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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001392_neg_0

8
standard_description: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
problem_activity: Warm-up
The purpose of this warm-up is for students to use their intuition to think about the upcoming unit on probability. In particular, students guess what type of fish might be caught after knowing the results of the previous 10 fish caught. Although no answer can be given with absolute certainty, the results being heavily skewed towards one type of fish should lead students to the idea that it is more likely to be the most commonly caught fish will be caught again.
Launch
It may be helpful to explain that there are many types of fish that are caught while fishing for fun or sport. The two types listed in this warm-up, bluegill and yellow perch, are typically found in lakes and caught with the same type of bait. Both of these types of fish are suitable for eating after being caught or release back into the water.
Student Facing
Andre and his dad have been fishing for 2 hours. In that time, they have caught 9 bluegills and 1 yellow perch.
The next time Andre gets a bite, what kind of fish do you think it will be? Explain your reasoning.
Student Response
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Activity Synthesis
The purpose of the discussion is to show students that no single answer can be certain for this problem, but previous results can help inform the likelihood of future outcomes.
Poll the class regarding the type of fish they think will be caught next. Begin by asking for students who think the next fish caught will be a bluegill followed by students who think the next fish caught will be a yellow perch followed by students who think that another type of fish will be caught (or that they will not catch another fish). Display the results from the poll for all to see. Following the poll, ask at least one student representing each group with more than 1 vote for their reasoning. Tell students that we cannot know for certain what the next type of fish will be, but based on the results we have available, it is most likely that a bluegill will be caught next.


aligns: no