few_shots: 
Example 1:
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.

Example 2:
Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Concept/skill: 
Solve quadratic equations in one variable.

Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Problem/activity:
Task
Suppose $A$ is an angle with vertex $P$, as pictured below:
[IMG]
Draw a circle with center $P$ and with  radius $r \gt 0$.  Explain why the circle
meets each ray of angle $A$ in a single point.  Label these points $Q$ and $R$ respectively.
Draw circles with centers $Q$ and $R$ respectively and radius $r$.  These circles meet at $P$ and a second point to be labelled $B$.
Show that ray $\overrightarrow{PB}$  bisects angle $P$.


Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

Answer: 
No. This task does not involve drawing lines that are tangent to circles. The only line that may be drawn is the ray between points P and B.

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

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Narrative
The purpose of this True or False is to elicit strategies and understandings students have for multiplying one-digit whole numbers by multiples of 10. The reasoning students do here helps to deepen their understanding of the associative property as they decompose multiples of ten to make multiplying easier.
Launch
Display one statement.
“Give me a signal when you know whether the statement is true and can explain how you know.”
1 minute: quiet think time
Activity
Share and record answers and strategy.
Repeat with each statement.
Student Facing
Decide if each statement is true or false. Be prepared to explain your reasoning.
\(2 \times 40 = 2 \times 4 \times 10\)
\(2 \times 40 = 8 \times 10\)
\(3 \times 50 = 15 \times 10\)
\(3 \times 40 = 7 \times 10\)
Student Response
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Activity Synthesis
“How can you justify your answer without finding the value of both sides?”
Consider asking:
“Who can restate _____’s reasoning in a different way?”
“Does anyone want to add on to _____’s reasoning?”
“Can we make any generalizations based on the statements?”


aligns: yes