Lesson 20

• Groups of 2
• Display subtraction calculations.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “How are the two examples alike? How are they different?” (In the second one the numbers are written in expanded form, including the numbers that show regrouping.)
• “We’ve seen subtraction problems with decomposed units before. How are these different?” (In the problems we have seen so far, only one place needed to be decomposed in order to subtract. In these examples, more than one place needs to be decomposed.)

The purpose of this activity is for students to add and subtract multi-digit numbers through the hundred-thousands place. To find the value of some differences, students will decompose more than one unit.

The last question includes problems with a missing addend and a missing subtrahend. Besides making use of the structure of the standard algorithm (MP7), students will need to rely on what they know about the relationship between addition and subtraction to find the missing numbers.

• Groups of 2
• Give students access to grid paper.

• 5–7 minutes: independent work time
• “Check your responses to the first problem with your partner and make any adjustments you need to make. Then work on the second problem together.”
• 2–3 minutes: partner discussion
• As students work on the second problem monitor for students who:
  • Find the missing addend by adding up from 67,182 to 129,400, or by subtracting \(129,\!400 - 67,\!182\).
  • Find the missing subtrahend by adding up from 193,710 to 234,650, or by subtracting \(234,\!650 - 193,\!710\)

• “How can you tell if your answers are correct? How can you check them?” (One way to check the result of subtraction is by adding it back to the number being subtracted. One way to check the result of addition is by subtracting one addend from the sum. Another way of checking is by performing the calculations with the numbers written in expanded form.)

In this activity, students analyze addition and subtraction calculations, identify errors, and explain what makes certain ways of calculating problematic. The work here gives students opportunities to construct logical arguments and critique the reasoning of others (MP3).

• Groups of 2
• Display the first problem.
• 2 minutes: quiet think time
• 2–3 minutes: partner discussion

• 5 minutes: independent work time to complete the second problem.
• 2 minutes: partner discussion
• Monitor for students who describe the errors using place value language and an understanding of how and when to decompose a unit.

• Select 2–3 students to share their responses and reasoning.
• Record responses as students share.
• “What are some errors that are commonly done when subtracting two numbers using the standard algorithm?” (Subtracting without lining up the numbers by place value. Using the notation of regrouping without decomposing a unit. Crossing out digits without including them in the regrouping. Subtracting from left to right without decomposing units.)
• “What ideas do you have for avoiding those errors?” (Use grid paper to line up the digits by place value. Decompose the unit before regrouping. Check answers using addition.)