few_shots: 
Example:
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: 
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Answer: 
No. Completing neither of these problems requires replacing one equation by the sum of that equation and a multiple of the other equation.

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_001392_neg_0

8
standard_description: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
problem_activity: Problem 1
Jack mixes yellow and blue paint to make a green paint that he will use to paint his basement. He uses a ratio of 3 pints of yellow paint for every 2 pints of blue paint. Jack pours 18 pints of yellow paint into a bucket.
a.   How many pints of blue paint should Jack add to the bucket?
b.   Jack's friend Kyle wants to help paint. Kyle said he has a green paint that is 9 parts yellow paint to 4 parts blue paint. Is Kyle's paint the same shade green as Jack's? Explain why or why not.
Problem 2
Terrance bikes 3.6 miles to school in 18 minutes. Jacqueline bikes 5.4 miles to school in 30 minutes. Assuming each student rode at a constant speed, who is traveling at a faster speed?
Problem 3
At the corner market, you can buy rice by the pound. The table below shows some weights and their corresponding costs.
| **           Rice (lbs.)          ** | **           Cost ($)          ** |
|--------------------------------------|-----------------------------------|
|                  2                   |                11                 |
|                  10                  |                55                 |
|                  13                  |                 ?                 |
|                  ?                   |                88                 |
a.   How much does 13 pounds of rice cost?
b.   How many pounds of rice can you buy with $88?


aligns: yes