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.


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.


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.


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: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is to reintroduce students to Put Together, Total Unknown story problems. In this type of problem, there is no action, so students must recognize the addends must be joined to make up the total. Students were introduced to this type of story problem in kindergarten and solved within 10 using objects or drawings. Students also solved Put Together, Total Unknown problems in Unit 1 in the context of data.
Students begin the activity by looking at the problem displayed, rather than in their books. The three reads routine gives students an opportunity to make sense of the problem before looking for a solution. Because there is no action in a put together problem, students identify the important quantities and think about how they might represent them before they solve the problem (MP1). At the end of the launch, students open their books and work on the problem. Students solve in any way they choose including using objects, drawings, words, or numbers, and write an equation to match the story problem.
This activity uses
MLR6 Three Reads.
Advances: reading, listening, representing.
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
Activity
MLR6 Three Reads
Display only the problem stem, without revealing the question(s).
“We are going to read this problem 3 times.”
1st Read: “Kiran has some fish in his fish tank. He has 4 red fish and 5 blue fish.”
“What is this story about?”
1 minute: partner discussion
Listen for and clarify any questions about the context.
2nd Read: “Kiran has some fish in his fish tank. He has 4 red fish and 5 blue fish.”
“What are all the things we can count in this story?” (the number of red fish, the number of blue fish, the total number of fish)
30 seconds: quiet think time
2 minutes: partner discussion
Share and record all quantities.
Reveal the question(s).
3rd Read: Read the entire problem, including question(s) aloud.
“What are different ways we can solve this problem?” (I can use red and blue connecting cubes. I can draw the fish and count them.)
30 seconds: quiet think time
1 minute: partner discussion
"Solve the problem."
3 minutes: independent work time
“Share your thinking with your partner.”
2 minutes: partner discussion
Monitor for students who solve in the following ways and can explain their thinking clearly:
objects or drawings and count all
objects or drawings and count on
numbers and count on
Student Facing
Kiran has some fish in his fish tank.
He has 4 red fish and 5 blue fish.
How many fish does he have in all?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Student Response
Teachers with a valid work email address can
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Activity Synthesis
Invite previously identified students to share in sequence above.
After each student shares, “How does this representation match the story problem?”
Display
\(4+5=\boxed{9}\)
.
"Where do you see the parts of this equation in this representation? The story problem?” (4 means the 4 red fish, 5 is the blue fish, 9 is how many he has altogether.)


correct_option_index: 1