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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_neg_0

HS_0
standard_description: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
problem_activity: Narrative
The purpose of this activity is for students to apply their knowledge from previous activities to draw arrays to match multiplication expressions. Have connecting cubes or counters available for students who need them. In the launch, students use their bodies to make an array for the expression
\(4\times6\)
. Feel free to adjust this expression to better fit the number of students in your class.
Launch
Groups of 2
Display
\(4\times6\)
“Work together as a class to use your bodies to create an array for this multiplication expression.”
If the number of students does not exactly match the product, ask extra students to monitor the array and be prepared to explain where they see parts of the expression in the array.
3–5 minutes: whole-class work time
Activity
“Work with your partner to draw an array for each multiplication expression. Be ready to share connections you notice between the multiplication expressions and arrays.”
2–3 minutes: partner work time
Student Facing
Draw an array for each multiplication expression. Be prepared to share your reasoning.
\(2\times3\)
\(5\times2\)
\(4\times4\)
Student Response
Teachers with a valid work email address can
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Advancing Student Thinking
If students draw equal groups that are not arrays, consider asking:
“How did you use the expression to create your drawing?”
“How could we rearrange your drawing into an array?”
Activity Synthesis
Share an array or two for each expression.
“What connections did you and your partner see between the multiplication expressions and arrays?” (The factors tell us how many things are in each row and column. For
\(2\times3\)
, we drew an array with 2 columns that have 3 things in each column. For
\(2\times3\)
, we drew an array with 2 rows that have 3 things in each row.)


aligns: no