# prompt_examples

example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBS1X9V6HS7G49R7NZ33E_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":"Which of the following is a one-to-one function?","answerOptions":["Each input maps to a unique output.","An input maps to multiple outputs.","Multiple inputs map to one output.","Outputs map to multiple inputs."],"answer":"Each input maps to a unique output.","difficulty":"mild"}


example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBS1X9V6HS7G49JX712EK_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":"A function where each input has a unique output is called what?","answerOptions":["one-to-one","many-to-one","not a function","relation"],"answer":"one-to-one","difficulty":"mild"}


example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBS1X9V6HS7G4A3T3M8MS_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: hot
example_output_json:
{"question":"Create a rule for a function. How would you check if it is one-to-one or many-to-one? Justify your reasoning.","teacherTips":["Test inputs: if distinct inputs give distinct outputs, it is one-to-one; otherwise, many-to-one."],"difficulty":"hot"}


example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBRM86E5DS4PTDVV6G75C_SCAFFOLDED_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: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore whether the following functions are one-to-one or many-to-one, using reasoning and mathematical analysis.","questions":[{"answer":"Determine injectivity using algebra and the horizontal line test.","question":"Determine whether the function $f(x) = x^2 - 3x + 2$ is one-to-one or many-to-one."},{"answer":"Many-to-one","question":"Is the piecewise function $f(x) = \\begin{cases} x + 1, \u0026 x \\leq 0 \\ 2x - 1, \u0026 x \u003e 0 \\end{cases}$ one-to-one or many-to-one?"},{"answer":"One-to-one","question":"Explain how you would determine if any given function is one-to-one or many-to-one. Include examples to support your reasoning."}],"difficulty":"extension"}


example_id: lp_01K94QBQX61WNZ9NBQANSW7SXZ_01K94QBRM86E5DS4PTDRFJ6FV5_SCAFFOLDED_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: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn to identify if a function is one-to-one or many-to-one. A one-to-one function maps each input to a unique output.","questions":[{"answer":"One-to-one","question":"Which of the following is an example of a one-to-one function?"},{"answer":"Each input maps to a unique output.","question":"Consider the function $f(x) = x^2$.\nIs this function one-to-one or many-to-one?"},{"answer":"Two inputs can share the same output.","question":"The function $g(x) = 3x + 5$ maps $x$ to $y$. Is this function one-to-one or many-to-one? Explain your reasoning."}],"difficulty":"enabling"}


example_id: lp_01K94QGZE99EQWZBC5HG7FFS25_01K94QH0HCNFSCGDN9TJZAPH23_THOUGHT_SPARKER
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: High Jump
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"In a high jump competition, the height of the bar, $h$, in inches is raised linearly over time, $t$, in minutes. This relationship is modeled by $h = 36 + 2t$, where $36$ inches is the starting height, and the bar is raised by $2$ inches every minute.","firstSentence":"How could you determine which graph matches this equation?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify key features of the equation, like the y-intercept and slope.","Ask students to consider how the slope affects the steepness of the line on the graph.","Discuss how to use points from the equation to verify which graph is correct."]}


example_id: lp_01K94QGZE99EQWZBC5HG7FFS25_01K94QH0HCNFSCGDN9SY72DY2B_APPLICATION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: High Jump
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Predicting High Jump Heights with Graphs","example1Header":"Situation\nHigh jump coaches use graphs of linear equations to predict how a jumper’s height improves with practice over time. This helps them set realistic goals and training plans.","example1Body":"Example\nIf the jumper's height follows $y = 0.2x + 1.5$, the graph starts at $1.5$ (intercept) and rises $0.2$ meters per week (slope). For $x = 5$, $y = 2.5$ meters.","example2Header":"","example2Body":""}


example_id: lp_01K94QGZE99EQWZBC5HG7FFS25_01K94QH0HCNFSCGDN9T2DA7ZMH_ACTIVITY
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: High Jump
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Graph Match Challenge\nTeams compete to match linear equations to graphs they create and solve.","scenario":"Steps\n1. Each team writes $3$ linear equations (e.g., $y=2x+1$) on slips of paper.\n2. Swap equations with another team and graph the equations on graph paper.\n3. Label each graph with a unique letter (e.g., A, B, C).\n4. Return graphs to the original team to match with the equations.\n5. Score $1$ point for each correct match. Highest score wins!","steps":["Discussion\n• What role does the slope play in identifying graphs?\n• How does the y-intercept help differentiate graphs?","Differentiation Opportunities\n• Support: Provide equations with simpler slopes (e.g., integers only).\n• Extend: Include equations with fractions or negative slopes for extra challenge."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94QGZE99EQWZBC5HG7FFS25_01K94QH0HCNFSCGDN9TDC7H4JM_CONTEMPLATIVE_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: High Jump
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You have 3 equations: $y = 2x + 1$, $y = -x + 4$, $y = \\frac{1}{2}x - 3$. Sketch possible graphs. How would you match each equation to its graph?","teacherTips":["Explain how slopes and intercepts affect the graph's direction and position.","Encourage students to test by substituting points in each equation.","Discuss differences between positive, negative, and fractional slopes."],"difficulty":"mild"}


example_id: lp_01K94QGZE99EQWZBC5HG7FFS25_01K94QH0HCNFSCGDN9TMKKX36W_EXIT_TICKET
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: High Jump
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$1$","question":"The graph of the high jumper's height follows $y = 2x + 1$. What is the $y$-intercept of this line?"},{"answer":"Downward","question":"The height $y$ of a high jumper over time $x$ is given by $y = -\\frac{1}{2}x + 4$. Does the graph slope upward or downward?"},{"answer":"$\\left(\\frac{2}{3}, 0\\right)$","question":"A high jumper's trajectory follows $y = 3x - 2$. At what point does the graph cross the $x$-axis?"}]}


example_id: lp_01K94QHETR668B6VDTR7181WW9_01K94QHG46ER8X6ZS9E1MFB3B6_MULTIPLE_CHOICE_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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 equations represents a line with a slope of $2$ and a $y$-intercept of $-3$?","answerOptions":["$y = 2x - 3$","$y = -2x + 3$","$y = 3x - 2$","$y = -3x + 2$"],"answer":"$y = 2x - 3$","difficulty":"mild"}


example_id: lp_01K94QHETR668B6VDTR7181WW9_01K94QHG46ER8X6ZS9E9S73VP9_MULTIPLE_CHOICE_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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: spicy
example_output_json:
{"question":"Which equation represents a line passing through $(2, 5)$ and having a slope of $-3$?","answerOptions":["$y = -3x + 11$","$y = -3x - 1$","$y = 3x - 1$","$y = 3x + 11$"],"answer":"$y = -3x + 11$","difficulty":"spicy"}


example_id: lp_01K94QHETR668B6VDTR7181WW9_01K94QHG46ER8X6ZS9EBTMBW4Y_CONTEMPLATIVE_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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":"Design three linear equations. How would you graph them to ensure they intersect at one point? Explain.","teacherTips":["Ensure the equations have different slopes. Solve simultaneously to find the intersection point."],"difficulty":"spicy"}


example_id: lp_01K94QHETR668B6VDTR7181WW9_01K94QHG46ER8X6ZS9E9E4773Z_CONTEMPLATIVE_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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":"Design a linear equation. Sketch its graph and explain how you matched the line to your equation.","teacherTips":["The slope $m$ sets the steepness, and $b$ gives the $y$-intercept where the line crosses $y$-axis."],"difficulty":"mild"}


example_id: lp_01K94QHETR668B6VDTR7181WW9_01K94QHFP52EEGTTY16B4T398X_SCAFFOLDED_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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 match linear equations with their graphs by understanding slopes and y-intercepts.","questions":[{"answer":"The graph rises steeply and crosses at $-2$.","question":"What is the y-intercept of the equation $y = 2x + 3$?\nHint: The y-intercept is the constant term in the equation."},{"answer":"$2$","question":"What is the slope of the equation $y = -x + 4$?\nHint: The slope is the coefficient of $x$."},{"answer":"$3$","question":"The equation $y = 3x - 2$ has a slope of $3$ and a y-intercept of $-2$.\nDescribe how the graph will look based on this information."}],"difficulty":"enabling"}


example_id: lp_01K94QHETR668B6VDTR7181WW9_01K94QHFP52EEGTTY16DGE5HRC_SCAFFOLDED_QUESTION
skills: ["Matching linear equations with their graphs"]
skill_ids: ["1wVDSzIDfAg9f5eNEn4j"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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 the connections between linear equations and their graphs by analyzing slopes, intercepts, and transformations.","questions":[{"answer":"The lines have the same y-intercept but different slopes, causing different directions and steepness.","question":"For the equation $y = -3x + 5$, what is the slope and the y-intercept?"},{"answer":"Slope: $-3$, y-intercept: $5$","question":"If the equation $y = -3x + 5$ is changed to $y = -3x - 2$, what happens to the graph?"},{"answer":"The line shifts down by $7$ units.","question":"Compare the graphs of $y = 2x + 3$ and $y = -\\frac{1}{2}x + 3$. How are they similar, and how are they different? Justify your answer."}],"difficulty":"extension"}


example_id: lp_01K94QQME3G661N3RCNX8QNE71_01K94QQNK33MAJ3ZYNAQE6P767_THOUGHT_SPARKER
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
context: Clownfish
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A young clownfish grows by $0.5$ cm per month, starting at a length of $2$ cm when it is born. A table shows its length over the first $6$ months: $x$ (months): $0, 1, 2, 3, 4, 5, 6$; $y$ (length in cm): $2, 2.5, 3, 3.5, 4, 4.5, 5$.","firstSentence":"How could you create a linear equation to represent the relationship shown in the table?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the rate of change (slope) and starting value (y-intercept) from the table.","Ask students to substitute values from the table into their equation to check for accuracy.","Discuss the real-world meaning of the slope and y-intercept in the context of clownfish growth."]}


example_id: lp_01K94QQME3G661N3RCNX8QNE71_01K94QQNK33MAJ3ZYNA8J9PYWB_APPLICATION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
context: Clownfish
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Tracking Clownfish Growth Patterns","example1Header":"Situation\nMarine biologists monitor clownfish growth over time. They use $x$ and $y$ tables to create equations that predict size based on age.","example1Body":"Example\nFrom the table: $x$ (age in months) as $1, 2, 3, 4$ and $y$ (length in cm) as $3, 5, 7, 9$. The equation $y = 2x + 1$ shows how clownfish grow over time.","example2Header":"","example2Body":""}


example_id: lp_01K94QQME3G661N3RCNX8QNE71_01K94QQNK33MAJ3ZYNABX6S5R7_ACTIVITY
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
context: Clownfish
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Business Equation Builder\nYour team is running a store. Use equations and tables to track sales!","scenario":"Steps\n1. Choose a product price (e.g., $y = 5x$ where $x$ is items sold).\n2. Create a table for $x = 1$ to $5$ to calculate total sales $y$.\n3. Swap tables with another team and find their equation.\n4. Check each other's work for accuracy and correct mistakes.\n5. Teams earn points for correct tables and equations!","steps":["Discussion\n• How does the equation show the relationship between $x$ and $y$?\n• What patterns did you notice in the $x$ and $y$ tables?","Differentiation Opportunities\n• Support: Limit $x$ values to $1$ through $3$ and use simple equations (e.g., $y = 2x$).\n• Extend: Include equations with constants (e.g., $y = 3x + 2$) and negative values for $x$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94QQME3G661N3RCNX8QNE71_01K94QQNK33MAJ3ZYNA5XZW277_WARM_UP_QUESTIONS_WITH_CONTEXT
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
context: Clownfish
class_year: 8
country: US
period_number: 8
node_type: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"You're a marine biologist tracking clownfish movements using coordinates on a grid to study their habitat patterns.","questions":[{"answer":"$4$","question":"A clownfish is spotted at $(4, 7)$. What is the $x$-coordinate of its location?"},{"answer":"$3$","question":"A clownfish moves from $(3, 5)$ to $(3, 8)$. How far did it travel vertically?"},{"answer":"$y = 2x$","question":"A clownfish's positions are $(1, 2)$, $(2, 4)$, and $(3, 6)$. What is the pattern in the $y$-values as $x$ increases?"}]}


example_id: lp_01K94QQME3G661N3RCNX8QNE71_01K94QQNK33MAJ3ZYNAXXE8QZJ_EXIT_TICKET
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
context: Clownfish
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$x=1, y=2; x=2, y=4; x=3, y=6$","question":"If a clownfish swims with speed $y = 2x$, create an $x$ and $y$ table for $x = 1, 2, 3$."},{"answer":"$x=0, y=1; x=2, y=7; x=4, y=13$","question":"A clownfish swims following $y = 3x + 1$. Fill the table for $x = 0, 2, 4$."},{"answer":"$y = 3x + 2$","question":"A clownfish swims such that $x$ and $y$ are related as $x = 1, y = 5$; $x = 2, y = 8$; $x = 3, y = 11$. What is the equation?"}]}


example_id: lp_01K94QQME3G661N3RCNX8QNE71_01K94QQNK33MAJ3ZYNAJXWW3FX_CONTEMPLATIVE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
context: Clownfish
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A car rental company charges $\\$50$ per day plus $\\$0.20$ per mile. Create an $x$ and $y$ table showing total cost $y$ for $x$ miles driven. Then write a linear equation connecting $x$ and $y$.","teacherTips":["Remind students $y = 50 + 0.20x$ connects miles ($x$) to total cost ($y$).","Encourage creating an $x$ and $y$ table with realistic $x$ values (e.g., $10, 20, 50$).","Discuss how the equation models the situation and checks the table."],"difficulty":"mild"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6YQQC8N09YS2N2XPMD4_MULTIPLE_CHOICE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"For the equation $y = 2x^2 - 3$, what is the value of $y$ when $x = -2$, $x = 0$, and $x = 3$?","answerOptions":["$y = 5, -3, 15$","$y = 8, -3, 21$","$y = 5, -3, 21$","$y = 8, -3, 15$"],"answer":"$y = 5, -3, 21$","difficulty":"spicy"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6YQQC8N09YS27FQJ1GE_CONTEMPLATIVE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create an $x$ and $y$ table for the equation $y = 3x + 2$. Choose five $x$ values and explain your reasoning.","teacherTips":["Substitute $x$ into $y = 3x + 2$ to find $y$. Example: if $x = 1$, $y = 3(1) + 2 = 5$."],"difficulty":"mild"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6YQQC8N09YS2BDWWZ8M_MULTIPLE_CHOICE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Given the equation $y = 2x + 1$, what is the value of $y$ when $x = 3$?","answerOptions":["$5$","$6$","$7$","$8$"],"answer":"$7$","difficulty":"mild"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6YQQC8N09YS2GYTVH5W_MULTIPLE_CHOICE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Given the equation $y = 2x + 3$, what is the value of $y$ when $x = 4$?","answerOptions":["$5$","$8$","$11$","$15$"],"answer":"$11$","difficulty":"hot"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6YQQC8N09YS1MBBJSKK_CONTEMPLATIVE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create an $x$ and $y$ table for a linear relationship of your choice. Write the equation. How would you verify your equation works for all values in your table? Can you find another table with a different equation that intersects yours?","teacherTips":["Use $y = mx + b$, test each $x$ and $y$ pair in the table. Graph equations to verify intersections."],"difficulty":"spicy"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6YQQC8N09YS1J8SDJCY_MULTIPLE_CHOICE_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A table shows $x$ values of $1$, $2$, $3$, $4$ and $y$ values of $5$, $7$, $9$, $11$. What is the linear equation that represents this relationship?","answerOptions":["$y = x + 4$","$y = 2x + 3$","$y = 2x + 1$","$y = 3x + 2$"],"answer":"$y = 2x + 1$","difficulty":"hot"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6CG2XGTN8QFRGT48PK0_SCAFFOLDED_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore how to create $x$ and $y$ tables from equations and derive equations from tables of values","questions":[{"answer":"Answers may vary; reasoning must be provided.","question":"Complete the $x$-$y$ table for $y = 2x - 3$ when $x = -2, -1, 0, 1, 2$."},{"answer":"$(-7, -5, -3, -1, 1)$","question":"The $x$-$y$ table has points $(0, 4), (1, 7), (2, 10), (3, 13)$. What is the linear equation connecting $x$ and $y$?"},{"answer":"$y = 3x + 4$","question":"Explain how you can derive a linear equation from an $x$-$y$ table with any given set of points. Use examples to support your explanation."}],"difficulty":"extension"}


example_id: lp_01K94QR56HBRH5FVQYT4PWN882_01K94QR6CG2XGTN8QFRDCE0YY7_SCAFFOLDED_QUESTION
skills: ["Creating $x$ and $y$ tables from equations","Creating linear equations from $x$ and $y$ tables"]
skill_ids: ["FOYJUQQ5wHPSDIPjbiCg","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
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 create $x$ and $y$ tables from linear equations. An $x$ and $y$ table shows how $x$ and $y$ values are related.","questions":[{"answer":"$1$, $3$, $5$, $7$","question":"In the equation $y = 2x + 1$, what is $y$ when $x = 2$?"},{"answer":"$3$","question":"Complete this table for $y = 2x + 1$: If $x = 3$, what is $y$?\n$x$: $1$, $2$, $3$\n$y$: $3$, $5$, ?"},{"answer":"$4$","question":"Complete the $x$ and $y$ table for $y = 2x + 1$.\n$x$: $0$, $1$, $2$, $3$\n$y$: ?, ?, ?, ?"}],"difficulty":"enabling"}


example_id: lp_01K94QX4G37B23P9D36GZDZWPW_01K94QX5BX99PJ647MQ7X73R7A_APPLICATION
skill_ids: ["wseaBMeBpJyz2JpoUkg5","nCtCal5qaXaCRHyK5xrh"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Martial Arts
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Using Functions in Martial Arts Scoring","example1Header":"Situation\nIn martial arts tournaments, judges score points based on specific moves. The scoring system ensures that each move has one unique score to maintain fairness.","example1Body":"Example\nIf 'punch' is scored as both 1 and 3, this violates the rule of functions where each input (move) must map to one output (score). This system is not a function.","example2Header":"","example2Body":""}

skills:
["Determining whether a relation is a function graphically or algebraically","Creating $x$ and $y$ tables from graphs"]


example_id: lp_01K94QX4G37B23P9D36GZDZWPW_01K94QX5BX99PJ647MQZC5HBP8_THOUGHT_SPARKER
skill_ids: ["wseaBMeBpJyz2JpoUkg5","nCtCal5qaXaCRHyK5xrh"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Martial Arts
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A martial artist practices by alternating between punches and kicks, completing $3$ punches for every $2$ kicks in a minute.","firstSentence":"How could you determine if the relationship between punches and kicks is a function?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Ask students to create an $x$ and $y$ table showing punches and kicks per minute to explore the relationship.","Encourage students to use the vertical line test if they graph the relationship.","Discuss how a function assigns exactly one output for each input and check this definition against their table or graph."]}

skills:
["Determining whether a relation is a function graphically or algebraically","Creating $x$ and $y$ tables from graphs"]


example_id: lp_01K94QX4G37B23P9D36GZDZWPW_01K94QX5BX99PJ647MQT1DPNP8_CONTEMPLATIVE_QUESTION
skill_ids: ["wseaBMeBpJyz2JpoUkg5","nCtCal5qaXaCRHyK5xrh"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Martial Arts
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create a graph showing a relation with 5 points. Make an $x$ and $y$ table for the graph. Is it a function? Explain.","teacherTips":["Guide students to plot 5 points clearly on the graph.","Help students organize the $x$ and $y$ values into a table.","Discuss why each $x$-value must pair with only one $y$-value for it to be a function."],"difficulty":"mild"}

skills:
["Determining whether a relation is a function graphically or algebraically","Creating $x$ and $y$ tables from graphs"]


example_id: lp_01K94QX4G37B23P9D36GZDZWPW_01K94QX5BX99PJ647MR122SBAH_EXIT_TICKET
skill_ids: ["wseaBMeBpJyz2JpoUkg5","nCtCal5qaXaCRHyK5xrh"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Martial Arts
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"A martial artist tracks kicks performed in $x$ minutes as $(1, 30), (2, 60), (3, 90)$. Is this a function?"},{"answer":"$3, 6, 9, 12$","question":"A graph shows a martial artist breaking $x$ boards, where $y = 3x$. What values of $y$ correspond to $x = 1, 2, 3, 4$?"},{"answer":"No","question":"A coach records martial artist's punches $(1, 20), (2, 40), (2, 50)$. Is this relation a function?"}]}


example_id: lp_01K94QX4G37B23P9D36GZDZWPW_01K94QX5BX99PJ647MQCEH7BGR_ACTIVITY
skill_ids: ["wseaBMeBpJyz2JpoUkg5","nCtCal5qaXaCRHyK5xrh"]
subtopics: ["Functions \u0026 Relations"]
subtopic_ids: ["subtopic_01GTC0BNG539A4BDKP49E441XD"]
topic: Functions
topic_id: 56029c0d-a8c1-4852-8a96-805863d4f00e
context: Martial Arts
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Mystery Graph Challenge\nYou are detectives solving mysteries! Each graph hides clues to whether it represents a function.","scenario":"Steps\n1. Draw a graph on graph paper with at least $5$ points.\n2. Record the points in an $x$ and $y$ table.\n3. Check if any $x$ values repeat with different $y$ values.\n4. Decide if the graph is a function based on your table.\n5. Compare answers with another team and discuss findings!","steps":["Discussion\n• Why does a function have only one $y$ for each $x$?\n• What patterns help you quickly spot non-functions?","Differentiation Opportunities\n• Support: Provide a pre-drawn graph for students to focus on creating the table.\n• Extend: Challenge students to create graphs of non-functions and explain why they fail the test."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXRAPZSKCJBYQJ3WCV1F6_MULTIPLE_CHOICE_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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":"If $y = 2x$, what is the $y$ value when $x = 3$?","answerOptions":["$3$","$5$","$6$","$9$"],"answer":"$6$","difficulty":"mild"}

skills:
["Creating $x$ and $y$ tables from graphs","Determining whether a relation is a function graphically or algebraically"]


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXRAPZSKCJBYQJD8P3VME_CONTEMPLATIVE_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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: spicy
example_output_json:
{"question":"Choose a graph of a real-world situation (e.g., distance vs. time). How would you create an $x$-$y$ table from the graph? What strategies ensure accurate points and calculations?","teacherTips":["Identify key points on the graph, record $x$ and $y$ values, and ensure units and context match."],"difficulty":"spicy"}

skills:
["Creating $x$ and $y$ tables from graphs","Determining whether a relation is a function graphically or algebraically"]


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXRAPZSKCJBYQJ7KGRJBE_MULTIPLE_CHOICE_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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":"A graph shows $y = 2x + 1$. What is $y$ when $x = 3$?","answerOptions":["$5$","$6$","$7$","$8$"],"answer":"$7$","difficulty":"mild"}

skills:
["Creating $x$ and $y$ tables from graphs","Determining whether a relation is a function graphically or algebraically"]


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXRAPZSKCJBYQH9ECEY9T_MULTIPLE_CHOICE_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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 relations is a function?","answerOptions":["$y = 2x + 3$","$x^2 + y^2 = 16$","$y = \\pm \\sqrt{x}$","$x = 5$"],"answer":"$y = 2x + 3$","difficulty":"mild"}


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXRAPZSKCJBYQHAVVE94K_CONTEMPLATIVE_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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":"Design a graph with at least 5 points. How would you decide if it represents a function? Explain.","teacherTips":["If each $x$ has one $y$, it's a function. Use the vertical line test for confirmation."],"difficulty":"mild"}


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXQW3PYE898G735SVT150_SCAFFOLDED_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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":"Analyze a relation, construct its table of values, and determine its function properties.","questions":[{"answer":"No, it is not a function.","question":"Construct a table of values for the relation $y = 2x - 3$, where $x = -2, -1, 0, 1, 2$."},{"answer":"$(-2, -7), (-1, -5), (0, -3), (1, -1), (2, 1)$","question":"The graph of $y = 2x - 3$ is a straight line. Is this relation a function? Justify algebraically."},{"answer":"Yes, it is a function.","question":"Consider the relation $x^2 + y^2 = 4$.\nIs this relation a function? Justify your answer graphically and algebraically."}],"difficulty":"extension"}


example_id: lp_01K94QXQ0F221E0TWRM2DS9JKT_01K94QXQW3PYE898G72Z97M6BT_SCAFFOLDED_QUESTION
skill_ids: ["nCtCal5qaXaCRHyK5xrh","wseaBMeBpJyz2JpoUkg5"]
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 how to create $x$ and $y$ tables and determine whether a relation is a function using graphs.","questions":[{"answer":"Yes, it is a function","question":"If $y = 2x + 3$, what is $y$ when $x = 2$?"},{"answer":"$4$","question":"Does a graph where a vertical line touches it in two places represent a function?\nUse the vertical line test."},{"answer":"$5$","question":"Does the equation $y = x^2$ represent a function? Explain your reasoning."}],"difficulty":"enabling"}


example_id: lp_01K94SGJVRAY8YD5W57R8QB9FW_01K94SGKWYPT3X75QG6XYCNBW2_THOUGHT_SPARKER
skill_ids: ["bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6","PDMK31LsJTBBdlsqNrVr"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"For Halloween, you create decorations by cutting out pumpkin shapes on orange paper. One pumpkin is reflected across the $y$-axis, and another is a duplicate that is dilated to twice its original size.","firstSentence":"How could you describe the differences between the reflected and dilated pumpkins based on their shapes and positions?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Use graph paper to help students visualize the reflections and dilations.","Encourage students to identify which properties of the shapes remain unchanged and which change after transformations.","Discuss the vocabulary of transformations like 'reflected,' 'dilated,' and 'axis' for clarity."]}

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


example_id: lp_01K94SGJVRAY8YD5W57R8QB9FW_01K94SGKWYPT3X75QG67TEN862_APPLICATION
skill_ids: ["bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6","PDMK31LsJTBBdlsqNrVr"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Reflections in Halloween Decorations","example1Header":"Situation\nHalloween designers create spooky window decorations. They use reflections to ensure symmetrical and eerie patterns for houses and storefronts.","example1Body":"Example\nTo reflect triangle $A(2, 3)$, $B(4, 1)$, $C(3, 5)$ across the $y$-axis, designers flip $x$-values: $A(-2, 3)$, $B(-4, 1)$, $C(-3, 5)$. This creates a symmetrical design.","example2Header":"","example2Body":""}

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


example_id: lp_01K94SGJVRAY8YD5W57R8QB9FW_01K94SGKWYPT3X75QG6DNBBCXB_ACTIVITY
skill_ids: ["bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6","PDMK31LsJTBBdlsqNrVr"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Transform It Challenge!\nYour team is transforming shapes on a grid to unlock the next level!","scenario":"Steps\n1. Draw a $10 \\times 10$ grid on paper and place a triangle at $(2,3)$, $(4,3)$, and $(3,5)$.\n2. Reflect the triangle across the $x$-axis and label the new coordinates.\n3. Dilate the reflected triangle by a scale of $2$ from the origin and label it.\n4. Repeat with a new triangle of your choice. Earn points for correct transformations!\n5. Compare shapes with other teams to verify answers and discuss strategies.","steps":["Discussion\n• How does a reflection affect the coordinates of a shape?\n• What happens to the size and position during dilation?","Differentiation Opportunities\n• Support: Use smaller grids and simpler shapes (e.g., squares) for practice.\n• Extend: Combine reflections and dilations with rotations for more challenge."],"discussion":[],"differentiation":{"support":"","extend":""}}

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


example_id: lp_01K94SGJVRAY8YD5W57R8QB9FW_01K94SGKWYPT3X75QG6TK80ZN3_CONTEMPLATIVE_QUESTION
skill_ids: ["bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6","PDMK31LsJTBBdlsqNrVr"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a pattern using shapes. Reflect some across the $x$-axis or $y$-axis, and dilate others. How does your pattern change with each transformation?","teacherTips":["Encourage students to sketch shapes before and after transformations.","Discuss how reflections and dilations change shape positions or sizes.","Ask students to explain transformations in their own words."],"difficulty":"mild"}


example_id: lp_01K94SGJVRAY8YD5W57R8QB9FW_01K94SGKWYPT3X75QG728E1E7Q_EXIT_TICKET
skill_ids: ["bjlSlQ0HinkyPVfklcTo","TyU67kr75ULQT84bAcQ6","PDMK31LsJTBBdlsqNrVr"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Halloween
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$(3, -5)$","question":"A pumpkin-shaped pattern is reflected across the $x$-axis. If a point on the pattern is $(3, 5)$, what is the reflected point's coordinate?"},{"answer":"$(4, 8)$","question":"A bat decoration at $(2, 4)$ is dilated by a scale factor of $2$ from the origin. Where is the new position of the bat?"},{"answer":"$(4, -6)$","question":"A witch's broomstick at $(-4, 6)$ is first reflected across the $x$-axis, then the $y$-axis. What is its final position?"}]}


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH86RVQHYHN8PG7JHA0B7_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What are the coordinates of the point $(5, -3)$ after being reflected across the $x$-axis, then the $y$-axis?","answerOptions":["$(-5,3)$","$(5,3)$","$(-5,-3)$","$(5,-3)$"],"answer":"$(-5,3)$","difficulty":"hot"}

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


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH86RVQHYHN8PG2WEG9WC_CONTEMPLATIVE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A rectangle is reflected over the $y$-axis. How would you determine the new coordinates of its vertices? Could the reflected shape look different? Why or why not?","teacherTips":["Flip the $x$-coordinates' signs; the reflected shape is congruent and does not change its appearance."],"difficulty":"mild"}

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


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH86RVQHYHN8PHNPY38FZ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following describes a dilated shape?","answerOptions":["The shape is flipped over a line","The shape is moved to a new position","The size of the shape is changed","The shape is turned around a point"],"answer":"The size of the shape is changed","difficulty":"mild"}

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


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH86RVQHYHN8PHQS8BCNC_CONTEMPLATIVE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You see a triangular sign and its dilated version. How could you confirm the shapes are similar?","teacherTips":["Check corresponding angles are equal and side lengths have the same ratio."],"difficulty":"hot"}


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH86RVQHYHN8PH5Q9VPNB_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"The point $(3, -5)$ is reflected across the $x$-axis, then across the $y$-axis. What are the coordinates of the resulting point?","answerOptions":["$(-3, -5)$","$(-3, 5)$","$(3, 5)$","$(3, -5)$"],"answer":"$(-3, 5)$","difficulty":"spicy"}


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH86RVQHYHN8PH24YEAWM_MULTIPLE_CHOICE_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What are the coordinates of the point $(-5, 3)$ after being reflected across the $x$-axis?","answerOptions":["$(-5,-3)$","$(5,3)$","$(-5,3)$","$(5,-3)$"],"answer":"$(-5,-3)$","difficulty":"hot"}


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH6N5R9KCJ7TWKB578PRR_SCAFFOLDED_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 shapes change when they are reflected across the $x$-axis or the $y$-axis.","questions":[{"answer":"$(3, 2)$","question":"When a shape is reflected across the $x$-axis, what happens to its $y$-coordinates?\nHint: Reflecting flips the shape vertically."},{"answer":"They stay the same","question":"When a shape is reflected across the $y$-axis, what happens to its $x$-coordinates?\nHint: The shape flips horizontally."},{"answer":"They double","question":"If a point $(3, -2)$ is reflected across the $x$-axis, what are its new coordinates?\nHint: Think about what happens to the $y$-coordinate."}],"difficulty":"enabling"}


example_id: lp_01K94SH5V9C959SNR57ZT6ZJG4_01K94SH6N5R9KCJ7TWKEFNKN0Z_SCAFFOLDED_QUESTION
skill_ids: ["PDMK31LsJTBBdlsqNrVr","TyU67kr75ULQT84bAcQ6","bjlSlQ0HinkyPVfklcTo"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore reflections and dilations: Analyze transformations of shapes across axes and their geometric properties.","questions":[{"answer":"The rectangle is congruent but rotated $180^\\circ$.","question":"A point $P(3, 5)$ is reflected across the $x$-axis. What are the coordinates of the reflected point?"},{"answer":"$(3, -5)$","question":"A triangle has vertices $A(2, 3)$, $B(4, -1)$, and $C(1, -2)$. After reflecting it across the $y$-axis, it is dilated by a factor of $2$. What are the new coordinates of $A$?"},{"answer":"$(-4, 6)$","question":"A rectangle is reflected across the $x$-axis and then the $y$-axis. Explain why the resulting rectangle is congruent to the original, and discuss any changes in orientation."}],"difficulty":"extension"}


example_id: lp_01K94SNTMNQN3C1ETT016FGCBX_01K94SNVGNBQ0GT0R0VWCQAPH1_EXIT_TICKET
skill_ids: ["92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Flowers
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"If two flower-shaped tiles have identical size and shape, are they congruent?"},{"answer":"Yes, $\\triangle ABC \\cong \\triangle DEF$","question":"In a flower garden, $\\triangle ABC$ and $\\triangle DEF$ have $\\overline{AB} = \\overline{DE}$, $\\overline{BC} = \\overline{EF}$, and $\\overline{CA} = \\overline{FD}$. Are they congruent?"},{"answer":"$8$ m","question":"A triangular flower bed $\\triangle XYZ$ is congruent to $\\triangle PQR$. If $\\overline{XY} = 8$ m, $\\overline{YZ} = 6$ m, $\\angle Z = 50^\\circ$, and $\\angle R = 50^\\circ$, find $\\overline{PQ}$."}]}

skills:
["Identifying congruent shapes","Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests","Solving for unknown triangle elements using congruency"]


example_id: lp_01K94SNTMNQN3C1ETT016FGCBX_01K94SNVGNBQ0GT0R0VGERVBZC_CONTEMPLATIVE_QUESTION
skill_ids: ["92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Flowers
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Two bridges have triangular supports. How would you prove they are congruent using SSS, SAS, AAS, or RHS?","teacherTips":["Discuss when each congruence test (SSS, SAS, AAS, RHS) is applicable.","Encourage students to identify corresponding sides and angles.","Help students connect congruence to real-world structural stability."],"difficulty":"mild"}

skills:
["Identifying congruent shapes","Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests","Solving for unknown triangle elements using congruency"]


example_id: lp_01K94SNTMNQN3C1ETT016FGCBX_01K94SNVGNBQ0GT0R0V8K82W4S_ACTIVITY
skill_ids: ["92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Flowers
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Triangle Match-Up Challenge\nYour team must match triangle pairs and prove they are congruent!","scenario":"Steps\n1. Each team draws $6$ triangles of different sizes and angles on paper.\n2. Cut out the triangles and mix them together with another team's triangles.\n3. Match pairs of congruent triangles using SSS, SAS, AAS, or RHS tests.\n4. Write a short proof for each pair to show how they are congruent.\n5. The team with the most correct matches and proofs wins!","steps":["Discussion\n• Why is it important to have specific tests for congruency?\n• What happens if two triangles share two equal sides but not an angle?","Differentiation Opportunities\n• Support: Provide pre-drawn triangles with measurements labeled for easier matching.\n• Extend: Challenge students to create triangles that are congruent but not identical in orientation."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Identifying congruent shapes","Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests","Solving for unknown triangle elements using congruency"]


example_id: lp_01K94SNTMNQN3C1ETT016FGCBX_01K94SNVGNBQ0GT0R0V396VHEY_APPLICATION
skill_ids: ["92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Flowers
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Congruence in Floral Arrangements","example1Header":"Situation\nFlorists design symmetrical arrangements using congruent flower shapes to create balanced, visually appealing displays for events.","example1Body":"Example\nA florist uses two triangular petals, each with sides $4$ cm, $5$ cm, $6$ cm. Identifying them as congruent ensures symmetry in the floral design.","example2Header":"","example2Body":""}


example_id: lp_01K94SNTMNQN3C1ETT016FGCBX_01K94SNVGNBQ0GT0R0VPKSBQW1_THOUGHT_SPARKER
skill_ids: ["92ldmsPXpH8q7E1XRHR8","Xc7MST441RlCy1oVEU5C","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Flowers
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Two triangular flower beds in a park have side lengths of $3$ m, $4$ m, and $5$ m for one bed, and $5$ m, $4$ m, and $3$ m for the other.","firstSentence":"How could you prove that these two flower beds are congruent?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the congruency test (SSS) and explain why it works.","Ask students to sketch the triangles to visualize their correspondence.","Discuss why side lengths alone are sufficient to prove congruency in this case."]}


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPBK1DTCTVCGHA6PGH7T2_MULTIPLE_CHOICE_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"In $\\triangle ABC$ and $\\triangle DEF$, $AB = DE = 5$ cm, $BC = EF = 6$ cm, and $AC = DF = 7$ cm. Which congruency test proves $\\triangle ABC \\cong \\triangle DEF$?","answerOptions":["SSS","SAS","ASA","RHS"],"answer":"SSS","difficulty":"spicy"}

skills:
["Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests","Identifying congruent shapes","Solving for unknown triangle elements using congruency"]


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPBK1DTCTVCGH9Z2GX7ZD_MULTIPLE_CHOICE_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Two triangles have three pairs of corresponding sides that are equal. Which rule proves they are congruent?","answerOptions":["SSS","SAS","AAS","RHS"],"answer":"SSS","difficulty":"mild"}

skills:
["Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests","Identifying congruent shapes","Solving for unknown triangle elements using congruency"]


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPBK1DTCTVCGH950TQX5E_CONTEMPLATIVE_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Imagine you are designing a tile floor. How would you use congruent shapes to ensure the tiles fit perfectly? What shapes could you use, and how would you confirm they are congruent?","teacherTips":["Use shapes with equal sides and angles. Confirm congruence by comparing all sides and angles."],"difficulty":"mild"}

skills:
["Proving that triangles are congruent using the SSS, SAS, AAS and RHS tests","Identifying congruent shapes","Solving for unknown triangle elements using congruency"]


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPBK1DTCTVCGH90SG8H8R_MULTIPLE_CHOICE_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If two shapes are congruent, what must they have in common?","answerOptions":["Size and shape","Color and shape","Size and orientation","Shape and position"],"answer":"Size and shape","difficulty":"mild"}


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPBK1DTCTVCGHAR909JHQ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In $\\triangle ABC$ and $\\triangle DEF$, $AB = DE$, $\\angle A = \\angle D$, and $\\angle B = \\angle E$. Which congruency test proves the triangles are congruent?","answerOptions":["SSS","SAS","ASA","AAS"],"answer":"ASA","difficulty":"hot"}


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPBK1DTCTVCGHAVM21WTV_CONTEMPLATIVE_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design two triangles with at least one pair of congruent sides or angles. How could you prove they are congruent? What unknown elements can you solve for using congruence, and how do you justify your reasoning?","teacherTips":["Use congruence rules (e.g., SAS) to prove. Solve unknowns by matching sides/angles in congruent pairs."],"difficulty":"spicy"}


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPB2YKFSDV2RWJ0HNSZH8_SCAFFOLDED_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will identify congruent triangles and understand how to prove congruency using SSS, SAS, AAS, or RHS tests.","questions":[{"answer":"Yes, they are congruent.","question":"What does it mean for two triangles to be congruent?"},{"answer":"They have the same size and shape","question":"What does the SSS test check to prove triangles are congruent?"},{"answer":"They have the same shape but different sizes","question":"Two right triangles have hypotenuses of $10$ cm and one corresponding side of $6$ cm. Are the triangles congruent using the RHS test? Explain."}],"difficulty":"enabling"}


example_id: lp_01K94SPAE798TRDT462Y3D9TK6_01K94SPB2YKFSDV2RWJ4X60THK_SCAFFOLDED_QUESTION
skill_ids: ["Xc7MST441RlCy1oVEU5C","92ldmsPXpH8q7E1XRHR8","m0na6OMpAVcpAdE0taHR"]
subtopics: ["Congruence"]
subtopic_ids: ["subtopic_01GTC0BP9HKAY36GZQVZGC2SHM"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the concept of congruent triangles using SSS, SAS, AAS, and RHS tests to solve advanced geometric problems.","questions":[{"answer":"AC = DF = approximately $6.3$ cm","question":"Two triangles have sides $AB = PQ$, $BC = QR$, and $AC = PR$.\nWhich congruence test proves the triangles are congruent?"},{"answer":"SSS","question":"In $\\Delta ABC$, $\\angle C = 90^\\circ$, $AC = 8$, and $BC = 6$.\nIn $\\Delta PQR$, $\\angle R = 90^\\circ$, $PR = 8$, and $QR = 6$.\nAre the triangles congruent?"},{"answer":"Yes","question":"Two triangles, $\\Delta ABC$ and $\\Delta DEF$, are congruent by the SAS test.\n$AB = DE = 7$ cm, $\\angle B = \\angle E = 50^\\circ$, and $BC = EF = 5$ cm.\nProve the triangles are congruent and find the length of $AC$ and $DF$."}],"difficulty":"extension"}


example_id: lp_01K94SV4PG2SPKY1JQN6Y76QQR_01K94SV5HMM43WYNA3M4E6TE7E_EXIT_TICKET
skills: ["Describing translations of shapes on a grid","Identifying dilated shapes"]
skill_ids: ["1x6ZgRLYcWdiEKgTjXiB","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Juggling
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$3$ units right, $3$ units up","question":"A juggler moves a juggling ball shape from $(2, 3)$ to $(5, 6)$. What are the horizontal and vertical shifts?"},{"answer":"$(2, 2)$, $(6, 4)$, $(4, 8)$","question":"A juggler draws a triangle with vertices at $(1, 1)$, $(3, 2)$, and $(2, 4)$. After dilation by scale factor $2$, where are the new vertices?"},{"answer":"$8$ units right, $6$ units up","question":"A juggling pin moves from $(4, 5)$ to $(8, 7)$ and then to $(12, 11)$. What single translation would give the same result?"}]}


example_id: lp_01K94SV4PG2SPKY1JQN6Y76QQR_01K94SV5HMM43WYNA3KVSYB494_CONTEMPLATIVE_QUESTION
skills: ["Describing translations of shapes on a grid","Identifying dilated shapes"]
skill_ids: ["1x6ZgRLYcWdiEKgTjXiB","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Juggling
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Design a pattern using 3 shapes on a grid. Translate or dilate the shapes to create a new pattern. How do the translations and dilations change the shapes' positions and sizes?","teacherTips":["Encourage students to describe changes in position using translation vectors.","Ask students to explain how dilation affects the shapes' sizes but not their angles.","Ensure students clearly connect transformations to their grid designs."],"difficulty":"mild"}


example_id: lp_01K94SV4PG2SPKY1JQN6Y76QQR_01K94SV5HMM43WYNA3KAD8X5Z3_ACTIVITY
skills: ["Describing translations of shapes on a grid","Identifying dilated shapes"]
skill_ids: ["1x6ZgRLYcWdiEKgTjXiB","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Juggling
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Shape Mural Challenge\nYou're designing a mural using shapes! Translate and resize them for your design.","scenario":"Steps\n1. Draw a $10 \\times 10$ grid on graph paper.\n2. Choose a shape (e.g., triangle, square) and draw it on the grid.\n3. Translate the shape by moving it $3$ units right and $2$ units up.\n4. Dilate the shape by doubling its size from the original.\n5. Combine translations and dilations to create a mural and describe the changes.","steps":["Discussion\n• How does dilating a shape affect its size and position?\n• What patterns did you notice when translating shapes multiple times?","Differentiation Opportunities\n• Support: Use only basic translations (e.g., $1$ unit up or down) and no dilations.\n• Extend: Combine multiple transformations (e.g., rotate, translate, and dilate)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94SV4PG2SPKY1JQN6Y76QQR_01K94SV5HMM43WYNA3K42V198P_APPLICATION
skills: ["Describing translations of shapes on a grid","Identifying dilated shapes"]
skill_ids: ["1x6ZgRLYcWdiEKgTjXiB","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Juggling
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Shape Transformations in Juggling Patterns","example1Header":"Situation\nProfessional jugglers design routines by visualizing how patterns change. They use shape transformations like dilation to adjust the size of juggling formations.","example1Body":"Example\nA triangle in the juggling pattern has sides $2$ m, $3$ m, and $4$ m. After dilation by $2$, the sides become $4$ m, $6$ m, and $8$ m, doubling the size of the pattern.","example2Header":"","example2Body":""}


example_id: lp_01K94SV4PG2SPKY1JQN6Y76QQR_01K94SV5HMM43WYNA3M3808531_THOUGHT_SPARKER
skills: ["Describing translations of shapes on a grid","Identifying dilated shapes"]
skill_ids: ["1x6ZgRLYcWdiEKgTjXiB","TyU67kr75ULQT84bAcQ6"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Juggling
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A juggler tosses three balls in a triangular pattern on a coordinate grid, with the points of the triangle at $(1,1)$, $(4,1)$, and $(2,4)$. After every cycle, the triangle is translated $3$ units to the right and dilated by a scale factor of $2$ from the origin.","firstSentence":"How do these transformations affect the positions of the triangle's vertices after each cycle?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to draw the original triangle and apply translations and dilations step by step.","Discuss the difference between translations (moving without changing size) and dilations (changing size relative to a point).","Ask students to explain how the scale factor influences the distance of each vertex from the origin."]}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVMA7W8V4PNNM3DATKNCE_MULTIPLE_CHOICE_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A shape is dilated by doubling its size. What happens to its angles?","answerOptions":["The angles double in size","The angles are halved","The angles stay the same","The angles disappear"],"answer":"The angles stay the same","difficulty":"mild"}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVMA7W8V4PNNM397HDMYR_CONTEMPLATIVE_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"How would you explain if a shape is a dilation of another? Create examples of dilated shapes.","teacherTips":["Dilated shapes have proportional sides and identical angles, scaled by a factor greater than 0."],"difficulty":"mild"}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVMA7W8V4PNNM3YVHN8VF_MULTIPLE_CHOICE_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A shape moves $3$ units right and $2$ units up. What is this type of movement called?","answerOptions":["Translation","Rotation","Reflection","Dilation"],"answer":"Translation","difficulty":"mild"}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVMA7W8V4PNNM3TAQDC1P_MULTIPLE_CHOICE_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A point moves from $(3, 4)$ to $(7, 8)$. What is the translation?","answerOptions":["$4$ units right and $4$ units up","$4$ units left and $4$ units up","$4$ units right and $4$ units down","$4$ units left and $4$ units down"],"answer":"$4$ units right and $4$ units up","difficulty":"mild"}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVMA7W8V4PNNM46Q1WHKS_CONTEMPLATIVE_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a shape on a $10 \\times 10$ grid. Describe a series of translations to move it to three new positions. How would you explain each movement clearly to someone else?","teacherTips":["A translation moves a shape by adding/subtracting values to $x$ and $y$ coordinates, e.g., $(x+3, y-2)$."],"difficulty":"spicy"}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVKVNG7EQ9HJSHMC7DPS1_SCAFFOLDED_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore transformations and dilations of shapes on a coordinate grid.","questions":[{"answer":"Order affects final position due to dilation's dependency on the origin.","question":"A triangle has vertices at $(2, 3)$, $(4, 5)$, and $(6, 3)$. Translate the triangle by the vector $\\langle -3, 2 \\rangle$. What are the new coordinates of the vertices?"},{"answer":"$(-1, 5)$, $(1, 7)$, $(3, 5)$","question":"Dilate the triangle from Question 1, with vertices $(-1, 5)$, $(1, 7)$, and $(3, 5)$, by a scale factor of $2$ about the origin. What are the new coordinates?"},{"answer":"$(-2, 10)$, $(2, 14)$, $(6, 10)$","question":"Explain why the order of applying a translation and a dilation matters. Use examples from the previous questions to support your reasoning."}],"difficulty":"extension"}


example_id: lp_01K94SVK3FN50KWBZVGBZ15EYT_01K94SVKVNG7EQ9HJSHGBXW0K2_SCAFFOLDED_QUESTION
skills: ["Identifying dilated shapes","Describing translations of shapes on a grid"]
skill_ids: ["TyU67kr75ULQT84bAcQ6","1x6ZgRLYcWdiEKgTjXiB"]
subtopics: ["Shape Transformations"]
subtopic_ids: ["subtopic_01GTC0BR9GMQXZVZ08VWYRK286"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 translations and dilations. A translation moves a shape on a grid, and a dilation changes its size.","questions":[{"answer":"The shape moves to a new position and changes size","question":"What happens to a shape during a translation?\nHint: Think about whether the shape changes or just moves."},{"answer":"The shape moves without changing size or direction","question":"What happens to a shape during a dilation?\nHint: Does the shape change size or stay the same?"},{"answer":"The shape gets bigger","question":"If a shape is translated and then dilated, describe what happens.\nHint: Think about how the shape moves and changes size."}],"difficulty":"enabling"}


example_id: lp_01K94T0TAJ1BZ2XQMK4A1PVG74_01K94T0V393DMGNJ9S5QZBY7D5_ACTIVITY
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Treehouse
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Shadow Triangle Challenge\nYour team is helping architects check if building shadows are proportional to their heights.","scenario":"Steps\n1. Draw two triangles: one with sides $6$ cm, $8$ cm, $10$ cm and another similar triangle.\n2. Use AAA, SSS, SAS, or RHS tests to prove the triangles are similar.\n3. Measure the corresponding sides and calculate their ratios.\n4. Discuss how the ratios confirm similarity.\n5. Apply the same method to analyze a new triangle your team creates.","steps":["Discussion\n• Which similarity test is easiest to use and why?\n• How do side ratios help confirm similarity in real-world problems?","Differentiation Opportunities\n• Support: Provide pre-drawn triangles with labeled dimensions for students to analyze.\n• Extend: Challenge students to find missing side lengths using the scale factor."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Applying similar triangles in $2$D problems","Proving triangle similarity using the AAA, SSS, SAS and RHS tests"]


example_id: lp_01K94T0TAJ1BZ2XQMK4A1PVG74_01K94T0V393DMGNJ9S65WEDQ57_CONTEMPLATIVE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Treehouse
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A tree casts a shadow 12 m long, while a 2 m stick casts a 3 m shadow. How can you use similar triangles to find the tree's height?","teacherTips":["Help students identify the corresponding sides of the triangles.","Encourage the use of the SSS or AAA similarity test.","Discuss how to set up and solve proportions for the height."],"difficulty":"mild"}

skills:
["Applying similar triangles in $2$D problems","Proving triangle similarity using the AAA, SSS, SAS and RHS tests"]


example_id: lp_01K94T0TAJ1BZ2XQMK4A1PVG74_01K94T0V393DMGNJ9S6CYR8JPB_EXIT_TICKET
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Treehouse
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"A treehouse ladder forms a triangle with angles $60^\\circ$, $60^\\circ$, and $60^\\circ$. Is this triangle similar to another triangle with the same angles?"},{"answer":"$9$","question":"A tree casts a shadow of $6$ m, and a $1.5$ m tall person casts a shadow of $1$ m. How tall is the tree?"},{"answer":"$2\\sqrt{6}$","question":"A treehouse $5$ m above the ground is supported by a $7$ m ladder leaning against it. How far is the ladder’s base from the tree?"}]}

skills:
["Applying similar triangles in $2$D problems","Proving triangle similarity using the AAA, SSS, SAS and RHS tests"]


example_id: lp_01K94T0TAJ1BZ2XQMK4A1PVG74_01K94T0V393DMGNJ9S68JAV9YC_THOUGHT_SPARKER
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Treehouse
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A treehouse casts a shadow of $12$ feet, while a $6$-foot ladder nearby casts a $3$-foot shadow.","firstSentence":"How could you prove that the triangles formed by the treehouse and ladder shadows are similar?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify corresponding sides and angles in the two triangles.","Discuss the importance of proportional relationships in proving similarity.","Use diagrams to help students visualize the scenario and justify their reasoning."]}


example_id: lp_01K94T0TAJ1BZ2XQMK4A1PVG74_01K94T0V393DMGNJ9S5KGCXXC1_APPLICATION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Treehouse
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Designing a Treehouse with Similar Triangles","example1Header":"Situation\nArchitects designing treehouses use triangle similarity to scale designs. They ensure stability and proper proportions by comparing smaller model triangles to larger structures.","example1Body":"Example\nA small triangle with angles $40^\\circ$, $50^\\circ$, and $90^\\circ$ is compared to a larger triangle of the same angles. By the AAA test, the triangles are similar, ensuring the design scales correctly.","example2Header":"","example2Body":""}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16Z3ES65SBZGKNZT57RH_MULTIPLE_CHOICE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If $\\Delta ABC$ is similar to $\\Delta DEF$, and side $AB = 6$ cm, side $DE = 3$ cm, and side $AC = 8$ cm, what is the length of side $DF$?","answerOptions":["$4$ cm","$6$ cm","$9$ cm","$12$ cm"],"answer":"$4$ cm","difficulty":"mild"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16Z3ES65SBZGKH3RW4BR_MULTIPLE_CHOICE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Two triangles are similar. If one side of the first triangle is $5$ cm and the corresponding side of the second triangle is $15$ cm, what is the ratio of their side lengths?","answerOptions":["$1:2$","$1:3$","$2:3$","$3:1$"],"answer":"$1:3$","difficulty":"mild"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16Z3ES65SBZGKRQ9G9F2_CONTEMPLATIVE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You see a tree and its shadow is 12 ft. Your height is 5 ft, and your shadow is 3 ft. How could you find the tree's height?","teacherTips":["Use $\\frac{\\text{tree height}}{12} = \\frac{5}{3}$. Solve: tree height $= 20$ ft."],"difficulty":"hot"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16Z3ES65SBZGKZQDHRYH_MULTIPLE_CHOICE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Two similar triangles have corresponding sides in the ratio $3:5$. If the smaller triangle's area is $27$ cm$^2$, what is the larger triangle's area?","answerOptions":["$45$ cm$^2$","$75$ cm$^2$","$125$ cm$^2$","$135$ cm$^2$"],"answer":"$75$ cm$^2$","difficulty":"spicy"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16Z3ES65SBZGJQ0G9BFV_CONTEMPLATIVE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a triangular garden. How can you prove two triangles in your design are similar using the AAA, SSS, SAS, or RHS tests? Which test would you use, and why?","teacherTips":["Use tests like AAA (equal angles) or SSS (proportional sides) to prove triangles are similar."],"difficulty":"mild"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16Z3ES65SBZGJVRCR2Q7_MULTIPLE_CHOICE_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Two triangles have angles $50^\\circ$, $60^\\circ$, and $70^\\circ$. Which similarity test proves they are similar?","answerOptions":["SSS","AAA","SAS","RHS"],"answer":"AAA","difficulty":"hot"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16F9GEY6Y2BX4CR30B86_SCAFFOLDED_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question set, you will learn how to prove triangles are similar using similarity tests like AAA, SSS, SAS, and RHS.","questions":[{"answer":"SAS","question":"If two triangles have all corresponding angles equal, which similarity test proves they are similar?"},{"answer":"AAA","question":"If two triangles have all three pairs of corresponding sides in the same ratio, which similarity test proves they are similar?"},{"answer":"SSS","question":"Two triangles have side ratios of $2:3$ and an equal angle between these sides.\nWhich similarity test proves these triangles are similar?"}],"difficulty":"enabling"}


example_id: lp_01K94T15FNES1BKTD70DHFAYEW_01K94T16F9GEY6Y2BX4EWEYHHW_SCAFFOLDED_QUESTION
skill_ids: ["7vmDhLdK32qFdOcSm51t","efVZBFKA3eLTuIVwRjqN"]
subtopics: ["Scale Factors"]
subtopic_ids: ["subtopic_01GZ13TNC6FRGKMQXQAF25YYHB"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore triangle similarity by proving relationships using AAA, SSS, SAS, and RHS tests.","questions":[{"answer":"RHS is the most efficient test","question":"Two triangles have angles measuring $50^\\circ$, $60^\\circ$, and $70^\\circ$.\nProve whether these triangles are similar using the AAA test."},{"answer":"Similar by AAA","question":"Triangle $ABC$ has sides $6$ cm, $8$ cm, and $10$ cm.\nTriangle $DEF$ has sides $9$ cm, $12$ cm, and $15$ cm.\nAre the triangles similar? Justify using the SSS test."},{"answer":"Similar by SSS","question":"Given two triangles, one with sides $5$ cm, $12$ cm, and $13$ cm, and another with a hypotenuse of $26$ cm and one angle $90^\\circ$, prove similarity.\nWhich similarity test is best suited for this proof, and why?"}],"difficulty":"extension"}


example_id: lp_01K94T5NSXT4MV3AWWWPM3998H_01K94T5Q1WFTWYFNPB9K03DMPA_CONTEMPLATIVE_QUESTION
skill_ids: ["r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi","FF5DGQOBbmpSuWNhPEB1"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Knitting
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"An isosceles triangle has two equal angles of $x^\\circ$. The third angle is bisected. How could you find the angles of the triangle? What happens if $x = 60^\\circ$?","teacherTips":["Guide students to use $x + x + \\text{third angle} = 180^\\circ$.","Discuss how bisection splits the third angle into equal parts.","Encourage exploring the case when $x = 60^\\circ$ for equilateral triangles."],"difficulty":"mild"}

skills:
["Understanding properties of angle bisectors in equilateral triangles","Understanding that angles in a triangle add up to $180$ degrees","Applying angle sum properties in isosceles triangles"]


example_id: lp_01K94T5NSXT4MV3AWWWPM3998H_01K94T5Q1WFTWYFNPB9RVHTJGH_EXIT_TICKET
skill_ids: ["r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi","FF5DGQOBbmpSuWNhPEB1"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Knitting
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$70^\\circ$","question":"Mary is knitting a triangular patch with angles $60^\\circ$ and $50^\\circ$. What is the measure of the third angle?"},{"answer":"$70^\\circ$","question":"Mary knits an isosceles triangle with a vertex angle of $40^\\circ$. What is the measure of each base angle?"},{"answer":"$30^\\circ$","question":"Mary divides an equilateral knitted triangle into two equal parts using an angle bisector. What is the measure of the smaller angles formed at the vertex?"}]}

skills:
["Understanding properties of angle bisectors in equilateral triangles","Understanding that angles in a triangle add up to $180$ degrees","Applying angle sum properties in isosceles triangles"]


example_id: lp_01K94T5NSXT4MV3AWWWPM3998H_01K94T5Q1WFTWYFNPB93AJFDAE_ACTIVITY
skill_ids: ["r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi","FF5DGQOBbmpSuWNhPEB1"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Knitting
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Triangle Angle Challenge\nYour team is designing puzzles using triangle angle rules for others to solve!","scenario":"Steps\n1. Draw an isosceles triangle and label its angles $x$, $y$, and $z$.\n2. Use $x + y + z = 180^\\circ$ to calculate one missing angle.\n3. Create a second triangle that is equilateral and draw its angle bisectors.\n4. Write a question about your triangles for another team to solve.\n5. Solve another team’s triangle puzzle and check their solution.","steps":["Discussion\n• Why do the angles in a triangle always add up to $180^\\circ$?\n• How do angle bisectors in an equilateral triangle show symmetry?","Differentiation Opportunities\n• Support: Focus only on isosceles triangles and provide one angle as a hint.\n• Extend: Challenge students to create scalene triangles with no equal angles."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Understanding properties of angle bisectors in equilateral triangles","Understanding that angles in a triangle add up to $180$ degrees","Applying angle sum properties in isosceles triangles"]


example_id: lp_01K94T5NSXT4MV3AWWWPM3998H_01K94T5Q1WFTWYFNPB9QV81RJY_THOUGHT_SPARKER
skill_ids: ["r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi","FF5DGQOBbmpSuWNhPEB1"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Knitting
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A knitting pattern includes an isosceles triangle with angles of $70^\\circ$, $70^\\circ$, and $40^\\circ$, and an equilateral triangle where each side is bisected to form smaller triangles.","firstSentence":"How could you use the angle properties of these triangles to ensure the pattern aligns perfectly when knitting the pieces together?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify the angle sum property of triangles before discussing specifics.","Guide them to explore how bisecting angles in an equilateral triangle affects the smaller triangles formed.","Discuss how aligning angles accurately ensures a seamless knitting pattern."]}


example_id: lp_01K94T5NSXT4MV3AWWWPM3998H_01K94T5Q1WFTWYFNPB91VW3YHK_APPLICATION
skill_ids: ["r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi","FF5DGQOBbmpSuWNhPEB1"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Knitting
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Designing Patterns in Knitting","example1Header":"Situation\nKnitting designers create triangular patterns for scarves, shawls, and decorations. They carefully plan the angles so the triangles fit perfectly into larger designs.","example1Body":"Example\nA triangular knitting design has angles $60^\\circ$ and $90^\\circ$. The third angle is $180^\\circ - (60^\\circ + 90^\\circ) = 30^\\circ$, ensuring the total is $180^\\circ$.","example2Header":"","example2Body":""}


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T66P6R8A1VKG564231TYJ_MULTIPLE_CHOICE_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"In an isosceles triangle, the vertex angle is $40^\\circ$. What is the measure of each base angle?","answerOptions":["$70^\\circ$","$80^\\circ$","$60^\\circ$","$50^\\circ$"],"answer":"$70^\\circ$","difficulty":"spicy"}

skills:
["Applying angle sum properties in isosceles triangles","Understanding properties of angle bisectors in equilateral triangles","Understanding that angles in a triangle add up to $180$ degrees"]


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T66P6R8A1VKG55X41RNM4_MULTIPLE_CHOICE_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In an isosceles triangle, two angles are $x^\\circ$ each. If the third angle is $40^\\circ$, what is the value of $x$?","answerOptions":["$70^\\circ$","$68^\\circ$","$60^\\circ$","$50^\\circ$"],"answer":"$70^\\circ$","difficulty":"hot"}

skills:
["Applying angle sum properties in isosceles triangles","Understanding properties of angle bisectors in equilateral triangles","Understanding that angles in a triangle add up to $180$ degrees"]


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T66P6R8A1VKG56RMZRWBF_MULTIPLE_CHOICE_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"True or false: In an equilateral triangle, the angle bisectors are also the medians.","answerOptions":["True","False"],"answer":"True","difficulty":"mild"}

skills:
["Applying angle sum properties in isosceles triangles","Understanding properties of angle bisectors in equilateral triangles","Understanding that angles in a triangle add up to $180$ degrees"]


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T66P6R8A1VKG56W23VK87_CONTEMPLATIVE_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"In an equilateral triangle, angle bisectors divide each angle into two equal parts. How could you use this property to locate the triangle's center? Justify your reasoning with a construction or explanation.","teacherTips":["The angle bisectors meet at a single point, the centroid, equidistant from all vertices."],"difficulty":"spicy"}


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T66P6R8A1VKG5551Z6DMB_MULTIPLE_CHOICE_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A triangle has angles measuring $50^\\circ$ and $70^\\circ$. What is the measure of the third angle?","answerOptions":["$50^\\circ$","$60^\\circ$","$70^\\circ$","$80^\\circ$"],"answer":"$60^\\circ$","difficulty":"mild"}


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T66P6R8A1VKG55C3GH1NF_CONTEMPLATIVE_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a triangle where one angle is twice the second angle, and the third angle is $10^\\circ$ more than the second. How would you calculate each angle? Are there multiple solutions?","teacherTips":["Set $x + 2x + (x + 10) = 180$. Solve: $x = 34$, so angles are $34^\\circ, 68^\\circ, 78^\\circ$."],"difficulty":"spicy"}


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T666EPM89RED4R18NM0DX_SCAFFOLDED_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 the angle sum property of triangles and special properties of isosceles and equilateral triangles.","questions":[{"answer":"$30^\\circ$","question":"What is the sum of all the angles in a triangle?"},{"answer":"$90^\\circ$","question":"An isosceles triangle has two angles equal to $70^\\circ$. What is the measure of the third angle?"},{"answer":"$180^\\circ$","question":"In an equilateral triangle, each angle is bisected. What is the measure of each smaller angle formed by the bisector?"}],"difficulty":"enabling"}


example_id: lp_01K94T65BW3RGA55BV9R9DR73K_01K94T666EPM89RED4R7DBCQEK_SCAFFOLDED_QUESTION
skill_ids: ["FF5DGQOBbmpSuWNhPEB1","r1w3kXHnW75irKvrKqXG","Rm9BWRIkUS3lnuuLSnpi"]
subtopics: ["Triangles"]
subtopic_ids: ["subtopic_01GTC0BE1M2EM8G83GK4C6NBYZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore angle sum properties in isosceles triangles and delve into angle bisectors in equilateral triangles.","questions":[{"answer":"Angle bisectors are medians and altitudes due to symmetry.","question":"In an isosceles triangle, two angles are equal, and the third angle is $40^\\circ$. What are the measures of the two equal angles?"},{"answer":"$70^\\circ$","question":"In an equilateral triangle, an angle bisector divides one angle into two smaller angles. What is the measure of each smaller angle?"},{"answer":"$30^\\circ$","question":"Explain why the angle bisectors of an equilateral triangle also act as its medians and altitudes. Use geometric reasoning in your explanation."}],"difficulty":"extension"}


example_id: lp_01K94TB6M60EVRTTWM1FEGZ16T_01K94TB7DTG88C8EAZ62S7K173_ACTIVITY
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: GPS
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Triple Triangle Test\nYour team needs to test building materials to find sets that form right triangles!","scenario":"Steps\n1. Write down $5$ sets of numbers (e.g., $(3, 4, 5)$, $(6, 8, 10)$).\n2. For each set, check if $a^2 + b^2 = c^2$ to verify if it's a Pythagorean triple.\n3. Circle the sets that are valid triples and cross out the invalid ones.\n4. Compare your results with another team to ensure accuracy.\n5. Discuss which sets worked and why others did not.","steps":["Discussion\n• Why do some sets fail to be Pythagorean triples?\n• How can you quickly spot if a set might be a triple?","Differentiation Opportunities\n• Support: Start with smaller numbers like $(3, 4, 5)$ or $(5, 12, 13)$ to simplify calculations.\n• Extend: Create your own larger triples by multiplying known triples by a constant (e.g., $2$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94TB6M60EVRTTWM1FEGZ16T_01K94TB7DTG88C8EAZ6S2EMC0Q_EXIT_TICKET
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: GPS
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"If a GPS calculates $3$, $4$, and $5$ as the sides of a triangle, does it form a Pythagorean triple?"},{"answer":"Yes","question":"A GPS estimates distances as $9$, $12$, and $15$. Do these distances form a Pythagorean triple?"},{"answer":"$17$","question":"If a GPS shows two sides of a right triangle as $8$ and $15$, what is the length of the hypotenuse?"}]}


example_id: lp_01K94TB6M60EVRTTWM1FEGZ16T_01K94TB7DTG88C8EAZ6ENRCFMC_CONTEMPLATIVE_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: GPS
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You know $3$, $4$, and $5$ form a Pythagorean triple. What other triples can you find? Explain how you know they work.","teacherTips":["Encourage students to test $a^2 + b^2 = c^2$ for their chosen triples.","Discuss how multiplying a triple by the same number keeps it valid.","Suggest starting with small numbers to find patterns."],"difficulty":"mild"}


example_id: lp_01K94TB6M60EVRTTWM1FEGZ16T_01K94TB7DTG88C8EAZ606PY51R_APPLICATION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: GPS
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Calculating Distances with GPS and Pythagoras","example1Header":"Situation\nGPS engineers calculate distances between two points. They use Pythagoras' theorem to check triangular paths and ensure accurate navigation data.","example1Body":"Example\nGPS systems confirm triangular distances using Pythagoras' theorem. For $(3, 4, 5)$: $3^2 + 4^2 = 5^2$, or $9 + 16 = 25$. This makes $(3, 4, 5)$ a valid triangle.","example2Header":"","example2Body":""}


example_id: lp_01K94TB6M60EVRTTWM1FEGZ16T_01K94TB7DTG88C8EAZ6K4MP937_THOUGHT_SPARKER
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: GPS
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A GPS shows that the distance between two towns is $50$ miles north and $120$ miles west. It calculates the shortest path between the two towns as $130$ miles.","firstSentence":"How could you verify that these distances form a Pythagorean triple?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall the Pythagorean theorem and how it applies to right triangles.","Guide students to calculate whether $50^2 + 120^2$ equals $130^2$.","Ask students to discuss why the Pythagorean theorem is useful in real-world applications like GPS calculations."]}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBKQ0YDERE8671KJ1NGHY_CONTEMPLATIVE_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You want to build a triangular garden. How can you use Pythagorean triples to pick side lengths? Justify your choice.","teacherTips":["Choose $a$, $b$, $c$ such that $a^2 + b^2 = c^2$, e.g., $3$, $4$, $5$. Scaled triples also work."],"difficulty":"hot"}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBKQ0YDERE8671ENHV1ZR_CONTEMPLATIVE_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Create three different sets of Pythagorean triples. How would you check if each set satisfies $a^2 + b^2 = c^2$?","teacherTips":["Check if $a^2 + b^2 = c^2$ for each set. Example: $3^2 + 4^2 = 9 + 16 = 25 = 5^2$."],"difficulty":"mild"}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBKQ0YDERE86712G34X6M_MULTIPLE_CHOICE_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 Pythagorean triple?","answerOptions":["$7, 24, 25$","$10, 24, 26$","$5, 12, 14$","$8, 15, 20$"],"answer":"$7, 24, 25$","difficulty":"mild"}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBKQ0YDERE86715D76WHB_MULTIPLE_CHOICE_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 Pythagorean triple?","answerOptions":["$\\{7, 24, 25\\}$","$\\{10, 24, 26\\}$","$\\{9, 12, 15\\}$","$\\{8, 13, 16\\}$"],"answer":"$\\{7, 24, 25\\}$","difficulty":"mild"}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBKQ0YDERE8671A65AT6R_MULTIPLE_CHOICE_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 Pythagorean triple?","answerOptions":["$7, 24, 25$","$10, 24, 26$","$8, 15, 20$","$5, 12, 14$"],"answer":"$7, 24, 25$","difficulty":"mild"}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBK9YJ5AFQ5H1Z2P2DNS4_SCAFFOLDED_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
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 identify Pythagorean triples. A Pythagorean triple consists of three whole numbers that satisfy $a^2 + b^2 = c^2$.","questions":[{"answer":"Yes","question":"Are $3$, $4$, and $5$ a Pythagorean triple?\nCheck if $3^2 + 4^2 = 5^2$."},{"answer":"Yes","question":"Are $6$, $8$, and $10$ a Pythagorean triple?\nCheck if $6^2 + 8^2 = 10^2$."},{"answer":"No","question":"Do $5$, $12$, and $13$ form a Pythagorean triple?\nShow your work."}],"difficulty":"enabling"}


example_id: lp_01K94TBJEA1RF708XWK066TPG9_01K94TBK9YJ5AFQ5H1Z6PNCSFB_SCAFFOLDED_QUESTION
skills: ["Identifying Pythagorean triples"]
skill_ids: ["YODiHrgWgz8Rlcbfg3ba"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the fascinating world of Pythagorean triples and uncover hidden patterns in right triangles.","questions":[{"answer":"Use $a = m^2 - n^2$, $b = 2mn$, $c = m^2 + n^2$","question":"Determine if $15$, $20$, and $25$ form a Pythagorean triple."},{"answer":"Yes","question":"A right triangle has legs $9$ and $12$, and a hypotenuse $x$. Find the value of $x$."},{"answer":"$15$","question":"Explain how to generate any Pythagorean triple using integers $m$ and $n$, and prove why the formula works."}],"difficulty":"extension"}


example_id: lp_01K94TFEVT4VS13W5RP2W62M4H_01K94TFFK9NNQMKH88TEHQPCJP_EXIT_TICKET
skills: ["Applying Pythagoras' theorem","Solving worded problems with Pythagoras' theorem"]
skill_ids: ["ofNmPkcXqPRVRa2SNOyk","YFcUVv6TmiRWQe1LBHLw"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Basketball
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5$ m","question":"A basketball hoop is $3$ m high, and a player stands $4$ m away from the base. What is the distance to the hoop?"},{"answer":"$31.8$ m","question":"A basketball court is $28$ m long and $15$ m wide. What is the diagonal distance across the court?"},{"answer":"$25$ m","question":"A player runs $7$ m forward and $24$ m sideways to catch the ball. What is the shortest distance to the starting point?"}]}


example_id: lp_01K94TFEVT4VS13W5RP2W62M4H_01K94TFFK9NNQMKH88T75A0V4T_CONTEMPLATIVE_QUESTION
skills: ["Applying Pythagoras' theorem","Solving worded problems with Pythagoras' theorem"]
skill_ids: ["ofNmPkcXqPRVRa2SNOyk","YFcUVv6TmiRWQe1LBHLw"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Basketball
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You want to build a ramp with a height of 3 ft and a base of 4 ft. How would you find the ramp length?","teacherTips":["Remind students to use $a^2 + b^2 = c^2$ for right triangles.","Encourage drawing a diagram to visualize the problem.","Ask students to explain their steps and reasoning."],"difficulty":"mild"}


example_id: lp_01K94TFEVT4VS13W5RP2W62M4H_01K94TFFK9NNQMKH88ST5ZK0PR_ACTIVITY
skills: ["Applying Pythagoras' theorem","Solving worded problems with Pythagoras' theorem"]
skill_ids: ["ofNmPkcXqPRVRa2SNOyk","YFcUVv6TmiRWQe1LBHLw"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Basketball
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Drone Delivery Challenge\nYou're managing a drone delivery service. Use Pythagoras' theorem to calculate if drones can deliver packages efficiently.","scenario":"Steps\n1. Draw a city grid on graph paper with $5 \\times 5$ blocks.\n2. Mark two locations as 'warehouse' and 'delivery point'.\n3. Measure the horizontal and vertical distances between these points.\n4. Use Pythagoras' theorem to find the shortest diagonal route.\n5. Compare the diagonal distance to the drone's maximum range.","steps":["Discussion\n• How does the diagonal route compare to the total block distance?\n• What happens if the drone's range is shorter than the diagonal distance?","Differentiation Opportunities\n• Support: Use grids with smaller blocks (e.g., $3 \\times 3$) for simpler calculations.\n• Extend: Add multiple delivery points and calculate total diagonal distances."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94TFEVT4VS13W5RP2W62M4H_01K94TFFK9NNQMKH88SM2BNWRE_APPLICATION
skills: ["Applying Pythagoras' theorem","Solving worded problems with Pythagoras' theorem"]
skill_ids: ["ofNmPkcXqPRVRa2SNOyk","YFcUVv6TmiRWQe1LBHLw"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Basketball
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Using Pythagoras' Theorem in Basketball Court Design","example1Header":"Situation\nBasketball court designers ensure the key dimensions are accurate. They use Pythagoras' theorem to measure diagonal distances for proper court alignment.","example1Body":"Example\nA free-throw lane is $12$ ft wide and $19$ ft long. Using Pythagoras' theorem, $c^2 = 12^2 + 19^2 = 505$, so $c \\approx \\sqrt{505} \\approx 22.5$ ft, the diagonal distance.","example2Header":"","example2Body":""}


example_id: lp_01K94TFEVT4VS13W5RP2W62M4H_01K94TFFK9NNQMKH88TBQ5695R_THOUGHT_SPARKER
skills: ["Applying Pythagoras' theorem","Solving worded problems with Pythagoras' theorem"]
skill_ids: ["ofNmPkcXqPRVRa2SNOyk","YFcUVv6TmiRWQe1LBHLw"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Basketball
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A basketball court is 28 metres long and 15 metres wide. A player makes a diagonal pass from one corner of the court to the opposite corner.","firstSentence":"How could you calculate the distance of the diagonal pass?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify and label the triangle formed by the diagonal pass.","Discuss how Pythagoras' theorem relates to the sides of a right triangle in this context.","Ask students to verify their calculations by estimating if the diagonal makes sense given the court's dimensions."]}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFRM3HJ00PBB532V0J6QJ_MULTIPLE_CHOICE_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A ladder is leaning against a wall. The bottom of the ladder is $6$ feet from the wall, and the ladder is $10$ feet long. How high up the wall does the ladder reach?","answerOptions":["$8$ feet","$7$ feet","$9$ feet","$6$ feet"],"answer":"$8$ feet","difficulty":"hot"}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFRM3HJ00PBB530K2FDTE_MULTIPLE_CHOICE_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A right triangle has one leg of $3$ units and the other leg of $4$ units. What is the length of the hypotenuse?","answerOptions":["$5$ units","$6$ units","$7$ units","$8$ units"],"answer":"$5$ units","difficulty":"mild"}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFRM3HJ00PBB536CJWQE3_CONTEMPLATIVE_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A ladder leans against a wall, 10 ft from its base to the wall's base. If the ladder is 26 ft, how high does it reach? What if the ladder's position or wall height changes? How would you calculate these scenarios?","teacherTips":["Use $a^2 + b^2 = c^2$. Solve $b = \\sqrt{26^2 - 10^2} = 24$ ft. Adjust $a$, $b$, or $c$ for changes."],"difficulty":"spicy"}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFRM3HJ00PBB52CYH45G4_MULTIPLE_CHOICE_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In a right-angled triangle, the legs are $6$ cm and $8$ cm. What is the length of the hypotenuse?","answerOptions":["$10$ cm","$12$ cm","$14$ cm","$16$ cm"],"answer":"$10$ cm","difficulty":"hot"}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFRM3HJ00PBB52FG21R4V_CONTEMPLATIVE_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are designing a triangular ramp for a skateboard park. The base is 12 ft, and the height is 5 ft. How would you calculate the length of the ramp? What if the base or height changed? How would this impact your calculations?","teacherTips":["Use $c = \\sqrt{a^2 + b^2}$; changing $a$ or $b$ alters $c$, affecting the ramp's steepness."],"difficulty":"spicy"}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFR5055V8DMFT4KXN72D8_SCAFFOLDED_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore challenging real-world problems using Pythagoras' theorem to calculate distances and justify solutions.","questions":[{"answer":"Explain using Pythagoras' theorem and calculations.","question":"A ladder leans against a wall, reaching a height of $12$ ft. The base of the ladder is $5$ ft from the wall. How long is the ladder?"},{"answer":"$13$ ft","question":"A triangular field has a hypotenuse of $25$ m and one side measuring $20$ m. Find the length of the other side of the triangle."},{"answer":"$15$ m","question":"A rectangular park is $50$ m long and $40$ m wide. A diagonal path divides it into two triangles. Explain how to find the diagonal's length and why this method works."}],"difficulty":"extension"}


example_id: lp_01K94TFQHMGZNK34KJ1BTPZJHZ_01K94TFR5055V8DMFT4GV23YQ7_SCAFFOLDED_QUESTION
skills: ["Solving worded problems with Pythagoras' theorem","Applying Pythagoras' theorem"]
skill_ids: ["YFcUVv6TmiRWQe1LBHLw","ofNmPkcXqPRVRa2SNOyk"]
subtopics: ["Pythagoras' Theorem"]
subtopic_ids: ["subtopic_01GTC0BH91VAHG0ZY159PCR54G"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will solve simple word problems using Pythagoras' theorem. Remember, $c^2 = a^2 + b^2$ for right triangles.","questions":[{"answer":"$15$ m","question":"A right triangle has legs of $3$ m and $4$ m. What is the length of the hypotenuse?"},{"answer":"$5$ m","question":"A right triangle has a hypotenuse of $10$ m and one leg of $6$ m. What is the length of the other leg?"},{"answer":"$6$ m","question":"A rectangle has a length of $9$ m and a width of $12$ m.\nWhat is the length of its diagonal?\nHint: The diagonal forms the hypotenuse of a right triangle."}],"difficulty":"enabling"}


example_id: lp_01K94TKNYY4V6AEYJD2P51A45P_01K94TKPTFW7Z2DAFXXK1SXSNT_EXIT_TICKET
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: The Solar System
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$5$","question":"A satellite travels between points $(3, 4)$ and $(7, 1)$ in space. What is the distance it covers?"},{"answer":"$(5, 1)$","question":"If a space probe starts at $(2, 6)$ and ends at $(8, -4)$, what is the midpoint of its journey?"},{"answer":"$8\\sqrt{10}$","question":"An astronaut travels from $(12, 15)$ to $(4, -9)$ on a planetary grid. How far does the astronaut travel?"}]}


example_id: lp_01K94TKNYY4V6AEYJD2P51A45P_01K94TKPTFW7Z2DAFXXDKD8PCD_CONTEMPLATIVE_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: The Solar System
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Two friends live at $(2,5)$ and $(8,1)$. How would you find the distance and midpoint of their houses? Explain.","teacherTips":["Guide students to use the distance formula: $d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.","Encourage explanation of midpoint: $\\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)$.","Discuss practical uses like measuring halfway points or travel distances."],"difficulty":"mild"}


example_id: lp_01K94TKNYY4V6AEYJD2P51A45P_01K94TKPTFW7Z2DAFXX2BTV3CT_ACTIVITY
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: The Solar System
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Delivery Route Planner\nYour team is planning delivery routes for a local business. You must find distances and midpoints between delivery points on a map.","scenario":"Steps\n1. Each team plots $4$ delivery points on graph paper with coordinates of their choice.\n2. Find the distance between each pair of consecutive points using the distance formula.\n3. Calculate the midpoint for each pair of consecutive points.\n4. Draw and label the route with distances and midpoints clearly marked.\n5. Compare routes with other teams to check for accuracy and efficiency.","steps":["Discussion\n• How can midpoints help optimize delivery routes?\n• What happens to the distance if points are closer together?","Differentiation Opportunities\n• Support: Provide pre-drawn points for students to calculate distances and midpoints.\n• Extend: Add a third dimension to calculate distances and midpoints in 3D space."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94TKNYY4V6AEYJD2P51A45P_01K94TKPTFW7Z2DAFXWZ8HSMKV_APPLICATION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: The Solar System
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Measuring the Distance Between Planets","example1Header":"Situation\nAstronomers calculate the distance between celestial objects to study their positions, orbits, and interactions in space.","example1Body":"Example\nIf Earth is at $(3, 2)$ and Mars at $(7, 6)$, the distance is $d = \\sqrt{(7 - 3)^2 + (6 - 2)^2} = \\sqrt{32} \\approx 5.66$ units.","example2Header":"","example2Body":""}


example_id: lp_01K94TKNYY4V6AEYJD2P51A45P_01K94TKPTFW7Z2DAFXXH9PK4ES_THOUGHT_SPARKER
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: The Solar System
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"The distance between Earth and Mars is approximately $225$ million km, and the distance between Mars and Jupiter is $550$ million km.","firstSentence":"How could you find the midpoint between Earth and Jupiter in this scenario?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to visualize the solar system as a number line to simplify the concept of distance and midpoint.","Discuss the importance of relative positions in space to help students connect the math to real-world astronomy.","Support students in breaking down the problem into smaller steps, like adding distances or dividing by two, to find the midpoint."]}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM0JY1VVC2KDD4ZJESCN7_CONTEMPLATIVE_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A park is shaped like a rectangle. The corners are at $(2,3)$, $(2,8)$, $(10,3)$, and $(10,8)$. How would you calculate the diagonal distance across the park? Can you find other ways to verify your result?","teacherTips":["Diagonal: $\\sqrt{(10-2)^2 + (8-3)^2} = \\sqrt{64 + 25} = \\sqrt{89}$. Verify via Pythagoras."],"difficulty":"spicy"}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM0JY1VVC2KDD4TP54E2R_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the distance between the points $(3,4)$ and $(7,4)$?","answerOptions":["$3$","$4$","$5$","$7$"],"answer":"$4$","difficulty":"mild"}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM0JY1VVC2KDD5T2G1TCN_CONTEMPLATIVE_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Design a park where the midpoint of the fountain and playground is the picnic table. Choose coordinates for these points and explain how you verify the picnic table's location.","teacherTips":["Use $\\left(\\frac{x_1+x_2}{2}, \\frac{y_1+y_2}{2}\\right)$ to verify the picnic table's location."],"difficulty":"spicy"}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM0JY1VVC2KDD5NFN5T22_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"What is the midpoint of the points $(3, 5)$ and $(7, 9)$?","answerOptions":["$(4, 6)$","$(5, 7)$","$(6, 8)$","$(10, 14)$"],"answer":"$(5, 7)$","difficulty":"hot"}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM0JY1VVC2KDD5HGWZT18_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the midpoint of the line segment joining the points $(2, 4)$ and $(6, 8)$?","answerOptions":["$(3, 6)$","$(4, 6)$","$(5, 7)$","$(4, 8)$"],"answer":"$(4, 6)$","difficulty":"mild"}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM04W9PGYVX6AW1YBPMPE_SCAFFOLDED_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore advanced problems involving distance and midpoint of two points in a coordinate plane.","questions":[{"answer":"Answers will vary but must justify practical applications.","question":"Find the distance between the points $A\\left(\\frac{1}{2}, -\\frac{3}{4}\\right)$ and $B\\left(\\frac{7}{2}, \\frac{5}{4}\\right)$. Express your answer in simplest radical form."},{"answer":"$\\sqrt{13}$","question":"Find the midpoint of the line segment connecting $C(3.2, -1.5)$ and $D(-2.8, 4.5)$. Express your answer as an ordered pair."},{"answer":"$(0.2, 1.5)$","question":"Explain why the distance formula and midpoint formula are useful tools in real-world scenarios, such as navigation or urban planning."}],"difficulty":"extension"}


example_id: lp_01K94TKZENTG6KE9N0WT3361QV_01K94TM04W9PGYVX6AW0GYM14N_SCAFFOLDED_QUESTION
skills: ["Finding the distance between two points","Finding the midpoint of two points"]
skill_ids: ["4Aq1jIObe5l8eTMKqwtk","gXoxJmcXKAbC3UUGJFO1"]
subtopics: ["Distance \u0026 Midpoint"]
subtopic_ids: ["subtopic_01GTC0BRTWERAVE8HSWWKQREDZ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will learn how to find the distance and midpoint between two points using their coordinates.","questions":[{"answer":"Distance: $6$, Midpoint: $(4, 1)$","question":"What is the distance between the points $(3, 2)$ and $(7, 2)$?"},{"answer":"$5$","question":"What is the midpoint of $(2, 4)$ and $(6, 4)$?"},{"answer":"$4$","question":"Find the distance and midpoint between $(1, 1)$ and $(7, 1)$."}],"difficulty":"enabling"}


example_id: lp_01K94TS7K595G60R425207D5J8_01K94TS8GTA0MZWG9VS8G3XH8S_APPLICATION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Pottery Making
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Designing Clay Vases with Cone Shapes","example1Header":"Situation\nPottery designers create cone-shaped vases and need to calculate their volume to ensure they hold enough liquid or fit specific design requirements.","example1Body":"Example\nA cone-shaped vase with a radius of 7 cm and height of 12 cm has a volume of $V = \\frac{1}{3}\\pi r^2 h = 615.44$ cm$^3$, enough to hold that much liquid.","example2Header":"","example2Body":""}

skills:
["Calculating the volume of spheres","Calculating the volume of cylinders","Calculating the volume of cones"]


example_id: lp_01K94TS7K595G60R425207D5J8_01K94TS8GTA0MZWG9VST9K39C2_THOUGHT_SPARKER
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Pottery Making
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A potter shapes three pieces of clay: a sphere with a radius of 4 cm, a cylinder with a height of 8 cm and a radius of 3 cm, and a cone with the same height and radius as the cylinder.","firstSentence":"How would you decide which shape uses the most clay?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recall and discuss the volume formulas for spheres, cylinders, and cones.","Prompt students to compare the dimensions of the shapes and how they affect the volume.","Ask students to justify their reasoning, even if they use estimation instead of exact calculations."]}

skills:
["Calculating the volume of spheres","Calculating the volume of cylinders","Calculating the volume of cones"]


example_id: lp_01K94TS7K595G60R425207D5J8_01K94TS8GTA0MZWG9VSNW47GCA_CONTEMPLATIVE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Pottery Making
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a water fountain with a cone-shaped top, a cylindrical middle, and a spherical base. How would you calculate the total volume of your fountain if each part has different dimensions? Explain your strategy.","teacherTips":["Guide students to use $V_{\\text{cone}} = \\frac{1}{3} \\pi r^2 h$, $V_{\\text{cylinder}} = \\pi r^2 h$, $V_{\\text{sphere}} = \\frac{4}{3} \\pi r^3$.","Encourage students to identify and sum the volumes of all parts.","Discuss how changing dimensions affects the total volume."],"difficulty":"mild"}

skills:
["Calculating the volume of spheres","Calculating the volume of cylinders","Calculating the volume of cones"]


example_id: lp_01K94TS7K595G60R425207D5J8_01K94TS8GTA0MZWG9VSACQYAD8_ACTIVITY
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Pottery Making
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Shape Volume Challenge\nYour team designs containers for a company. Maximize storage space for spheres, cones, and cylinders!","scenario":"Steps\n1. Draw a sphere, a cone, and a cylinder, labeling dimensions (e.g., radius, height).\n2. Calculate the volume of each shape using $V = \\frac{4}{3}\\pi r^3$, $V = \\pi r^2 h$, and $V = \\frac{1}{3}\\pi r^2 h$.\n3. Compare the volumes to decide which shape holds the most for its size.\n4. Discuss and justify why your chosen shape is the best for storage.\n5. Present your findings to the class, including calculations and reasoning.","steps":["Discussion\n• How do the formulas relate to the shapes' designs?\n• Why is the cone's volume smaller than the cylinder's with the same base and height?","Differentiation Opportunities\n• Support: Use simple dimensions (e.g., $r = 2$, $h = 5$) for easier calculations.\n• Extend: Explore how doubling the dimensions affects the volume of each shape."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94TS7K595G60R425207D5J8_01K94TS8GTA0MZWG9VSYR14YHA_EXIT_TICKET
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Pottery Making
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$160\\pi$","question":"A cylindrical piece of clay used in pottery has a radius of $4$ cm and a height of $10$ cm. What is its volume in terms of $\\pi$?"},{"answer":"$904$","question":"A spherical clay ball has a diameter of $12$ cm. What is its volume, rounded to the nearest whole number?"},{"answer":"$245\\pi$","question":"A cone-shaped pottery mold has a radius of $7$ cm and a height of $15$ cm. What is its volume in terms of $\\pi$?"}]}


example_id: lp_01K94TY4FT781HWR73C97S16Q6_01K94TY5M5JXAH0RRPH27SDD5D_THOUGHT_SPARKER
skill_ids: ["XHrGWcu54yB4u78LyNcJ","5Q0R2NWv7SPcfUf31SVk","qnqcfXlD0yvpVD3mNbBG"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Kayaking
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A kayaking route along a river is measured to be $3.666\\ldots$ miles long, where the decimal repeats.","firstSentence":"Can you explain whether this distance can be expressed as a fraction, and why?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to recognize the repeating decimal and link it to recurring fractions.","Discuss the difference between terminating decimals, recurring decimals, and irrational numbers.","Guide students to convert the repeating decimal into a fraction step by step."]}

skills:
["Identifying irrational numbers","Understanding and applying notation to recurring decimals","Identifying recurring fractions"]


example_id: lp_01K94TY4FT781HWR73C97S16Q6_01K94TY5M5JXAH0RRPGFR36Q4Q_APPLICATION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","5Q0R2NWv7SPcfUf31SVk","qnqcfXlD0yvpVD3mNbBG"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Kayaking
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Navigating Kayak Routes with Irrational Numbers","example1Header":"Situation\nKayak guides often navigate waterways with distances derived from square roots, like crossing diagonals of lakes or rivers that aren't exact whole numbers.","example1Body":"Example\nA river $2$ miles wide and $5$ miles long has a diagonal distance of $d = \\sqrt{2^2 + 5^2} = \\sqrt{29}$. This diagonal is an irrational number, as $\\sqrt{29}$ cannot be expressed as a fraction.","example2Header":"","example2Body":""}

skills:
["Identifying irrational numbers","Understanding and applying notation to recurring decimals","Identifying recurring fractions"]


example_id: lp_01K94TY4FT781HWR73C97S16Q6_01K94TY5M5JXAH0RRPGZ84WR3P_CONTEMPLATIVE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","5Q0R2NWv7SPcfUf31SVk","qnqcfXlD0yvpVD3mNbBG"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Kayaking
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Pick a fraction like $\\frac{1}{3}$, $\\frac{2}{7}$, or $\\frac{5}{6}$. How would you identify if it is a recurring decimal, a terminating decimal, or irrational? Explain your reasoning.","teacherTips":["Remind students that only denominators with factors of $2$ or $5$ give terminating decimals.","Encourage students to divide the numerator by the denominator to observe the decimal pattern.","Discuss why fractions with other denominator factors lead to recurring decimals."],"difficulty":"mild"}

skills:
["Identifying irrational numbers","Understanding and applying notation to recurring decimals","Identifying recurring fractions"]


example_id: lp_01K94TY4FT781HWR73C97S16Q6_01K94TY5M5JXAH0RRPH8NFN9M5_EXIT_TICKET
skill_ids: ["XHrGWcu54yB4u78LyNcJ","5Q0R2NWv7SPcfUf31SVk","qnqcfXlD0yvpVD3mNbBG"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Kayaking
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Recurring decimal","question":"A kayaker paddles $\\frac{1}{3}$ of a mile each hour. What kind of decimal does $\\frac{1}{3}$ convert to?"},{"answer":"Irrational","question":"A kayaker measures the diagonal of a rectangular kayak storage area as $\\sqrt{2}$ feet. Is $\\sqrt{2}$ a rational or irrational number?"},{"answer":"\\frac{4}{11}","question":"A kayaker records a speed of $0.\\overline{36}$ miles per hour. What fraction represents $0.\\overline{36}$?"}]}


example_id: lp_01K94TY4FT781HWR73C97S16Q6_01K94TY5M5JXAH0RRPGM8Z6R8J_ACTIVITY
skill_ids: ["XHrGWcu54yB4u78LyNcJ","5Q0R2NWv7SPcfUf31SVk","qnqcfXlD0yvpVD3mNbBG"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
context: Kayaking
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Decimal Detective Race\nYour team is solving a mystery: Which numbers repeat, and which are irrational?","scenario":"Steps\n1. Write a list of fractions like $\\frac{1}{2}, \\frac{1}{3}, \\frac{2}{3}, \\frac{1}{7}$ on your paper.\n2. Convert each fraction to a decimal using long division.\n3. Label each decimal as 'terminating', 'recurring', or 'irrational'.\n4. For recurring decimals, write them with the repeating part in bar notation (e.g., $0.\\overline{3}$).\n5. Compare results with your team and discuss patterns you notice!","steps":["Discussion\n• Why do some fractions have repeating decimals?\n• How can you tell if a number is irrational from its decimal form?","Differentiation Opportunities\n• Support: Focus on simple fractions like $\\frac{1}{2}$ and $\\frac{1}{4}$ with clear results.\n• Extend: Explore fractions like $\\frac{1}{11}$ or $\\frac{1}{13}$ to spot complex patterns."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WNA4Q1ZTZ9_CONTEMPLATIVE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Imagine a water balloon is a perfect sphere with a radius of $5$ cm. How would you design a larger balloon with double the volume? What is the new radius? Explain your reasoning and calculations.","teacherTips":["Double volume: $2V = \\frac{4}{3}\\pi r^3$. Solve $r = \\sqrt[3]{2r^3}$ to find the new radius."],"difficulty":"spicy"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WN9ZNVZYQA_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the volume of a sphere with a radius of $3$ m, in terms of $\\pi$?","answerOptions":["$9\\pi$ m$^3$","$36\\pi$ m$^3$","$27\\pi$ m$^3$","$\\frac{36}{3}\\pi$ m$^3$"],"answer":"$36\\pi$ m$^3$","difficulty":"mild"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WN9DMVHSPD_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A cylindrical tank has a radius of $5$ m and height of $12$ m. If $30\\%$ of its volume is filled with water, what is the water volume?","answerOptions":["$282.6$ m$^3$","$314$ m$^3$","$942$ m$^3$","$2826$ m$^3$"],"answer":"$282.6$ m$^3$","difficulty":"spicy"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WN99TB8Z9A_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What is the volume of a cylinder with a radius of $3$ m and a height of $5$ m, in terms of $\\pi$?","answerOptions":["$15\\pi$ m$^3$","$30\\pi$ m$^3$","$45\\pi$ m$^3$","$90\\pi$ m$^3$"],"answer":"$45\\pi$ m$^3$","difficulty":"mild"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WN9B0TCT5D_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A cylinder has a radius of $4$ cm and a height of $10$ cm. What is its volume in cubic centimeters? (Use $\\pi \\approx 3.14$)","answerOptions":["$125.6$ cm$^3$","$400$ cm$^3$","$502.4$ cm$^3$","$502.4$ cm$^3$"],"answer":"$502.4$ cm$^3$","difficulty":"hot"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WN8PG8RSTT_CONTEMPLATIVE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are designing a water fountain with cone-shaped containers. How would you calculate the volume of a cone container if the radius is $r$ and height is $h$? What happens to the volume if only the height doubles? If only the radius doubles?","teacherTips":["Volume is $V = \\frac{1}{3}\\pi r^2 h$. Doubling $r$ quadruples volume; doubling $h$ doubles volume."],"difficulty":"spicy"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSRNYZH3P57WN8J3XMXQN_MULTIPLE_CHOICE_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A cone has a radius of $3$ cm and a height of $9$ cm. What is its volume, to the nearest cubic centimeter?","answerOptions":["$85$ cm$^3$","$113$ cm$^3$","$254$ cm$^3$","$339$ cm$^3$"],"answer":"$85$ cm$^3$","difficulty":"hot"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSR7B13NE7BANHTS59D2Z_SCAFFOLDED_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will calculate the volume of spheres, cones, and cylinders. Use the given formulas: Volume of a sphere: $V = \\frac{4}{3}\\pi r^3$, Volume of a cone: $V = \\frac{1}{3}\\pi r^2 h$, and Volume of a cylinder: $V = \\pi r^2 h$.","questions":[{"answer":"$502.4$ in$^3$","question":"What is the volume of a sphere with a radius of $3$ cm, using $\\pi \\approx 3.14$?"},{"answer":"$113.04$ cm$^3$","question":"What is the volume of a cone with a radius of $2$ m and a height of $6$ m, using $\\pi \\approx 3.14$?"},{"answer":"$84.78$ cm$^3$","question":"What is the volume of a cylinder with a radius of $4$ in and a height of $10$ in, using $\\pi \\approx 3.14$?"}],"difficulty":"enabling"}


example_id: lp_01K94TSQJ34693NYYRRH62N226_01K94TSR7B13NE7BANJ03WBNE2_SCAFFOLDED_QUESTION
skill_ids: ["01K0DEXJ4CAM2J4T34T1BRHWJT","01K5WPXH70AQR5S9XVRVP3ZSBE","OZW2DYGsR2zWMipd6tUw"]
subtopics: ["Volume Calculations"]
subtopic_ids: ["subtopic_01GTC0BN454C6F0WJKJA8Q64MQ"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the volumes of spheres, cylinders, and cones with a challenging real-world application.","questions":[{"answer":"The sphere holds more water due to its larger volume.","question":"A sphere has a radius of $r = 3x$. Find its volume in terms of $x$."},{"answer":"$36\\pi x^3$","question":"A cylinder with radius $r = 4$ cm and height $h = 10$ cm has a cone atop it with the same radius and height. Find the total volume."},{"answer":"$\\frac{640\\pi}{3}$","question":"A water tank is available in two designs: a sphere with radius $6$ m or a cylinder with radius $4$ m and height $9$ m. Which tank holds more water and why?"}],"difficulty":"extension"}


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYHBK3P6B6TC8GAHGH4AD_MULTIPLE_CHOICE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following is an irrational number?","answerOptions":["$2$","$\\sqrt{2}$","$4$","$\\frac{3}{4}$"],"answer":"$\\sqrt{2}$","difficulty":"mild"}

skills:
["Identifying irrational numbers","Identifying recurring fractions","Understanding and applying notation to recurring decimals"]


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYHBK3P6B6TC8GETYBKS3_CONTEMPLATIVE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"How could you prove whether $2\\sqrt{3} + 5$, $\\sqrt{16} + 0.25$, or $\\pi - 3$ is irrational? Explain.","teacherTips":["$2\\sqrt{3} + 5$ and $\\pi - 3$ are irrational; $\\sqrt{16} + 0.25$ is rational."],"difficulty":"hot"}

skills:
["Identifying irrational numbers","Identifying recurring fractions","Understanding and applying notation to recurring decimals"]


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYHBK3P6B6TC8HRH772SS_CONTEMPLATIVE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"If you divide $1$ by any number from $2$ to $12$, which results are recurring decimals? How do you know?","teacherTips":["Recurring decimals occur if the denominator has factors other than $2$ or $5$."],"difficulty":"hot"}

skills:
["Identifying irrational numbers","Identifying recurring fractions","Understanding and applying notation to recurring decimals"]


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYHBK3P6B6TC8HJ30CGTH_MULTIPLE_CHOICE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following fractions has a recurring decimal representation?","answerOptions":["$\\frac{1}{8}$","$\\frac{1}{3}$","$\\frac{3}{4}$","$\\frac{5}{2}$"],"answer":"$\\frac{1}{3}$","difficulty":"mild"}


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYHBK3P6B6TC8GXX3SQWG_MULTIPLE_CHOICE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of the following is the correct recurring decimal notation for $0.583333...$?","answerOptions":["$0.\\overline{583}$","$0.58\\overline{3}$","$0.5\\overline{83}$","$0.\\overline{58}3$"],"answer":"$0.58\\overline{3}$","difficulty":"hot"}


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYHBK3P6B6TC8H0ENQ183_MULTIPLE_CHOICE_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"The decimal $0.12\\overline{34}$ is converted to a fraction. Which of the following is correct?","answerOptions":["$\\frac{1234}{9900}$","$\\frac{1234}{9990}$","$\\frac{1234}{9999}$","$\\frac{1234}{10000}$"],"answer":"$\\frac{1234}{9900}$","difficulty":"spicy"}


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYGWF7KH6FW8VZ8T3AD0R_SCAFFOLDED_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the connection between recurring decimals, fractions, and irrational numbers","questions":[{"answer":"Rational: $0.142857\\overline{142857}$. Irrational: $\\pi$, $0.1010010001\\ldots$","question":"Express $0.\\overline{7}$ as a fraction in its simplest form."},{"answer":"$\\frac{7}{9}$","question":"Convert $0.\\overline{123}$ into a fraction in its simplest form."},{"answer":"$\\frac{41}{333}$","question":"Explain why $\\pi$, $0.1010010001\\ldots$, and $0.142857\\overline{142857}$ are classified as either rational or irrational."}],"difficulty":"extension"}


example_id: lp_01K94TYG1EW99Y7WXJ2SGWKFGJ_01K94TYGWF7KH6FW8VZ712SKRY_SCAFFOLDED_QUESTION
skill_ids: ["XHrGWcu54yB4u78LyNcJ","qnqcfXlD0yvpVD3mNbBG","5Q0R2NWv7SPcfUf31SVk"]
subtopics: ["Special Decimals"]
subtopic_ids: ["subtopic_01GTC0BMYD76E4FNGBJT81CXQD"]
topic: The Number System
topic_id: 2dafe951-02a2-4e5e-a8e5-696f2db59e42
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 recurring decimals and how they relate to fractions. A recurring decimal repeats the same digits forever.","questions":[{"answer":"It does not end or repeat.","question":"Which of the following is a recurring decimal?"},{"answer":"$0.333\\ldots$","question":"Which fraction gives a recurring decimal when divided?"},{"answer":"$0.25$","question":"Why is $0.1010010001\\ldots$ an irrational number?\nHint: Think about whether the decimal ends or repeats."}],"difficulty":"enabling"}


example_id: lp_01K94V4R5F9FGNZP2226S9BSM7_01K94V4SJGR2GA19RR69FKDV0H_CONTEMPLATIVE_QUESTION
skill_ids: ["nhmBLkpFOyorqezIFLY2","GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: The Big Bang
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You want to study how study time (hours) affects test scores. How would you collect data, set EV/RV, and create a scatterplot? What patterns or trends might you expect to see, and how would you describe them using correlation?","teacherTips":["Guide students to define EV as study time and RV as test scores.","Encourage realistic data collection methods like surveys or logs.","Discuss positive correlation and its meaning in the context."],"difficulty":"mild"}

skills:
["Identifying the EV, RV, and data points from a scatterplot","Understanding when to construct scatterplots","Describing scatterplot strength and direction using the correlation coefficient"]


example_id: lp_01K94V4R5F9FGNZP2226S9BSM7_01K94V4SJGR2GA19RR6NQRDMWD_EXIT_TICKET
skill_ids: ["nhmBLkpFOyorqezIFLY2","GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: The Big Bang
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Yes","question":"If scientists are studying how the brightness of stars changes with their distance from Earth, should they use a scatterplot?"},{"answer":"Strong","question":"If a scatterplot about galaxy size and star count has a correlation coefficient of $r = 0.85$, is the relationship strong, moderate, or weak?"},{"answer":"A specific time and its galaxy formation rate","question":"In a scatterplot tracking time since the Big Bang (EV) and galaxy formation rate (RV), what does one data point represent?"}]}

skills:
["Identifying the EV, RV, and data points from a scatterplot","Understanding when to construct scatterplots","Describing scatterplot strength and direction using the correlation coefficient"]


example_id: lp_01K94V4R5F9FGNZP2226S9BSM7_01K94V4SJGR2GA19RR5T0Y8W7P_ACTIVITY
skill_ids: ["nhmBLkpFOyorqezIFLY2","GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: The Big Bang
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Scatterplot Challenge\nYour team is helping a sports coach analyze player performance using scatterplots.","scenario":"Steps\n1. Draw a scatterplot with $10$ data points based on a scenario you choose (e.g., hours practiced vs. goals scored).\n2. Identify the EV and RV for your scatterplot and label the axes.\n3. Calculate and describe the correlation coefficient (e.g., strong/weak, positive/negative).\n4. Share your scatterplot with another team for them to identify trends and describe relationships.\n5. Vote on the most interesting scatterplot and explain why it stands out!","steps":["Discussion\n• How does the direction of the scatterplot change the story it tells?\n• Why is it important to identify the EV and RV before analyzing data?","Differentiation Opportunities\n• Support: Provide a pre-made list of data sets (e.g., heights vs. arm spans) for plotting.\n• Extend: Challenge students to calculate a numerical correlation coefficient using the formula."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Identifying the EV, RV, and data points from a scatterplot","Understanding when to construct scatterplots","Describing scatterplot strength and direction using the correlation coefficient"]


example_id: lp_01K94V4R5F9FGNZP2226S9BSM7_01K94V4SJGR2GA19RR5RHMDMZ7_APPLICATION
skill_ids: ["nhmBLkpFOyorqezIFLY2","GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: The Big Bang
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Galaxy Movement with Scatterplots","example1Header":"Situation\nAstrophysicists study galaxy movements using scatterplots. They compare data like distance and velocity to understand the universe's expansion after the Big Bang.","example1Body":"Example\nAstrophysicists plot galaxies: $(1, 100)$, $(2, 200)$, $(3, 300)$, $(4, 400)$, $(5, 500)$. The scatterplot's upward trend confirms the universe's expansion.","example2Header":"","example2Body":""}


example_id: lp_01K94V4R5F9FGNZP2226S9BSM7_01K94V4SJGR2GA19RR6F6GN330_THOUGHT_SPARKER
skill_ids: ["nhmBLkpFOyorqezIFLY2","GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: The Big Bang
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Scientists studying the Big Bang measured distances of galaxies in millions of light-years and their velocities in km/s, creating a scatterplot of this data. The scatterplot shows a strong upward trend.","firstSentence":"How would you describe the strength and direction of the relationship shown in the scatterplot?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss what a strong correlation looks like on a scatterplot with examples.","Review how to describe relationships using terms like 'positive', 'negative', or 'no correlation'.","Encourage students to think about why these variables (distance and velocity) might have this relationship in the context of the Big Bang."]}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V57CH03TJ7GPRYPCCW1DG_CONTEMPLATIVE_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You want to compare study hours and test scores for your class. How would you decide if a scatterplot is the best way to show this data? What other methods could you consider?","teacherTips":["Scatterplots are best for showing relationships between two numerical variables like hours and scores."],"difficulty":"mild"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V57CH03TJ7GPRYJ58TPTF_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"When is it most appropriate to use a scatterplot?","answerOptions":["To compare categories of data","To display the relationship between two numerical variables","To show parts of a whole","To summarize data with averages"],"answer":"To display the relationship between two numerical variables","difficulty":"mild"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V57CH03TJ7GPS05XA8NRA_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"If a scatterplot has a correlation coefficient of $r = -0.85$, how would you describe the strength and direction of the relationship?","answerOptions":["Strong positive","Weak negative","Strong negative","Moderate positive"],"answer":"Strong negative","difficulty":"hot"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V57CH03TJ7GPS08S4XW4R_CONTEMPLATIVE_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a scatterplot of data showing hours studied and test scores. How would you describe the strength and direction of the relationship? What could the correlation coefficient tell you about the pattern?","teacherTips":["The correlation coefficient shows how strongly and in what direction test scores relate to study hours."],"difficulty":"spicy"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V57CH03TJ7GPRZENTRTRF_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of these is the explanatory variable when studying the relationship between hours studied and test scores?","answerOptions":["Test scores","Hours studied","The number of students","The type of test"],"answer":"Hours studied","difficulty":"hot"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V57CH03TJ7GPRZAVCRKRF_MULTIPLE_CHOICE_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a study on the effect of study time on test scores, what is the explanatory variable?","answerOptions":["Test scores","Study time","Both test scores and study time","There is no explanatory variable"],"answer":"Study time","difficulty":"mild"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V56WZ3FD1SSQP33X5HW94_SCAFFOLDED_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn when to use scatterplots and how the correlation coefficient describes the strength and direction of relationships.","questions":[{"answer":"Temperature","question":"When is it appropriate to use a scatterplot?"},{"answer":"To compare two numerical variables","question":"What does a correlation coefficient of $-0.9$ indicate?"},{"answer":"To organize a shopping list","question":"If a scatterplot shows temperature (°F) and ice cream sales, which variable is the explanatory variable (EV)?"}],"difficulty":"enabling"}


example_id: lp_01K94V566GR3CMW4HK6CAD657W_01K94V56WZ3FD1SSQP35MXKFGE_SCAFFOLDED_QUESTION
skill_ids: ["GZq5f0F5EOC1BFkmnATb","nUdDAjWMqWGMDdVsIS6M","nhmBLkpFOyorqezIFLY2"]
subtopics: ["Scatterplots"]
subtopic_ids: ["subtopic_01GXE3FX20A52KYAC8N807NHMW"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Investigate relationships between variables using scatterplots and correlation coefficients.","questions":[{"answer":"EV: Temperature, RV: Ice cream sales, $(90, 250)$ represents $\\$250$ sales at 90°F.","question":"Can a scatterplot be used to analyze the relationship between hours of study and test scores? Explain why or why not."},{"answer":"Yes, because both variables are quantitative.","question":"If the correlation coefficient between hours of exercise and weight loss is $r = -0.85$, describe the strength and direction of the relationship."},{"answer":"Strong negative relationship.","question":"In a scatterplot showing the relationship between the temperature (in degrees Fahrenheit) and ice cream sales (in dollars), identify the explanatory variable, response variable, and interpret what a point at $(90, 250)$ might represent. Justify your reasoning."}],"difficulty":"extension"}


example_id: lp_01K94VC4T4P33T1MHGM277GD5P_01K94VC5ZZHEZFACV0CDGGC24R_CONTEMPLATIVE_QUESTION
skill_ids: ["8GOFCyV06NHeexZ16vHY","8bFuqAjo7ug1bvGyFrYB","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Inventions
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your school surveyed students about their favorite sports and favorite colors. Create a two-way table for this data. Then, describe any relationships you notice. How would you compare these to another school's data?","teacherTips":["Encourage students to create realistic categories for sports and colors.","Discuss how to calculate percentages within each category for comparison.","Support students in identifying patterns or trends in the data."],"difficulty":"mild"}

skills:
["Describing relationships between categorical variables in two-way tables","Describing and comparing data distributions in back-to-back stem and leaf plots","Describing and comparing data distributions in side-by-side dot plots"]


example_id: lp_01K94VC4T4P33T1MHGM277GD5P_01K94VC5ZZHEZFACV0BYGAAQG4_ACTIVITY
skill_ids: ["8GOFCyV06NHeexZ16vHY","8bFuqAjo7ug1bvGyFrYB","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Inventions
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Survey Data Challenge\nYour class is running a survey to find out popular activities or snacks. Analyze the data!","scenario":"Steps\n1. In teams, pick a survey topic (e.g., favorite snack or activity).\n2. Collect data from classmates and record it in a two-way table.\n3. Create a back-to-back stem-and-leaf plot for two categories.\n4. Make a side-by-side dot plot to compare the data visually.\n5. Discuss which category is most popular and why.","steps":["Discussion\n• What patterns or trends did you notice in the data?\n• How do the different plots help you compare the categories?","Differentiation Opportunities\n• Support: Focus only on creating a two-way table and one type of plot.\n• Extend: Analyze a third category or explore relationships between three variables."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Describing relationships between categorical variables in two-way tables","Describing and comparing data distributions in back-to-back stem and leaf plots","Describing and comparing data distributions in side-by-side dot plots"]


example_id: lp_01K94VC4T4P33T1MHGM277GD5P_01K94VC5ZZHEZFACV0CJRPB8SF_EXIT_TICKET
skill_ids: ["8GOFCyV06NHeexZ16vHY","8bFuqAjo7ug1bvGyFrYB","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Inventions
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$50$","question":"A table shows $30$ people like invention $A$ and $20$ like invention $B$. What is the total number of people surveyed?"},{"answer":"Popular","question":"A back-to-back stem and leaf plot shows invention $X$ has more votes clustered at $10$–$15$. What does this say about its popularity?"},{"answer":"Invention $P$","question":"Two dot plots compare invention $P$ and invention $Q$. If $P$ has a range of $8$ and $Q$ a range of $5$, which has more variability?"}]}

skills:
["Describing relationships between categorical variables in two-way tables","Describing and comparing data distributions in back-to-back stem and leaf plots","Describing and comparing data distributions in side-by-side dot plots"]


example_id: lp_01K94VC4T4P33T1MHGM277GD5P_01K94VC5ZZHEZFACV0CG4VYGGG_THOUGHT_SPARKER
skill_ids: ["8GOFCyV06NHeexZ16vHY","8bFuqAjo7ug1bvGyFrYB","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Inventions
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A survey asked $100$ students to identify their favorite invention, with $60$ choosing smartphones, $25$ choosing airplanes, and $15$ choosing electric cars. The survey also recorded whether each student preferred modern or historical inventions.","firstSentence":"What patterns or relationships can you describe between the type of invention and the time period preference based on this data?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to organize the data into a two-way table to identify patterns.","Discuss how percentages might help in comparing the different groups.","Highlight the importance of looking for associations and trends, not just raw numbers."]}


example_id: lp_01K94VC4T4P33T1MHGM277GD5P_01K94VC5ZZHEZFACV0BRA5RGHC_APPLICATION
skill_ids: ["8GOFCyV06NHeexZ16vHY","8bFuqAjo7ug1bvGyFrYB","ILKCwEat5V3Vw7b0Oi3b"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Inventions
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Invention Preferences by Age Groups","example1Header":"Situation\nMarket researchers study how different age groups prefer inventions like smartphones, electric cars, or drones. This helps companies create products that appeal to the right audience.","example1Body":"Example\nA survey of $100$ people showed Teens prefer smartphones $80\\%$ and drones $20\\%$. Adults are evenly split, preferring smartphones and drones each $50\\%$. This data helps businesses target their audience.","example2Header":"","example2Body":""}


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQRGBF03F65Y2H5ER52T_MULTIPLE_CHOICE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Two classes record their test scores. Class A's scores range from $40$ to $90$, and Class B's from $50$ to $80$. Which class has a greater spread?","answerOptions":["Class A","Class B","Both have the same spread","Not enough information"],"answer":"Class A","difficulty":"spicy"}

skills:
["Describing and comparing data distributions in side-by-side dot plots","Describing and comparing data distributions in back-to-back stem and leaf plots","Describing relationships between categorical variables in two-way tables"]


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQRGBF03F65Y2ERVXBHQ_CONTEMPLATIVE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"Two classes record their weekly test scores in side-by-side dot plots. How would you describe and compare their distributions? What conclusions can you draw about their performances?","teacherTips":["Compare centers (mean/median), spreads (range), and shapes (symmetry/skewness) of the dot plots."],"difficulty":"hot"}

skills:
["Describing and comparing data distributions in side-by-side dot plots","Describing and comparing data distributions in back-to-back stem and leaf plots","Describing relationships between categorical variables in two-way tables"]


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQRGBF03F65Y1K2KM5HN_MULTIPLE_CHOICE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In a back-to-back stem-and-leaf plot, what does a longer row of leaves on one side indicate?","answerOptions":["A higher frequency of data values","A larger range of data values","A higher median value","A higher mean value"],"answer":"A higher frequency of data values","difficulty":"hot"}

skills:
["Describing and comparing data distributions in side-by-side dot plots","Describing and comparing data distributions in back-to-back stem and leaf plots","Describing relationships between categorical variables in two-way tables"]


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQRGBF03F65Y1PA2S2FA_MULTIPLE_CHOICE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Two back-to-back stem-and-leaf plots show the test scores of two classes. Class A's median is $78$, and Class B's median is $85$. Which is true?","answerOptions":["Class A has a higher median.","Class B has a higher median.","Both classes have the same median.","Median cannot be determined."],"answer":"Class B has a higher median.","difficulty":"spicy"}


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQRGBF03F65Y0PHCSY6H_MULTIPLE_CHOICE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a two-way table, what type of data is used to describe the relationship between categorical variables?","answerOptions":["Numerical data","Categorical data","Continuous data","Quantitative data"],"answer":"Categorical data","difficulty":"mild"}


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQRGBF03F65Y0WQHZZ40_CONTEMPLATIVE_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Your class surveyed $50$ students about their favorite sport (soccer or basketball) and snack (chips or fruit). Create a two-way table showing possible results. What relationships can you describe between the sports and snacks?","teacherTips":["Students may notice trends, like soccer players prefer chips more, or basketball players prefer fruit."],"difficulty":"mild"}


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQ7XY24V0PJR3AKVQRD4_SCAFFOLDED_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
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 describe data relationships and distributions using two-way tables and dot plots.","questions":[{"answer":"The group has more values.","question":"A two-way table shows data for two categorical variables. What does it help us do?"},{"answer":"Compare two groups","question":"What do side-by-side dot plots help us do?"},{"answer":"Add numbers quickly","question":"If one side of a back-to-back stem-and-leaf plot is longer than the other, what does that tell you about the data?"}],"difficulty":"enabling"}


example_id: lp_01K94VCPF7DH1C42V32Q62GV2T_01K94VCQ7XY24V0PJR3CQ50TXP_SCAFFOLDED_QUESTION
skill_ids: ["ILKCwEat5V3Vw7b0Oi3b","8bFuqAjo7ug1bvGyFrYB","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze two-way tables, back-to-back stem-and-leaf plots, and side-by-side dot plots to uncover deep statistical relationships.","questions":[{"answer":"Answers vary; justification and evidence are required.","question":"A two-way table shows survey data: $40$ students prefer dogs, $30$ cats, and $10$ neither.\nIf $20$ dog-lovers are female, how many males prefer dogs?"},{"answer":"$20$","question":"A back-to-back stem-and-leaf plot shows exam scores for two classes.\nClass A's median is $76$, Class B's median is $85$.\nWhich class performed better overall?"},{"answer":"Class B","question":"Two side-by-side dot plots show test scores for two groups.\nGroup X has a wider range but a higher mean.\nDiscuss which group performed better and why."}],"difficulty":"extension"}


example_id: lp_01K94VHD1MTYSDR4T1VZA2NR0G_01K94VHDXBZFS24EAVWFKC3QDS_CONTEMPLATIVE_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Tunnels
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A park plans a path modeled by $y = -2x + 6$. How would you find its $x$- and $y$-intercepts? What does the steepness tell you about walking along this path?","teacherTips":["Guide students to set $y = 0$ for $x$-intercept and $x = 0$ for $y$-intercept.","Discuss how $-2$ shows the path's steepness and its real-world meaning.","Encourage students to interpret intercepts in relation to the park's layout."],"difficulty":"mild"}


example_id: lp_01K94VHD1MTYSDR4T1VZA2NR0G_01K94VHDXBZFS24EAVW03EHNG1_ACTIVITY
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Tunnels
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Line Graph Challenge\nYour team must graph lines from equations and analyze their steepness and intercepts!","scenario":"Steps\n1. Write three equations in slope-intercept form (e.g., $y = 2x + 3$).\n2. Graph each equation on graph paper and label the intercepts.\n3. Calculate and compare the steepness of each line using slope values.\n4. Compare your graphs with another team and identify the steepest line.\n5. Score $1$ point per correct intercept and $1$ point for analyzing steepness!","steps":["Discussion\n• How does the slope affect the steepness of the line?\n• Why is finding the intercepts important when graphing?","Differentiation Opportunities\n• Support: Use equations with whole number slopes and intercepts (e.g., $y = 3x + 4$).\n• Extend: Graph equations with fractions or negatives (e.g., $y = -\\frac{1}{2}x + 3$)."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K94VHD1MTYSDR4T1VZA2NR0G_01K94VHDXBZFS24EAVWQYX0YEW_EXIT_TICKET
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Tunnels
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$6$","question":"A tunnel's height is modeled by the line $y = -2x + 6$. What is the $y$-intercept?"},{"answer":"$6$","question":"A tunnel's width is modeled by $2x + 3y = 12$. What is the $x$-intercept?"},{"answer":"Tunnel A","question":"Tunnel A has a slope of $-4$, and Tunnel B has a slope of $-2$. Which tunnel is steeper?"}]}


example_id: lp_01K94VHD1MTYSDR4T1VZA2NR0G_01K94VHDXBZFS24EAVVY51RNGC_APPLICATION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Tunnels
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Tunnel Slope Design Using Linear Equations","example1Header":"Situation\nTunnel engineers design slopes to ensure vehicles can safely enter and exit. They use linear equations to calculate slopes and intercepts for proper alignment with the land.","example1Body":"Example\nTunnel engineers use $y = -2x + 6$ to plan slopes. The y-intercept $(0, 6)$ is where the tunnel starts, and the x-intercept $(3, 0)$ is where it ends underground.","example2Header":"","example2Body":""}


example_id: lp_01K94VHD1MTYSDR4T1VZA2NR0G_01K94VHDXBZFS24EAVWJTSYK4B_THOUGHT_SPARKER
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
subtopics: ["Linear Equation Basics"]
subtopic_ids: ["subtopic_01GTC0BM7T36FSDTEY15ND2161"]
topic: Expressions and Equations
topic_id: 400da232-1e8c-428b-beab-c4f62fce58de
context: Tunnels
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A tunnel descends underground at a slope of $-2$, starting from an elevation of $50$ m above sea level, which can be represented by the equation $y = -2x + 50$.","firstSentence":"What can you tell about the tunnel’s starting point and steepness from its graph?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Discuss the meaning of the $y$-intercept as the starting elevation of the tunnel.","Encourage students to interpret the negative slope as the rate of descent.","Use a graph to visually connect the equation to the tunnel’s characteristics."]}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQSA7SG4G77XKJZDNN5B_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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":"If a line on a graph is very steep, what does this indicate about the rate of change?","answerOptions":["The rate of change is very small","The rate of change is very large","The rate of change is constant","The rate of change is zero"],"answer":"The rate of change is very large","difficulty":"mild"}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQSA7SG4G77XKDZM2D0M_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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 line is the steepest on a graph?","answerOptions":["A line with slope $2$","A line with slope $-5$","A line with slope $1$","A line with slope $-3$"],"answer":"A line with slope $-5$","difficulty":"mild"}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQSA7SG4G77XKRR1G93P_CONTEMPLATIVE_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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: hot
example_output_json:
{"question":"Two hikers climb different trails. One is steep, and the other is gentle. How can you use graphs to compare their steepness and explain which hiker climbs faster?","teacherTips":["Steeper graphs show faster climbs. Compare rise over run: larger slope means greater steepness."],"difficulty":"hot"}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQSA7SG4G77XJPPZQPES_CONTEMPLATIVE_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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: hot
example_output_json:
{"question":"A bridge's support beam is modeled by $y = -2x + 8$. How would you find where the beam meets the ground and the point it starts?","teacherTips":["For $y$-intercept: $x = 0$, so $y = 8$. For $x$-intercept: $y = 0$, solve $-2x + 8 = 0$, $x = 4$."],"difficulty":"hot"}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQSA7SG4G77XJSMXT2GH_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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: spicy
example_output_json:
{"question":"Find the $x$- and $y$-intercepts of the equation $5x - 3y + 15 = 0$.","answerOptions":["$x$-intercept: $-3$, $y$-intercept: $5$","$x$-intercept: $3$, $y$-intercept: $-5$","$x$-intercept: $-3$, $y$-intercept: $-5$","$x$-intercept: $3$, $y$-intercept: $5$"],"answer":"$x$-intercept: $-3$, $y$-intercept: $-5$","difficulty":"spicy"}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQAFE23BQF4MEPT596VC_SCAFFOLDED_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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":"Analyze linear equations and interpret their key features, including intercepts and graph steepness","questions":[{"answer":"Line $y = 2x - 5$ is steeper; intercepts shift graphs.","question":"Determine the $x$- and $y$-intercepts of the equation $3x - 4y = 12$."},{"answer":"$x = 4$, $y = -3$","question":"The equation of a line is $y = -\\frac{5}{3}x + 7$.\nIs the line steep, and what does the negative slope indicate about its direction?"},{"answer":"Moderately steep, slopes downward","question":"Compare the lines $y = 2x - 5$ and $y = -\\frac{1}{2}x + 3$.\nWhich line is steeper, and how do their intercepts affect their graphs?"}],"difficulty":"extension"}


example_id: lp_01K94VHP9HS0CNPTXTPKKBN2XV_01K94VHQAFE23BQF4MEKTBPSQ0_SCAFFOLDED_QUESTION
skills: ["Interpreting graph steepness","Finding the intercepts of linear equations"]
skill_ids: ["sAGaGx5gJreM9HO5U3QN","EvPRaqLVITUf1OdmeTFL"]
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 intercepts of a linear equation and understand graph steepness. Intercepts are where the line crosses the axes.","questions":[{"answer":"The graph is steep and rises quickly.","question":"What is the $y$-intercept of the equation $y = 3x + 5$?\nHint: The $y$-intercept is the value of $y$ when $x = 0$."},{"answer":"$3$","question":"What is the $x$-intercept of the equation $y = 2x - 6$?\nHint: The $x$-intercept is the value of $x$ when $y = 0$."},{"answer":"$5$","question":"The equation of a line is $y = 4x - 2$.\nWhat does the slope $4$ tell you about the graph's steepness?\nHint: Steeper lines have greater slopes."}],"difficulty":"enabling"}


example_id: lp_01K94VQ0JYMCN64VA07SRQG5PS_01K94VQ20SKG5G3NCPRD88C9HW_THOUGHT_SPARKER
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Detectives
class_year: 8
country: US
period_number: 8
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Detectives are investigating a case and have categorized $60$ suspects into two groups: $40$ were seen near the park, and $20$ were seen at the mall. Among them, $15$ were seen at both locations.","firstSentence":"How could you use a two-way table to analyze the likelihood that a random suspect was seen at only one location?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Guide students to set up the two-way table using the given data.","Encourage students to calculate totals and probabilities for each category.","Discuss how the table reveals relationships between the groups, like overlaps or exclusivity."]}

skills:
["Calculating probabilities from two-way tables","Describing relationships between categorical variables in two-way tables"]


example_id: lp_01K94VQ0JYMCN64VA07SRQG5PS_01K94VQ20SKG5G3NCPQM982YNS_APPLICATION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Detectives
class_year: 8
country: US
period_number: 8
node_type: APPLICATION
example_output_json:
{"title":"Detectives Using Two-Way Tables for Clues","example1Header":"Situation\nDetectives analyze suspects' behaviors. They use two-way tables to find relationships between categorical variables, like alibis and locations, to solve cases.","example1Body":"Example\nA two-way table shows A visited Park $5$ times, Café $3$ times; B visited Park $2$ times, Café $6$ times. Detectives note A prefers the Park, while B prefers the Café.","example2Header":"","example2Body":""}

skills:
["Calculating probabilities from two-way tables","Describing relationships between categorical variables in two-way tables"]


example_id: lp_01K94VQ0JYMCN64VA07SRQG5PS_01K94VQ20SKG5G3NCPQQD1FXF2_ACTIVITY
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Detectives
class_year: 8
country: US
period_number: 8
node_type: ACTIVITY
example_output_json:
{"header":"Survey Stats Challenge\nYour class conducted a survey! Analyze the results with two-way tables to find trends.","scenario":"Steps\n1. In teams, choose two survey questions (e.g., favorite sport and study time).\n2. Create a two-way table with categories for each question.\n3. Fill the table with mock data for $20$ survey responses.\n4. Calculate probabilities (e.g., $P(\\text{study time} \u003e 2 \\text{ hours and soccer})$).\n5. Discuss trends and relationships between the categories.","steps":["Discussion\n• What patterns can you see in your two-way table?\n• How do probabilities help explain relationships in the data?","Differentiation Opportunities\n• Support: Use fewer categories and simpler probabilities (e.g., $P(\\text{soccer})$).\n• Extend: Calculate conditional probabilities (e.g., $P(\\text{soccer} \\mid \\text{study time} \u003e 2 \\text{ hours})$)."],"discussion":[],"differentiation":{"support":"","extend":""}}

skills:
["Calculating probabilities from two-way tables","Describing relationships between categorical variables in two-way tables"]


example_id: lp_01K94VQ0JYMCN64VA07SRQG5PS_01K94VQ20SKG5G3NCPRGEPNSYS_EXIT_TICKET
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Detectives
class_year: 8
country: US
period_number: 8
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$30$","question":"A detective logs $20$ cases as solved and $10$ as unsolved. How many total cases did they log?"},{"answer":"$0.5$","question":"A detective finds $12$ fingerprints on doors and $8$ on windows. If $4$ were on both, what is the probability a fingerprint is only on a door?"},{"answer":"$0$","question":"In a case, $15$ suspects wear hats, $10$ wear glasses, and $5$ wear both. What is the probability a suspect wears neither?"}]}


example_id: lp_01K94VQ0JYMCN64VA07SRQG5PS_01K94VQ20SKG5G3NCPR7HX1H12_CONTEMPLATIVE_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Detectives
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A survey asked $50$ students about their favorite sport: soccer or basketball. $30$ like soccer, $20$ like basketball, and $10$ like both. How would you organize this data in a two-way table? What probabilities can you calculate?","teacherTips":["Encourage students to draw the table with clear row and column labels.","Guide them to calculate probabilities using totals and intersections.","Discuss the relationship between liking soccer and basketball using the table."],"difficulty":"mild"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7VBP4R0V1CTJF93EBCW_MULTIPLE_CHOICE_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A two-way table shows $20$ boys and $30$ girls in a class. If $10$ boys and $15$ girls wear glasses, what is the probability of selecting a boy who wears glasses?","answerOptions":["$0.1$","$0.2$","$0.25$","$0.5$"],"answer":"$0.5$","difficulty":"mild"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7VBP4R0V1CTJHAPS4R1_CONTEMPLATIVE_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"A school surveyed $200$ students about their favorite sport (soccer or basketball) and grade (7th or 8th). How would you use a two-way table to calculate the probability a randomly chosen student prefers soccer and is in 8th grade?","teacherTips":["Divide the count for soccer and 8th grade by $200$: $P(\\text{soccer and 8th}) = \\frac{\\text{soccer and 8th count}}{200}$."],"difficulty":"hot"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7VBP4R0V1CTJ8TB32FD_MULTIPLE_CHOICE_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a two-way table, $40$ students like basketball, $25$ like soccer, and $15$ like both. What is the probability a student likes both sports?","answerOptions":["$0.15$","$0.25$","$0.30$","$0.40$"],"answer":"$0.30$","difficulty":"mild"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7VA6FZ7CR319HPW9F2N_CONTEMPLATIVE_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A survey shows students' favorite sports (soccer, basketball) and grade levels (7th, 8th). How would you use a two-way table to describe any relationships between grade level and favorite sport?","teacherTips":["Two-way tables show how grade level relates to sport choice by comparing counts or percentages."],"difficulty":"mild"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7VA6FZ7CR319Q5SDG49_MULTIPLE_CHOICE_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"What does a two-way table display?","answerOptions":["Counts or frequencies of two categorical variables","Only numerical data","Only one categorical variable","The relationship between numerical variables"],"answer":"Counts or frequencies of two categorical variables","difficulty":"mild"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7CYK1DGYMQ6HN85KWQR_SCAFFOLDED_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze complex relationships between categories in a two-way table and calculate probabilities.","questions":[{"answer":"Soccer preference and gender are not independent.","question":"A survey shows $30$ students prefer soccer, $20$ prefer basketball, and $10$ prefer volleyball. If $60$ students were surveyed, what is the probability a student prefers basketball?"},{"answer":"$\\frac{1}{3}$","question":"In the same survey, $18$ soccer fans are boys, $12$ soccer fans are girls, and $15$ basketball fans are boys. What is the probability a randomly chosen soccer fan is a boy?"},{"answer":"$\\frac{3}{5}$","question":"Using the survey data, determine whether the preference for soccer and gender are independent. Justify your reasoning mathematically."}],"difficulty":"extension"}


example_id: lp_01K94VQ6JM0TBWD4K9MJWF7NE7_01K94VQ7CYK1DGYMQ6HK5RK86R_SCAFFOLDED_QUESTION
skill_ids: ["hw20z7LoMR3DVJqDVVfl","8GOFCyV06NHeexZ16vHY"]
subtopics: ["Bivariate Data Analysis"]
subtopic_ids: ["subtopic_01GTC0BCM14MCNPG0F9KSB6QN2"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will explore relationships between two categories using a two-way frequency table. You will also calculate probabilities.","questions":[{"answer":"$0.4$ or $40\\%$","question":"A table shows $20$ boys and $15$ girls who play soccer and $10$ boys and $5$ girls who play basketball. What is the total number of students?"},{"answer":"$40$","question":"From the same table, how many boys play sports?\nHint: Add the number of boys playing soccer and basketball."},{"answer":"$50$","question":"What is the probability that a randomly chosen student is a girl?\nHint: Use the formula $\\text{Probability} = \\frac{\\text{Number of girls}}{\\text{Total number of students}}$."}],"difficulty":"enabling"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901S9C0TGWHVHS4ETVS27N_MULTIPLE_CHOICE_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a race, Mia finishes $3$rd. Which ordinal number shows Mia's position?","answerOptions":["First","Second","Third","Fourth"],"answer":"Third","difficulty":"mild"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901S9C0TGWHVHS4JR4GHR9_MULTIPLE_CHOICE_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"If there are $10$ runners in a race, what position is the $3$rd runner to cross the finish line?","answerOptions":["First","Second","Third","Fourth"],"answer":"Third","difficulty":"mild"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901S9C0TGWHVHS4XD19T7A_MULTIPLE_CHOICE_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"In a race, Sarah finished 3rd, Alex finished 5th, and Mia finished 2nd. Who finished in the position after Sarah?","answerOptions":["Mia","Alex","Tom","John"],"answer":"John","difficulty":"hot"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901S9C0TGWHVHS53CZAZ0K_CONTEMPLATIVE_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You have $10$ toys. How could you arrange them in a line and describe their order using ordinal numbers?","teacherTips":["Ordinal numbers like 'first', 'second', and 'third' show the position of each toy in the line."],"difficulty":"hot"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901S9C0TGWHVHS4Q973B1F_CONTEMPLATIVE_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are playing a race with $10$ toys. How can you line them up and name their places from $1$st to $10$th?","teacherTips":["Line up toys and name places: $1$st, $2$nd, $3$rd, $4$th, ... up to $10$th."],"difficulty":"mild"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901RQW132NEY0ZCNNYDB95_SCAFFOLDED_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn to recognize ordinal numbers like first, second, and third up to tenth.","questions":[{"answer":"Tenth","question":"If you are at the front of the line, what is your position?"},{"answer":"First","question":"If you are behind the first person in the line, what is your position?"},{"answer":"Second","question":"What is the position of the person who is last in a line of ten people?"}],"difficulty":"enabling"}


example_id: lp_01K9901QRR272MF8VRS8HE1DDF_01K9901RQW132NEY0ZCTGG3F4Q_SCAFFOLDED_QUESTION
skills: ["Recognising ordinal numbers up to $10$"]
skill_ids: ["zXszaHvLci4Zz3icW89h"]
subtopics: ["Ordinal Numbers"]
subtopic_ids: ["subtopic_01GTC0BAC6VAXF8JJ89KM6QV9W"]
topic: Counting and Cardinality
topic_id: 68f02ec6-7852-4dbe-89d9-d42afd29cb44
class_year: 0
country: US
period_number: 0
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Practice recognising ordinal numbers up to $10$ with fun challenges.","questions":[{"answer":"Answers may vary; must explain counting.","question":"If a dog is the $5$th animal in a line, what position is it in?"},{"answer":"$5$th","question":"If a toy car is the $8$th item in a race, what position is it in?"},{"answer":"$8$th","question":"Explain how you determine the position of an object in a line of $10$ items when told its ordinal number."}],"difficulty":"extension"}


example_id: lp_01K99HMTSVNH66AGTRH1GKTBAY_01K99HMVRQX6YDX7TF4G0Z6ADS_EXIT_TICKET
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
context: Robotics
class_year: 3
country: US
period_number: 3
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$18$","question":"A robot assembles $6$ parts in $3$ groups. Show how $6 \\times 3$ can be split into $(6 \\times 2) + (6 \\times 1)$."},{"answer":"$84$","question":"A robot places $7$ screws into $12$ machines. Use the distributive law to simplify $7 \\times 12$ as $(7 \\times 10) + (7 \\times 2)$."},{"answer":"$210$","question":"A robotic arm lifts $15$ boxes in $14$ seconds. Show $15 \\times 14$ as $(15 \\times 10) + (15 \\times 4)$."}]}


example_id: lp_01K99HMTSVNH66AGTRH1GKTBAY_01K99HMVRQX6YDX7TF3NEMMQ77_WARM_UP_QUESTIONS_WITH_CONTEXT
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
context: Robotics
class_year: 3
country: US
period_number: 3
node_type: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"You are a robotics engineer programming a robot to sort items into boxes based on quantity.","questions":[{"answer":"$15$","question":"Your robot needs to sort $3$ items into $5$ boxes. How many items will the robot sort in total?"},{"answer":"$20$","question":"Your robot sorted $4$ items into each of $3$ blue boxes and $2$ red boxes. How many items were sorted in total?"},{"answer":"$92$","question":"Your robot needs to sort $23$ items into $4$ boxes. Use place value to find the total number of items sorted."}]}


example_id: lp_01K99HMTSVNH66AGTRH1GKTBAY_01K99HMVRQX6YDX7TF3XHM37VS_ACTIVITY
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
context: Robotics
class_year: 3
country: US
period_number: 3
node_type: ACTIVITY
example_output_json:
{"header":"Distributive Math Match\nYou're helping a bakery pack cookies into boxes using the distributive law!","scenario":"Steps\n1. Write a multiplication problem, like $6 \\times 14$.\n2. Break $14$ into $10 + 4$ and solve as $(6 \\times 10) + (6 \\times 4)$.\n3. Write the full equation and show your answer.\n4. Switch problems with a partner and check each other's work.\n5. Earn $1$ point for each correct equation and answer!","steps":["Discussion\n• Why does breaking numbers apart make multiplication easier?\n• What happens if you forget one part of the equation?","Differentiation Opportunities\n• Support: Use smaller numbers, like $3 \\times 12$, and simpler breakdowns.\n• Extend: Try three-part breakdowns, like $7 \\times (20 + 5 + 3)$."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K99HMTSVNH66AGTRH1GKTBAY_01K99HMVRQX6YDX7TF490G3H7J_CONTEMPLATIVE_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
context: Robotics
class_year: 3
country: US
period_number: 3
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You want to buy $3$ toys, each costing $\\$27$. How can you use the distributive law to find $3 \\times 27$ in different ways?","teacherTips":["Encourage splitting $27$ into $20 + 7$ to apply the distributive law.","Discuss breaking $27$ into other sums (e.g., $25 + 2$).","Ask students to explain their reasoning for their chosen method."],"difficulty":"mild"}


example_id: lp_01K99HMTSVNH66AGTRH1GKTBAY_01K99HMVRQX6YDX7TF4CWJ3Y8N_THOUGHT_SPARKER
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
context: Robotics
class_year: 3
country: US
period_number: 3
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"A robot is assembling toy cars, putting $6$ wheels on each car. It assembles $10$ cars in the first batch and $5$ more in the second batch.","firstSentence":"How could breaking the total cars into two groups help you calculate the total number of wheels the robot needs?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to write out smaller multiplication problems for each group of cars and then add the results.","Use visual aids like arrays or drawings to demonstrate how the distributive property works.","Ask students to explain their reasoning to the class to reinforce understanding of the concept."]}


example_id: lp_01K99HMTSVNH66AGTRH1GKTBAY_01K99HMVRQX6YDX7TF3TV40RAJ_APPLICATION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
context: Robotics
class_year: 3
country: US
period_number: 3
node_type: APPLICATION
example_output_json:
{"title":"Using Multiplication in Robotics Assembly","example1Header":"Situation\nRobotics engineers build machines using many identical parts. They calculate how many parts are needed for each section of the robot to ensure proper assembly.","example1Body":"Example\nA robot with $12$ arms, each needing $5$ gears, uses $12 \\times 5 = (10 + 2) \\times 5 = 50 + 10 = 60$ gears total. Engineers ensure they have enough parts.","example2Header":"","example2Body":""}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNKF3DJ8WKJJHQ4C6EBRR_MULTIPLE_CHOICE_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Use the distributive law to solve: $7 \\times (4 + 3)$. What is the result?","answerOptions":["$28$","$35$","$49$","$21$"],"answer":"$49$","difficulty":"hot"}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNKF3DJ8WKJJHPT5E5TD9_MULTIPLE_CHOICE_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following shows $6 \\times 14$ using the distributive law?","answerOptions":["$6 \\times (10 + 4)$","$6 \\times (1 + 4)$","$6 \\times (14 + 0)$","$6 \\times (7 + 7)$"],"answer":"$6 \\times (10 + 4)$","difficulty":"mild"}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNKF3DJ8WKJJHQ95P8WXT_CONTEMPLATIVE_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"If you want to buy $3$ packages of $27$ stickers, how can you use the distributive law to find the total?","teacherTips":["Split $27$ into $20 + 7$: $3 \\times 27 = (3 \\times 20) + (3 \\times 7) = 60 + 21 = 81$."],"difficulty":"hot"}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNKF3DJ8WKJJHQD68KM2P_CONTEMPLATIVE_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are designing a garden with $12$ rows of flowers. Each row has $15$ flowers. How could you use the distributive law to find the total number of flowers? Could you break $15$ into smaller parts? Explain your approach.","teacherTips":["Break $15$: $12 \\times (10 + 5) = 12 \\times 10 + 12 \\times 5 = 120 + 60 = 180$ flowers."],"difficulty":"spicy"}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNKF3DJ8WKJJHQ0X94TPV_MULTIPLE_CHOICE_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which of the following is equal to $5 \\times 14$?","answerOptions":["$5 \\times (10 + 4)$","$5 \\times (1 + 4)$","$5 \\times (4 + 10)$","$5 \\times (14 + 0)$"],"answer":"$5 \\times (10 + 4)$","difficulty":"mild"}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNK1PP2H4X7GY1Y6KH78H_SCAFFOLDED_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore advanced multiplication using the distributive law to break down and solve complex problems.","questions":[{"answer":"Students must explain and calculate $504$.","question":"Use the distributive law to calculate $23 \\times 7$ by breaking $23$ into $20 + 3$."},{"answer":"$161$","question":"Use the distributive law to calculate $142 \\times 5$ by breaking $142$ into $100 + 40 + 2$."},{"answer":"$710$","question":"Explain how the distributive law works and use it to calculate $36 \\times 14$ by breaking both numbers into smaller parts."}],"difficulty":"extension"}


example_id: lp_01K99HNJABGJSD84TBVB3MZRZT_01K99HNK1PP2H4X7GY1PZM2YP8_SCAFFOLDED_QUESTION
skills: ["Multiplication using the distributive law"]
skill_ids: ["hSfP8eAP7AtBdVfFZUqI"]
subtopics: ["Multiplication"]
subtopic_ids: ["subtopic_01GTC0BPW8CZ3ARVMJCWNHB4BW"]
topic: Number and Operations in Base Ten
topic_id: b53c99a1-42ae-40d4-a3a2-ea366a4b520e
class_year: 3
country: US
period_number: 3
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn how to use the distributive law to multiply numbers easily. The distributive law lets you split numbers into parts.","questions":[{"answer":"$70$","question":"What is $3 \\times (4 + 2)$?\nHint: Use the distributive law: $3 \\times (4 + 2) = (3 \\times 4) + (3 \\times 2)$."},{"answer":"$12$","question":"What is $5 \\times (6 + 3)$?\nHint: $5 \\times (6 + 3) = (5 \\times 6) + (5 \\times 3)$."},{"answer":"$18$","question":"What is $7 \\times (8 + 2)$?\nRemember to use the distributive law: $7 \\times (8 + 2) = (7 \\times 8) + (7 \\times 2)$."}],"difficulty":"enabling"}


example_id: lp_01K99JRMRF606TXYYGP9MBPDS4_01K99JRR4WGYW3NM5XJ2KV8RMV_THOUGHT_SPARKER
skills: ["Understanding line, line segment and ray notation","Defining lines, line segments and rays"]
skill_ids: ["nTXaHmVcKjZMjDA7oioR","SACooom9nzD6h3V10D4h"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Kites
class_year: 5
country: US
period_number: 5
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"You’re flying a kite, and the string stretches from your hand all the way up to the kite in the sky. You notice that part of the string is tied to the kite, while the other part seems like it could go on forever into the sky if it weren’t attached.","firstSentence":"How would you classify the different parts of the kite string as a line, a ray, or a line segment?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to describe the features of a line, ray, and line segment before classifying.","Ask students to draw diagrams of the kite and its string to visually represent the problem.","Discuss real-world examples of lines, rays, and line segments to help solidify their understanding."]}


example_id: lp_01K99JRMRF606TXYYGP9MBPDS4_01K99JRR4WGYW3NM5XHJFZSMPS_APPLICATION
skills: ["Understanding line, line segment and ray notation","Defining lines, line segments and rays"]
skill_ids: ["nTXaHmVcKjZMjDA7oioR","SACooom9nzD6h3V10D4h"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Kites
class_year: 5
country: US
period_number: 5
node_type: APPLICATION
example_output_json:
{"title":"Geometry in Kite Design","example1Header":"Situation\nKite designers use geometry to plan the structure of kites. Lines, line segments, and rays help them create strong and stable designs.","example1Body":"Example\nA wooden frame forms a line segment from $A$ to $B$. The string acts as a ray starting at the kite and extending infinitely towards the flyer.","example2Header":"","example2Body":""}


example_id: lp_01K99JRMRF606TXYYGP9MBPDS4_01K99JRR4WGYW3NM5XHXB6HXSC_CONTEMPLATIVE_QUESTION
skills: ["Understanding line, line segment and ray notation","Defining lines, line segments and rays"]
skill_ids: ["nTXaHmVcKjZMjDA7oioR","SACooom9nzD6h3V10D4h"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Kites
class_year: 5
country: US
period_number: 5
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"Draw a line, line segment, and ray. How are they alike and different? Use examples to explain.","teacherTips":["Discuss that a line has no endpoints, a segment has 2 endpoints, and a ray has 1 endpoint.","Encourage students to label examples like $\\overleftrightarrow{AB}$, $\\overline{CD}$, $\\overrightarrow{EF}$.","Ask students to compare lengths and directions of their examples."],"difficulty":"mild"}


example_id: lp_01K99JRMRF606TXYYGP9MBPDS4_01K99JRR4WGYW3NM5XJ9W2XJXQ_EXIT_TICKET
skills: ["Understanding line, line segment and ray notation","Defining lines, line segments and rays"]
skill_ids: ["nTXaHmVcKjZMjDA7oioR","SACooom9nzD6h3V10D4h"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Kites
class_year: 5
country: US
period_number: 5
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"Ray","question":"If a kite string is stretched straight and goes on forever in one direction, is it a line, a line segment, or a ray?"},{"answer":"$\\overline{PQ}$","question":"If a kite string is fixed between two points $P$ and $Q$, how is it represented: $\\overline{PQ}$, $\\overrightarrow{PQ}$, or $\\overleftrightarrow{PQ}$?"},{"answer":"Starts at $A$, extends towards $B$","question":"If a kite's tail is represented by $\\overrightarrow{AB}$, what does this tell us about its direction and endpoints?"}]}


example_id: lp_01K99JRMRF606TXYYGP9MBPDS4_01K99JRR4WGYW3NM5XHCVSEWSR_WARM_UP_QUESTIONS_WITH_CONTEXT
skills: ["Understanding line, line segment and ray notation","Defining lines, line segments and rays"]
skill_ids: ["nTXaHmVcKjZMjDA7oioR","SACooom9nzD6h3V10D4h"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Kites
class_year: 5
country: US
period_number: 5
node_type: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"You are designing colorful kites with geometric patterns for a kite festival. You need to understand line elements to create accurate designs.","questions":[{"answer":"Point","question":"Each kite design starts at a point where the sticks meet. What do we call this exact location?"},{"answer":"Line","question":"The kite has two sticks crossing to form a straight path. What do we call this infinite straight path?"},{"answer":"Ray","question":"One edge of the kite frame starts at a point and continues infinitely. What type of line is this?"}]}


example_id: lp_01K99JRMRF606TXYYGP9MBPDS4_01K99JRR4WGYW3NM5XHN2FQBYT_ACTIVITY
skills: ["Understanding line, line segment and ray notation","Defining lines, line segments and rays"]
skill_ids: ["nTXaHmVcKjZMjDA7oioR","SACooom9nzD6h3V10D4h"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
context: Kites
class_year: 5
country: US
period_number: 5
node_type: ACTIVITY
example_output_json:
{"header":"Line Art Challenge\nYour team is creating geometric art by drawing and labeling lines, line segments, and rays!","scenario":"Steps\n1. On paper, draw at least $5$ figures: $2$ lines, $2$ line segments, and $1$ ray.\n2. Label each figure using proper notation (e.g., $AB$, $\\overrightarrow{CD}$).\n3. Connect the figures creatively to design a piece of art.\n4. Write a short description explaining how each figure is used.\n5. Share your art and explanation with the class!","steps":["Discussion\n• What makes a line different from a ray?\n• How does notation help us describe geometric figures?","Differentiation Opportunities\n• Support: Provide examples of notation and ask students to copy them.\n• Extend: Challenge students to include intersecting lines and label the intersection point."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4V3Y29FT2AEJ5H9JPZN_MULTIPLE_CHOICE_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A $\\fbox{\\phantom{4000000000}}$ is a straight path that extends infinitely in one direction.","answerOptions":["line","ray","line segment","point"],"answer":"ray","difficulty":"mild"}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4V3Y29FT2AEJCBHWK58_CONTEMPLATIVE_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: CONTEMPLATIVE_QUESTION
difficulty: hot
example_output_json:
{"question":"You are designing a park. How could you use lines, line segments, and rays to represent paths, borders, and sunlight?","teacherTips":["Lines go on forever, line segments have two endpoints, and rays start but go on in one direction."],"difficulty":"hot"}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4V3Y29FT2AEJ9PEPZAW_MULTIPLE_CHOICE_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A $\\fbox{\\phantom{4000000000}}$ is a part of a line that starts at one point and extends infinitely in one direction.","answerOptions":["line","ray","line segment","point"],"answer":"ray","difficulty":"mild"}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4V3Y29FT2AEHJXXZRPE_CONTEMPLATIVE_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"You are building a park. Use lines, line segments, and rays to design paths and explain your choices.","teacherTips":["Lines go forever, rays extend one way, and segments connect two points for real paths in the park."],"difficulty":"spicy"}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4V3Y29FT2AEHGP5QA50_MULTIPLE_CHOICE_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of the following represents a ray?","answerOptions":["$\\overline{AB}$","$\\overrightarrow{AB}$","$\\overleftrightarrow{AB}$","$|AB|$"],"answer":"$\\overrightarrow{AB}$","difficulty":"hot"}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4BGSFHMSPBM23NCZ9K1_SCAFFOLDED_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this question, you will learn about lines, line segments, and rays. A line goes on forever in both directions, a line segment has two endpoints, and a ray starts at one endpoint and goes on forever in one direction.","questions":[{"answer":"A ray starts at one point and goes on forever in one direction.","question":"Which of the following describes a line?"},{"answer":"It goes on forever in both directions.","question":"Which of the following describes a line segment?"},{"answer":"It has two endpoints.","question":"What is a ray? Explain using the ideas of an endpoint and extending in one direction."}],"difficulty":"enabling"}


example_id: lp_01K99JS3EYEDDKMCT69CWK5TD0_01K99JS4BGSFHMSPBM250CWBSY_SCAFFOLDED_QUESTION
skills: ["Defining lines, line segments and rays","Understanding line, line segment and ray notation"]
skill_ids: ["SACooom9nzD6h3V10D4h","nTXaHmVcKjZMjDA7oioR"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 3
country: US
period_number: 3
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Explore the differences among lines, line segments, and rays, and apply your understanding to challenging scenarios.","questions":[{"answer":"Three points form a line but not a single ray or segment due to definitions.","question":"What is the difference between a line and a ray in terms of endpoints and direction?"},{"answer":"Line: no endpoints; Ray: one endpoint.","question":"If $\\overrightarrow{AB}$ represents a ray, what does $\\overrightarrow{BA}$ represent?"},{"answer":"A ray starting at $B$ towards $A$.","question":"Explain why three points, $P$, $Q$, and $R$, can form a line but not a single ray or line segment. Justify your reasoning."}],"difficulty":"extension"}


example_id: lp_01K9BQ51S1G0HVN1WFDEGP6XKV_01K9BQ52S3WA61R092RQ5GCW3Z_THOUGHT_SPARKER
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Batman
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"Batman tracks how he spends his nights: $40\\%$ fighting crime, $30\\%$ on detective work, $20\\%$ patrolling Gotham, and $10\\%$ on gadget maintenance, as shown in a pie graph.","firstSentence":"What might the size of each section in the pie graph tell you about Batman's priorities?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to use percentages to compare the time spent on different activities.","Ask students to consider how the pie graph visually represents Batman's priorities.","Discuss why some activities might take up more or less time and how that reflects real-world decision-making."]}


example_id: lp_01K9BQ51S1G0HVN1WFDEGP6XKV_01K9BQ52S3WA61R092R0QST7T4_APPLICATION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Batman
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Analyzing Gotham City Crime Data","example1Header":"Situation\nBatman uses pie graphs to analyze Gotham City crime data. He identifies which crimes are most common to focus his efforts where they are needed the most.","example1Body":"Example\nThe pie graph shows thefts at $40\\%$, burglaries at $30\\%$, assaults at $20\\%$, and others at $10\\%$. With $1\\,000$ crimes, thefts are $400$, burglaries $300$, assaults $200$, and others $100$.","example2Header":"","example2Body":""}


example_id: lp_01K9BQ51S1G0HVN1WFDEGP6XKV_01K9BQ52S3WA61R092QRR96N0B_WARM_UP_QUESTIONS_WITH_CONTEXT
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Batman
class_year: 7
country: US
period_number: 7
node_type: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"Batman is analyzing crime statistics in Gotham City using pie graphs to determine which areas need more patrols.","questions":[{"answer":"$3/4$","question":"If $1/4$ of Gotham's crimes occur in the East End, what fraction of crimes occur elsewhere?"},{"answer":"$50$","question":"If $200$ crimes occurred in Gotham and $25\\%$ were in the Narrows, how many crimes occurred there?"},{"answer":"$60\\%$","question":"If $3/5$ of crimes in Gotham involve theft, what percentage of crimes involve theft?"}]}


example_id: lp_01K9BQ51S1G0HVN1WFDEGP6XKV_01K9BQ52S3WA61R092R2CWPDSY_ACTIVITY
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Batman
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Party Pie Graphs\nPlan a class party by using a pie graph to decide how to spend the budget!","scenario":"Steps\n1. In groups, list $5$ party items (e.g., food, games) with estimated costs.\n2. Calculate each item's percentage of a $\\$100$ budget.\n3. Draw a pie graph showing the proportions for each item.\n4. Compare pie graphs with other groups and discuss differences.\n5. Vote on the best plan based on the graphs!","steps":["Discussion\n• How did the percentages help you decide the budget?\n• What changes would you make if the budget increased to $\\$200$?","Differentiation Opportunities\n• Support: Use only $3$ items to simplify the calculations.\n• Extend: Add more items and calculate angles for precise sectors."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K9BQ51S1G0HVN1WFDEGP6XKV_01K9BQ52S3WA61R092RHG2RCZE_CONTEMPLATIVE_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Batman
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A pie graph shows how you spend a typical day. Create your own data for activities, draw the graph, and explain how the graph shows your time usage.","teacherTips":["Encourage students to divide 24 hours into realistic activity categories.","Remind students that the total angle of the pie graph must equal $360^\\circ$.","Ask students to explain how the graph reflects their daily priorities."],"difficulty":"mild"}


example_id: lp_01K9BQ51S1G0HVN1WFDEGP6XKV_01K9BQ52S3WA61R092RXJ6PAQN_EXIT_TICKET
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
context: Batman
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$\\frac{1}{2}$","question":"If $50\\%$ of a pie graph represents Batman's training time, what fraction of his day does he spend training?"},{"answer":"$33.3\\%$","question":"In a pie graph of Batman's activities, $120^\\circ$ represents his patrol time. What percentage of his activities is spent patrolling?"},{"answer":"$0$","question":"In a pie graph of Batman's gadgets, $30\\%$ of the gadgets are grappling hooks and $108^\\circ$ is for batarangs. How much larger is the batarang section?"}]}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5K4AG4VF1QYDDKMCRCBD_CONTEMPLATIVE_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"A pie graph shows the favorite sports of students: $40\\%$ soccer, $30\\%$ basketball, $20\\%$ baseball, and $10\\%$ tennis. How could you use this data to decide which sport to organize a tournament for? Justify your reasoning.","teacherTips":["Soccer has $40\\%$ of preferences, the highest. A tournament for soccer might engage the most students."],"difficulty":"mild"}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5K4AG4VF1QYDDS6JY4VY_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A pie graph shows that 45$\\%$ of a class prefers soccer, 30$\\%$ prefers basketball, and the rest prefers tennis. If there are 60 students, how many prefer tennis?","answerOptions":["$10$","$15$","$18$","$20$"],"answer":"$15$","difficulty":"spicy"}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5K4AG4VF1QYDDJD1D4E8_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"In a pie graph, if a section represents $25\\%$ of the total, what fraction of the pie does it represent?","answerOptions":["$1/2$","$1/3$","$1/4$","$1/5$"],"answer":"$1/4$","difficulty":"mild"}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5K4AG4VF1QYDDD8YXS54_MULTIPLE_CHOICE_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 7
country: US
period_number: 7
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A pie graph shows that $50\\%$ of students prefer pizza. What fraction of the pie graph represents this preference?","answerOptions":["$1/3$","$1/2$","$1/4$","$3/4$"],"answer":"$1/2$","difficulty":"mild"}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5K4AG4VF1QYDDX9VETSM_CONTEMPLATIVE_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: spicy
example_output_json:
{"question":"Create a pie graph showing how you divide 24 hours in a day. How would it change on a holiday?","teacherTips":["Divide $360^\\circ$ proportionally to activities. Compare weekday vs holiday divisions."],"difficulty":"spicy"}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5JNSSTBJFGY0Y7K462D9_SCAFFOLDED_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
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 interpret pie graphs, which divide a circle into proportional sectors that represent parts of a whole.","questions":[{"answer":"$25\\%$","question":"A pie graph represents data as parts of a whole. What percentage does a full circle represent?"},{"answer":"$100\\%$","question":"If a sector of a pie graph represents $25\\%$, what fraction of the circle does it represent?"},{"answer":"$50\\%$","question":"A sector in a pie graph has an angle of $90^\\circ$. What percentage of the circle does this represent?\nRemember: A full circle has $360^\\circ$."}],"difficulty":"enabling"}


example_id: lp_01K9BQ5HPTG00QNFE7WN2DVVXB_01K9BQ5JNSSTBJFGY0YE82SQ5T_SCAFFOLDED_QUESTION
skills: ["Interpreting pie graphs"]
skill_ids: ["PL0JTXf7bamJeHNN4C8e"]
subtopics: ["Advanced Data Representation"]
subtopic_ids: ["subtopic_01GTC0BAC5VGSVWWXMW4XWZRP7"]
topic: Measurement and Data
topic_id: 29ebac64-21fc-4fc0-b874-d487d2657969
class_year: 7
country: US
period_number: 7
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyze the data distribution of a pie graph showing the percentages of votes received by four candidates in a class election.","questions":[{"answer":"Other candidates' percentages decrease to keep total at $100\\%$.","question":"If Candidate A received $40\\%$, Candidate B received $25\\%$, and Candidate C received $20\\%$, what percentage did Candidate D receive?"},{"answer":"$15\\%$","question":"If the total number of votes is $400$, how many votes did Candidate B receive, given they received $25\\%$ of the total?"},{"answer":"$100$","question":"If Candidate D's percentage increased to $25\\%$, explain how this would impact the percentages of the other candidates and why."}],"difficulty":"extension"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDPK3EG5A57Z67P1B4C8P_MULTIPLE_CHOICE_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 and then a six-sided die is rolled. How many outcomes are in the sample space?","answerOptions":["$6$","$12$","$8$","$10$"],"answer":"$12$","difficulty":"mild"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDPK3EG5A57Z67VZK6JFB_CONTEMPLATIVE_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 toss a coin 3 times and draw a card from a deck. How would you use a tree diagram to show all possible outcomes? What strategies could you use to organize and count these outcomes efficiently?","teacherTips":["Tree diagram has $2^3 \\times 52 = 416$ outcomes. Use branches for coin tosses, then add cards at the end."],"difficulty":"spicy"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDPK3EG5A57Z67T2SAP1C_MULTIPLE_CHOICE_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 you flip a coin and roll a six-sided die, how many possible outcomes are in the sample space?","answerOptions":["$6$","$8$","$12$","$24$"],"answer":"$12$","difficulty":"mild"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDPK2Z47BR0RVFZ9X6D59_MULTIPLE_CHOICE_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 sample space of an experiment represent?","answerOptions":["The set of all possible outcomes of the experiment","The set of only the desired outcomes of the experiment","The total number of outcomes observed in the experiment","The probability of the most likely outcome in the experiment"],"answer":"The set of all possible outcomes of the experiment","difficulty":"mild"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDPK2Z47BR0RVG2FMBKKQ_CONTEMPLATIVE_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 are designing a game with a spinner divided into $4$ colors and a die. How can you use the sample space to predict outcomes and ensure fairness?","teacherTips":["Sample space shows all $4 \\times 6 = 24$ outcomes. Fairness means each outcome has equal chance."],"difficulty":"hot"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDP2MPH2RD68KA5334ADP_SCAFFOLDED_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 how to represent sample space using a tree diagram in complex scenarios involving multiple events.","questions":[{"answer":"The diagram is incorrect; it should have $24$ outcomes.","question":"A coin is flipped, then a six-sided die is rolled. How many outcomes are in the sample space?\nList all outcomes."},{"answer":"$12$ outcomes: $H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6$","question":"A coin is flipped, a die is rolled, and then a spinner with $3$ sections (red, blue, green) is spun.\nHow many outcomes are in the sample space?"},{"answer":"$36$ outcomes","question":"A tree diagram represents flipping a coin twice and rolling a die. The diagram shows $12$ outcomes.\nExplain whether this is correct and why."}],"difficulty":"extension"}


example_id: lp_01K9BQDMNK1FQEVW62AV1PDZAZ_01K9BQDP2MPH2RD68KA1BJS89Z_SCAFFOLDED_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
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 sample spaces and how to use a tree diagram to show all possible outcomes of an event.","questions":[{"answer":"HH, HT, TH, TT","question":"What does a sample space represent in probability?"},{"answer":"All possible outcomes of an event","question":"How does a tree diagram help in probability?"},{"answer":"The most likely outcome","question":"If you flip a coin twice, list all possible outcomes using a tree diagram."}],"difficulty":"enabling"}


example_id: lp_01K9BQE45RBED3QX78NY0KMZE1_01K9BQE508SBT57RVBR6KG8ZZ5_ACTIVITY
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Mountaineering
class_year: 7
country: US
period_number: 7
node_type: ACTIVITY
example_output_json:
{"header":"Tree Diagram Challenge\nExplore all outcomes of flipping a coin and rolling a die in teams.","scenario":"Steps\n1. Draw a tree diagram for flipping a coin and rolling a die.\n2. Label all branches with heads or tails, then numbers $1$ to $6$.\n3. Write down all possible outcomes (e.g., $H1$, $T4$).\n4. Check another team's diagram for missing or incorrect outcomes.\n5. Score $1$ point for each error found or corrected!","steps":["Discussion\n• Why is a tree diagram helpful for finding all outcomes?\n• How does the sample space change with two dice instead?","Differentiation Opportunities\n• Support: Start with just flipping a coin twice before adding the die.\n• Extend: Add a second coin and find the new sample space."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K9BQE45RBED3QX78NY0KMZE1_01K9BQE508SBT57RVBQT03BJYC_WARM_UP_QUESTIONS_WITH_CONTEXT
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Mountaineering
class_year: 7
country: US
period_number: 7
node_type: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"You're a mountaineering guide planning routes and safety drills for a team climbing a challenging peak.","questions":[{"answer":"$3$","question":"Your team has $3$ different tents. How many tents are there for your team to choose from?"},{"answer":"$4$","question":"Each climber carries either a blue jacket or a red jacket. For $2$ climbers, how many possible jacket combinations are there?"},{"answer":"$12$","question":"Your team has $4$ different routes and $3$ types of safety kits. How many total combinations of route and safety kit are possible?"}]}


example_id: lp_01K9BQE45RBED3QX78NY0KMZE1_01K9BQE508SBT57RVBRHS5Y17K_CONTEMPLATIVE_QUESTION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Mountaineering
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 $6$-sided die. How can you use a tree diagram to show all outcomes? What does the sample space represent?","teacherTips":["Guide students to draw one branch for each coin outcome (Heads, Tails).","Add branches for die outcomes (1–6) under each coin outcome.","Explain that the sample space lists all $12$ possible outcomes."],"difficulty":"mild"}


example_id: lp_01K9BQE45RBED3QX78NY0KMZE1_01K9BQE508SBT57RVBRS261XCB_EXIT_TICKET
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Mountaineering
class_year: 7
country: US
period_number: 7
node_type: EXIT_TICKET
example_output_json:
{"questions":[{"answer":"$\\{A, B, C\\}$","question":"If a climber chooses between $3$ routes (A, B, C), what does the sample space represent for their choice?"},{"answer":"$4$","question":"A mountaineer flips a coin to decide climbing (heads = steep, tails = easy) and then chooses among $2$ paths (red or blue). How many outcomes are there?"},{"answer":"$4$","question":"A mountaineer tosses $2$ coins to decide between $4$ routes (H1, H2, T1, T2). How many outcomes are in the sample space?"}]}


example_id: lp_01K9BQE45RBED3QX78NY0KMZE1_01K9BQE508SBT57RVBRNFF8XZ3_THOUGHT_SPARKER
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Mountaineering
class_year: 7
country: US
period_number: 7
node_type: THOUGHT_SPARKER
example_output_json:
{"firstSentenceHeader":"While climbing a mountain, a team must decide between two paths: an easier trail or a steeper route. Additionally, the weather could be sunny, cloudy, or snowy during their ascent.","firstSentence":"How could a tree diagram help you represent all the possible outcomes for this climb?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Encourage students to identify all possible choices and outcomes before creating the tree diagram.","Discuss how the tree diagram visually shows the total sample space and helps organize possibilities.","Ask students to explain what each branch or level of the tree diagram represents in the context of the climb."]}


example_id: lp_01K9BQE45RBED3QX78NY0KMZE1_01K9BQE508SBT57RVBR0B90SWQ_APPLICATION
skills: ["Representing sample space using a tree diagram","Understanding what sample space represents"]
skill_ids: ["IWRYFhp62mlkdsnyBsUl","ux8pYd1mCi62lCuhatJf"]
subtopics: ["Sample Space"]
subtopic_ids: ["subtopic_01GTC0BBZ6GNGZFYAC1T18XQBJ"]
topic: Statistics and Probability
topic_id: 41ed7376-b132-47bb-8f15-e9e17e04e046
context: Mountaineering
class_year: 7
country: US
period_number: 7
node_type: APPLICATION
example_output_json:
{"title":"Sample Space in Mountaineering Weather Planning","example1Header":"Situation\nMountaineers plan for weather scenarios to stay safe. They list all possible conditions like sun, rain, or snow to prepare for each outcome.","example1Body":"Example\nMountaineers list morning and afternoon weather conditions. Sample space: (S, S), (S, R), (S, SN), (R, S), (R, R), (R, SN), (SN, S), (SN, R), (SN, SN) for $9$ outcomes.","example2Header":"","example2Body":""}


example_id: lp_01K9BQQ15MDZTAT3K8723P74YH_01K9BQQ6QMBM9D1CB1XXFH17VF_APPLICATION
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
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 Efficiency in Formula One","example1Header":"Situation\nFormula One pit crews must perform tasks like tire changes and refueling in seconds. They use precise calculations to decide the order of tasks, ensuring maximum efficiency.","example1Body":"Example\nA pit crew handles $5 \\times 4 + 10 + 8$ seconds for tasks. Using BODMAS: $5 \\times 4 = 20$, $20 + 10 = 30$, then $30 + 8 = 38$ seconds total.","example2Header":"","example2Body":""}


example_id: lp_01K9BQQ15MDZTAT3K8723P74YH_01K9BQQ6QMBM9D1CB1YCAWND2W_THOUGHT_SPARKER
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
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":"A Formula One race car driver needs to plan their pit stops. The first pit stop takes $10$ seconds, the second takes $12$ seconds, and the team estimates the total time as $10 + 12 \\times 2^2$ seconds.","firstSentence":"How should you calculate the total time using the correct order of operations?","secondSentenceHeader":"","secondSentence":"","teacherTips":["Review the BODMAS rule with students before starting the discussion.","Ask students to identify operations in the expression and their order of priority.","Encourage students to explain their reasoning step-by-step when solving the expression."]}


example_id: lp_01K9BQQ15MDZTAT3K8723P74YH_01K9BQQ6QMBM9D1CB1Y7H4PGWY_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
context: Formula One
class_year: 7
country: US
period_number: 7
node_type: CONTEMPLATIVE_QUESTION
difficulty: mild
example_output_json:
{"question":"You are designing a puzzle game where players solve expressions like $3 + 4 \\times 2^2$. Create three expressions with different answers. Explain how BODMAS helps solve them.","teacherTips":["Remind students to follow the order: brackets, orders, division/multiplication, addition/subtraction.","Encourage them to create expressions with at least one exponent.","Discuss how changing the order affects the final result."],"difficulty":"mild"}


example_id: lp_01K9BQQ15MDZTAT3K8723P74YH_01K9BQQ6QMBM9D1CB1XKMJ3GTW_WARM_UP_QUESTIONS_WITH_CONTEXT
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
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: WARM_UP_QUESTIONS_WITH_CONTEXT
example_output_json:
{"situation":"You are a Formula One race engineer calculating pit stop strategies and lap times for your team's driver during a race.","questions":[{"answer":"$150$","question":"A Formula One car travels $300$ km in $2$ hours. What is its average speed in km per hour?"},{"answer":"$100$","question":"Your driver completed three laps in $35$ s, $33$ s, and $32$ s. What is the total time for all three laps?"},{"answer":"$40$","question":"To calculate pit stop time, use $(15 + 5) \\times 2$. What is the total time in seconds?"}]}


example_id: lp_01K9BQQ15MDZTAT3K8723P74YH_01K9BQQ6QMBM9D1CB1YJQ8XGDB_EXIT_TICKET
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
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":"$11$","question":"In a Formula One race, the calculation $3 + 4 \\times 2$ is used to estimate pit stop times. What is the correct result?"},{"answer":"$16$","question":"A car's performance is calculated as $2^3 + (5 - 3) \\times 4$. What is the result?"},{"answer":"$32$","question":"For a race strategy, the formula $6 \\times (2^2 + 3) - 10$ is used to calculate lap efficiency. What is the result?"}]}


example_id: lp_01K9BQQ15MDZTAT3K8723P74YH_01K9BQQ6QMBM9D1CB1Y0Z4V9XE_ACTIVITY
skill_ids: ["PRzneDlw1cwNA49FES26","4YvrqlWW3njzqRq1ha4X","yXHIEJebSK69tH40B15K"]
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 Puzzle Race\nTeams race to solve BODMAS puzzles with exponents to reach the finish line!","scenario":"Steps\n1. Each team writes $5$ expressions with BODMAS and exponents on paper.\n2. Swap your expressions with another team to solve.\n3. Solve each expression step-by-step using BODMAS rules.\n4. Check answers with the original team to confirm correctness.\n5. The first team to solve all puzzles correctly wins!","steps":["Discussion\n• Why is the order of operations important in solving expressions?\n• How do exponents change the value of an expression?","Differentiation Opportunities\n• Support: Use simpler expressions with no exponents and fewer steps.\n• Extend: Include brackets and multiple exponents in the expressions."],"discussion":[],"differentiation":{"support":"","extend":""}}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQR95ZZDGWTN67Y0G5WEC_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 value of $2^3 + 4$ when applying BODMAS?","answerOptions":["$14$","$12$","$10$","$16$"],"answer":"$12$","difficulty":"mild"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQR966X2DW5WK45ND2X6G_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 math puzzle using BODMAS with at least one exponent. How could you make the answer $50$?","teacherTips":["Example: $(2^3 + 4) \\times 5 - 10 = 50$. Brackets first, then exponent, then operations."],"difficulty":"hot"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQR95ZZDGWTN66P3GRFWN_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 result of $3 + 6 \\times (5 - 2)^2 \\div 3$ following the order of operations?","answerOptions":["$27$","$21$","$45$","$30$"],"answer":"$21$","difficulty":"hot"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQR95ZZDGWTN66GZHJQRG_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: mild
example_output_json:
{"question":"Create an expression using $3$, $5$, and $7$ with brackets and operations. How would BODMAS affect the result?","teacherTips":["BODMAS ensures brackets first, then orders, division/multiplication, and addition/subtraction."],"difficulty":"mild"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQR95ZZDGWTN678MVWF3C_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 value of $6 + 2 \\times 3$ when following the order of operations (BODMAS)?","answerOptions":["$24$","$12$","$18$","$12$"],"answer":"$12$","difficulty":"mild"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQR95ZZDGWTN67D9CTRZG_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":"Evaluate the expression: $6 + 12 \\div (3 \\times 2) - 4$.","answerOptions":["$2$","$6$","$4$","$8$"],"answer":"$4$","difficulty":"hot"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQQSRAPBWCTKDMKDN2Y19_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":"Test your understanding of BODMAS by solving complex expressions with exponents and multiple operations.","questions":[{"answer":"Students must demonstrate step-by-step reasoning: $32.5$.","question":"Evaluate the expression: $3^2 + (6 \\div 2) \\times 4$."},{"answer":"$21$","question":"Evaluate the expression: $[(2^3 + 4) \\div 2] \\times (5 - 3)$."},{"answer":"$12$","question":"Explain how to correctly evaluate the expression $5 \\times [3 + (4^2 - 6)] \\div 2$, and why following BODMAS is necessary to get the correct result."}],"difficulty":"extension"}


example_id: lp_01K9BQQQ64K203F4NJ6081MGB2_01K9BQQQSRAPBWCTKDMFRJBQ5Y_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 question, you will learn about following the correct order of operations (BODMAS) to solve mathematical problems.","questions":[{"answer":"$11$","question":"What is the first operation to solve in $8 + (5 - 2)$?\nHint: BODMAS says parentheses come first."},{"answer":"Addition","question":"What is the result of $2^3 + 4$?\nHint: BODMAS says exponents come before addition."},{"answer":"Subtraction","question":"Solve $3 + (2^2 \\times 2)$.\nHint: Follow BODMAS: solve inside parentheses, do exponents, then multiply, and finally add."}],"difficulty":"enabling"}


example_id: wp_01KC3ZJR6FGMZ484YMMM4411D5_wpn_01KC3ZJSAEJT3V8NX2V1YRKY53_SCAFFOLDED_QUESTION
skills: ["Understanding the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{m}}$"]
skill_ids: ["TzHcgDpDhsqhIVyZRFKF"]
subtopics: ["Exponents"]
subtopic_ids: ["subtopic_01GTC0BDF2P4V675HQJEYBNFFK"]
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 explore the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{m}}$ and apply it to simple numbers.","questions":[{"answer":"$\\sqrt[4]{16^{3}}$","question":"Which expression correctly rewrites $8^{\\frac{2}{3}}$ using the index law?\nHint: numerator becomes the exponent, denominator the root."},{"answer":"$\\sqrt[3]{8^{2}}$","question":"What is the value of $27^{\\frac{1}{3}}$?\nHint: take the cube root of 27."},{"answer":"$\\sqrt[2]{8^{3}}$","question":"Rewrite $16^{\\frac{3}{4}}$ as a radical using the index law."}],"difficulty":"enabling"}


example_id: wp_01KC3ZJR6FGMZ484YMMM4411D5_wpn_01KC3ZJSAEJT3V8NX2VW1VGCBG_SCAFFOLDED_QUESTION
skills: ["Understanding the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{m}}$"]
skill_ids: ["TzHcgDpDhsqhIVyZRFKF"]
subtopics: ["Exponents"]
subtopic_ids: ["subtopic_01GTC0BDF2P4V675HQJEYBNFFK"]
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":"Apply the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{\\,m}}$ to solve and justify advanced exponent problems.","questions":[{"answer":"Even root of negative $a$ is undefined.","question":"If $a^{\\frac{3}{2}} = 27$, find the value of $a$."},{"answer":"$9$","question":"Given $a^{\\frac{3}{2}} = 27$, express $a^{\\frac{1}{6}}$ in simplest radical form."},{"answer":"$\\sqrt[3]{3}$","question":"Explain why the index law $a^{\\frac{m}{n}} = \\sqrt[n]{a^{\\,m}}$ holds for positive real $a$, and discuss what happens when $a$ is negative and $n$ is even."}],"difficulty":"extension"}


example_id: wp_01KC3ZV5SNT4HFADSAMYGYNQYE_wpn_01KC3ZV6W1E2XSS5TTYQ004N0A_SCAFFOLDED_QUESTION
skill_ids: ["D8SU6YkMOSkxfiN8twGd","01JZ9YHE925MZK7HY97JQG3GES","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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":"Advanced factorisation challenge: factor the expression $-6x^3y + 9x^2y^2 - 4x^2y + 6xy^2$.","questions":[{"answer":"$-1$, then $xy(2x-3y)(3x+2)$","question":"Factor out the overall negative common factor from $-6x^3y + 9x^2y^2 - 4x^2y + 6xy^2$."},{"answer":"$-(6x^3y-9x^2y^2+4x^2y-6xy^2)$","question":"Factor completely the polynomial $6x^3y - 9x^2y^2 + 4x^2y - 6xy^2$."},{"answer":"$xy(2x-3y)(3x+2)$","question":"Explain why the full factorisation $-xy(2x-3y)(3x+2)$ is valid for the original expression."}],"difficulty":"extension"}

skills:
["Factorising positive common factors from algebraic expressions","Factorising negative common factors from algebraic expressions","Factorising by grouping in pairs","Factorising using the difference of two squares"]


example_id: wp_01KC3ZV5SNT4HFADSAMYGYNQYE_wpn_01KC3ZV6W1E2XSS5TTXBARCS90_SCAFFOLDED_QUESTION
skill_ids: ["D8SU6YkMOSkxfiN8twGd","01JZ9YHE925MZK7HY97JQG3GES","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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":"Learn to factor out a negative common factor from a simple algebraic expression.","questions":[{"answer":"$-4a(3a-2)$","question":"What is the greatest common factor (including sign) of $-6x^{2}+9x$?"},{"answer":"$-3x$","question":"Factor $-6x^{2}+9x$ using the GCF you found."},{"answer":"$-6x$","question":"Factor $-12a^{2}+8a$ by pulling out the negative common factor."}],"difficulty":"enabling"}

skills:
["Factorising positive common factors from algebraic expressions","Factorising negative common factors from algebraic expressions","Factorising by grouping in pairs","Factorising using the difference of two squares"]


example_id: wp_01KC3ZV5SNT4HFADSAMYGYNQYE_wpn_01KC3ZV6W1E2XSS5TTX8QEY7AN_SCAFFOLDED_QUESTION
skill_ids: ["D8SU6YkMOSkxfiN8twGd","01JZ9YHE925MZK7HY97JQG3GES","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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":"Practice factorising using the difference of squares and grouping.","questions":[{"answer":"$2(y-2)(y+2)$","question":"Which statement is true about $x^{2}-16$?"},{"answer":"It is a difference of squares","question":"Factor $x^{2}-16$."},{"answer":"It is a sum of squares","question":"Factor $2y^{2}-8$ by grouping (show the fully factored form)."}],"difficulty":"enabling"}

skills:
["Factorising positive common factors from algebraic expressions","Factorising negative common factors from algebraic expressions","Factorising by grouping in pairs","Factorising using the difference of two squares"]


example_id: wp_01KC3ZV5SNT4HFADSAMYGYNQYE_wpn_01KC3ZV6W1E2XSS5TTXYW3ZC11_MULTIPLE_CHOICE_QUESTION
skill_ids: ["D8SU6YkMOSkxfiN8twGd","01JZ9YHE925MZK7HY97JQG3GES","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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":"Factorise $12x^2 - 27$ completely.","answerOptions":["$3(2x-3)(2x+3)$","$(3x-9)(4x+3)$","$(6x-9)(2x+3)$","$3(4x-9)(4x+9)$"],"answer":"$3(2x-3)(2x+3)$","difficulty":"hot"}


example_id: wp_01KC3ZV5SNT4HFADSAMYGYNQYE_wpn_01KC3ZV6W1E2XSS5TTXZATK4KR_MULTIPLE_CHOICE_QUESTION
skill_ids: ["D8SU6YkMOSkxfiN8twGd","01JZ9YHE925MZK7HY97JQG3GES","ncmZDTI2kMKFfZJMB6m7","bHjBWVYvEE1qRqXagbQ9"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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: spicy
example_output_json:
{"question":"Factorise $x^4 - 16$ completely over the integers.","answerOptions":["$(x-2)(x+2)(x^2+4)$","$(x^2-4)(x^2+4)$","$(x-4)(x+4)$","$(x^2-8)(x^2+8)$"],"answer":"$(x-2)(x+2)(x^2+4)$","difficulty":"spicy"}


example_id: wp_01KC401RA2Z3KYC7GHTK3RVT26_wpn_01KC401S4J8MVQAZQHNYWWYNNC_SCAFFOLDED_QUESTION
skills: ["Understanding how to complete the square"]
skill_ids: ["TCSMDxCtOwf0ntUUDOsh"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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 complete the square for quadratic expressions.","questions":[{"answer":"$(x+5)^2$","question":"What number must be added to $x^2 + 6x$ to make a perfect square trinomial?"},{"answer":"$9$","question":"Which constant completes $x^2 + 8x + \\underline{\\phantom{0}}$ as a perfect square?"},{"answer":"$3$","question":"Write the completed square form of $x^2 + 10x + 25$."}],"difficulty":"enabling"}


example_id: wp_01KC401RA2Z3KYC7GHTK3RVT26_wpn_01KC401S4J8MVQAZQHQ183EHWC_SCAFFOLDED_QUESTION
skills: ["Understanding how to complete the square"]
skill_ids: ["TCSMDxCtOwf0ntUUDOsh"]
subtopics: ["Factorisation"]
subtopic_ids: ["subtopic_01GTC0BAC1M2VF6SRR08VK9NN3"]
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":"A student wants to rewrite quadratic expressions in vertex form by completing the square to analyse their graphs.","questions":[{"answer":"Because the square-completion identity applies only to a coefficient-$1$ quadratic; without factoring $a$, the added term is mis-scaled, yielding an incorrect form.","question":"Rewrite $f(x)=2x^{2}+12x+7$ in the form $a(x-h)^{2}+k$."},{"answer":"$2(x+3)^{2}-11$","question":"From the form $2(x+3)^{2}-11$, state the vertex of the parabola and indicate whether it opens upward or downward."},{"answer":"Vertex $(-3,-11)$, opens upward","question":"Explain why, when completing the square for a quadratic with leading coefficient $a\neq1$, we must first factor out $a$ from the $x^{2}$ and $x$ terms. Discuss what would go wrong if we tried to complete the square without this step."}],"difficulty":"extension"}


example_id: wp_01KC405VSR5T37D7ZXEHMQEYMF_wpn_01KC405WNR7ZQQC80Q6B3949SA_SCAFFOLDED_QUESTION
skills: ["Matching linear inequalities with their graphs"]
skill_ids: ["4U2IYZuzbz1xBduBwKZh"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
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":"Match each linear inequality to the description of its graph.","questions":[{"answer":"$y \\le -x + 4$","question":"The graph shows a solid line through $(0,0)$ and $(2,2)$ with shading above the line. Which inequality matches?"},{"answer":"$y \u003e x$","question":"A dashed line passes through $(0,4)$ and $(4,0)$ with shading below the line. Which inequality fits?"},{"answer":"$y \\ge x$","question":"Write the inequality for a solid line through $(1,3)$ and $(3,1)$ with shading below the line."}],"difficulty":"enabling"}


example_id: wp_01KC405VSR5T37D7ZXEHMQEYMF_wpn_01KC405WNR7ZQQC80Q6ZCHBHW8_SCAFFOLDED_QUESTION
skills: ["Matching linear inequalities with their graphs"]
skill_ids: ["4U2IYZuzbz1xBduBwKZh"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
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":"Match each linear inequality to its correct graph region and explore how algebraic changes affect the shading.","questions":[{"answer":"See explanation above.","question":"Does the point $(\\! -2,\\,5)$ satisfy the inequality $3x-4y\u003c12$?  Answer “yes” or “no”."},{"answer":"yes","question":"Rewrite $-x+2y\\ge 8$ as $y=mx+b$ and give the slope $m$ and $y$-intercept $b$."},{"answer":"$\\dfrac{1}{2},\\;4$","question":"Explain why multiplying both sides of a linear inequality by a negative number reverses the inequality sign, and describe how this reversal changes the side of the boundary line that must be shaded on the graph."}],"difficulty":"extension"}


example_id: wp_01KC405VSR5T37D7ZXEHMQEYMF_wpn_01KC405WNR7ZQQC80Q6P3DARV1_MULTIPLE_CHOICE_QUESTION
skills: ["Matching linear inequalities with their graphs"]
skill_ids: ["4U2IYZuzbz1xBduBwKZh"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
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 description matches the graph of the inequality $y \\le 3x + 1$?","answerOptions":["Line $y=3x+1$, region on or below line","Line $y=3x+1$, region above line only","Line $y=-3x+1$, region on or below line","Line $y=3x-1$, region on or below line"],"answer":"Line $y=3x+1$, region on or below line","difficulty":"hot"}


example_id: wp_01KC405VSR5T37D7ZXEHMQEYMF_wpn_01KC405WNR7ZQQC80Q6VEV9RH8_MULTIPLE_CHOICE_QUESTION
skills: ["Matching linear inequalities with their graphs"]
skill_ids: ["4U2IYZuzbz1xBduBwKZh"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
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: spicy
example_output_json:
{"question":"Which description matches the graph of the inequality $2y - 4x \u003e 8$?","answerOptions":["Solid line $y=2x+4$, shading below (closed)","Dashed line $y=2x+4$, shading above (open)","Dashed line $y=2x-4$, shading above (open)","Solid line $y=2x+4$, shading above (closed)"],"answer":"Dashed line $y=2x+4$, shading above (open)","difficulty":"spicy"}


example_id: wp_01KC405VSR5T37D7ZXEHMQEYMF_wpn_01KC405WNR7ZQQC80Q6W302T3W_MULTIPLE_CHOICE_QUESTION
skills: ["Matching linear inequalities with their graphs"]
skill_ids: ["4U2IYZuzbz1xBduBwKZh"]
subtopics: ["Linear Inequalities"]
subtopic_ids: ["subtopic_01GTC0BMDSM8R5HNPYMZYR72T3"]
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: spicy
example_output_json:
{"question":"Which description matches the graph of the inequality $y \\ge -\\dfrac{1}{2}x + 3$?","answerOptions":["Dashed line $y=-\\dfrac{1}{2}x+3$, shading below","Solid line $y=-\\dfrac{1}{2}x+3$, shading below","Solid line $y=-\\dfrac{1}{2}x+3$, shading above","Dashed line $y=-\\dfrac{1}{2}x+3$, shading above"],"answer":"Solid line $y=-\\dfrac{1}{2}x+3$, shading above","difficulty":"spicy"}


example_id: wp_01KC40HPX2XR8146T59TAW8HM5_wpn_01KC40HR5MW2542TDTMWKWNS63_SCAFFOLDED_QUESTION
skills: ["Understanding and applying function notation"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG"]
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":"A startup models profit using two functions: $f(x)=2x-5$ and $g(x)=x^{2}$. Investigate their compositions and properties.","questions":[{"answer":"They differ except at special $x$ where the two expressions coincide.","question":"Calculate $f(g(2))$."},{"answer":"$3$","question":"Find all real $x$ satisfying $g(f(x))=9$."},{"answer":"$x=1\\text{ or }4$","question":"Explain why $f(g(x))$ and $g(f(x))$ are generally different functions and describe when they could be equal."}],"difficulty":"extension"}


example_id: wp_01KC40HPX2XR8146T59TAW8HM5_wpn_01KC40HR5MW2542TDTMDDFXTDQ_SCAFFOLDED_QUESTION
skills: ["Understanding and applying function notation"]
skill_ids: ["ohtqIqrWYM3phfAqYrEG"]
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 what function notation means and how to use it. A function $f$ maps an input $x$ to an output using a rule.","questions":[{"answer":"$3$","question":"What does the notation $f(3)$ represent?"},{"answer":"The input value $3$","question":"Suppose $f(x)=2x+1$. What is $f(4)$?\nHint: Replace $x$ with $4$ and evaluate."},{"answer":"The output when $x$ = $3$","question":"If $f(x)=5x-3$, what value of $x$ makes $f(x)=12$?\nHint: Solve $5x-3=12$."}],"difficulty":"enabling"}


example_id: wp_01KC41AHGJ2RFVHWANFCNV9T64_wpn_01KC41AJF58V00H1MK904MJENF_SCAFFOLDED_QUESTION
skill_ids: ["mm2yE7DGJT9x6vg92vbq","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity you will find the rule for a number sequence using a table of $x$ and $y$ values.","questions":[{"answer":"$y = 2x + 1$","question":"What is $y$ when $x = 2$?\nHint: Look at the table of pairs."},{"answer":"$5$","question":"What constant increase does $y$ have for each increase of $1$ in $x$?\nHint: Subtract successive $y$ values."},{"answer":"$4$","question":"Write the linear formula that gives $y$ from $x$ for this sequence."}],"difficulty":"enabling"}

skills:
["Determining the formula of a visual sequence","Creating linear equations from $x$ and $y$ tables"]


example_id: wp_01KC41AHGJ2RFVHWANFCNV9T64_wpn_01KC41AJF58V00H1MK9NDAKSXX_SCAFFOLDED_QUESTION
skill_ids: ["mm2yE7DGJT9x6vg92vbq","yFmzcRuhAnotvrEgdkIB"]
subtopics: ["Formulaic Patterns"]
subtopic_ids: ["subtopic_01GTC0BR8BDB9MQY5G8ANP1NH2"]
topic: Expressions, Equations, and Relationships
topic_id: 5ea8f007-b4b3-4a2c-bb40-1e87fc771c04
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Given the table of tile counts (x) and border length (y), determine the linear rule that relates them.","questions":[{"answer":"Constant differences imply a linear relation.","question":"Find the equation of the line $y = mx + b$ that passes through the points $(2,7)$, $(5,16)$, $(8,25)$, and $(11,34)$. Express your answer in simplest form."},{"answer":"$y = 3x + 1$","question":"Using the equation you found, what border length $y$ corresponds to $x = 20$ tiles?"},{"answer":"$61$","question":"Explain why the data in the table must be described by a linear function rather than a quadratic or another nonlinear model. Provide a clear logical argument."}],"difficulty":"extension"}

skills:
["Determining the formula of a visual sequence","Creating linear equations from $x$ and $y$ tables"]


example_id: wp_01KC41GW4A5TBWRGE1VA1CKBWV_wpn_01KC41GWYQ0G9WNY2HM71N71AK_SCAFFOLDED_QUESTION
skills: ["Finding the formula for a straight line from its graph"]
skill_ids: ["P9CAuN91k1PXigDfei7v"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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":"A straight line on a coordinate plane passes through the points $(2,5)$ and $(-4,-1)$. Determine its equation and explore related properties.","questions":[{"answer":"The slope fixes the direction and the intercept fixes the vertical position, yielding a single line.","question":"Find the slope of the line and write its equation in slope-intercept form."},{"answer":"$y = x + 3$","question":"If a line parallel to the one above passes through $(0,-2)$, what is its equation?"},{"answer":"$y = x - 2$","question":"Explain why any two distinct points determine a unique straight line and how the slope-intercept form reflects that uniqueness, referencing the equations you derived."}],"difficulty":"extension"}


example_id: wp_01KC41GW4A5TBWRGE1VA1CKBWV_wpn_01KC41GWYQ0G9WNY2HKK4YX8S5_SCAFFOLDED_QUESTION
skills: ["Finding the formula for a straight line from its graph"]
skill_ids: ["P9CAuN91k1PXigDfei7v"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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 activity, you will find the formula $y = mx + b$ for a line using its graph information.","questions":[{"answer":"$y = 2x + 3$","question":"The line passes through $(0,3)$ and $(4,11)$. What is its slope?\nUse $slope = rise/run$."},{"answer":"$2$","question":"Using the same line, what is its y-intercept?\nThe y-intercept is the point where $x = 0$."},{"answer":"$3$","question":"Write the equation of the line in slope-intercept form."}],"difficulty":"enabling"}


example_id: wp_01KC41GW4A5TBWRGE1VA1CKBWV_wpn_01KC41GWYQ0G9WNY2HKT11C5PZ_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the formula for a straight line from its graph"]
skill_ids: ["P9CAuN91k1PXigDfei7v"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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":"A line passes through $(2,3)$ and $(5,9)$. What is its equation in slope-intercept form?","answerOptions":["$y = 2x + 1$","$y = 2x - 1$","$y = -2x + 1$","$y = 2x - 3$"],"answer":"$y = 2x - 1$","difficulty":"mild"}


example_id: wp_01KC41GW4A5TBWRGE1VA1CKBWV_wpn_01KC41GWYQ0G9WNY2HM2V85N6D_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the formula for a straight line from its graph"]
skill_ids: ["P9CAuN91k1PXigDfei7v"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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":"A line crosses the y-axis at $(0,-4)$ and goes through $(3,2)$. What is its equation?","answerOptions":["$y = 2x - 4$","$y = 2x + 4$","$y = -2x - 4$","$y = 2x - 2$"],"answer":"$y = 2x - 2$","difficulty":"hot"}


example_id: wp_01KC41GW4A5TBWRGE1VA1CKBWV_wpn_01KC41GWYQ0G9WNY2HM0EKZPXN_MULTIPLE_CHOICE_QUESTION
skills: ["Finding the formula for a straight line from its graph"]
skill_ids: ["P9CAuN91k1PXigDfei7v"]
subtopics: ["Linear Equation Forms"]
subtopic_ids: ["subtopic_01GTC0BPJ1WVPVD1NN67YEC9MA"]
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":"A line has slope $-3$ and passes through $(4,5)$. Which equation represents the line?","answerOptions":["$y = -3x + 17$","$y = -3x - 17$","$y = 3x + 17$","$y = -3x + 7$"],"answer":"$y = -3x + 17$","difficulty":"hot"}


example_id: wp_01KC41MEZ6RNJAFCD09J1KRKB5_wpn_01KC41MFSVA3FYMK4P9W4S7YEA_MULTIPLE_CHOICE_QUESTION
skills: ["Defining parallel lines"]
skill_ids: ["FfqmtjKdxdkWHCLprmmd"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Which of the following statements correctly defines parallel lines?","answerOptions":["Lines that intersect at one point","Lines that never intersect","Lines that form right angles","Lines that are the same line"],"answer":"Lines that never intersect","difficulty":"hot"}


example_id: wp_01KC41MEZ6RNJAFCD09J1KRKB5_wpn_01KC41MFSVA3FYMK4P9F95J054_MULTIPLE_CHOICE_QUESTION
skills: ["Defining parallel lines"]
skill_ids: ["FfqmtjKdxdkWHCLprmmd"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"Which symbol indicates that line l is parallel to line m?","answerOptions":["$l \\parallel m$","$l \\perp m$","$l = m$","$l \\subset m$"],"answer":"$l \\parallel m$","difficulty":"mild"}


example_id: wp_01KC41MEZ6RNJAFCD09J1KRKB5_wpn_01KC41MFSVA3FYMK4P9SZ2ZMN6_MULTIPLE_CHOICE_QUESTION
skills: ["Defining parallel lines"]
skill_ids: ["FfqmtjKdxdkWHCLprmmd"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"Line A has slope $3$ and line B also has slope $3$. What is their relationship?","answerOptions":["They are perpendicular","They intersect at $(0,0)$","They are the same line","They are parallel"],"answer":"They are parallel","difficulty":"hot"}


example_id: wp_01KC41MEZ6RNJAFCD09J1KRKB5_wpn_01KC41MFSVA3FYMK4P97QKK0FN_SCAFFOLDED_QUESTION
skills: ["Defining parallel lines"]
skill_ids: ["FfqmtjKdxdkWHCLprmmd"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity you will define parallel lines and practice identifying them from descriptions.","questions":[{"answer":"No","question":"Which sentence correctly defines parallel lines?\nHint: Think about lines that never meet."},{"answer":"Lines that intersect at a right angle","question":"Two lines have equations $y = 2x + 3$ and $y = 2x - 5$. Which statement is true?\nHint: Compare slopes."},{"answer":"Lines that are in the same plane and never intersect","question":"Is the line $y = -4x + 1$ parallel to the line $y = 3x + 2$? Explain briefly."}],"difficulty":"enabling"}


example_id: wp_01KC41MEZ6RNJAFCD09J1KRKB5_wpn_01KC41MFSVA3FYMK4PA5JZEWPM_SCAFFOLDED_QUESTION
skills: ["Defining parallel lines"]
skill_ids: ["FfqmtjKdxdkWHCLprmmd"]
subtopics: ["Elements of Geometry"]
subtopic_ids: ["subtopic_01GTC0BPAVPDNESJ8H8N29FMTE"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Exploring the definition of parallel lines using algebraic equations and parameter analysis.","questions":[{"answer":"Equal slopes give identical direction vectors, preventing intersection; vertical lines are parallel when they share the same $x$-coordinate.","question":"Line L₁: $3x + k\\,y = 12$ and line L₂: $9x - 6y = 15$ are parallel. What value of $k$ satisfies this?"},{"answer":"$-2$","question":"Line L₃: $m x + 4y = 7$ and line L₄: $2x + n y = 5$ are parallel. List all integer pairs $(m,n)$ that satisfy this condition."},{"answer":"$(1,8), (2,4), (4,2), (8,1), (-1,-8), (-2,-4), (-4,-2), (-8,-1)$","question":"Provide a clear justification that two non-vertical lines with equal slopes are parallel. Then explain how the definition of parallel lines applies to vertical lines."}],"difficulty":"extension"}


example_id: wp_01KC41R11EWTTS4JPFYCVP1XXJ_wpn_01KC41R1SFFXP7918RTKHBH3CD_SCAFFOLDED_QUESTION
skills: ["Identifying perpendicular lines in triangles and quadrilaterals"]
skill_ids: ["xqAWi4Y6sYyQxzabQH6e"]
subtopics: ["Sine \u0026 Cosine Rule"]
subtopic_ids: ["subtopic_01GTC0BH971F0VB5KKT574AFVZ"]
topic: Trigonometry
topic_id: 7bJyaIjPhmbEyaJZK7qy
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity you will learn how to spot perpendicular lines in triangles and quadrilaterals. A perpendicular pair forms a right angle ($90^\\circ$).","questions":[{"answer":"the sides of length $3$ cm and $4$ cm","question":"Which statement describes a pair of perpendicular sides in a triangle?"},{"answer":"$\\;$ Two sides that meet at a $90^{\\circ}$ angle","question":"In a rectangle, which sides are perpendicular?"},{"answer":"Two sides that are equal in length","question":"A right triangle has legs measuring $3$ cm and $4$ cm. Which two sides are perpendicular?"}],"difficulty":"enabling"}


example_id: wp_01KC41R11EWTTS4JPFYCVP1XXJ_wpn_01KC41R1SFFXP7918RV9ZZET1W_SCAFFOLDED_QUESTION
skills: ["Identifying perpendicular lines in triangles and quadrilaterals"]
skill_ids: ["xqAWi4Y6sYyQxzabQH6e"]
subtopics: ["Sine \u0026 Cosine Rule"]
subtopic_ids: ["subtopic_01GTC0BH971F0VB5KKT574AFVZ"]
topic: Trigonometry
topic_id: 7bJyaIjPhmbEyaJZK7qy
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Exploring perpendicular lines in a triangle and extending to a rectangle on the coordinate plane","questions":[{"answer":"ABCD is a rectangle because opposite sides are parallel and each interior angle is a right angle.","question":"Given points $A(0,0)$ and $B(4,0)$, find an integer coordinate for point C such that line AB is perpendicular to line AC."},{"answer":"$(0,3)$","question":"With $A(0,0)$, $B(4,0)$ and $C(0,3)$ as found, which vertex of triangle ABC contains the right angle?"},{"answer":"Angle at A","question":"Define point D so that AD is parallel to BC and CD is parallel to AB. Prove that quadrilateral ABCD is a rectangle, giving a clear geometric justification."}],"difficulty":"extension"}


example_id: wp_01KC421BP0RJRBWSHDTZX9SK5P_wpn_01KC421CHKBVD645CY377C1KJ9_MULTIPLE_CHOICE_QUESTION
skill_ids: ["KitxTsAS1tedXqbLAVNO","pT3WwssvzqOGmafNZdQn"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: mild
example_output_json:
{"question":"A circle has radius $4$ cm. What is the area of the segment cut off by a $60^\\circ$ central angle?","answerOptions":["$1.45\\text{ cm}^2$","$2.00\\text{ cm}^2$","$3.14\\text{ cm}^2$","$4.00\\text{ cm}^2$"],"answer":"$1.45\\text{ cm}^2$","difficulty":"mild"}

skills:
["Finding the perimeter and area of a sector of a circle","Calculating the area of a segment of a circle"]


example_id: wp_01KC421BP0RJRBWSHDTZX9SK5P_wpn_01KC421CHKBVD645CY2TYV7M4R_SCAFFOLDED_QUESTION
skill_ids: ["KitxTsAS1tedXqbLAVNO","pT3WwssvzqOGmafNZdQn"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"A circular garden has radius $4$ cm and a central angle of $60^\\circ$. Find its sector perimeter and area, then the area of the corresponding segment.","questions":[{"answer":"$\\frac{8\\pi}{3} - 4\\sqrt{3}$ cm$^{2}$","question":"What fraction of a whole circle does a $60^\\circ$ sector represent?"},{"answer":"$\\frac{1}{6}$","question":"What is the perimeter of the sector? (Perimeter = $2r + \\text{arc length}$)"},{"answer":"$\\frac{1}{4}$","question":"What is the area of the circular segment (sector area minus triangle area)? Express your answer in terms of $\\pi$ and $\\sqrt{3}$."}],"difficulty":"enabling"}

skills:
["Finding the perimeter and area of a sector of a circle","Calculating the area of a segment of a circle"]


example_id: wp_01KC421BP0RJRBWSHDTZX9SK5P_wpn_01KC421CHKBVD645CY3HSE35YG_SCAFFOLDED_QUESTION
skill_ids: ["KitxTsAS1tedXqbLAVNO","pT3WwssvzqOGmafNZdQn"]
subtopics: ["Circles"]
subtopic_ids: ["subtopic_01GTC0BM0PEZ2BF9KMCA00XYCT"]
topic: Geometry
topic_id: 18149148-fce7-4a5f-8634-543f8436b13d
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"A circular garden of radius $12\\,$m has a paved sector whose curved edge measures $15\\,$m. Use this information to find the sector’s perimeter, its area, and justify the formula for the area of the resulting circular segment.","questions":[{"answer":"Explanation of the formula as sector area minus triangle area.","question":"What is the perimeter of the sector (the sum of the two radii and the curved edge) in meters?"},{"answer":"$39$ m","question":"Express the area of the circular segment (the part of the circle cut off by the chord) in exact form using $r$ and $\\theta$."},{"answer":"$72\\!\\left(\\tfrac54-\\sin\\!\\left(\\tfrac54\\right)\\right)$ m²","question":"Explain why the area of a circular segment can be written as $\\tfrac12 r^{2}(\\theta-\\sin\\theta)$. Discuss the geometric meaning of each term and why subtracting the triangle area from the sector area gives the segment area."}],"difficulty":"extension"}

skills:
["Finding the perimeter and area of a sector of a circle","Calculating the area of a segment of a circle"]


example_id: wp_01KC424HYKM4SBM9W9TTEHPBKV_wpn_01KC424JPH53051EPV6G370KRF_SCAFFOLDED_QUESTION
skill_ids: ["oWtLaiUDNgnkbaOFM4HR","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Parallel \u0026 Perpendicular Lines"]
subtopic_ids: ["subtopic_01GTC0BJ3SKWRMEDMFSCQDT0QQ"]
topic: Linear Relationships
topic_id: D5UAsG087XeI1JSa39fl
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"You will learn how to find the equation of a line that is parallel to a given line.","questions":[{"answer":"$y = 3x - 7$","question":"What is the slope of the line $y = 3x + 2$? (In $y = mx + b$, $m$ is the slope.)"},{"answer":"$3$","question":"Which equation represents a line parallel to $y = 3x + 2$?"},{"answer":"$2$","question":"Find the equation of the line parallel to $y = 3x + 2$ that passes through the point $(4,5)$. Write in $y = mx + b$ form."}],"difficulty":"enabling"}

skills:
["Determining if two lines are coincident or parallel","Finding the equation of a line parallel to a given line"]


example_id: wp_01KC424HYKM4SBM9W9TTEHPBKV_wpn_01KC424JPH53051EPV7FW9MW1F_SCAFFOLDED_QUESTION
skill_ids: ["oWtLaiUDNgnkbaOFM4HR","01K0DDPZS6JCWDG1TXPT5J06XX"]
subtopics: ["Parallel \u0026 Perpendicular Lines"]
subtopic_ids: ["subtopic_01GTC0BJ3SKWRMEDMFSCQDT0QQ"]
topic: Linear Relationships
topic_id: D5UAsG087XeI1JSa39fl
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Two lines are given by $3x − 4y = d$ and $6x − 8y = 18$. Determine values of $d$ that make the lines parallel or coincident, and justify the conditions.","questions":[{"answer":"Equal slopes give parallelism; equal scaled constants give coincidence.","question":"Give one value of $d$ that makes $3x − 4y = d$ parallel to $6x − 8y = 18$ but not coincident."},{"answer":"$d = 2$","question":"Find the value of $d$ that makes $3x − 4y = d$ coincident with $6x − 8y = 18$."},{"answer":"$d = 9$","question":"Explain why having proportional coefficients makes two lines parallel, and why the constant terms must also be proportional (with the same ratio) for the lines to be coincident."}],"difficulty":"extension"}

skills:
["Determining if two lines are coincident or parallel","Finding the equation of a line parallel to a given line"]


example_id: wp_01KC42A32D0Z315RWX4YQ7E3CP_wpn_01KC42A423J6QJGDBV2RQ3QBQR_MULTIPLE_CHOICE_QUESTION
skills: ["Classifying events as dependent or independent"]
skill_ids: ["RJpVc5NyOGtSiia0NLnE"]
subtopics: ["Likelihood"]
subtopic_ids: ["subtopic_01GTC0BN1TKJ293ZQG2PQAV0K5"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: spicy
example_output_json:
{"question":"A bag has $3$ red and $2$ blue marbles. Event A: first draw is red. Event B: second draw is red without replacement. Are A and B independent?","answerOptions":["Independent","Dependent","Mutually exclusive","Cannot be determined"],"answer":"Dependent","difficulty":"spicy"}


example_id: wp_01KC42A32D0Z315RWX4YQ7E3CP_wpn_01KC42A423J6QJGDBV2G601G20_MULTIPLE_CHOICE_QUESTION
skills: ["Classifying events as dependent or independent"]
skill_ids: ["RJpVc5NyOGtSiia0NLnE"]
subtopics: ["Likelihood"]
subtopic_ids: ["subtopic_01GTC0BN1TKJ293ZQG2PQAV0K5"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A fair die is rolled twice. Event X: first roll is 4. Event Y: the two rolls total 7. Are X and Y independent?","answerOptions":["Dependent","Mutually exclusive","Independent","Same outcome"],"answer":"Independent","difficulty":"hot"}


example_id: wp_01KC42A32D0Z315RWX4YQ7E3CP_wpn_01KC42A423J6QJGDBV2H77BW1T_MULTIPLE_CHOICE_QUESTION
skills: ["Classifying events as dependent or independent"]
skill_ids: ["RJpVc5NyOGtSiia0NLnE"]
subtopics: ["Likelihood"]
subtopic_ids: ["subtopic_01GTC0BN1TKJ293ZQG2PQAV0K5"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 8
country: US
period_number: 8
node_type: MULTIPLE_CHOICE_QUESTION
difficulty: hot
example_output_json:
{"question":"A standard $52$-card deck is shuffled. Event M: first card is a heart. Event N: after replacing and reshuffling, second card is a heart. Are M and N independent?","answerOptions":["Dependent","Mutually exclusive","Cannot be determined","Independent"],"answer":"Independent","difficulty":"hot"}


example_id: wp_01KC42A32D0Z315RWX4YQ7E3CP_wpn_01KC42A423J6QJGDBV2YAEGVFZ_SCAFFOLDED_QUESTION
skills: ["Classifying events as dependent or independent"]
skill_ids: ["RJpVc5NyOGtSiia0NLnE"]
subtopics: ["Likelihood"]
subtopic_ids: ["subtopic_01GTC0BN1TKJ293ZQG2PQAV0K5"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Analyzing whether two classroom events affect each other's outcomes helps students master dependent vs. independent events.","questions":[{"answer":"Because studying raises the chance of a high score, making P(B|A)≠P(B).","question":"Event A: flip a fair coin; Event B: draw a red marble from a bag of $3$ red and $2$ blue marbles (with replacement). Are A and B independent or dependent?"},{"answer":"Independent","question":"Event A: draw one marble from the same bag (no replacement). Event B: draw a second marble and it is red. Are A and B independent or dependent?"},{"answer":"Dependent","question":"Event A: a student studies for a math test. Event B: the student scores above $90\\%$ on the test. Explain why A and B are dependent, referencing the definition of dependent events."}],"difficulty":"extension"}


example_id: wp_01KC42A32D0Z315RWX4YQ7E3CP_wpn_01KC42A423J6QJGDBV23GDFMM9_SCAFFOLDED_QUESTION
skills: ["Classifying events as dependent or independent"]
skill_ids: ["RJpVc5NyOGtSiia0NLnE"]
subtopics: ["Likelihood"]
subtopic_ids: ["subtopic_01GTC0BN1TKJ293ZQG2PQAV0K5"]
topic: Data Analysis and Probability
topic_id: 8e63f966-9c4d-427f-af20-c680cae9e45f
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In this activity, you will decide whether two events affect each other, learning the difference between independent and dependent events.","questions":[{"answer":"Independent","question":"Which statement best describes an independent event?"},{"answer":"The outcomes do not affect each other","question":"Rolling a six-sided die and flipping a fair coin are:"},{"answer":"The outcome of one event changes the chance of the other","question":"If you draw a card, replace it, then draw another card, are the two draws independent or dependent? Provide the word."}],"difficulty":"enabling"}


example_id: wp_01KC42CR5KYHQ5B4Z1FY0N3MBM_wpn_01KC42CRW9QGMZMKSP0Z78C1SA_SCAFFOLDED_QUESTION
skills: ["Calculating probabilities from two-way tables"]
skill_ids: ["hw20z7LoMR3DVJqDVVfl"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: extension
example_output_json:
{"headline":"Survey of $120$ students on snack (Fruit or Chips) and breakfast (Yes/No). Data: Fruit-Yes $40$, Fruit-No $30$, Chips-Yes $20$, Chips-No $30$.","questions":[{"answer":"Not independent","question":"What is the probability a randomly chosen student likes Fruit? Give a reduced fraction."},{"answer":"$7/12$","question":"If a student eats breakfast, what is the probability they like Fruit? Give a reduced fraction."},{"answer":"$2/3$","question":"Are the events “likes Fruit” and “eats breakfast” independent? Explain using the table data."}],"difficulty":"extension"}


example_id: wp_01KC42CR5KYHQ5B4Z1FY0N3MBM_wpn_01KC42CRW9QGMZMKSP0ADVTF60_SCAFFOLDED_QUESTION
skills: ["Calculating probabilities from two-way tables"]
skill_ids: ["hw20z7LoMR3DVJqDVVfl"]
subtopics: ["Probability \u0026 Statistics Foundations"]
subtopic_ids: ["subtopic_01GTC0BPPFC7SK14KHJW3Y93PB"]
topic: Probability & Statistics
topic_id: 0cDr8PIJ3x1UHjGScbYX
class_year: 8
country: US
period_number: 8
node_type: SCAFFOLDED_QUESTION
difficulty: enabling
example_output_json:
{"headline":"In a class of $40$ students, the survey results are: Boys who like basketball = $10$, Boys who like soccer = $12$, Girls who like basketball = $8$, Girls who like soccer = $10$.","questions":[{"answer":"$\\dfrac{7}{10}$","question":"What is the probability of selecting a boy who likes basketball?\nHint: $\\text{probability}= \\frac{\\text{favorable outcomes}}{\\text{total outcomes}}$"},{"answer":"$\\dfrac{10}{40}$","question":"What is the probability that a randomly chosen student likes soccer?\nHint: add all soccer fans then divide by $40$."},{"answer":"$\\dfrac{12}{40}$","question":"If a student is selected at random, what is the probability the student is a girl **or** likes basketball? Give the answer as a reduced fraction."}],"difficulty":"enabling"}


