few_shots: 
Example:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


Answer: 
Yes. 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.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0
standard_description: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
problem_activity: Narrative
In this activity, students notice as the divisor increases for a given dividend, the quotient gets smaller. Students may recognize and explain the relationship between multiplication and division. For example, they may notice that dividing one quarter into two equal pieces is the same as finding the product of
\(\frac{1}{2}\times\frac{1}{4}\)
. This relationship is not explicitly brought up in the synthesis, but if students describe this relationship, connect it to the student work that is discussed in the synthesis, as appropriate. When students notice a pattern, they look for and express regularity in repeated reasoning (MP8).
Engagement: Provide Access by Recruiting Interest.
Invite students to share a situation in their own lives that could be used to represent one of the division expressions.
Supports accessibility for: Conceptual Processing, Language, Attention
Launch
Groups of 2
Activity
1–2 minutes: independent think time
3–5 minutes: partner work time
Student Facing
Find the value that makes each equation true. Use a diagram if it is helpful.
\(\frac {1}{4} \div 2 = \underline{\hspace{1 cm}}\)
\(\frac {1}{4} \div 3 = \underline{\hspace{1 cm}}\)
\(\frac {1}{4} \div 4 = \underline{\hspace{1 cm}}\)
What patterns do you notice?
How would you find the value of
\(\frac{1}{4}\)
divided by any whole number? Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students do not explain how they would find the value of
\(\frac{1}{4}\)
divided by any whole number, prompt them to find the value of
\(\frac{1}{4} \div 5\)
and
\(\frac{1}{4} \div 6\)
and ask, “What is the relationship between the divisor and the quotient?”
Activity Synthesis
Display:
\(\frac {1}{4} \div 2 = \frac {1}{8}\)
\(\frac {1}{4} \div 3 = \frac {1}{12}\)
\(\frac {1}{4} \div 4 = \frac {1}{16}\)
“What patterns do you notice?” (The quotient is getting smaller. The denominator of the quotient is getting bigger. The denominator in the quotient increases by 4. The denominator in the quotient is equal to 4 times the number you are dividing by.)
“Why is the quotient getting smaller?” (Because we are dividing
\(\frac {1}{4}\)
into more pieces each time, so the size of each piece will be smaller.)


aligns: no