How can you teach using doubles for addition?

Edward C. Rathmell
University of Northern Iowa

• Create a word problem where the parts being added are close together, that is, have a difference of one or two.
• 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 known double fact to help them solve the problem. If not, tell the students that you heard a student solve it by using a double, then explain how they were thinking. For 7 + 6, think 6 + 6 is 12, so 7 + 6 is 1 more or 13.
• You may want to model the double thinking by showing a the double then adding one or two (removing one or two).
• Verbalize the thinking and ask the class to verbalize the thinking.
• Then ask the class to use a known double fact 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 addition problem they did and how it could be written as an equation.
• Ask students what double could be used to help you solve problems, such as, 5 + 6 (5 + 5 or 6 + 6); 8 + 6 (6 + 6, 8 + 8, or 7 + 7)
• Discuss when doubles can be used efficiently, that is, when the parts are close together. Compare these problems to counting on problems where one of the numbers is small. Have the students choose whether they would count on or use doubles to solve several different problems.
• 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 doubles and near doubles problems in about 3 seconds. This will enable them to solve 24 additional problems beyond the 64 they can do because of the zero generalization and counting on. They can now easily solve 88 of the 100 addition facts.

Before students can use doubles to help them solve near-double facts, they obviously need to know some of the doubles. However, they do not need to know all of the doubles before they start learning this strategy. For example, most children already know that 5 + 5 is 10. That can be a good starting point for this strategy.

In order to help students learn to use doubles, start with a double, show both parts, ask how many there are in all, then add one more counter to one of the parts, repeat the double fact and ask the new fact that is shown. For example, show 5 and 5 on the overhead projector. Ask what the total is. Then put one more counter with one of the parts. Say five and five make ten, how much is 6 and 5? The students can easily see that only one more counter was added to the total, so they know the answer is just one more than ten.

Create examples like that described in the paragraph above. Each time show a double, add (or remove) one or two more counters, repeat the double fact, and ask how many there are now. Just like with counting on, students are more likely to use the information that is given and compensate for the change if the numbers are large. If the numbers are small, the students may tend to count them all.

Write several near doubles problems on the board. Ask which doubles can be used with each of the problems. Note that there is not a single answer for any of these problems. The smaller number can be doubled, then you can count on one or two more. Or, the larger number can be doubled, then you can count back one or two. Or, if there is a difference of two, some students learn to double the middle number. One group of second graders called this the Robin Hood method. In each case, the thinking can be illustrated with counters to show others in the class exactly what a student is thinking.

Return to Questions