few_shots: Example:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response, in json format:
{
  "explanation": "An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation. Solving this problem does not require use of the Pythagorean identity.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS
options: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = �� ÷ 3, 6 × 6 = ?.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to draw arrays from a given arrangements of dots. Students draw an array from dots in equal groups to reinforce the definition of an array and then draw as many arrays as they can from 16 randomly placed dots. Having cubes or counters for students to physically rearrange would be helpful in this activity.
MLR8 Discussion Supports.
To support partner discussion, display the following sentence frames: “This array matches the diagram because . . .”, and “This array shows multiplication because . . . .”
Advances: Conversing, Representing
Required Materials
Materials to Gather
Connecting cubes or counters
Launch
Groups of 2
Give students access to connecting cubes or counters.
Activity
“Work independently to draw a way that the first group of dots in problem 1 could be arranged into an array.”
2 minutes: independent work time
“Discuss how you arranged your dots and how the array is related to multiplication with your partner.”
1 minute: partner discussion
“How did you rearrange the dots to make an array?” (Since there were 3 in each group, I put 3 dots in each row. I saw 2 groups of 6, so I made 2 rows of 6.)
Consider asking:
“Did anyone create a different array?”
“Now you are going to make as many arrays as you can from 16 dots.”
2–3 minutes: independent work time
“Share how you rearranged the dots into arrays with your partner. See if together you can come up with any other arrays.”
3–5 minutes: partner work time
Student Facing
Draw 1 way the dots could be rearranged into an array.
[IMG]
Explain or show how the array is related to multiplication.
Draw ways that the dots could be arranged into arrays. Draw as many ways as you can.
[IMG]
Explain or show how each array is related to multiplication.
Student Response
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Activity Synthesis
“What kinds of equal groups did you make from 16 dots? How can you see the equal groups in the arrays you made?” (I can make 2 groups of 8. I drew it as 2 rows of 8 dots.)


correct_option_index: 0