few_shots: 
Example 1:
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.

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


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:
Concept/skill: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

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


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_neg_0

HS_0

im_task_000870_neg_0

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im_task_001160_neg_0

HS_2
standard_description: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
problem_activity: Narrative
The purpose of this lesson is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem in the context of putting together pattern blocks (MP2). If students finish early, invite them to find multiple solutions to the story problem.
MLR8 Discussion Supports.
Synthesis: For each decomposition that is shared, invite students to turn to a partner and restate the recorded equation.
Advances: Listening, Speaking
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Pattern blocks
Launch
Groups of 2
Give students access to connecting cubes or two-color counters, 10-frames, and pattern blocks.
Read and display the task statement.
“Tell your partner what happened in the story.”
30 seconds: quiet think time
1 minute: partner discussion
Monitor for students who accurately retell the story. Choose at least one student to share with the class.
Reread the task statement.
“Show your thinking using drawings, numbers, words, or objects.”
Activity
2 minutes: independent work time
2 minutes: partner discussion
“If you haven’t already, write an expression to show how many square pattern blocks and triangle pattern blocks Diego used.”
2 minutes: independent work time
Student Facing
Diego built a shape with 10 pattern blocks.
He only used squares and triangles.
How many square pattern blocks did Diego use?
Then how many triangle pattern blocks did Diego use?
Expression: _________________________________
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
Invite students who found different decompositions of 10 to share.
As students share, record each solution with an equation, such as
\(10 = 7 + 3\)
.
“Did _____ and _____ both show what happened in the story? How do you know?” (Yes. They both have 10 pattern blocks, with some triangles and some squares.)
“In the next activity, we will find more ways that we can make shapes with 10 pattern blocks.”


aligns: no