How can you teach making ten for addition?

Edward C. Rathmell
University of Northern Iowa

• Create a word problem where one of the parts being added is an 8 or a 9 and the other makes the total more than 10.
• 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 added to make ten, then added the rest to get the total. If not, tell the students that you heard a student solve it by making ten. For 9 + 6, think 9 and 1 is 10, then 5 more is 15.
• You may want to model the make ten thinking by showing the 8 or 9 objects in a ten frame (a 2 by 5 grid), show the other part outside the ten frame, then fill the empty spots in the ten frame as you add to ten, then add the rest.
• Verbalize the thinking and ask the class to verbalize the thinking.
• Then ask the class to use make 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 make ten. 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 to create problems where make ten can be used.
• Discuss when make ten can be used efficiently, that is, when one of the parts is close to ten and the other makes the whole more than ten.
• Compare these problems to counting on and using double problems. Have the students choose whether they would count on, use doubles, or make ten to solve several different problems.
• After the students can make ten, a few minutes of practice on a regular basis for two or three weeks will enable them to solve make ten problems in about 3 seconds. This strategy will enable them to solve the remainder of the addition facts. They now have an efficient way to solve each of the 100 addition facts. With practice of these strategies, the students should easily be able to respond to any addition fact in less than 3 seconds.

Before the make ten strategy can be used successfully by students, they will need to know how to add ten and a single digit number. This is a prerequisite for the make ten strategy. The students should understand adding ten and a single digit number from their work with place value. If not, or as a review, use a ten frame or place value materials, such as base ten blocks, etc., to show how easy it is to add these numbers. Even some quick mental computation problems, such as, 10 + 6; 3 + 10; 40 + 7; 4 + 30; etc, can help students recognize how place value ideas can help them solve these problems easily.

The students should also know how many more it takes to make ten when you start with 8 or 9. These are relatively easy since it only takes one or two more. This same thinking can be used with numbers other than 8 or 9. But, students may not be as sure about how many more it will take to make ten and they may have more difficulty subtracting that number from the other part to determine how many extras need to be added to ten to get the whole.

Familiarity with the ten frame will help students learn these partitions of ten. Make a transparency of a ten frame. Put it on the overhead projector. Turn the projector off and hide the counters. Hide what you are doing. Put some counters in the ten frame. Flash the projector on for about 1 or 2 seconds. Then quickly turn it off and ask the students what number was shown. Also ask how many more it will take to make ten, that is, completely fill the ten frame. Repeat using different numbers. The students should quickly learn 6 is five and one more, 7 is five and two more, etc. It is a small step from that to know how many more it will take to make ten.

Other activities that can help students learn partitions of ten include the following. Start with 10 counters. Hide them and put some in one hand with the others in your other hand. Show how many counters there are in one hand. Ask how many there are in your other hand.

This strategy is a little more difficult for some children to learn, partly because of the prerequisites described above. But that does not make it less important. It just means that a few more activities need to be provided over an extended period of time.

Show some counters (less than ten). Ask how many more it will take to make ten. Have the students predict, then use counters to check. Repeat starting with other numbers. A similar question can be asked for larger numbers. For 37, ask how many more will it take to make 40. This is a question that can be asked just to help promote number sense.

It is easy to concretely illustrate the make ten strategy with the ten frame. Simply show an addition problem by putting 8 or 9 counters in the ten frame and some others outside the ten frame. The whole should be more than ten. Ask the students to show how they can use the ten frame to help them add the numbers. Then have them verbalize the thinking, for example, 8 and 2 more is 10, then 4 more is 14. Repeat with other numbers. Use this activity a few minutes each day for several days.

Another way to illustrate this thinking is to use a number line. For example, start at 8, jump 2 to make 10, then jump 4 more to get the whole of 14. If you draw the number line on the board, you can make it "numberless" except for the 8 and the 10. As the students explain the make ten thinking, draw an arrow showing a jump of 2 to make ten, then draw another arrow showing a jump of 4 more to get to the whole of 14. Discuss how you added 6 more by adding 2 to make ten, then 4 more to make 14.

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