Strategies for Adding and Subtracting Decimals

Est. Class Sessions: 3

Developing the Lesson

Part 2. Subtracting Decimals

Subtract with Patterns on Number Lines. Display the Number Line Patterns 2 Master and direct students' attention to the first number line. Ask students to find the next three numbers in the sequence 3.5, 3.0, 2.5, 2.0, and to describe the pattern that helped them determine the next numbers. Students should see that the pattern is subtracting 0.5. Then ask a volunteer to write the answers in their approximate places on the number line, explaining why they placed the numbers 1.5, 1.0, and 0.5 where they did. Repeat the process for the remaining three number lines.

Invent Strategies. Display the following number sentence:

0.5

− 0.5

Ask:

How would you estimate this difference? (Possible response: 0.9 is close to 1, and 0.5 is one-half, so about 1 minus one-half is about one-half.)
Who can think of a way to find the exact difference? Show us. (Possible response: We could use a number line, fraction circle pieces, or base-ten pieces like we did when we added decimals. For example, if I had nine skinnies, 0.9, and took 5 skinnies 0.5, away there would be 4 skinnies, 0.4, left.)
Use your Hundredths Circle Wheels to solve 0.9 − 0.5. (Show nine-tenths and then turn the wheel to cover five of the tenths to leave fourtenths showing. The difference is four-tenths.)
How do you know if that answer is reasonable? (Possible response: I estimated a difference of about one-half. 0.4 is about one-half.)
Who would like to show another way to solve 0.9 − 0.5?

Display the following problem vertically:

0.85

− 0.2

Ask:

Explain how to estimate the difference. (Possible response: 0.85 is close to 0.9. If I count back two-tenths it is seven-tenths.)

Ask students to show a partner how they would solve 0.85 − 0.2. Students should recognize that they cannot model 0.85 with fraction circle pieces. However, they can use base-ten pieces, their Hundredths Circle Wheel, or a number line to solve the problem.

After students have had a chance to talk with a partner about solving the problem, display and direct their attention to the Subtracting Decimals section of the Strategies for Adding and Subtracting Decimals pages in the Student Guide. Discuss the various strategies for subtracting decimals as presented on the page by asking students to explain how the hundredths circle, number line, and base-ten pieces are used to subtract 0.85 − 0.2.

Use Models to Subtract. Next have student pair complete Questions 1–2 on the Subtract Decimals with Grids and Number Lines pages in the Student Activity Book. These pages follow the same procedure as the pages on addition. Students solve 0.85 − 0.2 again, this time using a number line to estimate and a hundredths grid to find the exact difference.

When they are done, ask:

Demonstrate how you used the hundredths grid to solve 0.85 − 0.2. (See Figure 4. Possible response: Fill in 0.85 and then erase 0.2 to find the solution, 0.65.)
Explain what Jason did wrong in Question 2. (Jason erased 0.02 instead of 0.2. He erased two squares on the hundredths grid instead of two rows. He didn't subtract enough.)

Refer to the equation you displayed and ask:

Is 0.2 the same as 0.20? Is 2/10 equivalent to 20/100? (yes)

Show students that because two-tenths is equivalent to twenty-hundredths, you can write:

0.85

− 0.20

The problem is 85 hundredths minus 20 hundredths.

Discuss Subtraction Strategies. Assign Questions 3–9 to student pairs. Upon completion, choose a few problems and ask student volunteers to explain how they estimated the difference. Then ask a volunteer to demonstrate how they used a grid to find the difference. After each problem, ask a different student to show how to use a hundredths circle, number line, or base-ten pieces to solve the same problem. Use displays of the Decimal Number Lines, Decimal Grids, and Hundredths Circles Masters as needed throughout the discussion.

Assign the Homework section of the Subtract Decimals with Grids and Number Lines pages in the Student Activity Book.

Student Guide: 389