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: Work with numbers 11–19 to gain foundations for place value.

Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Extend the counting sequence.

Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)

Understand place value.

Understand the place value system.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Use place value understanding and properties of operations to add and subtract.

Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is for students to choose an algorithm or other strategy to add within 1,000. Students should attend to the details of numbers in the problems that could indicate whether a particular strategy or algorithm is most useful. The important thing is that students choose an algorithm or strategy that they can use efficiently and accurately for the given problem.
Engagement: Develop Effort and Persistence.
Check in and provide each group with feedback that encourages collaboration and community. For example, check that students are staying on task, using math vocabulary, and sharing how they solved the problem.
Supports accessibility for: Social-Emotional Functioning
Launch
Groups of 2
“We’ve been learning about addition algorithms for the last few lessons. Recall that an algorithm is a set of steps that works every time as long as the steps are carried out correctly. But, you know lots of ways to add numbers and lots of representations for showing your work like base-ten diagrams, number lines, and writing words or equations. If it’s not a set of steps that would work every time, we call it a strategy.”
“In this activity, you’re going to have an opportunity to find the value of each of these sums using an algorithm or other strategy of your choice.”
Activity
“Find the value of each sum. Later, you’ll have a chance to share your work.”
7-10 minutes: independent work time
Identify students who used the same strategy to add and those who used different strategies.
Choose a few problems for students to discuss. Consider selecting
\(264 +359\)
(the second expression) and
\(399 + 499\)
(the last expression), which lend themselves to be evaluated with an algorithm and another strategy, respectively.
“Find a partner that added the same way you did. Discuss your reasoning.”
1-2 minutes: partner discussion
“Now find a partner who found the sum in a different way from you. Discuss your reasoning.”
2-3 minutes: partner discussion
Repeat the discussion with 1-2 expressions or as many as time permits.
Student Facing
Use a strategy of your choice to find the value of each sum. Show your reasoning. Organize it so it can be followed by others.
\(199 + 348\)
\(264 + 359\)
\(203 + 75\)
\(316 + 198\)
\(399 + 499\)
[IMG]
Student Response
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Activity Synthesis
Invite 4-5 students to share a strategy or algorithm that someone they talked to used.
“What strategies or algorithms do you want to practice more?”


correct_option_index: 3