":"During a lunar eclipse, Earth's shadow on the Moon has a diameter of $12\\,000$ km. What is the circumference of Earth's shadow?"},{"answer":"$\\frac{98\\pi}{3}$","question":"If a solar eclipse creates a circular shadow with a radius of $14$ km and a $60^\\circ$ central angle, what is the area of the shadow segment?"}]}


example_id: lp_01K94KG89CXS40F6S9ZEKEE0E3_01K94KG9AWH85A0TC4E31HRN8R_ACTIVITY
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Eclipses
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Circle Pizza Challenge\nYou're designing the perfect pizza! Calculate areas and circumferences to compare sizes.","scenario":"Steps\n1. Draw three circles with radii $5$ cm, $7$ cm, and $10$ cm on paper.\n2. Label each circle with its radius, diameter, and center point.\n3. Calculate the circumference of each circle using $C = 2\\pi r$.\n4. Calculate the area of each circle using $A = \\pi r^2$.\n5. Compare and discuss which pizza size offers the most value.","steps":["Discussion\n• How does doubling the radius affect the area and circumference?\n• Why is it useful to know both the area and circumference of a circle?","Differentiation Opportunities\n• Support: Use $\\pi \\approx 3$ for simpler calculations.\n• Extend: Find the cost per cm$^2$ if the pizzas cost $\\$10$, $\\$15$, and $\\$20$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94KG89CXS40F6S9ZEKEE0E3_01K94KG9AWH85A0TC4EG38T24X_CONTEMPLATIVE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Eclipses
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a circular garden with a path along the edge. How would you calculate the area of the garden, the circumference for the path, and the area of a segment if part of the garden is reserved for flowers? Explain your steps.","teacherTips":["Encourage students to use the formulas $A = \\pi r^2$ and $C = 2\\pi r$.","Remind them to define the radius and explain their reasoning.","Discuss real-world examples of garden design to inspire ideas."],"difficulty":"mild"}


example_id: lp_01K94KG89CXS40F6S9ZEKEE0E3_01K94KG9AWH85A0TC4E090A3DY_APPLICATION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Eclipses
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Geometry in Eclipses: Calculating Circumference","example1Header":"Situation\nAstronomers calculate the circumference of Earth's shadow during a lunar eclipse to predict how long the Moon will remain in shadow.","example1Body":"Example\nAstronomers use $C = \\pi d$ for Earth's shadow. For $d = 12,742$ km: $C = 3.14 \\times 12,742 = 40,030.88$ km, predicting eclipse duration.","example2Header":"","example2Body":""}


example_id: lp_01K94KG89CXS40F6S9ZEKEE0E3_01K94KG9AWH85A0TC4EMVGT7R6_THOUGHT_SPARKER
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Eclipses
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"During a solar eclipse, the moon covers part of the sun, appearing as a circle with a radius of 700 km. The shaded region of the sun’s surface forms a segment of the circle, and the sun's full radius is 695\\,700 km.","firstSentence":"How could you compare the area of the shaded part of the sun to the unshaded part during the eclipse?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to visualize the problem by sketching the circle and segment.","Guide students to calculate the total area of the sun and relate it to the segment's area.","Discuss how the geometry of circles applies to real-world phenomena like eclipses."]}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGY8R75S0MTY08ZMWGQRE_MULTIPLE_CHOICE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A circle has a radius of $7$ cm. A segment is formed by a central angle of $60^\\circ$. What is the area of the segment, rounded to $1$ decimal place?","answerOptions":["$25.6$ cm$^2$","$32.1$ cm$^2$","$28.6$ cm$^2$","$30.5$ cm$^2$"],"answer":"$25.6$ cm$^2$","difficulty":"hot"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGY8R75S0MTY08Y5T968K_CONTEMPLATIVE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A pizza is cut into $8$ equal slices. If one slice has a crust length of $5$ cm, how would you calculate the area of the crusted segment? What assumptions or measurements would you need?","teacherTips":["Use the central angle $\\theta = 360^\\circ/8$ to find sector area, then subtract the triangle area."],"difficulty":"mild"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGY8R75S0MTY07B8KA9B8_MULTIPLE_CHOICE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A circle has a radius of $7$ cm. What is its circumference? (Use $\\pi \\approx 3.14$)","answerOptions":["$21.98$ cm","$43.96$ cm","$49.00$ cm","$153.86$ cm"],"answer":"$43.96$ cm","difficulty":"mild"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGY8R75S0MTY07CTAFRTE_CONTEMPLATIVE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"A circular park has a diameter of 50 m. How would you find the distance around it? What if its diameter doubled?","teacherTips":["Use $C = \\pi d$. For $d = 50$ m, $C = 50\\pi$ m. Doubling $d$ doubles $C$ to $100\\pi$ m."],"difficulty":"hot"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGY8R75S0MTY084WA1AMM_MULTIPLE_CHOICE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A circle has a radius of $6$ cm. Calculate the area of the circle, and then subtract the area of a square with a side length of $6$ cm. What is the result?","answerOptions":["$36\\pi - 36$ cm$^2$","$36\\pi - 6$ cm$^2$","$18\\pi - 36$ cm$^2$","$18\\pi - 6$ cm$^2$"],"answer":"$36\\pi - 36$ cm$^2$","difficulty":"spicy"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGY8R75S0MTY0814A81PV_MULTIPLE_CHOICE_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the area of a circle with a radius of $7$ cm? (Use $\\pi \\approx 3.14$)","answerOptions":["$49$ cm$^2$","$153.86$ cm$^2$","$314$ cm$^2$","$21.98$ cm$^2$"],"answer":"$153.86$ cm$^2$","difficulty":"mild"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGXRAJ6V9RC0GRWA4Z61Y_SCAFFOLDED_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to calculate the area and circumference of a circle. The formulas are: Area = $\\pi r^2$ and Circumference = $2\\pi r$.","questions":[{"answer":"$28.26$","question":"Find the circumference of a circle with radius $4$. Use $\\pi \\approx 3.14$."},{"answer":"$12.56$","question":"What is the area of a circle with radius $3$? Use $\\pi \\approx 3.14$."},{"answer":"$25.12$","question":"Find the area of a segment of a circle with radius $6$ and angle $90^\\circ$. Use $\\pi \\approx 3.14$."}],"difficulty":"enabling"}


example_id: lp_01K94KGX0QK9G4TE603GGHPH0B_01K94KGXRAJ6V9RC0GS0BEFXG8_SCAFFOLDED_QUESTION
skill_ids: ["pT3WwssvzqOGmafNZdQn","fNzMZxRMkJZom1e7kkXQ","AhnDNL4mr5MBKyolRQ7d"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the relationships between the area, circumference, and segments of a circle using advanced reasoning and calculations.","questions":[{"answer":"$\\frac{100\\pi}{3} - 25\\sqrt{3}$ cm$^2$","question":"What is the exact area of a circle with a radius of $7$ cm?"},{"answer":"$49\\pi$ cm$^2$","question":"What is the ratio of the area to the circumference of a circle with radius $7$ cm, in terms of $\\pi$?"},{"answer":"$\\frac{7}{2}$","question":"A circle has radius $10$ cm. A chord divides it into a segment where the central angle is $120^\\circ$.\nCalculate and justify the exact area of the segment."}],"difficulty":"extension"}


example_id: lp_01K94KW51M9MGQRK0PKMG0V3Y0_01K94KW67Q2T2KVDNCMYWCMW4N_EXIT_TICKET
skill_ids: ["BXI214aJy5HoZfAWeszE","bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Origami
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"If an origami fold creates two adjacent angles measuring $65^\\circ$ and $25^\\circ$, are these angles complementary?"},{"answer":"$45^\\circ$","question":"An origami design has intersecting creases where one angle measures $45^\\circ$. What is the measure of the vertically opposite angle?"},{"answer":"$70^\\circ$","question":"An origami fold creates two parallel creases and a transversal, where one corresponding angle measures $70^\\circ$. What is the measure of the other angle?"}]}

skills:
["Identifying vertically opposite angles","Understanding corresponding angles in transversals","Defining complementary and supplementary angles"]


example_id: lp_01K94KW51M9MGQRK0PKMG0V3Y0_01K94KW67Q2T2KVDNCMCW1EV42_ACTIVITY
skill_ids: ["BXI214aJy5HoZfAWeszE","bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Origami
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Intersecting Roads Puzzle\nDesign a road intersection and identify key angle relationships!","scenario":"Steps\n1. Draw two intersecting roads on paper, forming two pairs of parallel lines crossed by a transversal.\n2. Label all angles formed at the intersection points (e.g., $1$, $2$, $3$, etc.).\n3. Identify and label complementary, supplementary, vertically opposite, and corresponding angles.\n4. Write down equations to show how the angles relate (e.g., $x + y = 90^\\circ$, $a = b$).\n5. Score $1$ point for each correct angle relationship. The team with the highest score wins!","steps":["Discussion\n• Why are vertically opposite angles always equal?\n• How can we use complementary and supplementary angles to find missing values?","Differentiation Opportunities\n• Support: Focus only on labeling complementary and supplementary angles.\n• Extend: Add a second transversal and identify more complex angle relationships."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Identifying vertically opposite angles","Understanding corresponding angles in transversals","Defining complementary and supplementary angles"]


example_id: lp_01K94KW51M9MGQRK0PKMG0V3Y0_01K94KW67Q2T2KVDNCMPJZ5J3P_CONTEMPLATIVE_QUESTION
skill_ids: ["BXI214aJy5HoZfAWeszE","bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Origami
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You design a park with paths forming intersecting lines and parallel walkways. How can you identify complementary, supplementary, vertically opposite, and corresponding angles in your design? Justify your reasoning.","teacherTips":["Encourage students to use real-world visuals, like park layouts.","Guide students to label angles clearly and identify relationships.","Discuss how angle relationships apply to real-world designs."],"difficulty":"mild"}

skills:
["Identifying vertically opposite angles","Understanding corresponding angles in transversals","Defining complementary and supplementary angles"]


example_id: lp_01K94KW51M9MGQRK0PKMG0V3Y0_01K94KW67Q2T2KVDNCMTCJ0KME_THOUGHT_SPARKER
skill_ids: ["BXI214aJy5HoZfAWeszE","bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Origami
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In an origami project, you fold a square sheet of paper to create intersecting lines that form angles of $50^\\circ$, $130^\\circ$, $50^\\circ$, and $130^\\circ$ at the intersection.","firstSentence":"How would you identify which angles are complementary in this origami design?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Use diagrams of the folded paper to help students visualize the angles formed.","Review the definitions of complementary and supplementary angles before the discussion.","Encourage students to explain their reasoning for identifying angle pairs, focusing on their sums."]}


example_id: lp_01K94KW51M9MGQRK0PKMG0V3Y0_01K94KW67Q2T2KVDNCMA80NDPM_APPLICATION
skill_ids: ["BXI214aJy5HoZfAWeszE","bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Origami
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Angles in Origami Design","example1Header":"Situation\nOrigami artists fold paper to create precise shapes. Accurate angles ensure designs like animals or flowers look realistic and symmetrical.","example1Body":"Example\nA fold creates a $40^\\circ$ angle. The complementary angle is $90^\\circ - 40^\\circ = 50^\\circ$. Another fold has $115^\\circ$, with its supplementary angle $180^\\circ - 115^\\circ = 65^\\circ$.","example2Header":"","example2Body":""}


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXHRAHDS0KG6JZNYR1D5T_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"When a transversal intersects two parallel lines, corresponding angles are always $[?]$.","answerOptions":["Equal","Supplementary","Complementary","Acute"],"answer":"Equal","difficulty":"mild"}

skills:
["Understanding corresponding angles in transversals","Defining complementary and supplementary angles","Identifying vertically opposite angles"]


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXHRAHDS0KG6JZTGTECVC_CONTEMPLATIVE_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"A bridge has support beams forming parallel lines with a transversal. How can you find all pairs of corresponding angles? Justify your reasoning.","teacherTips":["Corresponding angles are equal when a transversal intersects parallel lines, e.g., top-right angles."],"difficulty":"hot"}

skills:
["Understanding corresponding angles in transversals","Defining complementary and supplementary angles","Identifying vertically opposite angles"]


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXHRAHDS0KG6JYDKWN1GZ_CONTEMPLATIVE_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have an angle of $70^\\circ$. How could you create a complementary angle and a supplementary angle? Explain your reasoning.","teacherTips":["Complementary: $90^\\circ - 70^\\circ = 20^\\circ$. Supplementary: $180^\\circ - 70^\\circ = 110^\\circ$."],"difficulty":"mild"}

skills:
["Understanding corresponding angles in transversals","Defining complementary and supplementary angles","Identifying vertically opposite angles"]


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXHRAHDS0KG6JYHKDPMQX_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the sum of two supplementary angles?","answerOptions":["$90^\\circ$","$180^\\circ$","$270^\\circ$","$360^\\circ$"],"answer":"$180^\\circ$","difficulty":"mild"}


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXHRAHDS0KG6JZ7QWXQN6_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Two intersecting lines form angles $x$, $y$, $z$, and $w$. If $x = 110^\\circ$ and $y = 70^\\circ$, what is the value of $z$?","answerOptions":["$70^\\circ$","$110^\\circ$","$90^\\circ$","$50^\\circ$"],"answer":"$110^\\circ$","difficulty":"spicy"}


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXHRAHDS0KG6JZ0ED6HJ5_MULTIPLE_CHOICE_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Two intersecting lines form four angles: $50^\\circ$, $130^\\circ$, $50^\\circ$, and $130^\\circ$. Which pair of angles are vertically opposite?","answerOptions":["$50^\\circ$ and $130^\\circ$","$50^\\circ$ and $50^\\circ$","$130^\\circ$ and $130^\\circ$","$50^\\circ$ and $130^\\circ$ (at opposite positions)"],"answer":"$50^\\circ$ and $130^\\circ$ (at opposite positions)","difficulty":"hot"}


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXH93RAV7VPM0NFH014E8_SCAFFOLDED_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore relationships between complementary, supplementary, vertically opposite, and corresponding angles in geometric configurations.","questions":[{"answer":"Corresponding angles are equal due to parallel line properties.","question":"Two angles are complementary. One angle measures $65^\\circ$. What is the measure of the other angle?"},{"answer":"$25^\\circ$","question":"Two intersecting lines form vertically opposite angles. If one angle measures $45^\\circ$, what is the measure of its vertically opposite angle?"},{"answer":"$45^\\circ$","question":"A transversal cuts two parallel lines, forming corresponding angles. Explain why corresponding angles are equal, and provide a real-world example of this property."}],"difficulty":"extension"}


example_id: lp_01K94KXG4VVDPZSEBF3A8FMFAC_01K94KXH93RAV7VPM0NEW02FP3_SCAFFOLDED_QUESTION
skill_ids: ["bHjhBjEZPCgueX8D0BpR","A9DjPz8IN1vpL2RSuMcM","BXI214aJy5HoZfAWeszE"]
subtopics: ["Classifying Angles"]
subtopic_ids: ["subtopic_01GTC0BAC0NMKXM043SD8M1AXA"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn about complementary, supplementary, and vertically opposite angles. Complementary angles add to $90^\\circ$, supplementary angles add to $180^\\circ$, and vertically opposite angles are equal.","questions":[{"answer":"$45^\\circ$","question":"Two angles add up to $90^\\circ$. If one angle is $30^\\circ$, what is the other angle?"},{"answer":"$50^\\circ$","question":"Two angles are supplementary. If one angle is $120^\\circ$, what is the other angle?"},{"answer":"$60^\\circ$","question":"Two straight lines intersect, forming four angles. If one angle is $45^\\circ$, what is the measure of the vertically opposite angle?"}],"difficulty":"enabling"}


example_id: lp_01K94M453KG9K1DEX763EAVZV2_01K94M4649E843JP4C2H6BH22Q_EXIT_TICKET
skills: ["Solving for volume using $V=Ah$","Calculating the total surface area of composite solids"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Archaeology
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$12$","question":"An archaeologist discovers a rectangular stone slab with a base area of $6$ m$^2$ and height of $2$ m. What is its volume in m$^3$?"},{"answer":"$16\\pi + 2\\sqrt{20}\\pi$","question":"A statue is made of a cylinder with height $3$ m and base radius $2$ m, topped by a cone with height $4$ m. What is the total surface area?"},{"answer":"$50$","question":"An ancient artifact is a composite solid: a rectangular prism base $(5$ m $\\times 3$ m $\\times 2$ m$)$ topped by a pyramid with height $4$ m. What is the total volume?"}]}


example_id: lp_01K94M453KG9K1DEX763EAVZV2_01K94M4649E843JP4C233DNP1G_ACTIVITY
skills: ["Solving for volume using $V=Ah$","Calculating the total surface area of composite solids"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Archaeology
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Packing Box Challenge\nYou work at a shipping company designing boxes to fit items efficiently.","scenario":"Steps\n1. In teams, draw a composite solid made of a cylinder and a rectangular prism.\n2. Label dimensions (e.g., height, radius, length) and find the total surface area.\n3. Calculate the volume of the composite solid using $V=Ah$ for each part.\n4. Compare results with other teams to decide which box is most efficient.\n5. Present your design and explain your calculations to the class.","steps":["Discussion\n• How does changing one dimension affect surface area and volume?\n• Why might a smaller surface area be better for shipping?","Differentiation Opportunities\n• Support: Provide simpler shapes (e.g., cubes and cylinders) with whole-number dimensions.\n• Extend: Add a cone or sphere to your solid and calculate the new surface area and volume."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94M453KG9K1DEX763EAVZV2_01K94M4649E843JP4C29QGJ8CE_CONTEMPLATIVE_QUESTION
skills: ["Solving for volume using $V=Ah$","Calculating the total surface area of composite solids"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Archaeology
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a water tank made of a cylinder and a hemisphere on top. How would you calculate the total surface area and volume of the tank if the cylinder's height is $4$ ft and radius is $2$ ft?","teacherTips":["Guide students to calculate separate areas for the cylinder and hemisphere.","Remind students to include the curved surface area of the hemisphere.","Discuss combining the volumes of both shapes to get the total volume."],"difficulty":"mild"}


example_id: lp_01K94M453KG9K1DEX763EAVZV2_01K94M4649E843JP4C2CR49WQA_THOUGHT_SPARKER
skills: ["Solving for volume using $V=Ah$","Calculating the total surface area of composite solids"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Archaeology
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Archaeologists uncover an ancient artifact shaped like a cylinder with a hemispherical top. The cylinder has a height of $30$ cm and a base radius of $10$ cm, the same as the radius of the hemisphere.","firstSentence":"How would you calculate the total volume of this artifact?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the shapes that make up the composite solid before calculating.","Discuss the formula for the volume of a hemisphere and how it relates to the formula for a sphere.","Guide students to add the volumes of the cylinder and hemisphere to find the total volume."]}


example_id: lp_01K94M453KG9K1DEX763EAVZV2_01K94M4649E843JP4C1YZVQ8GY_APPLICATION
skills: ["Solving for volume using $V=Ah$","Calculating the total surface area of composite solids"]
skill_ids: ["PAGdRpS75rtjcjOLRc0q","01K0DFTCK11Q05EV7EBF6QD1KM"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Archaeology
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Calculating Surface Areas in Archaeological Excavations","example1Header":"Situation\nArchaeologists uncover ancient storage jars made of composite shapes. To restore or replicate them, they calculate the surface area for cleaning or crafting replicas.","example1Body":"Example\nAn ancient jar combines a cylinder (height $10$ cm, radius $4$ cm) and a hemisphere (radius $4$ cm). Its total surface area is $351.68$ cm$^2$.","example2Header":"","example2Body":""}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZZBE8B0DFW2XENSWA9J_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A cylinder has a radius of $3$ cm and a height of $5$ cm. Ignore the top and bottom circles. What is the lateral surface area?","answerOptions":["$15\\pi$ cm$^2$","$30\\pi$ cm$^2$","$45\\pi$ cm$^2$","$60\\pi$ cm$^2$"],"answer":"$30\\pi$ cm$^2$","difficulty":"mild"}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZZBE8B0DFW2XBN6MW0F_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangular prism has dimensions $4$ m by $3$ m by $2$ m. What is its total surface area?","answerOptions":["$24$ m$^2$","$52$ m$^2$","$72$ m$^2$","$84$ m$^2$"],"answer":"$72$ m$^2$","difficulty":"mild"}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZZBE8B0DFW2XJQRRJ2G_CONTEMPLATIVE_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a storage box combining a cube and a cylinder. How would you calculate its total surface area, including the areas where they connect? What factors might affect your design?","teacherTips":["Add areas of cube and cylinder, subtract overlapping region. Consider all visible surfaces."],"difficulty":"spicy"}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZZBE8B0DFW2WRD0TED3_CONTEMPLATIVE_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A fish tank has a base area of $150$ cm$^2$ and is partially filled with water to a height of $10$ cm. How would you calculate the volume of water if more water is added to fill the tank to $15$ cm? What strategies could you use?","teacherTips":["For $h = 10$ cm, $V = 150 \\times 10 = 1\\,500$ cm$^3$. At $h = 15$ cm, $V = 150 \\times 15 = 2\\,250$ cm$^3$."],"difficulty":"mild"}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZZBE8B0DFW2WM92CJEV_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"The base area of a rectangular prism is $20$ cm$^2$ and its height is $5$ cm. What is the volume of the prism?","answerOptions":["$25$ cm$^3$","$50$ cm$^3$","$100$ cm$^3$","$200$ cm$^3$"],"answer":"$100$ cm$^3$","difficulty":"mild"}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZG41AEC5SN2KVW5W5Q8_SCAFFOLDED_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the surface area and volume of composite solids combining cylinders and rectangular prisms","questions":[{"answer":"Volume increases by a greater proportion.","question":"A composite solid consists of a cylinder with radius $3$ cm and height $5$ cm attached to the top of a rectangular prism with dimensions $6$ cm by $6$ cm by $5$ cm. Find the total surface area of the composite solid."},{"answer":"$45\\pi + 156$","question":"Using the composite solid from Question 1, calculate its total volume."},{"answer":"$45\\pi + 180$","question":"If the radius of the cylinder in the composite solid is doubled while keeping all other dimensions unchanged, justify whether the surface area or the volume increases by a greater proportion."}],"difficulty":"extension"}


example_id: lp_01K94M4Y60HVY1CCMGGSX1GN85_01K94M4ZG41AEC5SN2KNY9V3F4_SCAFFOLDED_QUESTION
skills: ["Calculating the total surface area of composite solids","Solving for volume using $V=Ah$"]
skill_ids: ["01K0DFTCK11Q05EV7EBF6QD1KM","PAGdRpS75rtjcjOLRc0q"]
subtopics: ["Surface Area"]
subtopic_ids: ["subtopic_01GTC0BM527TT0RTJPR44JJBRN"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to calculate the volume of composite solids using $V = A h$, where $A$ is the base area and $h$ is the height.","questions":[{"answer":"$84$ cm$^3$","question":"A rectangular prism has a base area of $10$ cm$^2$ and a height of $5$ cm. What is its volume?\nUse $V = A h$."},{"answer":"$15$ cm$^3$","question":"A composite solid is made of two rectangular prisms. The first has $A = 8$ cm$^2$, $h = 4$ cm, and the second has $A = 6$ cm$^2$, $h = 3$ cm. What is the total volume?"},{"answer":"$50$ cm$^3$","question":"A composite solid has a base area of $12$ cm$^2$ and a height of $7$ cm. What is its volume?\nExplain your steps using $V = A h$."}],"difficulty":"enabling"}


example_id: lp_01K94MCS22KY95KRHW2K5510QG_01K94MCT3ZCS1ASWXN25EVMSN7_APPLICATION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Reforestation
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Random Sampling in Reforestation Projects","example1Header":"Situation\nForesters use random sampling to estimate tree growth in reforested areas. They cannot count every tree, so they randomly choose small sections to study.","example1Body":"Example\nForesters randomly sample $10$ sections. With $12$, $15$, $14$, $13$, $16$, $11$, $14$, $13$, $15$, and $12$ trees, the average is $135 \\div 10 = 13.5$ trees per acre.","example2Header":"","example2Body":""}

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


example_id: lp_01K94MCS22KY95KRHW2K5510QG_01K94MCT3ZCS1ASWXN2QWE34SZ_THOUGHT_SPARKER
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Reforestation
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A reforestation project involves planting $10\\,000$ trees, and a team samples $100$ trees to estimate the project's success rate.","firstSentence":"How might the way the $100$ trees are chosen affect the conclusions drawn about the entire project?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss different sampling methods such as random sampling, cluster sampling, and convenience sampling.","Encourage students to share examples of biased versus unbiased sampling methods.","Use visual aids or simulations to show how sampling methods can impact the representativeness of data."]}

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


example_id: lp_01K94MCS22KY95KRHW2K5510QG_01K94MCT3ZCS1ASWXN2A36KAWB_ACTIVITY
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Reforestation
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Survey Sampling Game\nYour team is designing surveys to collect fair and unbiased opinions in class.","scenario":"Steps\n1. In teams, write $3$ survey questions (e.g., favorite food).\n2. Pick $10$ classmates using two methods: $1$ random and $1$ biased.\n3. Collect answers for both surveys and record the results.\n4. Compare the results to identify sampling bias.\n5. Discuss how random sampling creates fairer data.","steps":["Discussion\n• What made the biased sample unfair?\n• How does random sampling improve accuracy?","Differentiation Opportunities\n• Support: Give examples of biased methods, like only asking close friends.\n• Extend: Design a stratified sample, ensuring all groups are represented."],"discussion":[],"differentiation":{"support":"","extend":""}}

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


example_id: lp_01K94MCS22KY95KRHW2K5510QG_01K94MCT3ZCS1ASWXN2JZDEZSM_CONTEMPLATIVE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Reforestation
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your school wants to know students' favorite lunch. How would you design a fair random sample? What sampling method would you use, and how would you avoid bias?","teacherTips":["Discuss different sampling methods like random or stratified sampling.","Explain how bias affects the accuracy of survey results.","Encourage students to justify their sampling choices."],"difficulty":"mild"}


example_id: lp_01K94MCS22KY95KRHW2K5510QG_01K94MCT3ZCS1ASWXN2WS8M13D_EXIT_TICKET
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Reforestation
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"If a team randomly selects $10$ trees from a forest to measure height, is this a random sample?"},{"answer":"Yes","question":"If only tall trees near the edge of a forest are sampled, would this sampling method cause bias?"},{"answer":"Stratified sampling","question":"A reforestation project divides a forest into $5$ zones and samples $10$ trees from each zone. What type of sampling is this?"}]}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDGMHGX65A6YXPPQCQC2N_MULTIPLE_CHOICE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If a survey is conducted only in a luxury mall to find average income, what type of sampling bias might occur?","answerOptions":["Location bias","Selection bias","Response bias","Non-response bias"],"answer":"Location bias","difficulty":"mild"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDGMHGX65A6YXPRGD27AS_CONTEMPLATIVE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You want to know students' favorite school subject. How would you avoid sampling bias in your survey?","teacherTips":["Avoid bias by including a diverse group, like students from all grades, genders, and interests."],"difficulty":"hot"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDGMHGX65A6YXN3AD2PM9_CONTEMPLATIVE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You want to survey $50$ students about their favorite sport. How would you pick a random sample, and why?","teacherTips":["Choose by chance, like drawing names. This avoids bias and gives all students an equal chance."],"difficulty":"hot"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDGMHGX65A6YXN76DXG9R_MULTIPLE_CHOICE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A company surveys every $10$th customer entering a store. Is this a random sample?","answerOptions":["Yes, because it is unbiased","No, because it is systematic","Yes, because every customer has a chance","No, because it is biased"],"answer":"No, because it is systematic","difficulty":"spicy"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDGMHGX65A6YXP665FA41_MULTIPLE_CHOICE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A researcher selects every 10th person entering a store to participate in a survey. Which sampling method is being used?","answerOptions":["Simple random sampling","Systematic sampling","Stratified sampling","Convenience sampling"],"answer":"Systematic sampling","difficulty":"hot"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDGMHGX65A6YXNYHDXWXC_MULTIPLE_CHOICE_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which sampling method involves selecting individuals who are easiest to reach?","answerOptions":["Simple random sampling","Systematic sampling","Cluster sampling","Convenience sampling"],"answer":"Convenience sampling","difficulty":"mild"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDG4QNDC17HR495K4BY5V_SCAFFOLDED_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore sampling bias, random samples, and sampling methods to determine the fairness and validity of data collection.","questions":[{"answer":"Random reduces bias, convenience is easier but less representative.","question":"A survey asks only students in the school band about their favorite music genre. Why might this sample be biased?"},{"answer":"The sample is unrepresentative of all students.","question":"How can you select a random sample of $50$ students from a school with $500$ students to ensure everyone has an equal chance of being chosen?"},{"answer":"Use a random number generator on all $500$ students.","question":"A city wants to survey residents about public transportation. Compare the advantages and disadvantages of using random sampling versus convenience sampling."}],"difficulty":"extension"}


example_id: lp_01K94MDFCG4JEJKA2Y7HBDBJQ7_01K94MDG4QNDC17HR4932X30C7_SCAFFOLDED_QUESTION
skill_ids: ["8Tcl65LGb78533gvhcwn","A2vaRoxM2u0gdY9tIxka","EynlqRpby7HISkWORU26"]
subtopics: ["Sampling"]
subtopic_ids: ["subtopic_01GTC0BHQKB2ZWJAA244FAWNEB"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn about sampling bias and how random sampling ensures fairness.","questions":[{"answer":"It doesn't include all students, so it's not fair.","question":"Why might asking only soccer players about their favorite sport create bias?"},{"answer":"It includes only soccer players, so it's not fair.","question":"What makes a random sample fair?"},{"answer":"Everyone likes soccer, so it's fair.","question":"Explain why asking only students who arrive early to school might lead to biased survey results."}],"difficulty":"enabling"}


example_id: lp_01K94MQ5G3XB7W4WK5CF7KRPPW_01K94MQ6KQ7T3R44QYCQDSA18C_APPLICATION
skills: ["Calculating range","Defining interquartile range"]
skill_ids: ["ZwAp7NuWvkPA19vCjp1z","d0mkj2iDtlgQJ2rI1Dte"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Cars
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Car Speeds with Range","example1Header":"Situation\nAutomotive engineers analyze speed data from test drives to ensure cars perform consistently. They calculate the range to understand speed variations.","example1Body":"Example\nEngineers record speeds: $50$, $52$, $48$, $60$, $55$ mph. The range is $60 - 48 = 12$ mph, showing a $12$ mph variation in test speeds.","example2Header":"","example2Body":""}


example_id: lp_01K94MQ5G3XB7W4WK5CF7KRPPW_01K94MQ6KQ7T3R44QYDAQBN1AT_THOUGHT_SPARKER
skills: ["Calculating range","Defining interquartile range"]
skill_ids: ["ZwAp7NuWvkPA19vCjp1z","d0mkj2iDtlgQJ2rI1Dte"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Cars
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A car dealer records the distances that eight different cars travel on a full tank of gas: $380$, $410$, $450$, $470$, $490$, $520$, $550$, $600$ miles.","firstSentence":"How might you analyze this data to describe the spread of the car ranges?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to recall how to find the interquartile range and why it is useful.","Encourage students to discuss the benefits of using the interquartile range rather than the total range.","Have students identify the quartiles visually by plotting the data on a number line."]}


example_id: lp_01K94MQ5G3XB7W4WK5CF7KRPPW_01K94MQ6KQ7T3R44QYCTQFDGB1_ACTIVITY
skills: ["Calculating range","Defining interquartile range"]
skill_ids: ["ZwAp7NuWvkPA19vCjp1z","d0mkj2iDtlgQJ2rI1Dte"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Cars
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Statistical Score Showdown\nYour team is analyzing test scores to find the range and interquartile range for student data.","scenario":"Steps\n1. Create a list of $10$ test scores (e.g., $45$, $78$, $56$, etc.).\n2. Arrange the scores in ascending order.\n3. Calculate the range as the highest score minus the lowest score.\n4. Find $Q_1$, $Q_3$, and calculate the IQR as $Q_3 - Q_1$.\n5. Compare your results with other teams to discuss data spread.","steps":["Discussion\n• Why is the IQR more useful than the range for understanding data spread?\n• What happens to the range if an outlier is added to the data?","Differentiation Opportunities\n• Support: Provide a pre-sorted data set and highlight $Q_1$ and $Q_3$ for easier calculations.\n• Extend: Analyze how adding extreme values impacts both the range and IQR."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94MQ5G3XB7W4WK5CF7KRPPW_01K94MQ6KQ7T3R44QYD4Z9J2C1_CONTEMPLATIVE_QUESTION
skills: ["Calculating range","Defining interquartile range"]
skill_ids: ["ZwAp7NuWvkPA19vCjp1z","d0mkj2iDtlgQJ2rI1Dte"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Cars
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A group of friends recorded their weekly allowances: $12$, $15$, $22$, $10$, $18$, $25$, and $14$. What is the range and interquartile range? How do these help describe their allowances?","teacherTips":["Guide students to arrange data in order to find range and quartiles.","Encourage students to interpret the spread of the data using IQR.","Explain the importance of range and IQR in describing variability."],"difficulty":"mild"}


example_id: lp_01K94MQ5G3XB7W4WK5CF7KRPPW_01K94MQ6KQ7T3R44QYDDD6JEHE_EXIT_TICKET
skills: ["Calculating range","Defining interquartile range"]
skill_ids: ["ZwAp7NuWvkPA19vCjp1z","d0mkj2iDtlgQJ2rI1Dte"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Cars
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$60$","question":"A car travels $150$ miles on its first trip and $90$ miles on its second trip. What is the range of these trip distances?"},{"answer":"$70$","question":"The distances travelled by cars in a day are $30$, $50$, $60$, $80$, $90$, $120$, and $150$ miles. What is the interquartile range?"},{"answer":"$20$","question":"Car speeds on a highway are recorded as $65$, $70$, $75$, $80$, $85$, $90$, and $95$ mph. What is the range of these speeds in mph if the lowest speed is increased by $10$ mph?"}]}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQQ2NAC0GNJGZYQ0GQQE_MULTIPLE_CHOICE_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"The interquartile range (IQR) is calculated as the difference between which two values in a data set?","answerOptions":["Maximum and minimum","Q1 and Q3","Mean and median","Q2 and Q4"],"answer":"Q1 and Q3","difficulty":"mild"}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQQ3R9GJSK1RXWH4P9FT_CONTEMPLATIVE_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a data set of $10$ numbers where the interquartile range (IQR) is exactly $6$. How can you change the data to keep the IQR the same but increase the range?","teacherTips":["IQR is $Q_3 - Q_1$. Adjust numbers outside $Q_1$ and $Q_3$ to increase range while keeping IQR constant."],"difficulty":"spicy"}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQQ2NAC0GNJH059HPJSE_MULTIPLE_CHOICE_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What does the interquartile range (IQR) represent in a dataset?","answerOptions":["The range of the entire data set","The difference between Q3 and Q1","The average of all data points","The middle value of the data set"],"answer":"The difference between Q3 and Q1","difficulty":"mild"}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQQ2NAC0GNJGZ9NWDAVJ_MULTIPLE_CHOICE_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the range of the data set: $12, 7, 15, 10, 8$?","answerOptions":["$8$","$5$","$7$","$15$"],"answer":"$8$","difficulty":"mild"}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQQ2NAC0GNJGZCDMEGSJ_CONTEMPLATIVE_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A zoo tracks daily temperatures for a month. Design a data set with a range of 15°F. What happens to the range if you add a new highest or lowest temperature? Explain.","teacherTips":["Range $=$ highest $-$ lowest. Adding new extremes increases the range; others may not affect it."],"difficulty":"spicy"}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQ893E467K9JWKR334DA_SCAFFOLDED_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the concepts of range and interquartile range with challenging datasets.","questions":[{"answer":"Dataset A, because it has a larger range and IQR.","question":"Given the data set: $12$, $7$, $19$, $5$, $14$, $11$, $8$, what is the range?"},{"answer":"$14$","question":"For the dataset $4$, $8$, $10$, $12$, $15$, $18$, $20$, $22$, $25$, find the interquartile range."},{"answer":"$12$","question":"Two datasets are given: Dataset A: $3$, $6$, $8$, $12$, $15$, $18$, $22$ and Dataset B: $7$, $8$, $9$, $10$, $11$, $12$, $13$.\nWhich dataset has a greater spread of data? Justify your answer using both the range and interquartile range."}],"difficulty":"extension"}


example_id: lp_01K94MQPD1W8NF58Y91XZVGXB6_01K94MQQ893E467K9JWHDSDX13_SCAFFOLDED_QUESTION
skills: ["Defining interquartile range","Calculating range"]
skill_ids: ["d0mkj2iDtlgQJ2rI1Dte","ZwAp7NuWvkPA19vCjp1z"]
subtopics: ["Measures of Spread"]
subtopic_ids: ["subtopic_01GTC0BPGZE9SFAJ6WTJ3KZBKF"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to calculate the range of a data set. The range is found by subtracting the smallest number from the largest number.","questions":[{"answer":"$12$","question":"What is the range of the data set $3, 7, 5, 10$?\nHint: Range = Largest number - Smallest number."},{"answer":"$3$","question":"What is the range of the data set $12, 18, 15, 9, 21$?\nHint: Range = Largest number - Smallest number."},{"answer":"$5$","question":"What is the range of the data set $5, 11, 8, 14, 2$?\nShow your work."}],"difficulty":"enabling"}


example_id: lp_01K94MW5Q2TYGEW2KMD9M9KQF3_01K94MW6HFC79CJN7BBK4KEM8S_APPLICATION
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Card Games
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Using Averages to Analyze Card Game Scores","example1Header":"Situation\nProfessional card game players analyze scores to improve strategies. Calculating the mean score helps them track performance over several rounds.","example1Body":"Example\nA player scores $12$, $18$, $15$, $20$, and $10$ over $5$ rounds. The total is $75$. Dividing by $5$ rounds gives $75 \\div 5 = 15$. The mean score is $15$.","example2Header":"","example2Body":""}


example_id: lp_01K94MW5Q2TYGEW2KMD9M9KQF3_01K94MW6HFC79CJN7BC6BH06SA_THOUGHT_SPARKER
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Card Games
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a card game, four players scored the following points over five rounds: $15$, $20$, $20$, $25$, and $30$.","firstSentence":"Which measure—mean, median, or mode—would you use to describe the typical score in this game, and why?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Prompt students to calculate the mean, median, and mode before deciding on their answer.","Discuss the strengths and limitations of each measure in representing the data.","Encourage students to explain their reasoning by connecting the measures to the context of the game."]}


example_id: lp_01K94MW5Q2TYGEW2KMD9M9KQF3_01K94MW6HFC79CJN7BBPB1CHQG_ACTIVITY
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Card Games
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Game Night Stats\nYour team is analyzing game scores to determine who had the best performance!","scenario":"Steps\n1. In teams, list $10$ scores between $1$ and $100$ on paper.\n2. Arrange the scores in ascending order.\n3. Find the mode (most frequent score) from your list.\n4. Calculate the median (middle score) of your data.\n5. Calculate the mean (average) of your scores.","steps":["Discussion\n• How does the data change if one score is much higher or lower?\n• Why might the mode, median, or mean be most useful in this case?","Differentiation Opportunities\n• Support: Work with $5$ scores instead of $10$ to simplify calculations.\n• Extend: Add an extra outlier score and analyze how it affects the results."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94MW5Q2TYGEW2KMD9M9KQF3_01K94MW6HFC79CJN7BC87PPCM8_EXIT_TICKET
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Card Games
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$","question":"In a card game, the scores are $3$, $5$, $3$, $7$, $3$, and $5$. What is the mode of the scores?"},{"answer":"$12$","question":"During a card game, the players scored $8$, $12$, $15$, $20$, $10$. What is the median score?"},{"answer":"$20$","question":"If the card game scores are $18$, $22$, $16$, $20$, and $24$, what is the mean score?"}]}


example_id: lp_01K94MW5Q2TYGEW2KMD9M9KQF3_01K94MW6HFC79CJN7BC1Q0RRQD_CONTEMPLATIVE_QUESTION
skills: ["Finding the median","Finding the mode","Calculating the mean"]
skill_ids: ["WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf","koijWmj27uJSkzJwd8R5"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Card Games
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a list of $10$ numbers (like test scores). Find the mean, median, and mode. How do they compare?","teacherTips":["Ensure students understand mean: sum divided by count.","Highlight median as the middle value when sorted.","Explain mode is the most frequent number in the list."],"difficulty":"mild"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWY80B0XPZD2E64QV5KH0_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the mean of the numbers $4$, $6$, and $8$?","answerOptions":["$5$","$6$","$7$","$8$"],"answer":"$6$","difficulty":"mild"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWY80B0XPZD2E69QAEW3F_CONTEMPLATIVE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You recorded your daily screen time: $2.5$, $3$, $2$, $4$, $3.5$ hours. How would you find the mean? What does it tell you about your habits?","teacherTips":["Add $2.5 + 3 + 2 + 4 + 3.5 = 15$, then divide by $5$: mean = $3$ hours, a typical daily habit."],"difficulty":"mild"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWY80B0XPZD2E7KRE3JTN_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is the median of the dataset $7, 12, 9, 5, 15, 10, 8$?","answerOptions":["$9$","$10$","$8$","$12$"],"answer":"$9$","difficulty":"hot"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWY80B0XPZD2E7PMGZK4M_CONTEMPLATIVE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a dataset of $9$ numbers with a median of $15$. How would adding $1$ number change the median? Explain.","teacherTips":["Adding $1$ number makes the dataset size even, so the median becomes the average of the two middle values."],"difficulty":"spicy"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWY80B0XPZD2E6XF7TCCZ_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is the mode of the dataset $7,\\ 5,\\ 9,\\ 5,\\ 7,\\ 3,\\ 7,\\ 2,\\ 9,\\ 5$?","answerOptions":["$5$","$7$","$9$","There is no mode"],"answer":"There is no mode","difficulty":"hot"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWY80B0XPZD2E6YB79PMV_MULTIPLE_CHOICE_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A dataset has the mode $15$. If three more $15$s and two $20$s are added, what must be true about the new mode?","answerOptions":["The mode is $20$","The mode is $15$","There is no mode","Both $15$ and $20$ are modes"],"answer":"The mode is $15$","difficulty":"spicy"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWXRH9N46QT9JH775FAB1_SCAFFOLDED_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze a data set to find the mode, median, and mean, and explain the relationships between these measures.","questions":[{"answer":"Mean: $6.57$, Mode: $4$, Median: $6$","question":"Given the data set: $3, 7, 5, 7, 9, 7, 5$, what is the mode?"},{"answer":"$7$","question":"For the data set $4, 8, 2, 6, 10, 8, 12$, what is the median?"},{"answer":"$8$","question":"Given the data set $2, 4, 4, 6, 8, 10, 12$, calculate the mean, and compare it to the mode and median. Explain the significance of any differences."}],"difficulty":"extension"}


example_id: lp_01K94MWX0B21F74HWZQ0EH5V7Q_01K94MWXRH9N46QT9JH1P56KPP_SCAFFOLDED_QUESTION
skills: ["Calculating the mean","Finding the median","Finding the mode"]
skill_ids: ["koijWmj27uJSkzJwd8R5","WxRTCwFjmo5jYWe7ts6S","FBdt1Ik4ATJRioMa3oIf"]
subtopics: ["Measures of Centre"]
subtopic_ids: ["subtopic_01GTC0BQAK7Z0VA1M5KJPE2BN7"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to find the mode, median, and mean of a dataset. These are ways to describe data.","questions":[{"answer":"$6$","question":"What is the mode of this dataset: $3,\\ 5,\\ 5,\\ 7,\\ 8$?\nThe mode is the number that appears most often."},{"answer":"$3$","question":"What is the median of this dataset: $4,\\ 6,\\ 9,\\ 10,\\ 12$?\nThe median is the middle number when the data is ordered."},{"answer":"$5$","question":"What is the mean of this dataset: $2,\\ 4,\\ 6,\\ 8,\\ 10$?\nRemember: Add all the numbers, then divide by how many there are."}],"difficulty":"enabling"}


example_id: lp_01K94N320JGXG58QPFBF3F4F62_01K94N32WEQ8RDBE17W4NEF5SW_THOUGHT_SPARKER
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Frisbee
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"When throwing a frisbee, there are different outcomes: it can land in a target zone, land outside, or be caught by someone. Each outcome has a probability between $0$ and $1$.","firstSentence":"Why do you think probabilities are always represented as numbers between $0$ and $1$?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss how probabilities represent likelihood, ranging from impossible ($0$) to certain ($1$).","Provide examples of real-life events with probabilities close to $0$, $1$, or somewhere in between.","Encourage students to explain their reasoning using familiar examples like rolling dice or flipping coins."]}


example_id: lp_01K94N320JGXG58QPFBF3F4F62_01K94N32WEQ8RDBE17VMCCY4ED_APPLICATION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Frisbee
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Probability in Frisbee Practice","example1Header":"Situation\nFrisbee players analyze probabilities to improve their accuracy. They calculate success chances to adjust their throws and strategies in practice.","example1Body":"Example\nA player lands $7$ of $10$ throws, so the success probability is $0.7$. With $3$ misses, the failure probability is $0.3$. These add up to $1$, covering all outcomes.","example2Header":"","example2Body":""}


example_id: lp_01K94N320JGXG58QPFBF3F4F62_01K94N32WEQ8RDBE17VQCGYEE4_ACTIVITY
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Frisbee
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Probability Sorting Game\nYour team is tasked with sorting events by how likely they are to happen.","scenario":"Steps\n1. In teams, write $10$ events (e.g., 'It will rain tomorrow').\n2. Classify each event as impossible ($0$), unlikely, even, likely, or certain ($1$).\n3. Assign a probability to each event (e.g., 'likely' is $0.8$).\n4. Compare your classifications with another team’s list.\n5. Score points for matching probabilities with the other team!","steps":["Discussion\n• Why must all probabilities be between $0$ and $1$?\n• How can you decide if an event is 'likely' or 'unlikely'?","Differentiation Opportunities\n• Support: Provide example events to help classify probabilities.\n• Extend: Include compound events and calculate their combined probabilities."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94N320JGXG58QPFBF3F4F62_01K94N32WEQ8RDBE17W9MVMEC2_EXIT_TICKET
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Frisbee
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.4$","question":"If a frisbee lands in the goal $4$ out of $10$ times, what is the probability of it landing in the goal?"},{"answer":"Yes","question":"During a frisbee game, the probability that Alex catches the frisbee is $0.7$. Is this probability valid?"},{"answer":"$0.75$","question":"If the probability of a frisbee missing the target is $0.25$, what is the probability of it hitting the target?"}]}


example_id: lp_01K94N320JGXG58QPFBF3F4F62_01K94N32WEQ8RDBE17W0RC9XMX_CONTEMPLATIVE_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Frisbee
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A spinner has 4 equal sections: red, blue, green, and yellow. How would you describe the probability of landing on each color? Can you think of events with probabilities of $0$ or $1$ involving this spinner?","teacherTips":["Guide students to recognize equal probabilities for each section: $0.25$ or $\\frac{1}{4}$.","Encourage discussion of impossible events (e.g., landing on purple) with $0$ probability.","Have students connect certain events (e.g., landing on any color) to probability $1$."],"difficulty":"mild"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NSPCE58WEHBNVX4P6KK_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following could represent the probability of an event?","answerOptions":["$1.5$","$0.75$","$-0.3$","$1.2$"],"answer":"$0.75$","difficulty":"mild"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NSPCE58WEHBP6MKW0CY_CONTEMPLATIVE_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"Design a game with 3 events. Assign probabilities to each event, ensuring they add to $1$. Explain why.","teacherTips":["Probabilities represent chances, must be between $0$ and $1$, and total $1$ for all outcomes."],"difficulty":"hot"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NSPCE58WEHBP4QWKJ7B_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of the following values can represent a valid probability?","answerOptions":["$1.2$","$-0.5$","$0.75$","$1.5$"],"answer":"$0.75$","difficulty":"hot"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NSPCE58WEHBNZ5SM5MS_CONTEMPLATIVE_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip a coin and roll a die. What are the possible probabilities of events, and why do they fall between $0$ and $1$?","teacherTips":["Probabilities show likelihood: $0$ means impossible, $1$ means certain, and all events fall in between."],"difficulty":"mild"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NSPCE58WEHBNN5Y4AAZ_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"True or false: The probability of an event can be $0.75$.","answerOptions":["True","False"],"answer":"True","difficulty":"mild"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NCM13JC1DJD21E59RPA_SCAFFOLDED_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore probabilities as numbers between $0$ and $1$ using real-world and abstract scenarios","questions":[{"answer":"The probabilities are invalid because $-0.2$ is not in $[0,1]$ and the total sum is less than $1$.","question":"What is the range of numbers that probabilities can take?"},{"answer":"$0$ to $1$","question":"A spinner has four regions with probabilities $0.3$, $0.2$, $0.4$, and $x$. What value of $x$ makes this a valid probability distribution?"},{"answer":"$0.1$","question":"A die is rolled, and the probabilities assigned to its outcomes are $0.1$, $0.2$, $0.3$, $0.4$, $0.1$, and $-0.2$.\nExplain why this set of probabilities is invalid."}],"difficulty":"extension"}


example_id: lp_01K94N3MHTM3YVS0R4NZ532XWX_01K94N3NCM13JC1DJD1W8NMZ18_SCAFFOLDED_QUESTION
skills: ["Understanding that probabilities are represented as numbers between $0$ and $1$"]
skill_ids: ["epyyn8wG9aa0qbIvsxmE"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn that probabilities are represented as numbers between $0$ and $1$. A probability of $0$ means impossible, and $1$ means certain.","questions":[{"answer":"It is certain to happen.","question":"Which of these could be a probability value?"},{"answer":"$1.5$","question":"If the probability of an event is $0$, what does it mean?"},{"answer":"$-0.2$","question":"What does it mean if a probability is $1$? Explain in your own words."}],"difficulty":"enabling"}


example_id: lp_01K94N89JHCX1M6NAX4RH59YHA_01K94N8ACG12APVZT7S0K0HAYF_ACTIVITY
skills: ["Comparing theoretical and experimental probabilities","Finding probability from experiments"]
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Pickleball
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Dice Probability Challenge\nYour team is tasked with rolling dice and finding probabilities to solve a mystery!","scenario":"Steps\n1. In teams, roll a 6-sided die $30$ times and record each outcome.\n2. Calculate the experimental probability for each number ($1$ to $6$).\n3. Compare these to the theoretical probability of $\\frac{1}{6}$ for each number.\n4. Discuss why experimental probabilities may differ from theoretical ones.\n5. Repeat $30$ more rolls and see if the probabilities get closer to $\\frac{1}{6}$.","steps":["Discussion\n• Why do experimental probabilities change with more rolls?\n• What patterns do you notice when comparing experimental and theoretical probabilities?","Differentiation Opportunities\n• Support: Roll the die $10$ times instead of $30$ and focus on fewer outcomes.\n• Extend: Use two dice and calculate probabilities for sums (e.g., $2$ to $12$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94N89JHCX1M6NAX4RH59YHA_01K94N8ACG12APVZT7SNSTVJ33_EXIT_TICKET
skills: ["Comparing theoretical and experimental probabilities","Finding probability from experiments"]
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Pickleball
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$\\frac{7}{10}$","question":"In $10$ pickleball matches, Sarah won $7$ times. What is the experimental probability of her winning?"},{"answer":"Higher","question":"In a pickleball game, the theoretical probability of hitting the target is $\\frac{1}{4}$. If Emma hits the target $6$ times out of $20$ shots, is the experimental probability higher or lower?"},{"answer":"Higher","question":"If the theoretical probability of winning a pickleball rally is $\\frac{3}{5}$ and you win $16$ out of $25$ rallies, how do the probabilities compare?"}]}


example_id: lp_01K94N89JHCX1M6NAX4RH59YHA_01K94N8ACG12APVZT7SE54V61N_CONTEMPLATIVE_QUESTION
skills: ["Comparing theoretical and experimental probabilities","Finding probability from experiments"]
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Pickleball
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip a coin $50$ times and record heads $28$ times. How does this compare to the theoretical probability of flipping heads? Why might they differ?","teacherTips":["Guide students to compare $28/50$ to $1/2$.","Discuss how sample size affects experimental results.","Encourage explanations for differences, like randomness."],"difficulty":"mild"}


example_id: lp_01K94N89JHCX1M6NAX4RH59YHA_01K94N8ACG12APVZT7RZWFYF8G_APPLICATION
skills: ["Comparing theoretical and experimental probabilities","Finding probability from experiments"]
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Pickleball
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Shot Accuracy in Pickleball","example1Header":"Situation\nPickleball coaches analyze player performance by observing shot accuracy during practice. Understanding probabilities helps players improve their game strategies.","example1Body":"Example\nA player tries $20$ shots, hitting $14$. The probability of hitting a shot is $14 \\div 20 = 0.7$ ($70\\%$), and missing is $6 \\div 20 = 0.3$ ($30\\%$).","example2Header":"","example2Body":""}


example_id: lp_01K94N89JHCX1M6NAX4RH59YHA_01K94N8ACG12APVZT7SGW6Z4H3_THOUGHT_SPARKER
skills: ["Comparing theoretical and experimental probabilities","Finding probability from experiments"]
skill_ids: ["kDNBwnJhdI048d9aPqjl","5NnKW7lV6y0B1BFGfUmG"]
subtopics: ["Probability Calculations"]
subtopic_ids: ["subtopic_01GTC0BN3HQY6DPNXYKFKCXAYZ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Pickleball
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A pickleball player has a theoretical probability of $75\\%$ of winning a point on their serve. In a practice match, they serve $40$ times and win $28$ points.","firstSentence":"Why might the experimental probability differ from the theoretical probability in this situation?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate both the theoretical and experimental probabilities to compare them.","Discuss factors like randomness and sample size that impact experimental probability.","Ask students to consider real-life influences, such as player fatigue or skill level, on results."]}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8XP5VJ6D0CVFRXP7QGAZ_SCAFFOLDED_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore probability using experiments involving dice rolls and card draws.","questions":[{"answer":"Answers will vary; must describe trials and calculations.","question":"A six-sided die is rolled $60$ times, and the number $3$ appears $15$ times.\nWhat is the experimental probability of rolling a $3$?"},{"answer":"$0.25$","question":"In the same experiment, the number $5$ appeared $10$ times.\nWhat is the combined experimental probability of rolling a $3$ or $5$?"},{"answer":"$0.4167$","question":"Design an experiment involving $50$ trials of drawing a card from a shuffled deck.\nExplain how you would calculate the experimental probability of drawing a red card."}],"difficulty":"extension"}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8XP5VJ6D0CVFRRWZF3ST_SCAFFOLDED_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to calculate probabilities from experiments. Probability is the chance of an event happening, calculated as the number of favorable outcomes divided by the total number of outcomes.","questions":[{"answer":"$0.6$","question":"A coin is flipped $10$ times and lands heads up $6$ times. What is the probability of getting heads?\nRemember: Probability = Favorable outcomes / Total outcomes."},{"answer":"$0.6$","question":"A die is rolled $20$ times, and a $4$ is rolled $5$ times. What is the probability of rolling a $4$?\nHint: Use the formula Probability = Favorable outcomes / Total outcomes."},{"answer":"$0.4$","question":"In an experiment, a spinner is spun $15$ times and lands on red $9$ times. What is the probability of landing on red?\nWrite your answer as a fraction or decimal."}],"difficulty":"enabling"}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8Y55NKHAM4PCTBTDCF5A_CONTEMPLATIVE_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design an experiment with a spinner divided into 4 equal colors. How would you estimate the probability of landing on each color after 100 spins? What would you infer if results differ from theoretical probability?","teacherTips":["Experimental probability is $\\frac{\\text{favorable outcomes}}{\\text{total spins}}$. Variations show randomness."],"difficulty":"spicy"}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8Y55NKHAM4PCT6J1JF8C_MULTIPLE_CHOICE_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A coin is tossed $10$ times, resulting in $7$ heads and $3$ tails. What is the experimental probability of getting heads?","answerOptions":["$0.7$","$0.3$","$0.5$","$0.9$"],"answer":"$0.7$","difficulty":"hot"}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8Y55NKHAM4PCV66D39GJ_MULTIPLE_CHOICE_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If a coin is flipped $50$ times and lands on heads $22$ times, which type of probability does $22/50$ represent?","answerOptions":["Theoretical probability","Experimental probability","Predicted probability","Calculated probability"],"answer":"Experimental probability","difficulty":"mild"}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8Y55NKHAM4PCVCBP0368_CONTEMPLATIVE_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You flip a coin $50$ times and get $32$ heads. How could you compare this result to the theoretical probability?","teacherTips":["Theoretical probability is $\\frac{1}{2}$. Experimental probability is $\\frac{32}{50} = 0.64$."],"difficulty":"hot"}


example_id: lp_01K94N8WWTNW0G8RNJM6MAJ1WV_01K94N8Y55NKHAM4PCV0XXCAVN_MULTIPLE_CHOICE_QUESTION
skills: ["Finding probability from experiments","Comparing theoretical and experimental probabilities"]
skill_ids: ["5NnKW7lV6y0B1BFGfUmG","kDNBwnJhdI048d9aPqjl"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which type of probability is based on actual results from an experiment?","answerOptions":["Theoretical probability","Experimental probability","Predicted probability","Calculated probability"],"answer":"Experimental probability","difficulty":"mild"}


example_id: lp_01K94NH03753CKKJ3VRPYPKH55_01K94NH13CSD7HSNKTTD87H774_EXIT_TICKET
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Fencing
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.3$","question":"If a fencer lands $3$ hits out of $10$ attempts, what is the experimental probability of landing a hit?"},{"answer":"$0.2$","question":"A fencer expects to land $5$ hits in $10$ attempts, but actually lands $7$. What is the difference between the experimental and expected probabilities?"},{"answer":"$10\\%$","question":"If a fencer lands $18$ hits out of $30$ attempts but the theoretical probability is $50\\%$, how much higher is the experimental probability in percentage?"}]}

skills:
["Comparing theoretical and experimental probabilities","Comparing experimental results to expected outcomes"]


example_id: lp_01K94NH03753CKKJ3VRPYPKH55_01K94NH13CSD7HSNKTSPM0VS04_ACTIVITY
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Fencing
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Coin Flip Probability Race\nTeams flip coins to see how their results compare to theoretical probabilities.","scenario":"Steps\n1. Each team flips a coin $50$ times and records heads and tails counts.\n2. Calculate the experimental probability of heads and tails.\n3. Compare these probabilities to the theoretical $0.5$ for heads and tails.\n4. Discuss as a team why your results might differ from theoretical predictions.\n5. Teams with results closest to $0.5$ win bonus points!","steps":["Discussion\n• Why might experimental results differ from theoretical probabilities?\n• How would increasing the number of flips affect your results?","Differentiation Opportunities\n• Support: Flip the coin $20$ times instead of $50$ for simpler calculations.\n• Extend: Calculate probabilities for combinations like $2$ heads in a row."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Comparing theoretical and experimental probabilities","Comparing experimental results to expected outcomes"]


example_id: lp_01K94NH03753CKKJ3VRPYPKH55_01K94NH13CSD7HSNKTT0S6Q5F4_CONTEMPLATIVE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Fencing
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip a coin $50$ times and record heads $28$ times. How does this compare to the theoretical probability of $\\frac{1}{2}$ for heads? What might explain any differences?","teacherTips":["Discuss how experimental results may differ from theoretical probabilities due to chance.","Encourage students to consider sample size and randomness.","Ask students to explain why results might get closer with more trials."],"difficulty":"mild"}

skills:
["Comparing theoretical and experimental probabilities","Comparing experimental results to expected outcomes"]


example_id: lp_01K94NH03753CKKJ3VRPYPKH55_01K94NH13CSD7HSNKTT780787Y_THOUGHT_SPARKER
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Fencing
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A fencer lands $12$ hits out of $20$ attempts in a match. Based on practice, their expected success rate is $70\\%$.","firstSentence":"What might comparing the experimental success rate to the expected success rate reveal about the fencer's performance?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to calculate both the experimental and expected success rates before comparing them.","Discuss possible reasons for differences, such as pressure during a match or varying levels of difficulty.","Ask students to consider how larger sample sizes (more matches) might affect the comparison."]}


example_id: lp_01K94NH03753CKKJ3VRPYPKH55_01K94NH13CSD7HSNKTSKQ1XVJV_APPLICATION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Fencing
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Probability in Fencing Tournaments","example1Header":"Situation\nFencing coaches analyze match data to estimate the likelihood of winning certain moves. They compare predicted probabilities with actual outcomes to refine training strategies.","example1Body":"Example\nA fencer expects $70\\%$ success but hits $6$ out of $10$ targets, so experimental probability is $6 \\div 10 = 0.6$ or $60\\%$. This differs from $70\\%$ by $10\\%$.","example2Header":"","example2Body":""}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHPQ615BDW2NR8CZ7KKSJ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"True or false: Experimental probability is based on actual trials, while theoretical probability is based on expected outcomes.","answerOptions":["True","False"],"answer":"True","difficulty":"mild"}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHPQ615BDW2NR8F3J4D9G_CONTEMPLATIVE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"If you flip a coin $20$ times, how could you compare the experimental probability of heads to the theoretical probability? How would the comparison change with $100$ flips? Why?","teacherTips":["Experimental probability approaches theoretical ($0.5$) as flips increase due to reduced random variation."],"difficulty":"hot"}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHPQ615BDW2NR9D335X32_CONTEMPLATIVE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You roll a fair die $50$ times. How could you compare the observed results to the expected outcomes? What might explain any differences?","teacherTips":["Expected: $50 \\div 6 \\approx 8.33$ per side. Differences arise due to random variation in small samples."],"difficulty":"spicy"}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHPQ615BDW2NR98N1TC5H_MULTIPLE_CHOICE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A coin is flipped $100$ times and lands on heads $40$ times. Does the experimental result match the expected result?","answerOptions":["Yes, it matches","No, it does not match","It matches half the time","It is impossible to tell"],"answer":"No, it does not match","difficulty":"mild"}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHPQ615BDW2NR961AQC11_MULTIPLE_CHOICE_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A coin is flipped $50$ times. Heads appears $18$ times. Is the experimental result equal to the expected result?","answerOptions":["Yes, because $18$ is close to $25$","No, because $18$ is less than $25$","Yes, because $18$ is exactly half of $50$","No, because $18$ is more than $25$"],"answer":"No, because $18$ is less than $25$","difficulty":"mild"}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHP7YFR00GQ25099CY6ZF_SCAFFOLDED_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Compare experimental results and theoretical probabilities in a dice-rolling game.","questions":[{"answer":"Sample size affects consistency; randomness causes variation.","question":"What is the theoretical probability of rolling a $6$ on a fair $6$-sided die?"},{"answer":"$\\frac{1}{6}$","question":"In $120$ rolls of a fair die, the number $6$ appeared $25$ times.\nWhat is the experimental probability of rolling a $6$?"},{"answer":"$\\frac{5}{24}$","question":"Explain why the experimental probability of rolling a $6$ in $120$ rolls may differ from the theoretical probability.\nDiscuss the role of sample size."}],"difficulty":"extension"}


example_id: lp_01K94NHNCFK8WGEEDGP6DM6X4R_01K94NHP7YFR00GQ2506792SAF_SCAFFOLDED_QUESTION
skill_ids: ["kDNBwnJhdI048d9aPqjl","J9KPnL04ABSLPfuh26DV"]
subtopics: ["Experimental Probability"]
subtopic_ids: ["subtopic_01GTC0BB73P3T54919P9B494GC"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will compare experimental results and theoretical probability. Theoretical probability predicts outcomes based on math, while experimental probability comes from actual trials.","questions":[{"answer":"Experimental is $70\\%$, theoretical is $50\\%$","question":"Theoretical probability is calculated by:"},{"answer":"Dividing favorable outcomes by total outcomes","question":"Experimental probability is calculated by:"},{"answer":"Counting the number of trials","question":"If a coin is flipped $10$ times and lands on heads $7$ times, how does the experimental probability compare to the theoretical probability?"}],"difficulty":"enabling"}


example_id: lp_01K94NPQDXMFH0H4YJC5BPCC9G_01K94NPRHN2ZWVBEFEM2WESBZM_ACTIVITY
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Paralympics
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Probability Challenge!\nYour team is figuring out probabilities for dice rolls and coin flips in a game.","scenario":"Steps\n1. Each team rolls a die and flips a coin $10$ times.\n2. Record all outcomes (e.g., $3$ and heads, $5$ and tails).\n3. Calculate the probability of rolling a $6$ and getting heads.\n4. Calculate the probability of rolling an even number and getting tails.\n5. Compare probabilities and discuss why some events are more likely.","steps":["Discussion\n• Why do we multiply probabilities for independent events?\n• How do the results change if we use a loaded die?","Differentiation Opportunities\n• Support: Use a smaller sample set (e.g., $5$ rolls and flips).\n• Extend: Include additional events, like rolling a prime number."],"discussion":[],"differentiation":{"support":"","extend":""}}

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


example_id: lp_01K94NPQDXMFH0H4YJC5BPCC9G_01K94NPRHN2ZWVBEFEMPVVH5RA_EXIT_TICKET
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Paralympics
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$0.8$","question":"At a Paralympics event, there is a $50\\%$ chance it rains and a $60\\%$ chance a swimmer wins gold. What is the probability one or both happen?"},{"answer":"$0.343$","question":"A Paralympics archer hits the target with a $70\\%$ chance. What is the probability they hit it $3$ times in a row?"},{"answer":"$0.3$","question":"At a Paralympics race, $2$ runners independently finish within $10$ seconds with probabilities $0.4$ and $0.5$. What is the probability neither finishes in time?"}]}

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


example_id: lp_01K94NPQDXMFH0H4YJC5BPCC9G_01K94NPRHN2ZWVBEFEMGSXRAWN_CONTEMPLATIVE_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Paralympics
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You flip 2 coins and roll a die. How would you find the probability of getting 2 heads and a 6? Can you explain your reasoning?","teacherTips":["Remind students that coin flips and die rolls are independent events.","Encourage students to multiply probabilities for independent events.","Ask students to explain how they calculate each probability."],"difficulty":"mild"}

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


example_id: lp_01K94NPQDXMFH0H4YJC5BPCC9G_01K94NPRHN2ZWVBEFEM0YTY9HB_APPLICATION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Paralympics
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Predicting Medal Outcomes in the Paralympics","example1Header":"Situation\nCoaches at the Paralympics analyze the probability of athletes winning medals in multiple events. They use this data to fine-tune training plans and focus on events with the best chances of success.","example1Body":"Example\nAn athlete has a $50\\%$ chance in event A and a $30\\%$ chance in event B. The probability of winning both is $0.5 \\times 0.3 = 0.15$, or $15\\%$.","example2Header":"","example2Body":""}


example_id: lp_01K94NPQDXMFH0H4YJC5BPCC9G_01K94NPRHN2ZWVBEFEMK7DY9YP_THOUGHT_SPARKER
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
context: Paralympics
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In the Paralympics, a certain athlete has a $40\\%$ chance of winning a gold medal in swimming and a $30\\%$ chance of winning a gold medal in track and field. These events are independent of each other.","firstSentence":"How would you calculate the probability of the athlete winning gold medals in both events?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Emphasize the concept of independent events and how their probabilities are calculated.","Encourage students to explain why multiplying probabilities is appropriate for independent events.","Discuss real-life examples of independent events to reinforce understanding."]}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQF01ZC8J6414J5JFSA52_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A coin is flipped, and a die is rolled. What is the probability of getting heads and a number greater than $4$?","answerOptions":["$\\dfrac{1}{6}$","$\\dfrac{1}{3}$","$\\dfrac{1}{4}$","$\\dfrac{1}{12}$"],"answer":"$\\dfrac{1}{6}$","difficulty":"hot"}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQF01ZC8J6414J84GSD47_CONTEMPLATIVE_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You randomly draw $3$ cards from a shuffled deck of $52$. How would you calculate the probability of getting exactly $2$ hearts and $1$ spade? What if you change the number of cards drawn or suits required?","teacherTips":["Use $P = \\frac{\\text{desired outcomes}}{\\text{total outcomes}}$. Apply combinations for each case."],"difficulty":"spicy"}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQF01ZC8J6414K0DT9YYZ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A coin is flipped and a die is rolled. What is the probability of getting heads on the coin and a $3$ on the die?","answerOptions":["$1/12$","$1/6$","$1/2$","$1/3$"],"answer":"$1/12$","difficulty":"mild"}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQF01ZC8J6414K6XSB5DN_CONTEMPLATIVE_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You roll a fair die and flip a coin. How can you calculate the probability of rolling a $6$ and getting heads? What other outcomes are possible, and how would their probabilities compare?","teacherTips":["The probability is $P(6 \\text{ and heads}) = \\frac{1}{6} \\times \\frac{1}{2} = \\frac{1}{12}$. Multiply for others similarly."],"difficulty":"hot"}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQF01ZC8J6414K43ZVPEF_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A coin is flipped and a die is rolled. What is the probability of getting heads on the coin and a $4$ on the die?","answerOptions":["$\\frac{1}{2}$","$\\frac{1}{6}$","$\\frac{1}{12}$","$\\frac{1}{8}$"],"answer":"$\\frac{1}{12}$","difficulty":"mild"}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQEHMYVM0BD6KYFMMD7BE_SCAFFOLDED_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to find the probability of combined events when the events are independent.","questions":[{"answer":"$\\frac{1}{4}$","question":"A coin is flipped. What is the probability of landing on heads?"},{"answer":"$1$","question":"A coin is flipped and a six-sided die is rolled. What is the probability of getting heads and rolling a $4$?"},{"answer":"$\\frac{1}{2}$","question":"What is the probability of flipping heads on a coin and rolling an odd number on a six-sided die?"}],"difficulty":"enabling"}


example_id: lp_01K94NQDT52BA7KRPCB1CEAJWP_01K94NQEHMYVM0BD6KYJ3FMWDC_SCAFFOLDED_QUESTION
skill_ids: ["GE5sCMlhlaZ6mYjuN6NM","qTPzvnTNx4XiHQqpMART"]
subtopics: ["Multiple Events"]
subtopic_ids: ["subtopic_01GTC0BDZ20N809GCAM551MQ0D"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the probability of multiple independent events in a challenging real-world scenario","questions":[{"answer":"The probability is $3/8$, based on the binomial formula.","question":"A fair coin is flipped, and a six-sided die is rolled. What is the probability of getting heads and rolling a $4$?"},{"answer":"$1/12$","question":"A coin is flipped twice, and a six-sided die is rolled. What is the probability of getting two heads and rolling a $5$?"},{"answer":"$1/24$","question":"Three cards are drawn randomly from a deck of $52$ cards with replacement. What is the probability of drawing exactly one red card?\nExplain your reasoning."}],"difficulty":"extension"}


example_id: lp_01K94PABF3BM7NT7NTYWHRSH79_01K94PACBYGZX4BP8V5BJ95TYQ_THOUGHT_SPARKER
skills: ["Defining linear equations","Finding the equation of a line parallel to a given line"]
skill_ids: ["3cYrE4D2Z8OSmbGQnEHL","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Superfoods
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The price of quinoa increases at a steady rate, modeled by the equation $y = 2x + 5$, where $x$ is the number of weeks and $y$ is the price in dollars.","firstSentence":"How would you write an equation for a line parallel to this one that starts at a different initial price?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the concept of slope and its role in parallel lines.","Discuss how changing the $y$-intercept affects the graph of the line.","Encourage students to test their equations by graphing and comparing with the original line."]}


example_id: lp_01K94PABF3BM7NT7NTYWHRSH79_01K94PACBYGZX4BP8V4TJ056T1_APPLICATION
skills: ["Defining linear equations","Finding the equation of a line parallel to a given line"]
skill_ids: ["3cYrE4D2Z8OSmbGQnEHL","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Superfoods
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Modeling Nutrient Trends in Superfoods","example1Header":"Situation\nNutritionists analyze nutrient levels in superfoods. They track protein or vitamin content over time, using linear equations to model trends and make predictions.","example1Body":"Example\nA line parallel to $y = 3x + 5$ passing through $(2, 4)$ has slope $3$. Using $y - 4 = 3(x - 2)$ gives $y = 3x - 2$, modeling a similar nutrient trend.","example2Header":"","example2Body":""}


example_id: lp_01K94PABF3BM7NT7NTYWHRSH79_01K94PACBYGZX4BP8V57HH2QJ6_CONTEMPLATIVE_QUESTION
skills: ["Defining linear equations","Finding the equation of a line parallel to a given line"]
skill_ids: ["3cYrE4D2Z8OSmbGQnEHL","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Superfoods
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A line passes through $(2, 3)$ and is parallel to $y = 4x + 1$. What could its equation be? How do you know?","teacherTips":["Parallel lines have the same slope, here $m = 4$.","Use the point-slope form $y - y_1 = m(x - x_1)$.","Substitute $(2, 3)$ and solve for $y$ to find the equation."],"difficulty":"mild"}


example_id: lp_01K94PABF3BM7NT7NTYWHRSH79_01K94PACBYGZX4BP8V4Y7P1PPS_ACTIVITY
skills: ["Defining linear equations","Finding the equation of a line parallel to a given line"]
skill_ids: ["3cYrE4D2Z8OSmbGQnEHL","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Superfoods
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Parallel Streets Design\nDesign parallel streets for a city grid while following specific rules for spacing.","scenario":"Steps\n1. Draw a city grid on graph paper with axes labeled $x$ and $y$.\n2. Start with a given line, e.g., $y = 2x + 3$.\n3. In teams, write equations for $3$ streets parallel to the given line.\n4. Plot the parallel lines and label them on the grid.\n5. Check another team's work for accuracy and give feedback.","steps":["Discussion\n• What stays the same for all parallel lines?\n• How does changing the $y$-intercept affect the graph?","Differentiation Opportunities\n• Support: Provide a step-by-step guide to identify slopes and write equations.\n• Extend: Write equations for lines parallel to $y = 2x + 3$ and passing through specific points."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94PABF3BM7NT7NTYWHRSH79_01K94PACBYGZX4BP8V5FSQGJZK_EXIT_TICKET
skills: ["Defining linear equations","Finding the equation of a line parallel to a given line"]
skill_ids: ["3cYrE4D2Z8OSmbGQnEHL","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Superfoods
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5$","question":"A store sells superfoods with total cost represented by $y = 5x + 10$, where $x$ is the quantity. What is the slope of the line?"},{"answer":"$y = 3x + 3$","question":"A superfood's price increases follow the line $y = 3x + 7$. What is the equation of a line parallel to this line that passes through $(2, 9)$?"},{"answer":"$y = -2x - 11$","question":"A farm uses revenue projections modeled by $y = -2x + 4$. What is the equation of a parallel line passing through $(-3, -5)$?"}]}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPVDF9DK4YSPSVGTSAKB_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the equation of a line parallel to $y = 3x + 2$?","answerOptions":["$y = 3x - 5$","$y = -3x + 2$","$y = 2x + 3$","$y = -2x - 3$"],"answer":"$y = 3x - 5$","difficulty":"mild"}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPVDF9DK4YSPSPYCVCD8_CONTEMPLATIVE_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A line has the equation $y = 3x + 2$. What could be the equation of a line parallel to it? How do you know?","teacherTips":["A parallel line has equation $y = 3x + b$ where $b$ is any number. The slope remains $3$."],"difficulty":"mild"}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPVDF9DK4YSPTSCG50EX_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following is a linear equation?","answerOptions":["$y = 2x + 5$","$y = x^2 + 3$","$y = 3x^{-1} + 4$","$y = x^{\\frac{1}{2}} + 2$"],"answer":"$y = 2x + 5$","difficulty":"mild"}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPVDF9DK4YSPTXXWRRYX_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of the following represents a linear equation?","answerOptions":["$3x + 2 = 0$","$x^2 + 4 = 0$","$2x + y^2 = 5$","$x + 3x^{-1} = 7$"],"answer":"$3x + 2 = 0$","difficulty":"hot"}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPVDF9DK4YSPTP4WTRQJ_CONTEMPLATIVE_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A taxi company charges $\\$5$ as a base fare plus $\\$2$ per mile. How would you write a linear equation to represent the total cost for a ride of $x$ miles? What would the cost be for $10$ miles?","teacherTips":["The equation is $y = 2x + 5$. For $10$ miles, $y = 2(10) + 5 = 25$, so the cost is $\\$25$."],"difficulty":"mild"}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPCKPE92EAAXMA0KFJ49_SCAFFOLDED_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore parallel lines and their equations by working with slopes and y-intercepts","questions":[{"answer":"Parallel lines share the same slope because different slopes would cause intersection.","question":"What is the slope of the line represented by the equation $3x - 4y = 8$?"},{"answer":"$\\frac{3}{4}$","question":"Find the equation of a line parallel to $3x - 4y = 8$ that passes through the point $(1, 2)$. Write your answer in slope-intercept form."},{"answer":"$y = \\frac{3}{4}x + \\frac{5}{4}$","question":"Explain why parallel lines must have the same slope. Use both geometric reasoning and algebraic evidence in your explanation."}],"difficulty":"extension"}


example_id: lp_01K94PBNDF4VFQNS510BF44XK0_01K94PBPCKPE92EAAXM3GCRCJC_SCAFFOLDED_QUESTION
skills: ["Finding the equation of a line parallel to a given line","Defining linear equations"]
skill_ids: ["01K0DDPZS6JCWDG1TXPT5J06XX","3cYrE4D2Z8OSmbGQnEHL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to find the equation of a line parallel to a given line. Parallel lines have the same slope.","questions":[{"answer":"$y = 4x + 3$","question":"What is the slope of the line $y = 3x + 5$?\nRemember: the slope is the coefficient of $x$ in $y = mx + b$."},{"answer":"$3$","question":"What is the slope of a line parallel to $y = -2x + 4$?\nHint: Parallel lines share the same slope."},{"answer":"$5$","question":"Find the equation of a line parallel to $y = 4x + 1$ that passes through the point $(0, 3)$.\nHint: Use the same slope and substitute the point."}],"difficulty":"enabling"}


example_id: lp_01K94PKTP9AF34FABT0CGN2EPK_01K94PKVPV9PM7VPAWACSN9EN5_THOUGHT_SPARKER
skill_ids: ["jeKVaNbqKcfZTANagQdL","CxQJSGgY0VuakzASgffH"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Insects
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A collection of insects has a total of $48$ legs, and each insect has $6$ legs.","firstSentence":"How would you determine the number of insects in the collection?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to set up a simple equation like $6x = 48$ and solve for $x$.","Discuss why division is the appropriate operation to use in this context.","Ask students to explain their reasoning and compare different solution methods."]}


example_id: lp_01K94PKTP9AF34FABT0CGN2EPK_01K94PKVPV9PM7VPAW9RKNV3F6_APPLICATION
skill_ids: ["jeKVaNbqKcfZTANagQdL","CxQJSGgY0VuakzASgffH"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Insects
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Tracking Bug Populations Using Equations","example1Header":"Situation\nEntomologists (insect scientists) track bug populations to protect ecosystems. They use equations to estimate the number of insects in a habitat after observing partial data.","example1Body":"Example\nAn entomologist counted $50$ beetles and knows $x + 50 = 120$ insects in total. Subtracting $50$: $x = 70$. There are $70$ other insects in the habitat.","example2Header":"","example2Body":""}


example_id: lp_01K94PKTP9AF34FABT0CGN2EPK_01K94PKVPV9PM7VPAWAG8BDBRA_EXIT_TICKET
skill_ids: ["jeKVaNbqKcfZTANagQdL","CxQJSGgY0VuakzASgffH"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Insects
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$7$","question":"A bee collected $x$ grams of pollen and then $5$ more grams, totaling $12$ grams. What is the value of $x$?"},{"answer":"$7$","question":"An ant carries $4x$ milligrams of food, which equals $28$ milligrams. What is the value of $x$?"},{"answer":"$18$","question":"A spider spins $x/6$ webs in $3$ hours. If each web takes $6$ hours, what is the value of $x$?"}]}


example_id: lp_01K94PKTP9AF34FABT0CGN2EPK_01K94PKVPV9PM7VPAWA62MSY23_CONTEMPLATIVE_QUESTION
skill_ids: ["jeKVaNbqKcfZTANagQdL","CxQJSGgY0VuakzASgffH"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Insects
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You spend $x$ dollars on a gift and have $\\$45$ left. How would you solve $x + 45 = 75$? Explain.","teacherTips":["Encourage students to isolate $x$ by subtracting $45$ from both sides.","Ask students to explain why subtraction maintains equality.","Have students check their solution by adding $x$ and $45$."],"difficulty":"mild"}


example_id: lp_01K94PKTP9AF34FABT0CGN2EPK_01K94PKVPV9PM7VPAW9W0MJ0C3_ACTIVITY
skill_ids: ["jeKVaNbqKcfZTANagQdL","CxQJSGgY0VuakzASgffH"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Insects
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Zoo Feeding Frenzy\nSolve equations to earn food for zoo animals! Each correct answer feeds a hungry animal.","scenario":"Steps\n1. Each team writes $5$ one-step equations on their paper (e.g., $x + 3 = 10$).\n2. Swap equations with another team to solve their problems.\n3. Solve each equation and check answers with the other team.\n4. For every correct solution, earn $1$ food token for your animal.\n5. The team with the most food tokens wins!","steps":["Discussion\n• How do you know your solution is correct?\n• Why is balancing both sides of the equation important?","Differentiation Opportunities\n• Support: Use only addition or subtraction equations (e.g., $x + 5 = 12$).\n• Extend: Include equations with fractions or decimals (e.g., $0.5x = 2.5$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNSC2PB82F3JJHDDA5N12_CONTEMPLATIVE_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You have $\\$50$ to spend. You buy a gift and have $\\$18$ left. How would you calculate the gift's cost? What if you had $\\$30$ left instead? Create equations for both scenarios and solve.","teacherTips":["Use $x + 18 = 50$. Subtract $18$: $x = 50 - 18$. For $\\$30$ left: $x + 30 = 50$, solve $x = 20$."],"difficulty":"spicy"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNSC2PB82F3JJH7K7S6A0_MULTIPLE_CHOICE_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Solve for $x$: $x + 7 = 12$.","answerOptions":["$x = 5$","$x = 19$","$x = 4$","$x = 7$"],"answer":"$x = 5$","difficulty":"mild"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNSC2PB82F3JJH5K9TP3G_MULTIPLE_CHOICE_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Solve for $x$: $x + 7 = 12$.","answerOptions":["$x = 5$","$x = 7$","$x = 12$","$x = 19$"],"answer":"$x = 5$","difficulty":"mild"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNSC2PB82F3JJJ882G1C4_MULTIPLE_CHOICE_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Solve for $x$: $5x = 60$.","answerOptions":["$x = 10$","$x = 12$","$x = 15$","$x = 18$"],"answer":"$x = 12$","difficulty":"hot"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNSC2PB82F3JJJ5Y65Z7V_MULTIPLE_CHOICE_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Solve for $x$ if $5x = 20$.","answerOptions":["$x = 2$","$x = 4$","$x = 5$","$x = 10$"],"answer":"$x = 4$","difficulty":"mild"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNSC2PB82F3JJJ24DAMVV_CONTEMPLATIVE_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a recipe where $3x = 21$ cups of flour are needed. How would you solve for $x$? What if $5x = 40$? Explain your steps and reasoning for both.","teacherTips":["For $3x = 21$, divide both sides by $3$: $x = 7$. For $5x = 40$, divide by $5$: $x = 8$."],"difficulty":"mild"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNRWH6M4HP7C1V0Q9K4A5_SCAFFOLDED_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will solve one-step algebraic equations. Remember, to solve an equation, isolate the variable by performing the opposite operation.","questions":[{"answer":"$5$","question":"If $x + 5 = 12$, what is the value of $x$?"},{"answer":"$6$","question":"If $y - 3 = 10$, what is the value of $y$?"},{"answer":"$7$","question":"If $4z = 20$, what is the value of $z$?\nRemember, divide both sides by $4$ to isolate $z$."}],"difficulty":"enabling"}


example_id: lp_01K94PNQX937239JRZR6AGNS6D_01K94PNRWH6M4HP7C1V6298K4H_SCAFFOLDED_QUESTION
skill_ids: ["CxQJSGgY0VuakzASgffH","jeKVaNbqKcfZTANagQdL"]
subtopics: ["Solving Basic Equations"]
subtopic_ids: ["subtopic_01GTC0BJN0FMS2XBQJX8F1AK86"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Solve challenging one-step equations and explore their underlying structure.","questions":[{"answer":"Divide by $-4$, $x = -6$.","question":"Solve for $x$: $x - 15 = -8$."},{"answer":"$7$","question":"Solve for $y$: $\\frac{2}{3}y = 10$."},{"answer":"$15$","question":"Explain how you would solve the equation $-4x = 24$. Why does your method work for all such equations?"}],"difficulty":"extension"}


example_id: lp_01K94PTW7E5AMEX6MB82JAHRT7_01K94PV0D65RYGKGHN0ZZEGM94_APPLICATION
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Robotics
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Path Planning in Robotics","example1Header":"Situation\nRobotics engineers create robots that navigate spaces autonomously. They use equations of lines to plan paths and find where paths intersect to avoid collisions.","example1Body":"Example\nTwo robots travel along $y = 2x + 1$ and $y = -x + 7$. Solving $2x + 1 = -x + 7$, $x = 2$. Substituting $x = 2$, $y = 5$. They meet at $(2, 5)$.","example2Header":"","example2Body":""}


example_id: lp_01K94PTW7E5AMEX6MB82JAHRT7_01K94PV0D65RYGKGHN1JEKXWQR_THOUGHT_SPARKER
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Robotics
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Two robots are programmed to move in straight lines. Robot A moves according to the equation $y = 2x + 3$, while Robot B moves according to $y = -x + 8$.","firstSentence":"What does the point where their paths intersect represent in this scenario?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to graph both equations to visualize the intersection point.","Discuss how the intersection relates to the physical paths of the robots.","Explore different methods to solve the equations algebraically, then verify graphically."]}


example_id: lp_01K94PTW7E5AMEX6MB82JAHRT7_01K94PV0D65RYGKGHN1CVE1TAR_CONTEMPLATIVE_QUESTION
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Robotics
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Two friends are comparing phone plans. Plan A costs $y = 10x + 20$, and Plan B costs $y = 15x + 10$. How would you graph these equations to determine for what $x$ (number of months) the costs are the same?","teacherTips":["Encourage students to calculate a few points for each equation.","Guide students to graph both lines on the same axis.","Discuss the meaning of the intersection point."],"difficulty":"mild"}


example_id: lp_01K94PTW7E5AMEX6MB82JAHRT7_01K94PV0D65RYGKGHN1NZ4PKT2_EXIT_TICKET
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Robotics
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$y = 7$","question":"A robot's movement is modeled by $y = 2x + 1$. What is $y$ when $x = 3$?"},{"answer":"$(1, 3)$","question":"The paths of two robots are $y = x + 2$ and $y = -x + 4$. At which point do their paths intersect?"},{"answer":"$\\left(\\frac{7}{3}, \\frac{1}{3}\\right)$","question":"A robot's position is $2x + y = 5$ and another robot's position is $x - y = 2$. What are the coordinates of their meeting point?"}]}


example_id: lp_01K94PTW7E5AMEX6MB82JAHRT7_01K94PV0D65RYGKGHN14D0W35E_ACTIVITY
skill_ids: ["uUlz9G2lq4RxIdGb2JCQ","mCBIb1V8GokoYiTHL7hD","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Robotics
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Graphing Intersection Hunt\nYou're city planners designing roads. Find where two roads (lines) intersect.","scenario":"Steps\n1. On graph paper, draw axes and label them from $-10$ to $10$.\n2. Graph the first equation: $y = 2x + 3$.\n3. Graph the second equation: $y = -x + 1$.\n4. Find and circle the intersection point of the two lines.\n5. Write the coordinates of the intersection point as the solution.","steps":["Discussion\n• Why does the intersection point solve both equations?\n• What happens if the lines are parallel?","Differentiation Opportunities\n• Support: Use equations with simpler integers, like $y = x + 1$ and $y = -x + 2$.\n• Extend: Try graphing a system with three equations and find their common intersection."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBX0XB21RQ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Solve the simultaneous equations $y = 2x + 1$ and $y = -x + 4$. What is the value of $x$?","answerOptions":["$x = 1$","$x = 2$","$x = 0$","$x = -1$"],"answer":"$x = 1$","difficulty":"mild"}

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


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBX8V2SCSJ_CONTEMPLATIVE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You design two lines, $y = m_1x + c_1$ and $y = m_2x + c_2$. How would you adjust $m_1$, $m_2$, $c_1$, and $c_2$ to ensure the lines intersect at $(3,5)$? Can you create another pair of lines that also intersect at $(3,5)$?","teacherTips":["At $(3,5)$, $5 = m_1(3) + c_1$ and $5 = m_2(3) + c_2$. Solve to find consistent $m$ and $c$ values."],"difficulty":"spicy"}

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


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBX3H52CJW_MULTIPLE_CHOICE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Solve the simultaneous equations: $y = 2x + 1$ and $y = -x + 7$. What is the value of $x$?","answerOptions":["$x = 2$","$x = 1$","$x = 3$","$x = 4$"],"answer":"$x = 2$","difficulty":"mild"}

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


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBY3662322_MULTIPLE_CHOICE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Solve the system of equations: $2x + y = 7$ and $x - y = 1$. What is the value of $x$?","answerOptions":["$x = 2$","$x = 3$","$x = 4$","$x = 5$"],"answer":"$x = 3$","difficulty":"hot"}


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBY07H0AWJ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Solve the simultaneous equations: $x + y = 7$ and $x - y = 1$. What are the values of $x$ and $y$?","answerOptions":["$x = 4$, $y = 3$","$x = 3$, $y = 4$","$x = 5$, $y = 2$","$x = 6$, $y = 1$"],"answer":"$x = 4$, $y = 3$","difficulty":"mild"}


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBYQE58R79_MULTIPLE_CHOICE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the solution to the simultaneous equations $y = x + 2$ and $y = -x + 4$?","answerOptions":["$x=1, y=3$","$x=2, y=4$","$x=0, y=2$","$x=-1, y=1$"],"answer":"$x=1, y=3$","difficulty":"mild"}


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVH90VS0VENFBYYXTPA6H_CONTEMPLATIVE_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A city has two bus companies. Company A charges $\\$2$ per ride plus $\\$0.25$ per mile. Company B charges $\\$3$ per ride plus $\\$0.15$ per mile. For what distances are the costs of both companies equal? How would you represent this graphically?","teacherTips":["Set $2 + 0.25x = 3 + 0.15x$. Solve for $x$ to find the distance. Graph lines to find the intersection."],"difficulty":"spicy"}


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVGSWBNB79SY75HAJ5WRZ_SCAFFOLDED_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze and solve simultaneous equations graphically for lines $y = mx + c$ involving two variables.","questions":[{"answer":"Three intersection points exist.","question":"Find the point of intersection of $y = 2x + 1$ and $y = -x + 4$."},{"answer":"$(1, 3)$","question":"Determine if $y = 3x - 2$ and $y = 3x + 5$ intersect. If not, explain why."},{"answer":"No, the lines are parallel.","question":"Three equations are given: $y = x + 2$, $y = -x - 2$, and $y = 2x - 1$.\nExplain how many points of intersection exist among the three lines and justify your reasoning."}],"difficulty":"extension"}


example_id: lp_01K94PVG22W580AKKH7J7EC3JQ_01K94PVGSWBNB79SY75F4SZ59B_SCAFFOLDED_QUESTION
skill_ids: ["mCBIb1V8GokoYiTHL7hD","uUlz9G2lq4RxIdGb2JCQ","jqjvecPA66bvSDoBrLNn"]
subtopics: ["Solving Simultaneous Equations"]
subtopic_ids: ["subtopic_01GTC0BHM3NXRF3FMVBR100M0H"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to solve simultaneous equations graphically by finding their point of intersection.","questions":[{"answer":"$(1, 5)$","question":"The lines $y = 2x + 1$ and $y = -x + 4$ intersect at which point?"},{"answer":"$(1, 3)$","question":"The lines $y = 3x - 2$ and $y = x + 4$ intersect at which point?"},{"answer":"$(0, 1)$","question":"Find the point of intersection of the lines $y = 2x + 3$ and $y = -x + 6$. Show your steps."}],"difficulty":"enabling"}


example_id: lp_01K94Q096YW3D7DTMX9P109TSF_01K94Q0AK8XSNED90K2PJKDNAS_CONTEMPLATIVE_QUESTION
skills: ["Defining a function","Understanding and applying function notation"]
skill_ids: ["ZEUCDm9sFWJgXHSQqKbc","ohtqIqrWYM3phfAqYrEG"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Tigers
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a function $f(x)$ that represents the cost of buying $x$ items, each costing $\\$5$. How does $f(x)$ change if the price per item increases to $\\$6$?","teacherTips":["Guide students to define $f(x) = 5x$ for the initial cost function.","Encourage students to redefine $f(x)$ for the increased price, $f(x) = 6x$.","Discuss how the slope changes when the price per item increases."],"difficulty":"mild"}


example_id: lp_01K94Q096YW3D7DTMX9P109TSF_01K94Q0AK8XSNED90K27QZ13HW_ACTIVITY
skills: ["Defining a function","Understanding and applying function notation"]
skill_ids: ["ZEUCDm9sFWJgXHSQqKbc","ohtqIqrWYM3phfAqYrEG"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Tigers
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Function Machine Challenge\nYou’re designing a secret function machine. Can others figure out your machine’s rule?","scenario":"Steps\n1. Each team creates a 'function rule' (e.g., $f(x) = 2x + 3$).\n2. Write $5$ inputs and calculate their outputs using your rule.\n3. Share only your inputs and outputs with another team.\n4. The other team guesses your function rule based on the data.\n5. Switch roles and repeat for multiple rounds!","steps":["Discussion\n• Why can each input have only one output in a function?\n• How does function notation make it easier to describe rules?","Differentiation Opportunities\n• Support: Provide examples of simple functions like $f(x) = x + 1$ to guide students.\n• Extend: Challenge students to include exponents or fractions in their function rules."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94Q096YW3D7DTMX9P109TSF_01K94Q0AK8XSNED90K2VC0BC2V_EXIT_TICKET
skills: ["Defining a function","Understanding and applying function notation"]
skill_ids: ["ZEUCDm9sFWJgXHSQqKbc","ohtqIqrWYM3phfAqYrEG"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Tigers
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$7$","question":"If a tiger's roar can be heard up to $x$ miles and $f(x) = 2x + 1$, what is $f(3)$?"},{"answer":"$6$","question":"If a tiger's daily food consumption $f(x)$ in pounds is modeled by $f(x) = x^2 - 3x + 2$, what is $f(4)$?"},{"answer":"$2$","question":"If $f(x) = 5x + 4$ represents a tiger's running speed in mph given $x$ minutes of rest and $f(2) = g(k)$, find $k$ if $g(k) = 14$."}]}


example_id: lp_01K94Q096YW3D7DTMX9P109TSF_01K94Q0AK8XSNED90K23BFHVSX_APPLICATION
skills: ["Defining a function","Understanding and applying function notation"]
skill_ids: ["ZEUCDm9sFWJgXHSQqKbc","ohtqIqrWYM3phfAqYrEG"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Tigers
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Tracking Tiger Populations with Functions","example1Header":"Situation\nWildlife conservationists track tiger populations over time. They use functions to model population changes based on factors like births, deaths, and habitat conditions.","example1Body":"Example\nConservationists use $f(x) = 2x + 5$ to predict tiger births. In $3$ years: $f(3) = 2(3) + 5 = 11$ tigers. This helps plan conservation efforts.","example2Header":"","example2Body":""}


example_id: lp_01K94Q096YW3D7DTMX9P109TSF_01K94Q0AK8XSNED90K2T9FQF11_THOUGHT_SPARKER
skills: ["Defining a function","Understanding and applying function notation"]
skill_ids: ["ZEUCDm9sFWJgXHSQqKbc","ohtqIqrWYM3phfAqYrEG"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Tigers
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A wildlife conservation group tracks the population of tigers in a forest using the function $P(t) = 50 + 12t$, where $P(t)$ is the population after $t$ years since $2020$.","firstSentence":"How would you use this function to find the tiger population in the year $2025$?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the meaning of each part of the function, including the constant and the coefficient of $t$.","Encourage students to identify the value of $t$ for the year $2025$ before substituting into the function.","Use examples of other linear functions to reinforce the concept of input-output relationships."]}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q27B687F2P8J6RVD6XAK0_CONTEMPLATIVE_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A function maps $x$ to $f(x)$. Create your own function $f(x)$ and choose 5 values of $x$. Show inputs and outputs. How does $f(x)$ behave?","teacherTips":["For $f(x) = x + 2$, inputs $x = 0, 1, 2$, outputs are $f(x) = 2, 3, 4$. Function adds $2$ to $x$."],"difficulty":"mild"}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q27B687F2P8J6S1FP4A8M_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"If $f(x) = x^2 - 4x + 7$, what is the value of $f(2a)$?","answerOptions":["$4a^2 - 8a + 7$","$4a^2 - 16a + 7$","$2a^2 - 4a + 7$","$4a^2 - 4a + 7$"],"answer":"$4a^2 - 8a + 7$","difficulty":"spicy"}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q27B687F2P8J6RXXAD8GQ_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"If $f(x) = 3x + 5$, what is $f(4)$?","answerOptions":["$12$","$17$","$19$","$14$"],"answer":"$17$","difficulty":"hot"}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q27B687F2P8J6R2R9HFGY_MULTIPLE_CHOICE_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following best defines a function?","answerOptions":["A relation where each input has exactly one output","A relation where outputs can have multiple inputs","A relation where inputs can have multiple outputs","A relation where all inputs are equal to all outputs"],"answer":"A relation where each input has exactly one output","difficulty":"mild"}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q27B687F2P8J6R7NYVRA1_CONTEMPLATIVE_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A function assigns an output to each input. Create a function rule for calculating a total cost if each item costs $x$ dollars and a fixed fee of $y$ dollars is added. Explain your reasoning.","teacherTips":["A function could be $f(x) = x + y$, where $x$ is item cost and $y$ is the fixed fee added."],"difficulty":"mild"}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q26WZYVVCKHA84TBH59QS_SCAFFOLDED_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore functions and function notation to identify relationships and solve complex problems.","questions":[{"answer":"$h(x) = 4x + 10$","question":"If $f(x) = 3x^2 - 2x + 5$, what is $f(2)$?"},{"answer":"$13$","question":"If $f(x) = 2x + 3$ and $g(x) = x^2 - 1$, find $f(g(2))$."},{"answer":"$9$","question":"Define a function $h(x)$ that represents the total cost in dollars of buying $x$ items, each costing $\\$4$, with a fixed shipping fee of $\\$10$.\nExplain why your function accurately models the scenario."}],"difficulty":"extension"}


example_id: lp_01K94Q25TXC39QVGQAB5TQRKAN_01K94Q26WZYVVCKHA84QREZ44J_SCAFFOLDED_QUESTION
skills: ["Understanding and applying function notation","Defining a function"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG","ZEUCDm9sFWJgXHSQqKbc"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn about functions and how to use function notation. A function connects inputs to outputs using a rule.","questions":[{"answer":"$0$","question":"If a function takes $x$ and adds $3$, what does $f(2)$ equal?"},{"answer":"$2$","question":"If $f(x) = 2x + 1$, what does $f(3)$ equal?"},{"answer":"$3$","question":"If $f(x) = x^2 - 4$, what is $f(-2)$?"}],"difficulty":"enabling"}


example_id: lp_01K94QB6DF5JMZ1EYZKWKGXTY9_01K94QB78KCC5TKQJ91Q6SBE3W_THOUGHT_SPARKER
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Mount Everest
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"On Mount Everest, the temperature at various elevations is recorded. At $3\\,000$ m, it is $-5^\\circ$C, and at $7\\,000$ m, it is $-15^\\circ$C, but at $5\\,000$ m and $8\\,000$ m, the temperature is also $-15^\\circ$C.","firstSentence":"Do you think the relationship between elevation and temperature on Mount Everest is one-to-one?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to define what makes a function one-to-one before discussing the scenario.","Ask students to explain how repeated temperature values at different elevations affect the classification of the function.","Use a graph to visually represent the relationship between elevation and temperature to support reasoning."]}


example_id: lp_01K94QB6DF5JMZ1EYZKWKGXTY9_01K94QB78KCC5TKQJ911FDN61A_APPLICATION
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Mount Everest
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Mapping Climbers on Mount Everest","example1Header":"Situation\nMount Everest expedition planners use functions to assign climbers to camps. They track climbers' progress, ensuring each has a unique camp or shares it with others.","example1Body":"Example\nExpedition planners map $4$ climbers: Climber A to Camp 1, B to Camp 2, C to Camp 2, and D to Camp 3. B and C share a camp, so the function is many-to-one.","example2Header":"","example2Body":""}


example_id: lp_01K94QB6DF5JMZ1EYZKWKGXTY9_01K94QB78KCC5TKQJ9128KVBV2_ACTIVITY
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Mount Everest
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Function Detective\nYou are detectives solving the mystery of one-to-one and many-to-one functions!","scenario":"Steps\n1. Write three equations like $y = x^2$, $y = 2x$, $y = |x|$ in your notebook.\n2. For each equation, create a table of values for $x$ from $-3$ to $3$.\n3. Plot the points from each table on graph paper to draw the functions.\n4. Analyze: Does each $x$ give a unique $y$? Is each $y$ from one $x$?\n5. Label functions as one-to-one or many-to-one based on your analysis.","steps":["Discussion\n• What patterns help identify a one-to-one function?\n• Why does $y = x^2$ fail to be one-to-one?","Differentiation Opportunities\n• Support: Focus on simpler functions like $y = x + 1$ or $y = 2x$ only.\n• Extend: Test more complex functions like $y = x^3 - x$ or $y = \\sin(x)$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94QB6DF5JMZ1EYZKWKGXTY9_01K94QB78KCC5TKQJ91K2QND8Y_CONTEMPLATIVE_QUESTION
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Mount Everest
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a rule for a function. How would you test if it is one-to-one or many-to-one? Explain why.","teacherTips":["Encourage students to test different inputs to see if outputs are unique.","Discuss examples of one-to-one and many-to-one functions for clarity.","Use graphs or tables to visualize the relationship between inputs and outputs."],"difficulty":"mild"}


example_id: lp_01K94QB6DF5JMZ1EYZKWKGXTY9_01K94QB78KCC5TKQJ91T90NXAN_EXIT_TICKET
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Mount Everest
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Many-to-one","question":"If a climber's altitude on Mount Everest is given by $f(x) = x^2$, where $x$ represents time in hours, is $f(x)$ one-to-one?"},{"answer":"One-to-one","question":"The altitude of climbers on Mount Everest is modeled by $g(x) = 3x + 5$. Is $g(x)$ a one-to-one function?"},{"answer":"Many-to-one","question":"A climber's oxygen levels on Mount Everest are given by $h(x) = x^3 - x$. Is $h(x)$ one-to-one?"}]}


example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBS1X9V6HS7G49DNTSPX7_MULTIPLE_CHOICE_QUESTION
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a function, if every input has a unique output, what type of function is it?","answerOptions":["One-to-one","Many-to-one","Not a function","Relation"],"answer":"One-to-one","difficulty":"mild"}


example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBS1X9V6HS7G49XR0D1DN_CONTEMPLATIVE_QUESTION
skills: ["Determining if a function is one-to-one or many-to-one"]
skill_ids: ["yvTLb6aZV69ibrRz0zSt"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a vending machine where each button selects a unique item. How would you ensure the machine's button-to-item mapping is one-to-one? Could it ever be many-to-one? Explain your reasoning.","teacherTips":["A one-to-one mapping ensures each button selects a unique item. Many-to-one occurs if buttons share outputs."],"difficulty":"mild"}


