How can we teach using ten for subtraction?

Edward C. Rathmell
University of Northern Iowa

• Create a word problem where the whole is greater than ten and one of the parts is 8 or 9.
• Give the students an opportunity to think about this problem.
• Then ask several students to share how they figured the problem out. One of them probably will explain how they used ten. If not, then tell the students that you heard a student solve it by using ten, then explain how they were thinking. For 13 - 9, think 9 and 1 more is 10, and 3 more is 13. That's 4 more. Or, start at 13 and subtract. Think 13 minus 3 is 10, then subtract 1 more to get 9. That's 4 less, so the answer is 4.
• You may want to model the use ten thinking by showing the whole, then covering it and reminding the students how many there are, then start with 9 and add 1 to make ten, then 3 more to make 13. That's 4 more. You can also start at the 13 and subtract to ten, then subtract 1 more to get to 9.
• Verbalize the thinking and ask the class to verbalize the thinking.
• Then ask the class to use ten to solve another problem.

Using a similar procedure for a few minutes everyday for two or three weeks will help nearly all of the class learn to use ten. Besides the routine described in the bullets above, sometimes do the following.

• Ask what subtraction problem they did and how it could be written as an equation.
• Ask students to start at 8 and count up to 15 for the fact problem 15 - 8 and compare it to using ten. Reinforce the efficiency of using ten.
• Discuss when using ten can be used efficiently, that is, when one of the parts being subtracted close to ten.
• After the students can use ten, a few minutes of practice on a regular basis for two or three weeks will enable them to solve these problems in about 3 seconds. If they also know the generalizations and can count back, count up, using doubles, they will be able to solve 88 of the 100 basic subtraction facts quickly.

Using make ten for addition will help students learn to use ten for subtraction. It is also important for them to understand the part-part-whole concept and/or comparison situations so that adding from the part to the whole makes sense as a way to solve subtraction problems.

One way to help students learn this strategy is to provide subtraction situations where the whole is greater than ten and one of the parts is eight or nine. Then create a situation where the part that is left after subtracting is hidden. Then as a student is explaining the use ten strategy, you can put counters back with the hidden set as you add on. For example, 9 and 1 more is 10, then 4 more is 14.

Another way to illustrate this thinking is to use a ten frame. If the part being subtracted is close to ten, show it in the ten frame. Then add on as a student explains, 1 more is 10 and 4 more is 14.

The ten frame can also be used by showing the whole in the ten frame. Note that it will fill the ten frame and there will be some extras. Then subtract to ten and subtract the rest from ten as you remove counters from the ten frame.

The number line can also be used. Draw a number line on the board. For 14 - 9, just mark the numbers 9, 10, and 14 on the number line. Then draw arrows as you add to show 9 and 1 is 10, then 4 more is 14. That's 5 more. Or, subtract from 14 to 10, then subtract to 9.

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