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

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im_task_001160_neg_0

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standard_description: Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.
problem_activity: Stage 1: Factors
Required Preparation
Materials to Gather
Centimeter cubes
Materials to Copy
Blackline Masters
Find the Number Stage 1 Directions and Gameboard

Narrative
Students find all the factors for a given number. One player chooses a number on the gameboard (1–36) and they get that many points. The other player covers all the factors of that number. Their score is the sum of all the covered factors. Students take turns choosing the starting number. If a player chooses a number that doesn’t have any uncovered factors, they lose their next turn. When there are no numbers remaining with uncovered factors, the player with the most points wins.
Additional Information
Each group of 2 needs 36 centimeter cubes.


aligns: no