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:
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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: 
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Answer: 
Yes. This task asks students to draw a ray that bisects an angle. The act of drawing circles and rays may involve compass and straightedge or dynamic geometric software.

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_pos_0

HS_2
standard_description: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the How Close center which was introduced in grade 1. In this stage, each student picks 7 cards and chooses 4 of them to create 2 two-digit numbers. Each student adds the numbers and the student whose sum is closest to 100 wins a point for the round. It is recommended that at this point in the year, students begin with a target number of 50 instead of 100 in this stage.
If students are not yet able to make 2 numbers that get close to 50, encourage them to choose 2 cards, make a 2 digit number and represent the number with cubes. Then determine how many more cubes they need to get to 50 and choose the 2 cards that will get closest to that number.
Representation: Internalize Comprehension.
Begin by asking, “Do you remember the game, ‘How Close?’” Invite students to recall strategies that helped them work within 20. Ask them to think about how the game will change when the target is 50.
Supports accessibility for: Memory, Attention, Organization
Required Materials
Materials to Gather
Number cards 0–10
Materials to Copy
How Close? Stage 3 Recording Sheet
Launch
Groups of 2
Give one set of digit cards to each group.
“Today we are going to play another game of How Close. This time we will play Close to 50.”
Display the digit cards at the top of the student page.
“We start with 7 cards again. Think about what cards you would choose to make 2 two-digit numbers that have a sum close to 50.”
1 minute: quiet think time
2-3 minutes: partner work time
Share responses.
“After you make your two-digit numbers, you will write an equation showing the sum.”
Demonstrate writing an equation on the recording sheet.
“Now, we see whose sum is closer to 50. Talk to your partner about how you could figure it out.” (You can count up or back from 50 and see whose number is closer.)
30 seconds: quiet think time
1 minute: partner discussion
“Then you will replace the cards you used and play again.”
Activity
"Now play How Close with your partner."
10 minutes: partner work time
Student Facing
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Activity Synthesis
Display digit cards from the student page.
“Diego made the number 38. What number could Diego make next to get close to 50?”


aligns: no