few_shots: 
Example 1:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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


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:
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).

Problem/activity:
Task
Solve the quadratic equation
$$ x^2 = (2x - 9)^2 $$
using as many different methods as possible.


Answer: 
No. This task does not involve an equation in two variables. There is only one variable, x.

Example 3:
Concept/skill: 
Construct a tangent line from a point outside a given circle to the circle.

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 $P$.


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

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: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
problem_activity: Optional activity
Students measure their proposed 5K courses with their trundle wheels. They compare their measurements with their estimates and make final adjustments to their proposed courses. Then they draw a finalized version of their course on the map (or a second copy of the map) including all the details necessary to organize the race: start and finish locations, walking direction, and number of laps.
Launch
Keep students in the same groups. Provide access to trundle wheels. Tell students to measure their proposed race course twice, record their measurements, and then to come back to the classroom to finish the computations and revisions.
Student Facing
Measure your proposed race course with your trundle wheel at least two times. Decide what distance you will report to the class.
Revise your course, if needed.
Create a visual display that includes:
A map of your final course
The starting and ending locations
The number of laps needed to walk 5 km
Any other information you think would be helpful to the race organizers
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
The map your teacher gave you didn't include a scale. Create one.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Ask students to display their maps and explain their proposed race courses. Consider doing a gallery walk. Encourage students to discuss any assumptions they made to complete their calculations as well as any revisions they made to their plan after measuring their proposed course.
Representing, Conversing: MLR7 Compare and Connect.
Use this routine to help students consider audience when preparing a visual display of their work. Ask students to consider how to display their proposed race courses so that another student can interpret them. Groups may wish to add notes or details to their drawings to help communicate their thinking. Provide 2–3 minutes of quiet think time for students to read and interpret each other's displays before they discuss any assumptions they made to complete their calculations as well as any revisions they made to their plan after measuring their proposed course.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


aligns: no