few_shots: 
Example 1:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Concept/skill: 
Recognize and represent proportional relationships between quantities.

Answer: 
No. Usually problems that teach recognizing and representing proportional relationships between quantities involve deciding whether two quantities are in a proportional relationship or identifying the constant of proportionality, and then representing proportional relationships by equations or explaining proportional relationship using coordinate graphs.

Example 2:
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
$$-\frac{1}{4}$$


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

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

Example 3:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

Answer: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

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_000972_neg_0

6

fl_problem_001097_neg_0

7

fl_problem_001392_pos_0

8
standard_description: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
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