Lesson 5

Subtraction

Est. Class Sessions: 2–3

Developing the Lesson

Part 3. Subtracting with the Traditional Algorithm

The opening pages of the Subtraction pages in the Student Guide provide a written record of a problem solved with base-ten pieces and on a recording sheet, similar to the problems the students solved in Part 2. Ask students to read through the solution in the Student Guide and use their base-ten pieces to follow the steps in the first problem solved by Mrs. Haddad. Ask them to discuss Question 1 with a partner and then with the class.

  • Do you agree with Mrs. Haddad that you don't need a table to record subtraction problems? (Yes. The columns tell the place value. I know the number on the right is in the ones place. The next number is in the tens place.)

Have students read through the next scenario. Students should talk with partners about the trades recorded in Joe's solution to 1237 − 459.

  • Explain to each other the meaning of the little marks in Joe's solution. (He is showing his trades.)

It is an important skill to be able to read and understand a solution in a math book. However, it is sometimes hard to understand someone else's marks when you do not know the order in which they were written. If students follow along with their own base-ten pieces as they read Joe's solution to the problem, they will be better able to understand the written solution.

Use Questions 2–6 on the Subtraction pages in the Student Guide to assess students' abilities to subtract multidigit numbers using paper-and-pencil methods [E7].

The Lesson 7 Workshop provides targeted practice.

Ask students to solve the problems in Questions 2–6. They can solve these problems on their own paper instead of on a recording sheet, using the traditional algorithm as Mrs. Haddad did. Use your judgment about whether some students would benefit from continuing to use the Base-Ten Recording Sheet to solve these problems.

  • Are there any problems in Question 6 that you can check using a mental math strategy?

If the strategy is not suggested by a student, show Joan's strategy in Figure 13 for Question 6H. Joan's strategy avoids regrouping.

After discussing the strategy, try a similar strategy for 702 − 346 and on the problem in Question 6D, 392 − 169.

  • How can you use Joan's strategy to solve 702 − 346? (One possible strategy: I subtracted 3 from the 702 to make it 699, so I would not have to regroup. Then I subtracted 346 and got 353. Then I added the 3 back in so the answer is 356.
  • How can you use Joan's strategy or a different mental math strategy to solve Question 6D? (Joan's strategy: I added 7 to 392 to make it 399, so I would not have to regroup. Then I subtracted 399 − 169 and got 230. I had to subtract 7 from 230 because I had added it to 392 earlier. 230 − 7 = 223. Using a number line: I used a number line. I started at 169. First I moved forward 1 to 170 then I moved 200 to 370. From 370 I move 22 to 392. I added my moves in my head, 1 + 200 + 22 = 223, so my answer is 223.)
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Joan's strategy to avoid regrouping when solving 802 − 567
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