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: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
problem_activity: Task
Your teacher was just awarded \$1,000 to spend on materials for your classroom.  She asked all 20 of her students in the class to help her decide how to spend the money.  Think about which supplies will benefit the class the most.
|                                                    Supplies                                                    | Cost  |
|----------------------------------------------------------------------------------------------------------------|-------|
|                                              A box of 20 markers                                               |  \$5  |
|                                              A box of 100 crayons                                              |  \$8  |
|                                              A box of 60 pencils                                               |  \$5  |
|                                     A box of 5,000 pieces of printer paper                                     | \$40  |
|                                      A package of 10 pads of lined paper                                       | \$15  |
|                                    A box of 50 pieces of construction paper                                    | \$32  |
|                                                 Books and maps                                                 |       |
|                                        A set of 20 books about science                                         | \$250 |
|                                       A set of books about the 50 states                                       | \$400 |
|                                   A story book (there are 80 to choose from)                                   |  \$8  |
| A map: there is one of your city, one for every state, one of the country, and one of the world to choose from | \$45  |
|                                               Puzzles and games                                                |       |
|                                     Puzzles (there are 30 to choose from)                                      | \$12  |
|                                   Board games (there are 40 to choose from)                                    | \$15  |
|                                 Interactive computer games (math and reading)                                  | \$75  |
|                                                 Special Items                                                  |       |
|                                    A bean bag chair for the reading corner                                     | \$350 |
Write down the different items and how many of each you would choose. Find the total for each category.
Supplies
Books and maps
Puzzles and games
Special items
Create a bar graph to represent how you would spend the money.  Scale the vertical axis by \$100.  Write all of the labels.
What was the total cost of all your choices?  Did you have any money left over?  If so, how much?
Compare your choices with a partner. How much more or less did you choose to spend on each category than your partner? How much more or less did you choose to spend in total than your partner?


aligns: no