few_shots: 
Example:
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.

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.
{"table": [{"_attributes": {"align": "center", "class": ["table", "table-bordered"], "style": "table-layout:fixed; width:70%"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "No solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Exactly 1 solution"}]}, {"_attributes": {"style": "text-align:center"}, "strong": [{"_value": "Infinite number of solutions"}]}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9=4x+7}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y=3y+5}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${y={x\\over2}}$$"}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${3x+6y-9=0}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${x=y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${1.25x=1.25y}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9.9=6x+8y}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${9x=2.5y-8.8}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}]}, {"td": [{"p": [{"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=1.5}$$"}]}, {"_attributes": {"style": "text-align:center"}, "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${11x-2y=2.5}$$"}]}]}, {"_attributes": {"style": "text-align:center"}}, {"_attributes": {"style": "text-align:center"}}, {}]}]}]}]}
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?


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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: fl_problem_001392_neg_0

8
standard_description: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
problem_activity: Narrative
The purpose of this activity is for students to add or subtract to find unknown addends within 20. Students will find unknown addends when the total is 20. The known addends may encourage students to think about ways to make a ten and to use the sums and differences that they know (MP7).
MLR7 Compare and Connect.
Synthesis: After all strategies have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, “Why did the different approaches lead to the same outcome? What did the methods have in common? How were they different?”
Advances: Representing, Conversing
Engagement: Develop Effort and Persistence.
Students may benefit from feedback that emphasizes effort and time on task. For example, give feedback on the partner relationship and how students are able to work together to complete a task. Encourage both partners to share ideas and speak up to agree or disagree.
Supports accessibility for: Social-Emotional Functioning, Attention
Required Materials
Materials to Copy
Number Cards 0-19
Required Preparation
Create a set of cards for each group of 2.
Launch
Groups of 2
Give each group a set of cards.
Activity
“Let’s play another game to find unknown addends.”
Select a volunteer to be your partner.
“Partner A will draw a card and hold it on their forehead without looking.”
Prompt the volunteer to demonstrate.
“Partner B names a number that you can add to the number on the card to get to 20.”
Think aloud finding and naming the number.
“Partner A then names the number they are holding on their head.”
Prompt the volunteer to find the number.
“Check your work and write an equation to represent how you found an unknown addend in the turn. Share your equation with your partner. Switch roles and play again.”
12 minutes: partner work time
Monitor for students who:
use place value reasoning or look to make 10
use known addition or subtraction facts
make equivalent, but easier sums or differences
Student Facing
Directions:
Partner A holds a card on their forehead without looking.
Partner B names the number that you can add to the number on the card to get 20.
Partner A says the number on their card.
Record an equation to represent how you found the unknown addend.
{"table": [{"_attributes": {"border": "1", "style": "width:100%"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "my equations"}, {"_attributes": {"scope": "col", "style": "text-align:center; width:50%"}, "_value": "my partner\u2019s equations"}]}]}], "tbody": [{"tr": [{"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}, {"td": [{}, {}]}]}]}]}
Student Response
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Activity Synthesis
“Mai thought of trying to make 2 tens. What number needs to be added to 12 to make 2 tens?”
“What other methods did you use to find the unknown addend?”
Invite previously identified students to share methods.
“Pull out the number cards for 0–9, as you will use them in the next activity.”


aligns: no