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: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
problem_activity: Narrative
The purpose of this activity is for students to decompose 6 into 2 parts. Students see that the total number of cubes remains the same when it is decomposed into 2 parts. Although students may notice that they can do this in different ways, that idea is not the focus until the next activity.
MLR8 Discussion Supports.
Display and encourage students to use the following sentence frames: “I have _____ cubes in my hand”, “I have _____ cubes on my desk,” and “I have _____ cubes altogether.”
Advances: Speaking, Reading, Representing
Required Materials
Materials to Gather
Connecting cubes
Required Preparation
Each student needs 6 connecting cubes.
Launch
Groups of 2
Give each student 6 connecting cubes.
Activity
“You have 6 cubes. Put some of the cubes in your hand and some on your desk.”
30 seconds: independent work time
“Tell your partner how many cubes are in your hand. Show them the cubes.”
“Tell your partner how many cubes are on your desk. Show them the cubes.”
“Tell your partner how many cubes you have altogether.”
Student Response
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Activity Synthesis
Invite a student to share.
“How many cubes did you have in your hand? How many cubes were on your desk?”
Write an expression to represent the parts.
“How many cubes did you have in all?” (6)
“The total number of cubes stays the same when we break them up into 2 parts.”


aligns: yes