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: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
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
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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