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: 
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).

Answer: 
No. This task does not involve an equation in two variables. There is only 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_neg_0

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im_task_001160_neg_0

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standard_description: Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)
problem_activity: Narrative
The purpose of this activity is for students to subtract a two-digit number from a two-digit number in a way that makes sense to them. Students build on their understanding of decomposing a ten when subtracting a one-digit number from a two-digit number to subtract two-digit numbers. The synthesis is devoted to presenting and comparing techniques students use to find the difference, including diagrams and equations (MP3).
This activity uses
MLR8 Discussion Supports
. Advances: listening, speaking, conversing
Representation: Develop Language and Symbols.
Synthesis: Make connections between representations visible. Ask students to verbalize the connection between the expression and the blocks.
Supports accessibility for: Visual-Spatial Processing, Language, Memory
Required Materials
Materials to Gather
Base-ten blocks
Connecting cubes
Launch
Groups of 2
Give students access to connecting cubes and base-ten blocks.
Activity
“Find the value of each difference and share your method and solution with your partner.”
7 minutes: independent work time
MLR8 Discussion Supports
“After your partner shares their method, repeat back what they told you.”
Display the sentence frames:
“I heard you say . . . .”
“Our methods are alike because . . . .”
“Our methods are different because . . . .”
5 minutes: partner discussion
Monitor for students who use base-ten blocks to show decomposing a ten.
Student Facing
Find the value of each difference. Show your thinking. Use blocks if it helps.
\(46 - 28 =\underline{\phantom{\hspace{1.05cm}}}\)
\(93 - 54 =\underline{\phantom{\hspace{1.05cm}}}\)
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
Some students may not use base-ten blocks to find the difference. Prompt them to show their thinking in a way that could help others understand. Ask them to write expressions to show the steps they took when appropriate. Consider asking:
“How did you find the value of the difference?”
“What could you add to your diagram to help your partner understand what you did?”
“How could you use equations to show the steps you used?”
Activity Synthesis
Invite previously identified students to share.
“What did _____ do to solve the problem? How can we record it?”
30 seconds: quiet think time
Share responses.
Show how to represent solving with base-ten blocks with drawings and equations.
“How are these representations like the way _____ used base-ten blocks to find the value of the difference? How are they different?”


aligns: yes