few_shots: 
Example:
Concept/skill: 
Analyze and solve pairs of simultaneous linear equations.

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: 
Yes. The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.

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

shot_info: fl_problem_001392_pos_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 compose and decompose 10 using objects, images, and equations. Students work with equations with the total before and after the equal sign.
MLR8 Discussion Supports.
Synthesis: For each question, invite students to turn to a partner and share their response. This gives all students an opportunity to produce language.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each student needs the bead tool that they created in the previous activity.
Launch
Groups of 2
“We can use the bead tool we made to show different ways to make and break apart 10. Show your partner one way that you can break apart 10 into 2 groups.”
“Take turns playing with your partner. Use your beads to show each equation. When your partner shows you their beads, tell them the equation to make 10 and draw a picture to show what the beads look like.”
Activity
4 minutes: partner work time
“Fill in each equation to match the pictures of beads. You can use your bead tool if it’s helpful."
3 minutes: independent work time
Student Facing
\(7 + 3 = 10\)
\(10 = 4 + 6\)
\(9 + 1 = 10\)
\(10 = 2 + 8 \)
\(\underline{\hspace{1 cm}} + \underline{\hspace{1 cm}} = 10\)
[IMG]
\(10 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)
[IMG]
\(\underline{\hspace{1 cm}} + \underline{\hspace{1 cm}} = 10\)
[IMG]
\(\underline{\hspace{1 cm}} + \underline{\hspace{1 cm}} = 10\)
[IMG]
Student Response
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Activity Synthesis
Display
\(2 + 8 = 10\)
.
Invite a student to demonstrate
\(2 + 8 = 10\)
with their beads.
“What 2 parts do you see? What total do you see?” (2 and 8, 10)
“How will the beads look different if we show
\(10 = 2 + 8\)
?" (The beads will look the same. There are still 10. 2 and 8 are still the parts.)


aligns: yes