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 statistics as a process for making inferences about population parameters based on a random sample from that population.
problem_activity: Task
Many researchers have studied chimpanzees to learn about their problem solving skills. In 1978, researchers Premack and Woodruff published an article in Science magazine, reporting findings from a study on an adult chimpanzee named Sarah, who had been raised in captivity and had received extensive training using photos and symbols. In one experiment, Sarah was shown videotapes of eight different situations in which a human being was faced with a problem. After each videotape showing, Sarah was presented with two photographs, one of which depicted a possible solution to the problem. The researchers ensured that the order in which the photographs were presented was randomized (for example, the correct answer was not always presented first, etc.) and that the photographs had similar visuals (for example. similar colors, etc.) Of the eight problems, Sarah picked the photograph with the correct solution seven times. Could Sarah have been merely guessing and just lucky with her responses, or is there evidence that Sarah does better than just guessing?
Give two possible explanations for why Sarah might have answered seven out of eight correctly.
If Sarah were just guessing, and was just likely to pick one photograph compared to the other, how many would you expect her to get right out of eight problems?
Give an example of how you could use basic classroom tools (coins, dice, calculators, cards, etc.) to simulate one trial of Sarah “just guessing” to pick a photograph for one problem.
A student, James, decides to use simulation to investigate whether the study data provide evidence that Sarah was doing better than just randomly guessing, and so James tosses a coin eight times, and obtains six heads. Explain why James should repeat the process of tossing the coin eight times and recording the number of heads, many times.
James repeats the process of eight coin-tosses 100 times, each time recording the number of heads on the eight coin-tosses. The following is a dotplot of his results.
[IMG]
Based on the above dotplot, what was the most common result for “number of heads” in eight coin-tosses? Why does this make sense?
Based on this dotplot, would you say that a score of 7 out of 8 would be unusual if Sarah has just been guessing? Why or why not?
Which of the following is a possible explanation for Sarah’s performance?
Sarah had been just guessing and got lucky with her responses.
Sarah does better than just guessing.
Both (i) and (ii) are possible explanations.
Based on the simulation results, which of the following appears to be a plausible (likely) explanation for Sarah’s performance?
Sarah had been just guessing and got lucky with her responses.
Sarah does better than just guessing.
Both (i) and (ii) are possible explanations.
Based on the results of this study, would it be reasonable to say that all chimpanzees do better than just guessing when faced with the kind of problems posed to Sarah? Explain why or why not.


aligns: no