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: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
problem_activity: Narrative
The purpose of this activity is for students to order numbers. Students estimate the location and label numbers on a number line, and then write them in order from least to greatest or greatest to least. For the third set of numbers, students may order the numbers using any method that makes sense to them. Students reflect on how the number line can help us organize numbers (MP5). Throughout the activity, monitor for the way students explain their reasoning based on place value and the relative position of numbers on the number line.
Representation: Access for Perception.
Use index cards, clothespins, and string to demonstrate the number line. Give students the numbers on the index cards and have them physically act it out by finding their place on the number line.
Supports accessibility for: Memory, Organization, Conceptual Processing
Launch
Groups of 2
Activity
“Now you will have a chance to order numbers.”
“Sometimes you will put them in order from least to greatest, and sometimes it will be from greatest to least.”
10 minutes: independent work time
“Compare with a partner. Explain your thinking.”
5 minutes: partner discussion
Monitor for students who order the last set of numbers by:
explaining their reasoning using precise place value language
placing each number on the number line before ordering the numbers
Student Facing
Estimate the location of 839, 765, 788, 815, and 719 on the number line.
Mark each number with a point. Label the point with the number it represents.
[IMG]
Order the numbers from
least to greatest.
_______, _______, _______, _______, _______
Estimate the location of 199, 245, 173, 218, and 137 on the number line.
Mark each number with a point. Label the point with the number it represents.
[IMG]
Order the numbers from
greatest to least.
_______, _______, _______, _______, _______
Order the numbers from
least to greatest.
545, 454, 405, 504, and 445
_______, _______, _______, _______, _______
Explain or show your thinking. Use the number line if it helps.
[IMG]
Was it more helpful for you to put the numbers in order first or put them on the number line first? Explain.
[IMG]
Student Response
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Advancing Student Thinking
If students locate the numbers on the number line, but reverse the order given in the problem, consider asking:
“How did you decide the order of your numbers?”
“Does your list show the numbers in order from least to greatest or greatest to least?”
Activity Synthesis
Invite previously identified students to share their reasoning.
“How are the numbers you labeled on the number line the same as the list of numbers you wrote? How are they different?” (For least to greatest, its the same. The difference is the number line shows the distance between each number, but the list of numbers shows them right next to each other.)


aligns: yes