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: 
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: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
problem_activity: Narrative
The purpose of this activity is for students to add or subtract to find unknown addends within 20. Students will find unknown addends when the total is 20. The known addends may encourage students to think about ways to make a ten and to use the sums and differences that they know (MP7).
MLR7 Compare and Connect.
Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “Why did the different approaches lead to the same outcome? What did the methods have in common? How were they different?”
Advances: Representing, Conversing
Engagement: Develop Effort and Persistence.
Students may benefit from feedback that emphasizes effort and time on task. For example, give feedback on the partner relationship and how students are able to work together to complete a task. Encourage both partners to share ideas and speak up to agree or disagree.
Supports accessibility for: Social-Emotional Functioning, Attention
Required Materials
Materials to Copy
Number Cards 0-19
Required Preparation
Create a set of cards for each group of 2.
Launch
Groups of 2
Give each group a set of cards.
Activity
“Let’s play another game to find unknown addends.”
Select a volunteer to be your partner.
“Partner A will draw a card and hold it on their forehead without looking.”
Prompt the volunteer to demonstrate.
“Partner B names a number that you can add to the number on the card to get to 20.”
Think aloud finding and naming the number.
“Partner A then names the number they are holding on their head.”
Prompt the volunteer to find the number.
“Check your work and write an equation to represent how you found an unknown addend in the turn. Share your equation with your partner. Switch roles and play again.”
12 minutes: partner work time
Monitor for students who:
use place value reasoning or look to make 10
use known addition or subtraction facts
make equivalent, but easier sums or differences
Student Facing
Directions:
Partner A holds a card on their forehead without looking.
Partner B names the number that you can add to the number on the card to get 20.
Partner A says the number on their card.
Record an equation to represent how you found the unknown addend.
| my equations | my partner’s equations |
|--------------|------------------------|
|              |                        |
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|              |                        |
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Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
“Mai thought of trying to make 2 tens. What number needs to be added to 12 to make 2 tens?”
“What other methods did you use to find the unknown addend?”
Invite previously identified students to share methods.
“Pull out the number cards for 0–9, as you will use them in the next activity.”


aligns: no