standard_description: Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
problem_activity: Narrative
The purpose of this activity is for students to practice using the subtraction algorithm introduced in a previous lesson. Provide base-ten blocks for students who choose to use them to support their reasoning about the algorithm.
MLR8 Discussion Supports:
Synthesis: Before students share their reasoning, remind them to use words such as decompose, ones, tens, and hundreds.
Advances: Speaking, Representing
Engagement: Provide Access by Recruiting Interest.
Leverage choice around perceived challenge. Invite students to select at least 3 of 5 problems to complete.
Supports accessibility for: Organization, Attention, Social-emotional skills
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Display Kiran’s algorithm from the previous lesson.
“Here’s a subtraction algorithm you saw in an earlier lesson. What might be the first thing you’d do if you are to use this algorithm to find the value of the subtraction expressions in the activity?” (Write the numbers in expanded form and stack them.)
1 minute: quiet think time
Share responses.
Give students access to base-ten blocks.
Activity
“Take some quiet time to try this algorithm. Check in with your partner if you have questions.”
5–7 minutes: independent work time
If students have questions about the notation used to record the decomposition of a hundred or ten into more tens or ones, consider asking:
“Is there any place in the problem where you don’t have enough tens or ones?”
“How could you get more tens (or ones)?”
“How could you record a hundred being decomposed into 10 tens (or a ten decomposed into 10 ones)?”
Student Facing
Here is a subtraction algorithm you saw in an earlier lesson:
[IMG]
Try using this algorithm to find the value of each difference. Show your reasoning. Organize it so it can be followed by others.
\(283 - 159\)
\(425 - 192\)
\(639 - 465\)
\(591 - 128\)
\(832 - 575\)
Student Response
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Advancing Student Thinking
If students do not record the multiple decompositions in the last problem, consider asking:
“What units did you need to decompose in this problem?”
“Where would it make the most sense to you to record how you decomposed a hundred into more tens? A ten into more ones?”
Activity Synthesis
Select students to share their reasoning for 2–3 problems. Choose problems to focus on based on common questions that came up. Be sure to discuss the last problem, which requires decompositions of both a ten and a hundred.
For the last problem, ask: “How did you decide how to record the ten and hundred that needed to be decomposed?” (I started subtracting the ones and decomposed a ten into 10 ones so I had already crossed off the 30 and written 20. When I decomposed the hundred into tens, I just decided to write the 120 on top of the 20 like I wrote the 20 on top of the 30.)
Record the completed algorithm, showing the decompositions of tens and hundreds.
Consider asking:
“Where were there not enough tens or ones to subtract?”
“What was decomposed and how was it recorded?”
“Did you notice any places where you might have made the error we saw in Lin's work?"


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