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: Extend the counting sequence.

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.

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

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.

Understand place value.

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

Understand the place value system.

Use place value understanding and properties of operations to add and subtract.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 2 of the Greatest of Them All center. Students use digit cards to create the greatest possible number. As each student draws a card, they choose where to write it on the recording sheet. Once a digit is placed, it can’t be moved. Students compare their numbers using
\(<\)
,
\(>\)
, or
\(=\)
. The player with the greater number in each round gets a point.
Students should remove cards that show 10 from their deck.
MLR2 Collect and Display.
Synthesis: Direct attention to the words collected and displayed on the anchor chart from the previous lessons. Invite students to borrow place value language from the display as needed.
Advances: Conversing, Reading
Required Materials
Materials to Gather
Number cards 0–10
Materials to Copy
Greatest of Them All Stage 2 Recording Sheet
Launch
Groups of 2
Give each group a set of number cards and each student a recording sheet.
“Now you will be playing the Greatest of Them All center with your partner.”
“You will try to make the greatest three-digit number you can.”
Display number cards and recording sheet.
Demonstrate picking a card.
“If I pick a (2), I need to decide whether I want to put it in the hundreds, tens, or ones place to make the largest three-digit number.”
“Where do you think I should put it?” (I think it should go in the ones place because it is a low number. In the hundreds place, it would only be 200.)
30 seconds: quiet think time
Share responses.
“At the same time, my partner is picking cards and building a number, too.”
“Take turns picking a card and writing each digit in a space.”
“Read your comparison aloud to your partner.”
Activity
“Now play a few rounds with your partner.”
15 minutes: partner work time
Activity Synthesis
Select a group to share a comparison statement. For example:
\(654 > 349 \)
and
\(349 < 654\)
.
“I noticed that partners had different comparison statements for the same numbers. How can they both be true?”
“If I draw an 8, where should I choose to place it and why?” (I would put it in the hundreds place since it’s almost the highest number I could
draw
. I might not get 9. With 800, I have a good chance for my number to be larger than my partner’s.)


correct_option_index: 5