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: 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.

Understand place value.

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

Understand the place value system.

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.

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

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

Extend the counting sequence.
problem_activity: Narrative
The purpose of this warm-up is to elicit students’ prior knowledge of area and the idea that a rectangle can be decomposed into smaller rectangular regions. Students look at 4 different area diagrams they used in grade 3. The reasoning here will be useful when students use diagrams to multiply two- and one-digit numbers in a later activity. While students may notice and wonder many things about the number of units within the area of the gridded region, focus on the connections between the diagrams with a grid and those without.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice? What do you wonder?
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Student Response
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Activity Synthesis
“What do you know about the 13 and 4 in the first ungridded rectangle?” (They are side lengths. They correspond to the number of squares across and the number of squares down in the first rectangle.)
“What about the 10, 3, and 4 in the second ungridded rectangle?” (The 10 and 3 are numbers that add up to 13. The 4 is the length of the shorter side.)
“How are the four diagrams related? Name as many connections as you see.” (Sample responses:
They all represent the same rectangle. They have the same side lengths and the same area.
The first two show the number of square units that fit in the rectangle. The last two don’t show it but we can tell by multiplying the side lengths.
The shaded portion in the second gridded rectangles shows the
\(4 \times 10\)
portion in the fourth rectangle.)
If no students mentioned the area of the rectangles in their analysis, ask: “How might we find the area of the rectangles?” (For the gridded rectangles, we can count the unit squares or multiply the number of units across and down. For the other two, we can multiply the side lengths.)


correct_option_index: 5