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# “Subtract One” Strategy: Subtracting From Zeros Without Borrowing

Many students cringe when they see a subtraction problem with multiple zeros. The “Subtract One” strategy in this lesson involves reducing the top number by one to turn the 0 digits into 9’s and then adding the one back in at the end.

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Students will be able to use the Subtract One strategy to subtract from numbers with multiple zeros (i.e. 4,000 - 347).

(5 minutes)
• Write the problem 5,000 - 2,384 on the board. Ask for a student to come to the board and make a tally mark for each step you perform to solve the problem. Use the traditional borrowing method and count the steps. It’s not important that these are exact.
• Observe how many steps it took to borrow, just to be able to perform the subtraction in each column.
• Tell students that with each step involved, the chances of an error increases, and it takes more time.
• Explain that they are going to learn a more efficient strategy for subtracting from numbers with multiple zeros in the “top number,” called the Subtract One strategy.
(10 minutes)
• Rewrite the problem 5,000 - 2,384 on the board. This time subtract one from the top number, making it 4,999 and the one from the bottom number making it 2,383. Write '-1' next to each number as you go.
• Explain that, since you are finding the difference, as long as you subtract the same thing from both numbers the difference won’t be affected - the answer will still be correct.
• After subtracting one from both numbers, subtract as usual with no need to borrow.
(10 minutes)
• Now write 8,000 - 6,586 on the board. Invite a student to come to the board and try to solve using the Subtract One strategy.
• While the student does the problem, you (or a student) should record how many steps it takes to solve the problem.
• Ask students to compare the two methods of subtracting with zeros in the top number and share their observations.
(10 minutes)
• Distribute Subtract One Strategy worksheet.
• Instruct students to do the first row with a partner or table group, helping each other as they try it on their own.
• Then have them do the second two rows on their own checking answers with a partner or using a calculator when they are done.

Support

• Do the first row of problems as a class on the whiteboard or projector.
• Provide problems with smaller numbers before starting the worksheet, such as 50 - 7.

Enrichment

• Have students try this strategy with larger numbers to six or seven digits. When doesn’t this strategy make the calculation easier? Does it make problems with non-zero numbers on the top easier to solve, such as 9,231 - 5,898?
(5 minutes)
• Distribute half sheets of paper or use student whiteboards. Write sample problems on the board, such as 6,000 - 576 and collect sheets or spot check student responses.
(5 minutes)
• Review the answer to a few problems and address any questions that arise. Ask students to explain why this strategy works, "Why does it still give you the correct answer when you change the numbers you are subtracting?"

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