How can we teach using doubles for subtraction?

Edward C. Rathmell
University of Northern Iowa

• Create a word problem where the part being subtracted is about half as large as the whole.
• 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 a double. If not, then tell the students that you heard a student solve it by using a double, then explain how they were thinking. For 13 - 6, think 6 and 6 make 12, so it must be 1 more or 7.
• You may want to model the use doubles thinking by showing the whole, then covering it and reminding the students how many there are, then subtract the part by removing all of them at the same time. Then ask if the hidden part could be the same as the part that is showing. Double that number to check. Adjust by one or two to make any needed corrections.
• Verbalize the thinking and ask the class to verbalize the thinking.
• Then ask the class to use doubles 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 doubles. 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 doubles. Reinforce the efficiency of using doubles.
• Discuss when using doubles can be used efficiently, that is, when the part being subtracted about half as large as the whole.
• After the students can use doubles, 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 and count up, they will be able to solve 70 of the 100 basic subtraction facts quickly.

Before you can expect success with this strategy, students should begin to understand that subtraction is more than just take away. There are two kinds of experiences that can help prepare students. The teacher can informally use the part-part-whole language as they work with addition and subtraction situations. The teachers can also present word problems and other problem solving situations that involve problem structures which are comparisons between numbers.

If helping children learn to count up is a leap in the direction of helping children learn to use addition to help them solve subtraction facts, using doubles is almost there. In fact, the strategy requires you to double the number you are subtracting, then adjust. You are adding. The double might not be the whole, and, if not, you have to go back and adjust the number you are adding.

The students also need to know some of the doubles before they will be able to use this strategy successfully. They can still learn the strategy by using known doubles, such as, 5 + 5 = 10, but they will not be able to use the strategy with many facts until they know the doubles well.

The most important teaching strategy is to hide the part that is left so the students cannot count what is left. This procedure can be used in situations where the number being subtracted is about half as large as the whole.

Show a set of counters. Create a situation where they will be covered or hidden. Remove about half of the counters, all at the same time. Ask how many are still covered. After a student suggests doubling the part, try it and adjust by one or two as needed. For 12 - 5, think 5 + 5 is 10, so you need to try a number that is 2 more than 5. The answer is 7.

Create other situations where the part that is left after subtracting is hidden. Remove nearly all the counters. Verify the answers by doubling the part that is subtracted. From this point, it is not a very large step to begin using known addition facts to help with subtraction facts.

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