few_shots: 
Example 1:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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 problem or activity shown below enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_pos_0

HS_2
standard_description: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Narrative
The purpose of this activity is for students to learn stage 1 of the What’s Behind My Back center. Students find multiple decompositions of a number. Students snap a tower of connecting cubes into 2 parts and record each decomposition with a drawing and an expression. It may be helpful to give each group of students a single color of connecting cubes so the color of the cubes doesn’t distract students from identifying the two parts. In future stages of this center students hide cubes behind their back after snapping a tower. If needed, you can choose not to use the name What’s Behind My Back when playing this stage or let students know they will do that in future stages of this center.
The recording sheet is printed in the student book for this activity. There is a blackline master available for students to use during centers in future activities and lessons.
When students write an expression to match the connecting cubes, they reason abstractly and quantitatively (MP2).
MLR8 Discussion Supports.
Display and read aloud the following sentence frame to support small-group discussion: “You broke your tower into a group of ____ and a group of ____.” invite students to chorally repeat this sentence in unison 1–2 times.
Advances: Speaking, Conversing, Representing
Required Materials
Materials to Gather
Connecting cubes
Crayons
Materials to Copy
What's Behind My Back Stage 1 Recording Sheet
Required Preparation
Each group of 2 needs 8 connecting cubes of the same color.
Launch
Groups of 2
Give each group of students at least 8 connecting cubes and access to 2 different color crayons.
“We are going to learn a center called What’s Behind My Back?”
Display a cube tower with 8 cubes.
“Start with a tower of 8 cubes. One partner breaks the tower into 2 parts.”
Demonstrate breaking the tower into 2 parts.
“The other partner describes what happened to the tower. Tell your partner what happened to my tower.” (You broke your tower into a group of 5 and a group of 3.)
30 seconds: partner discussion
Share responses.
“Both partners record the two parts with a drawing and an expression.”
Demonstrate completing the recording sheet with a drawing and an expression.
“Then put your tower back together, and play again. Take turns snapping the tower of 8 cubes into 2 parts.”
Activity
5 minutes: partner work time
Student Facing
8 cubes
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8 cubes
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Student Response
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Advancing Student Thinking
If students snap the cubes the same way each time, consider asking:
“Are there any other ways that you can snap the tower into 2 parts?”
“What if you snapped only 1 cube off of the tower?”
Activity Synthesis
“What did you notice each time you snapped the tower?” (There were always 8 cubes. The 2 parts that we broke the tower into were different each time.)
“What are the different ways that you and your partner found to break the tower of 8 cubes into 2 parts?”
Display a tower of 2 and a tower of 6.
“What expression can we write to represent the 2 parts of this tower?” (
\(2 + 6\)
)


aligns: yes