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: Understand the relationship between numbers and quantities; connect counting to cardinality.
problem_activity: Narrative
The purpose of this activity is for students to make groups with more or fewer objects than a given group of objects. When asking students to make a group that has more objects than the given group, the given group will have very few objects. Similarly, when asking them to make a group that has fewer objects than the given group, the given group will have many objects. This should allow students to create and compare the groups visually. In a future lesson, students will create groups with more or fewer objects than a given group when the quantities are closer, where it will be helpful for students to match or count the objects in each group.
Required Materials
Materials to Gather
Counters
Materials from a previous activity
Required Preparation
Each group of 2 needs a bag of green triangle and orange square pattern blocks from the previous activity.
Launch
Groups of 2
Give each group of students a bag of 8–10 green triangle pattern blocks and a bag of 1–3 orange square pattern blocks.
Activity
“Make a group with counters that has more than the group of orange squares.”
30 seconds: quiet think time
1 minute: partner work time
“Figure out and tell your partner how many counters you have. Then figure out and tell your partner how many orange squares you have.”
2 minutes: partner work time
“Make a group with counters that has fewer than the group of green triangles.”
30 seconds: quiet think time
1 minute: partner work time
“Figure out and tell your partner how many counters you have. Then figure out and tell your partner how many green triangles you have.”
2 minutes: partner work time
Activity Synthesis
Invite 2–3 students to share the groups of counters that they made that have fewer than the green triangles.
“What is the same about the groups they made? What is different?” (They all made groups with different numbers of counters. They all have fewer than the green triangles.)


aligns: no