standard_description: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^(2 )+ y^(2) = 3.
problem_activity: Narrative
The purpose of this activity is for students to subtract a two-digit number from a two-digit number in a way that makes sense to them. Students build on their understanding of decomposing a ten when subtracting a one-digit number from a two-digit number to subtract two-digit numbers. The synthesis is devoted to presenting and comparing techniques students use to find the difference, including diagrams and equations (MP3).
This activity uses
MLR8 Discussion Supports
. Advances: listening, speaking, conversing
Representation: Develop Language and Symbols.
Synthesis: Make connections between representations visible. Ask students to verbalize the connection between the expression and the blocks.
Supports accessibility for: Visual-Spatial Processing, Language, Memory
Required Materials
Materials to Gather
Base-ten blocks
Connecting cubes
Launch
Groups of 2
Give students access to connecting cubes and base-ten blocks.
Activity
“Find the value of each difference and share your method and solution with your partner.”
7 minutes: independent work time
MLR8 Discussion Supports
“After your partner shares their method, repeat back what they told you.”
Display the sentence frames:
“I heard you say . . . .”
“Our methods are alike because . . . .”
“Our methods are different because . . . .”
5 minutes: partner discussion
Monitor for students who use base-ten blocks to show decomposing a ten.
Student Facing
Find the value of each difference. Show your thinking. Use blocks if it helps.
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[IMG]
Student Response
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Advancing Student Thinking
Some students may not use base-ten blocks to find the difference. Prompt them to show their thinking in a way that could help others understand. Ask them to write expressions to show the steps they took when appropriate. Consider asking:
“How did you find the value of the difference?”
“What could you add to your diagram to help your partner understand what you did?”
“How could you use equations to show the steps you used?”
Activity Synthesis
Invite previously identified students to share.
“What did _____ do to solve the problem? How can we record it?”
30 seconds: quiet think time
Share responses.
Show how to represent solving with base-ten blocks with drawings and equations.
“How are these representations like the way _____ used base-ten blocks to find the value of the difference? How are they different?”


aligns: no