few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Your response:
Thought: In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Construct and compare linear and exponential models and solve problems.

Use functions to model relationships between quantities.

Build new functions from existing functions.

Understand the concept of a function and use function notation.

Interpret functions that arise in applications in terms of the context.

Interpret expressions for functions in terms of the situation they model.

Define, evaluate, and compare functions.

Extend the domain of trigonometric functions using the unit circle.

Prove and apply trigonometric identities.

Model periodic phenomena with trigonometric functions.
problem_activity: Activity
First, students examine several examples of functions and non-functions from the perspective of “Can we figure out . . . ?” Then, they decide which of the functions can be represented by a given expression.
Launch
Allow quiet think time to consider the situations in the first question and answer yes or no. Ensure students understand which ones are functions, and which are not. Then, give students time to complete the table.
Student Facing
For each question, answer yes or no.
It is 50 miles to Tucson. Can we figure out how many kilometers it is to Tucson?
It is 200 kilometers to Saskatoon. Can we figure out how many miles it is to Saskatoon?
A number is -3. Can we figure out its absolute value?
The absolute value of a number is 8. Can we figure out the number?
A circle has a diameter of 8 cm. Can we figure out its circumference?
A circle has a circumference of
\(10\pi\)
cm. Can we figure out its diameter?
A square has a side length of 6 units. Can we figure out its perimeter?
A rectangle has a perimeter of 30 meters. Can we figure out its width?
Which of the relationships are functions?
For each function definition in the table, match it with the situation, write a statement explaining which variable depends on which, and write an example using function notation. An example is done for you.
|    function definition     |                  situation                  |                                                      statement                                                      |    example    |
|----------------------------|---------------------------------------------|---------------------------------------------------------------------------------------------------------------------|---------------|
|     \(m(x) = 0.62x \)      | You know kilometers and want to find miles. | Distance in miles depends on distance in kilometers, or, distance in miles is a function of distance in kilometers. | \(m(100)=62\) |
| \(f(x) = x \boldcdot \pi\) |                                             |                                                                                                                     |               |
|      \(g(x) = 1.6x\)       |                                             |                                                                                                                     |               |
|       \(h(x) = 4x\)        |                                             |                                                                                                                     |               |
|       \(k(x) = |x|\)       |                                             |                                                                                                                     |               |
Student Response
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Activity Synthesis
Invite students to share their responses in the table, and how they know. Emphasize that there are many correct examples one could choose—the thing to understand is how function notation communicates an input and output to the function (or a value of the independent variable and corresponding value of the dependent variable.)


correct_option_index: 8