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: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.
problem_activity: Narrative
The purpose of this warm-up is for students to extend the verbal count sequence to 30. Students also see the numbers written as they say each number to help connect the number names to the written numbers. In the synthesis, students determine the next number in a count, which prepares them to count on from a given number. This deepens their understanding of the structure of the counting sequence (MP7).
Launch
Groups of 2
“Let’s count to 30.”
Activity
Count to 30 together.
Record as students count.
Count to thirty 1–2 times. Point to the numbers as students count.
Student Response
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Activity Synthesis
“I’m going to count. When I stop counting, whisper to your partner what number comes next when we count.”
Count to 5.
“What number comes next when we count?”
Count to 11.
“What number comes next when we count?”


aligns: no