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

HS_1

im_task_001160_pos_0

HS_2
standard_description: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
problem_activity: Narrative
The purpose of this activity is for students to compare decimals using the context of distance. Students should have access to hundredths grids, if they choose to use them. Monitor for students who compare the decimals using
place value reasoning to compare the 1 tenth for Diego's throw with the 1 hundredth for Jada's throw
hundredths grids for the decimal part of the throws
number lines, recalling work from a previous course
When students decide to compare the decimals using number lines or hundredths grids, they are using appropriate tools strategically (MP5).
MLR8 Discussion Supports.
Encourage students to begin partner discussions by reading their written responses aloud. If time allows, invite students to revise or add to their responses based on the conversation that follows.
Advances: Conversing, Speaking
Required Materials
Materials to Copy
Small Grids
Launch
Groups of 2
Display the image in student workbook.
“Have you ever thrown a frisbee?”
Poll the class.
“A frisbee is a disc. In the Olympics, there is an event called the discus throw. Participants try to throw a metal disc as far as they can.”
Activity
2 minutes: independent work time
5 minutes: partner work time
Monitor for students who use reasoning named in the activity narrative.
Student Facing
Diego and Jada were competing to see who could throw the frisbee further. Diego threw the frisbee 5.10 meters. Jada threw the frisbee 5.01 meters.
Who threw the frisbee further?
Be prepared to explain your thinking.
[IMG]
Tyler and Han were competing to see who could swim the length of the pool faster. Tyler swam the length of the pool in 35.15 seconds. Han swam the length of the pool in 35.30 seconds. Who swam the length of the pool faster? Be prepared to explain your thinking.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Ask previously selected students to share their solutions.
“Both problems are about comparing decimals. How are the problems different?” (The units are different in the two problems. One is meters and the other is seconds. In one problem, the winner has the greater number and in the other problem, the winner has the lesser number.)


aligns: no