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

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im_task_001160_pos_0

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standard_description: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
problem_activity: Narrative
The purpose of this activity is for students to solve a variety of Add to and Take from Result or Change Unknown story problems. Students solve the story problems any way they choose and write an equation that matches the story and has a box around the answer to the question. During the activity synthesis, students consider the different ways to write equations for a story problem.
MLR8 Discussion Supports.
Synthesis: For each method that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language.
Advances: Listening, Speaking
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Social-Emotional Functioning, Attention
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.
"We are going to solve some more story problems about books other kids like to read."
Activity
Read the problems.
5 minutes: independent work time
5 minutes: partner discussion
Student Facing
Mai has read 3 books about dogs.
Diego gives her 4 more books to read.
How many books about dogs will Mai read all together?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Noah has 4 books of poetry.
His sister gives him some more books.
Now he has 10 books of poetry.
How many books did his sister give him?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Tyler has 7 books about spiders.
He gives 3 of his books to Kiran.
How many books does Tyler have left?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Lin has 5 books about outer space.
Her teacher gives her some more books.
Now she has 10 books about outer space.
How many books did Lin's teacher give her?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
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 to share the equation for each problem.
"Why is the answer in different places in our equations?" (Because in some stories we know the two numbers to add together and then the answer is the total. In other problems we know the starting number and the total and the answer is the other number we added.)


aligns: no