few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
Concept/skill: 
Solve quadratic equations in one variable.

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


Answer: 
Yes. This task shows one quadratic equation with one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_001894_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
problem_activity: Narrative
The purpose of this activity is for students to learn a new variation of stage 2 of the Math Stories center. Students use two-color counters to act out and tell stories involving addition or subtraction with the background mats. Students use objects or drawings to represent and solve the story problem that is told to them by their partner.
After they participate in the center, students choose from any stage of previously introduced centers.
Bingo
Math Fingers
Subtraction Towers
5-frames
Counting Collections
Required Materials
Materials to Gather
Materials from previous centers
Two-color counters
Materials to Copy
Math Stories Stage 2 Recording Sheet
Math Stories Stage 2 Backgrounds
Required Preparation
Each group of 2 needs 10 two-color counters.
Gather materials from:
Bingo, Stages 1-3
Math Fingers, Stages 1-3
Math Stories, Stages 1 and 2
Subtraction Towers, Stage 1
5-frames, Stages 1 and 2
Counting Collections, Stage 1
Launch
Groups of 2
Give each group of students 10 two-color counters and a set of background mats. Give each student a recording sheet.
“We are going to learn a new way to do the Math Stories center.”
Display the background mat with a playground.
“This time I need to think of a story to go with the background mat. I also need to think of a question to ask at the end of the story.”
“My story is: 6 kids were playing on the rings. Then 2 of the kids left to go play on the slide.”
“What question can I ask at the end of my story?” (How many kids are still playing on the rings?)
30 seconds: quiet think time
Share responses.
“Now I’ll tell my partner my story and ask the question.”
“You can use the background mats to help you act out the story if it is helpful. You can also draw a picture on the recording sheet. Write a number to show the answer to the story problem.”
“Take turns telling story problems to go with the background mats. Remember to include a question for your partner at the end of your story problem.”
Activity
8 minutes: partner work time
“Now you can choose another center. You can also continue playing Math Stories.”
Display the center choices in the student book.
Invite students to work at the center of their choice.
8 minutes: center work time
If time, invite students to choose another center.
Student Facing
Choose a center.
Bingo
[IMG]
Math Fingers
[IMG]
Subtraction Towers
[IMG]
5-frames
[IMG]
Math Stories
[IMG]
Counting Collections
[IMG]
Activity Synthesis
Invite 2 students to share different story problems about the same background mat.
As each student shares, record the action with words and numbers and an expression. For example: “3 and 6” and “
\(3 + 6\)
”.
“What was the same about the stories? What was different?”


aligns: yes