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).

• “How would you describe Lin’s mistake?” (She tried to subtract 20 from 50 when subtracting 50 from 20. She needed to decompose a hundred to get more tens.)
• Select previously identified students to share what they would tell or show Lin to help her revise her work.
• If no students suggest the following revision to Lin's work, display the algorithm and ask students to explain the revision:

• “Keep Lin’s mistake in mind as we practice using this subtraction algorithm in the next activity.”

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.

• Select students to share their reasoning for 2 or 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 record the ten and the hundred that needed to be decomposed?” (I started subtracting the ones by decomposing a ten into 10 ones, so I crossed off the 30 and wrote 20. When I decomposed the hundred into tens, I 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:
  • “In which expressions were there not enough tens or ones to subtract?”
  • “What units were decomposed, and how were they recorded?”
  • “Did you notice any places where you might have made the error we saw in Lin's work?"