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: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to ten objects).
problem_activity: Narrative
The purpose of this warm-up is for students to experience a new part of the Questions About Us routine. Students consider concepts of number in a familiar context. This warm-up focuses on cardinality, or knowing that the last number tells us how many, and keeping track of which images have been counted. In the activity, students share methods for counting the images. After counting the group of images as a class or inviting a student to demonstrate how to count the images, ask students,  “How many students chose cats?” to confirm that students know that the last number tells us how many.
The images included in the Questions About Us Chart blackline master K.2.B are examples of what to display for the Questions About Us warm-ups in Section B. In order to create a display that will be visible to the whole class, print and cut out enough 5-frames so that there is a square for each student in the class. For example, if there are 23 students in the class, cut out four 5-frames and 3 squares out of a fifth 5-frame. Consider laminating the display and using a dry erase marker to write the two choices and record students' responses. If available, the provided images can also be enlarged.
Required Materials
Materials to Copy
Questions About Us Chart
Launch
Groups of 2
Display Questions About Us Chart.
“Which animal do you like better: dogs or cats?”
30 seconds: quiet think time
Record each student's choice with a circle in a 5-frame.
Activity
“How can we figure out how many students like cats better?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students like cats better?”
“How can we figure out how many students like dogs better?”
30 seconds: quiet think time
30 seconds: partner discussion
Share responses.
Demonstrate or invite students to demonstrate counting.
“How many students like dogs better?”
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Count how many students chose cats again. After counting 10 dots, pause and ask, “How many dots have I counted?” and “Which dots have I already counted? Which dots do I still need to count?”


aligns: no