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

Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Define, evaluate, and compare functions.

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

Build a function that models a relationship between two quantities.

Use functions to model relationships between quantities.

Prove and apply trigonometric identities.

Construct and compare linear and exponential models and solve problems.

Model periodic phenomena with trigonometric functions.

Build new functions from existing functions.

Analyze functions using different representations.
problem_activity: Problem 1
Prove the cofunction identity of:
$${\mathrm{cos}\left({\pi\over2}-x\right)=\mathrm{sin}x}$$
Using the sum or difference formula.
Problem 2
Solve:
$${\mathrm{sin}\left(x+{\pi\over4}\right)+1=\mathrm{sin}\left({\pi\over4}-x\right)}$$
for
$${0 \leq x \leq 2\pi}$$
.


correct_option_index: 7