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:
{
  "explanation": "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: Use place value understanding and properties of operations to add and subtract.

Extend the counting sequence.

Understand place value.

Understand the place value system.

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

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.

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

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.

Work with numbers 11–19 to gain foundations for place value.
problem_activity: Narrative
The purpose of this activity is for students to find combinations of coins with a value of 100 cents and understand that a dollar is the same as 100 cents. They add within 100 by grouping like coins, using a ten, or using counting on strategies. They find coin combinations that add up to 100 cents or 1 dollar and write the leftover amount as cents. This work builds on students’ understanding of a hundred.
Engagement: Develop Effort and Persistence.
Chunk the tasks by question and check in with students to provide feedback and encouragement after each question. Look for the students to be using a strategy and ask them to verbalize their solution to ensure they are on the right track.
Supports accessibility for: Language; Organization
Required Preparation
Add a dollar bill to the money poster showing the front and back to display in the launch.
Launch
Groups of 2
Display the poster with the dollar added.
[IMG]
“We just saw that there are many different ways to use coins to make 100 cents. One dollar is also the same as 100 cents.”
“If I have a dollar and I found a quarter, how much money would I have?” (125 cents or \$1 and 25¢)
30 seconds: quiet think time
Display a dollar and a quarter and write $1 and 25¢.
[IMG]
“When you write dollar amounts you use the \$ symbol. Use the ¢ symbol for the amount that cannot be grouped to make a dollar.”
Activity
“Now, you are going to work with a partner to make dollars and cents.”
10 minutes: partner work time
Monitor for students who show Priya's money in different ways to share in the Lesson Synthesis.
Student Facing
[IMG]
Andre emptied his pockets and found these coins.
[IMG]
How much money does he have? Show your thinking.
Han emptied his pockets and found these coins.
[IMG]
How much money does he have? Show your thinking.
Priya has $1 and 18¢ in her pocket.
If Priya only had coins in her pocket, what coins could she have?
Represent Priya’s coins:
If Priya had 1 dollar bill and some coins, what coins could she have?
Represent Priya's money:
Student Response
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Advancing Student Thinking
If students show the value of Andre and Han's coins only in cents, consider asking:
“How did you find the total value of the coins?”
“How many dollars does _______ have? How many leftover cents would he have?”
“How could you say how much money _______has using dollars and cents?”
Activity Synthesis
“I noticed that when you were creating a coin collection for Priya, there were different solutions.”
“How is it possible that everyone represented the same amount of money?” (Different coins can show the same amount, but you need a different number of coins.)
Invite students to share different combinations of coins they used to make $1.
Share and record responses.


correct_option_index: 0