Unit 3, Lesson 9
Subtraction Algorithms (Part 2)
Grade 3
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The purpose of this True or False? is to elicit insights students have about how the commutative property applies to addition and to multiplication, but does not apply to subtraction. The reasoning of students here helps to deepen their understanding of the properties of operations and how they apply to subtracting within 1,000. It also will be helpful later when students recognize the need to decompose a hundred or a ten to get more tens or ones.
This is the first time students experience the True or False? routine in grade 3. Students are familiar with this routine from a previous grade, however, they may benefit from a brief review of the steps involved.
Decide if each statement is true or false. Be prepared to explain your reasoning.
To Gather
Base-ten blocks
The purpose of this activity is for students to examine an error in an algorithm in which a larger digit is subtracted from a smaller digit in the same place-value position. In such a case, it is common for students to subtract the smaller digit from the larger digit instead, not realizing that subtraction is not commutative. The given algorithm here shows the numbers in expanded form to help students see that it is necessary to first decompose a hundred into tens before the 50 can be subtracted from 20.
When students make sense of and correct Lin’s mistake, they construct viable arguments and critique the reasoning of others (MP3).
To Gather
Base-ten blocks
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.
Here is a subtraction algorithm you saw in an earlier lesson:
Try using this algorithm to find the value of each difference. Show your reasoning. Organize your work so it can be followed by others.
Display students' work from a problem in the second activity, such as:
“Suppose a classmate says this problem has been changed into a completely different problem because the 832 has been crossed out. How would you explain the crossed-out numbers to them?” (The 832 is still there. It’s just been reorganized as 700 plus 120, which is 820, and then 820 plus 12 is 832. So, it’s still 832. It’s been grouped differently so we can subtract in every place value.)
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Lin’s work for finding the value of