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 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

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
problem_activity: Narrative
The purpose of this lesson is for students to learn stage 1 of the center, How Close? Students pick a given number of digit cards and then choose a subset of those to make an expression that yields a number as close as possible to 20.
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Double 10-frames
Number cards 0–10
Materials to Copy
How Close? Stage 1 Recording Sheet
Launch
Groups of 2
Give each group a set of number cards, two recording sheets, and access to double 10-frames and connecting cubes or two-color counters.
“We are going to learn a game called How Close? Add to 20. Let's play the first round together.”
“First we take out any card that has the number 10. We will not use those cards for the game.”
Display 5 cards.
“I can choose two or three of these cards to add to get as close to 20 as I can. What cards should I choose?”
1 minute: quiet think time
2 minutes: partner discussion
Share responses.
“I write an equation with the numbers I chose and the sum of the numbers.”
Demonstrate writing the equation on the recording sheet.
“The person who gets a sum closer to 20 gets a point for the round. Then you each get more cards so you always have five cards to choose from. Play again. The person who gets more points wins.”
Activity
10 minutes: partner work time
Activity Synthesis
Invite students to share their methods for making a sum close to 20.


aligns: no