few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Mathematical concept/skill options: 
A. Prove and apply trigonometric identities.
B. Model periodic phenomena with trigonometric functions.
C. Interpret functions that arise in applications in terms of the context.
D. Build a function that models a relationship between two quantities.
E. Define, evaluate, and compare functions.
F. Use functions to model relationships between quantities.
G. Understand the concept of a function and use function notation.
H. Analyze functions using different representations.
I. Extend the domain of trigonometric functions using the unit circle.
J. Interpret expressions for functions in terms of the situation they model.
K. Build new functions from existing functions.
L. Construct and compare linear and exponential models and solve problems.


Your response:
Thought: This problem applies trigonometric identities, including the angle addition formula for cosine.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001894

HS
options: Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

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.

Use equivalent fractions as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

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.

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.
problem_activity: Narrative
This optional activity gives students an additional opportunity to practice using number lines to decompose fractions into sums of other fractions and to record the decompositions as equations.
The fractions on the cards (shown here) contain no whole numbers or mixed numbers, but some students may use them to help them find the second addend (and to avoid counting tick marks on the number line). Some may also choose to label each number line with whole numbers beyond 1 to facilitate their reasoning and equation writing.
\(\frac{1}{3} \qquad \frac{2}{3} \qquad \frac{3}{3} \qquad \frac{4}{3} \qquad \frac{5}{3} \qquad \frac{6}{3} \qquad \frac{7}{3} \qquad \frac{8}{3}\)
Required Materials
Materials to Copy
Make Two Jumps
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Give each group a set of fraction cards from the blackline master.
Display the four number lines.
“What do you notice? What do you wonder?”
30 seconds: quiet think time
30 seconds: partner discussion
Activity
“Label each point on the number line with a fraction it represents.”
1–2 minutes: independent work time
“You will make two jumps on the number line to go from 0 to the point and write an equation to represent your moves.”
Explain how to use the cards and how to complete the task. Consider demonstrating with an example and allowing students to ask clarifying questions before they begin.
Monitor for students who:
use whole numbers and mixed numbers in their equations and those who don’t
label their number lines with whole numbers beyond 1
Student Facing
Here are four number lines, each with a point on it.
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For each number line, label the point. This is your target. Make two forward jumps to get from 0 to the target.
Pick a card from the set given to you. Use the fraction on it for your first jump. Draw the jump and label it with the fraction.
From there, draw the second jump to reach the target. What fraction do you need to add? Label the jump with the fraction.
Write an equation to represent the sum of your two fractions.
Student Response
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Activity Synthesis
Select previously identified students to share their responses to the first couple of diagrams (or more if time permits). Start with students who used no whole numbers or mixed numbers. Ask them to explain why they chose to write the numbers the way they did.
Consider discussing the merits and challenges (if any) of expressing the fractions as whole or mixed numbers.


correct_option_index: 4