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: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.
problem_activity: Narrative
In this activity, students use the context of paper flowers to analyze patterns and solve multi-step problems. The patterns are fairly straightforward, but to use them to solve problems, students will need to represent or otherwise reason about them mathematically. Their earlier experience of making flowers supports students in making sense and visualizing each step of the problem.
MLR7 Compare and Connect.
Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “Did anyone solve the problem the same way, but would explain it differently?” and “Why did the different approaches lead to the same (or different) outcome(s)?”
Advances: Representing, Conversing
Launch
Groups of 2
“The paper flowers are strung together to make a garland.”
Activity
2 minute: independent work time
10 minutes: partner work time
Monitor for students who:
Use equations to show their thinking.
Organize the multi-step process
Student Facing
[IMG]
Priya and Jada are making paper flower garlands for their friend’s quinceañera. Each garland uses 12 flowers.
Priya wants 2 big flowers, followed by 2 small flowers. Jada wants 1 big flower, followed by 2 small flowers. Use their patterns to draw the garlands.
Priya and Jada make 25 garlands of each type. How many large and small flowers will they need altogether?
Diego and Kiran also made flowers. They made a total of 155 flowers for garlands that require 16 flowers each. How many garlands can they make?
It takes 1 minute to cut the strips for a flower and 2 minutes to finish it. How long did it take Diego and Kiran to make the 155 flowers, if they each make about the same number of flowers?
Student Response
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Activity Synthesis
Display student work of selected students and invite them to share.
“What specific part of the work makes their explanation clear?”
Consider asking:
“What suggestion do you have to make it clearer?”
“How can you revise your own work to make it more clear or organized?”


correct_option_index: 0