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: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
problem_activity: Narrative
The purpose of this activity is for students to learn stage 3 of the Capture Squares center. Capture Squares was introduced in grade 1. In this stage, students spin to get a number (6
–
10) and flip a card (0
–
10) and find the value of the sum. The spinner includes a wild space where students can choose their own number. They find the value of the sum on the game board and connect 2 dots that are adjacent to the number. If that line closes the square, they capture it and shade it in their color. The player to shade in 3 squares first is the winner.
Required Materials
Materials to Gather
Colored pencils or crayons
Number cards 0–10
Paper clips
Materials to Copy
Capture Squares Stage 3 Gameboard
Capture Squares Stage 3 Spinner
Launch
Groups of 2
Give each pair of students a copy of the game board, the spinner and a paper clip, a set of cards, and access to crayons or colored pencils.
“We are going to play a game.”
Spin the spinner and draw a card.
“How could I find the value of the sum of these two numbers?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Use a suggested method or select a volunteer to show how to find the value.
“Now, I find the square that has the value of my sum. I draw a line connecting two dots on that square.”
“If the spinner lands on the wild space, you can pick any number to be one of your addends.”
Repeat 1–2 more times, as needed.
“If I draw the line that completes the square, I shade in that square with my color. The first player to shade in 3 squares is the winner.”
Activity
12 minutes: partner work time
Monitor for a variety of student strategies to share in the synthesis.
Activity Synthesis
Invite selected students to share their strategies.
“When the spinner landed on the wild spot, how did you decide what number to pick?”


aligns: no