few_shots: 
Example 1:
Concept/skill: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Example 3:
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.

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

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.)
problem_activity: Categorize each representation of a function as linear, exponential, or quadratic. Explain your reasoning for each one.
|                                                                                                                               a.                                                                                                                               |                                                                                                                             $$x$$                                                                                                                              | $$y$$ | 1 | -2 | 2 | 1 | 3 | 6 | 4 | 13 | 5 | 22 | b. | $$x$$ | $$y$$ | 1 | 48 | 2 | 24 | 3 | 12 | 4 | 6 | 5 | 3 |
|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------|---|----|---|---|---|---|---|----|---|----|----|-------|-------|---|----|---|----|---|----|---|---|---|---|
|                                                                                                                             $$x$$                                                                                                                              |                                                                                                                             $$y$$                                                                                                                              |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               1                                                                                                                                |                                                                                                                               -2                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               2                                                                                                                                |                                                                                                                               1                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               3                                                                                                                                |                                                                                                                               6                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               4                                                                                                                                |                                                                                                                               13                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               5                                                                                                                                |                                                                                                                               22                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                             $$x$$                                                                                                                              |                                                                                                                             $$y$$                                                                                                                              |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               1                                                                                                                                |                                                                                                                               48                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               2                                                                                                                                |                                                                                                                               24                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               3                                                                                                                                |                                                                                                                               12                                                                                                                               |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               4                                                                                                                                |                                                                                                                               6                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                                               5                                                                                                                                |                                                                                                                               3                                                                                                                                |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
|                                                                                                            c.                       $$f(x)=x(x-4)$$                                                                                                            |                                                                                                         d.                       $$f(x)=4-{x\over2}$$                                                                                                          |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |
| e.            |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_tte.PNG | f.            |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG|  |https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG| image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2018/07/02/alg1_u7_l1_ttf.PNG |       |   |    |   |   |   |   |   |    |   |    |    |       |       |   |    |   |    |   |    |   |   |   |   |


aligns: no