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


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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: 
Construct a tangent line from a point outside a given circle to the circle.

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, 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_neg_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
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 add 2 two-digit numbers within 100 and show their thinking with equations. Although some students may write each step of their thinking with equations, it is not required that they do so. Students can write one equation that shows the sum and represent their solution pathway in their drawings. In the activity synthesis, students present their method verbally to a new partner.
This activity uses
MLR8 Discussion Supports. Advances: listening, speaking, conversing
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Launch
Groups of 2
Give students access to connecting cubes in towers of 10 and singles.
“We have been learning about different ways to add within 100. You are going to find sums using a method that makes most sense to you for each problem. Record equations to show your thinking.”
Activity
5 minutes: independent work time
“Compare your work with your partner’s. Did you use the same method? Did you represent your method in the same way? How is your work the same? How is it different?"
5 minutes: partner work time
Monitor for a student who wrote equations related to making ten and one who wrote equations related to adding by place.
Student Facing
Find the value of each sum using any method that you want.
Show your thinking using drawings, numbers, or words.
Write equations to represent your thinking.
\(48 + 15\)
\(57 + 36\)
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
MLR8 Discussion Supports:
Display sentence frames to support students when they explain their method as equations:
“First, I _____ because . . .”
“I noticed _____ so I . . .”
“You are going to explain your method to another student in the class. Practice what you will say with your partner. Use these sentence starters to help you.”
3 minutes: partner discussion
“Find a new partner and explain your method.”
2 minutes: partner discussion


aligns: no