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


Standard options: 
A. Prove the Pythagorean identity sin^(2)(θ) + cos^(2)(θ) = 1 and use it to find sin(θ), cos(θ),or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
B. Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.


Your response:
Thought: 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. Solving this problem does not require use of the Pythagorean identity.
Answer: B

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


Standard options: 
A. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
B. Solve quadratic equations in one variable.


Your response:
Thought: This task shows one quadratic equation with one variable, x.
Answer: B

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 $P$.


Standard options: 
A. 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.
B. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Your response:
Thought: 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.
Answer: A

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001894

HS_0

im_task_000870

HS_1

im_task_001160

HS_2
options: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) ^( )Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
problem_activity: Narrative
The purpose of this activity is for students to solve problems that involve multiplication where one factor is a teen number. Students may solve and represent the problem any way they choose. In problem 3, look for different ways in which students are using area diagrams to highlight in the posters for the gallery walk in the next activity. Students reason abstractly and quantitatively when they interpret the stories and represent them with diagrams, expressions, or equations (MP2).
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 2 of the 4 problems to complete.
Supports accessibility for: Organization, Attention, Social-emotional Skills
Required Materials
Materials to Gather
Base-ten blocks
Tools for creating a visual display
Materials to Copy
Centimeter Grid Paper - Standard
Launch
Groups of 2
“Where are some places that you see art in your community?”
30 seconds: quiet think time
Share responses.
“These problems are about a student visiting a local art festival. This is where local artists come to display and sell their work.”
Give students access to grid paper and base-ten blocks.
“Turn and talk to your partner about how you might solve these problems.”
1–2 minutes: partner discussion
Activity
“Solve these problems. Explain or show your reasoning.”
6–8 minutes: independent work time
As students work, consider asking:
“How can you represent your thinking about the problem?”
“Where can you see _____ in your work?”
Monitor for:
different ways that students use the area diagram in the third problem
students who represent the third problem in the same way to pair to create a poster together
“Now you are going to create a poster to show your thinking on the third problem. You are going to work with a partner who solved the problem in the same way you did.”
Give each group tools for creating a visual display.
6–8 minutes: partner work time
Student Facing
Solve each problem. Explain or show your reasoning.
Noah sees a large painted mural that has side lengths of 15 feet and 4 feet. What is the area of the mural?
Noah’s family buys a mosaic that has 12 rows and 8 columns of 1 inch tiles. What is the area of the mosaic?
At the art festival, Noah uses sidewalk chalk to help decorate a rectangular piece of sidewalk that is 6 feet by 14 feet. What is the area of the piece of sidewalk that Noah helped decorate?
At the art festival, Noah buys a pack of stickers. There are 5 sheets and each sheet has 16 stickers. How many stickers are in the pack?
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
If students don’t find a solution to the problems, consider asking: “What is this problem about?” and “How could you represent the problem?”
Activity Synthesis
Display posters around the room.


correct_option_index: 1