How can we teach counting back for subtraction?

Edward C. Rathmell
University of Northern Iowa

• Create a word problem where the part being subtracted is small (1 or 2).
• 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 counted back. If not, then tell the students that you heard a student solve it by counting back, then explain how they were thinking. For 6 - 2, think 6, … then count back two, … 5, 4.
• You may want to model the counting back thinking by showing the whole, then covering it and reminding the students how many there are, then subtract the small part one at a time as you count back to get the whole.
• Verbalize the thinking and ask the class to verbalize the thinking.
• Then ask the class to use counting back 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 counting back. 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 back 2 and compare it to take away and count what's left. Reinforce the efficiency of counting back.
• Discuss when counting back can be used efficiently, that is, when one of the parts being subtracted is small.
• After the students can count back, a few minutes of practice on a regular basis for two or three weeks will enable them to solve counting back problems in about 3 seconds. If they also know the generalizations, they will be able to solve 37 of the 100 basic subtraction facts quickly.

Helping children learn to count back is just a step in the direction of helping them learn to use addition to help them solve subtraction facts. 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 a small number is being subtracted.

Show a set of counters. Create a situation where they will be covered or hidden. Remove one or two of them, one at a time. Ask how many are still covered. By uncovering the counters one at a time, the students will be encouraged to count back to determine how many are still covered.

Create other situations where the part the is left after subtracting is hidden. Remove the counters one at a time. Perhaps redo the problem and have the students verbalize the counting back as you remove the counters one at a time.

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