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: 
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_pos_0

HS_0

im_task_000870_pos_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.
problem_activity: Narrative
The purpose of this activity is for students to consider two different equations that represent the same story problem. Put Together, Result Unknown problems help students make sense of the commutative property because the two parts can be combined in different orders. This property, as well as the associative property, is referred to as “add in any order” to students. Students contextualize the problem and see that each number represents a specific object’s quantity, no matter which order it is presented, and connect these quantities to written symbols (MP2). Students will work more with the “add in any order” property in future lessons.
Representation: Access for Perception.
Students may benefit from hearing the instructions read aloud more than once.
Supports accessibility for: Language, 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 just solved a problem about pet fish. What else do you know about pets?”
30 seconds: quiet think time
1 minute: partner discussion
If needed ask, “What kinds of pets are there?”
Activity
Read the task statement.
3 minutes: independent work time
2 minutes: partner discussion
Monitor for a student who uses objects or drawings to show that each equation matches the story.
Student Facing
Tyler and Clare want to know how many pets they have together.
Tyler has 2 turtles.
Clare has 4 dogs.
Tyler wrote the equation
\(4 + 2= \boxed{6}\)
.
Clare wrote the equation
\(2 + 4 = \boxed{6}\)
.
Do both equations match the story?
Why or why not?
Show your thinking using drawings, numbers, or words.
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 explain that both equations match the story using only numbers, consider asking:
"How do you know that both equations match the story?"
"How could you use connecting cubes to show that they both match?"
Activity Synthesis
Invite previously identified students to share.
“How does their work show us that Tyler’s equation matches the story?”
“How does their work show us that Clare’s equation matches the story?”


aligns: no