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: 
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Answer: 
No. This task does not involve an equation in two variables. There is only 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_neg_0

HS_1

im_task_001160_neg_0

HS_2
standard_description: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
problem_activity: Narrative
The purpose of this activity is for students to convert from meters to centimeters using the context of a standing broad jump, a common test for physical fitness. Students may multiply by 100 to convert from meters to centimeters or divide by 100 to convert from centimeters to meters. Students should be encouraged to use whatever strategy makes sense to them. Future lessons will focus specifically on conversion from centimeters to meters. Give students access to meter sticks.
MLR8 Discussion Supports.
Synthesis: Provide students with the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Required Materials
Materials to Gather
Metersticks
Launch
Groups of 2
Display the image from student workbook.
Give students access to meter sticks.
“What do you notice? What do you wonder?” (The girl is jumping. There are numbers on the mat. Did she start where the footprints are? How far did she jump?)
Activity
1–2 minutes: quiet think time
6–8 minutes: partner work time
Monitor for students who:
use their result for Tyler’s jump in centimeters to find his jump in millimeters
use the result in meters to find how far Tyler jumped in millimeters
Student Facing
[IMG]
[IMG]
Here are the distances that each student jumped.
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "student"}, {"_attributes": {"scope": "col"}, "_value": "distance"}]}]}], "tbody": [{"tr": [{"td": [{"_value": "Mai"}, {"_value": "1.61 meters"}]}, {"td": [{"_value": "Tyler"}, {"_value": "1.43 meters"}]}, {"td": [{"_value": "Clare"}, {"_value": "1.57 meters"}]}]}]}]}
The average standing broad jump distance for 5th graders is 148 centimeters. Are each of the students in the table below, at, or above the average? Explain or show your reasoning.
The world record for the standing broad jump is 337 centimeters. Jada says that’s more than Mai and Clare jumped combined. Do you agree with Jada? Explain or show your reasoning.
Tyler says his jump sounds more impressive if he reports it in millimeters.
How far is Tyler’s jump in millimeters? What about Mai’s and Clare’s jumps?
Which unit do you think is best for reporting the jumps? Explain your reasoning.
Student Response
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Advancing Student Thinking
If students do not know the relationship between millimeters, centimeters, and meters, show them a meter stick and ask “How can you use the meter stick to figure out how many millimeters are in 1 meter?”
Activity Synthesis
Display the expression:
\(1.43 \times 100\)
.
“How does this expression represent Tyler’s jump in centimeters?” (There are 100 centimeters in a meter.)
Invite students to share how they found Tyler’s jump in millimeters.
Display the expression:
\((1.43 \times 100) \times 10\)
.
“In what unit of measurement does this expression represent Tyler's jump? How do you know?” (It represents Tyler’s jump in millimeters. There are 10 millimeters in a centimeter and
\(1.43\times100\)
represents the centimeters, so if we multiply the number of centimeters by 10, we will get the number of millimeters.)
Display the expression:
\(1.43 \times 1,\!000\)
.
“How does this expression represent Tyler’s jump in millimeters?” (There are 1,000 millimeters in a meter so I have to multiply by 1,000 to get millimeters from meters.)
Display the equation:
\(1.43 \times 1,\!000 = (1.43 \times 100) \times 10\)
.
Invite students to share which unit they prefer to express the distances that the students jumped.
“It’s important to choose a unit that makes sense to you.”


aligns: yes