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.

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

Understand 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.

Understand the place value system.

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

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

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 practice adding within 1,000 with an emphasis on adding by place. Throughout the activity, students have opportunities to explain their methods and representations to peers. In the synthesis, students have opportunities to question and critique the work of their peers as they compare different methods for adding three-digit numbers and different representations that show composing units when adding by place (MP3).
This activity uses
MLR8 Discussion Supports
. Advances: conversing
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to decide which problem to start with and the strategy they feel most comfortable solving with.
Supports accessibility for: Social-Emotional Functioning, Organization, Attention
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students access to base-ten blocks.
Activity
“We are going to practice adding 2 three-digit numbers. You can find the value of each sum in any way that makes sense to you. After some time working independently, you can continue working with a partner.”
MLR8 Discussion Supports
Display sentence frames to support students when they explain their strategy:
“First, I _____ because . . .”
“I noticed _____ so I . . .”
5 minutes: independent work time
4 minutes: partner work time
“Choose one expression and share how you found the value of the sum with a new partner.”
3 minutes: partner discussion
Monitor for students who use base-ten blocks, base-ten diagrams, or other representations that clearly show adding by place.
Student Facing
Find the value of each expression. Show your thinking.
\(384 + 409\)
\(757 + 152\)
\(262 + 438\)
\(575 + 166\)
Student Response
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Advancing Student Thinking
If students lose track of the tens or hundreds they compose (for example,
\(384 + 409 = 783\)
) or do not compose a ten or hundred, prompt students to explain their thinking and any representations they use. Consider asking:
“How does your representation show that you composed a new unit?”
“What could you add to your representation to help you keep track of any tens or hundreds you compose?”
“How could you use base-ten blocks to show your thinking?”
Activity Synthesis
Invite 2–3 previously identified students to share their representations and how they found the value of the sums.
“How are these methods the same? How are they different?”


correct_option_index: 6