What are some important thinking strategies for addition?

Edward C. Rathmell
University of Northern Iowa

Initially, children count all. This means that they count or show both parts of the problem and then proceed to count them all from one to the total. This is only efficient if both of the parts being added are very small. This is an appropriate method for solving addition problems initially, but children should be encouraged to learn more efficient ways of solving problems with larger numbers. Students soon learn that adding zero is easy. n + 0 = n is a generalization that enables them to solve problems they have never seen before. They just know that adding zero does not change the other part.

As children progress from counting all, they begin to count on. This means they start with one part and count on by ones to get the total. They soon learn to use the commutative property and start with the larger part before they count on the smaller number. Generally, children will not need to count on more than three, but some children can do it easily. For a problem like 3 + 8, the students just think 9, 10, 11.

Students can then learn to use a fact that they already know to help them figure out facts they do not yet know. These are called derived fact strategies. For example, counting on will soon help children memorize some facts. If they know that 7 + 3 is 10, it is not too difficult to understand that 7 + 4 is just one more.

One derived fact strategy to help students learn some of the larger facts, is to use doubles to help them with near doubles. For example, to solve 6 + 7, many students will think 6 + 6 = 12, so 6 + 7 is just 1 more or 13. Students soon are using this with problems where the parts have a difference of one or two. In fact, some students learn to use the "Robin Hood" method for numbers with a difference of two. For 8 + 6, you can take one from the 8 and put it with the 6 to make 7 + 7. Similar thinking can be used with any fact that a student knows. Many children use this thinking with ten. For example, for 9 + 6, since 10 and 6 is 16, 9 and 6 is just one less.

Another derived fact strategy involves making ten. When one of the parts is nearly 10, you can just add on to get 10, then add the extras. For example, for 9 + 5, you can think 9 and 1 more is 10, then 4 more is 14. This thinking is a powerful strategy to use with mental computation with larger numbers. It also is very helpful when students are beginning to learn the hard multiplication facts. For example, for 3 x 9, you can think 2 nines is 18, now just add on another nine, 18 and 2 more is 20, then 7 more is 27.

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