How can you teach counting on for addition?

Edward C. Rathmell
University of Northern Iowa

• Create a word problem where one of the parts being added is small (1, 2, or 3).
• 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 on. If not, then tell the students that you heard a student solve it by counting on, then explain how they were thinking. For 6 + 2, think 6, … then count on two more, … 7, 8.
• You may want to model the counting on thinking by showing the large part, then covering it and reminding the students how many there are, then add the small part one at a time as you count on to get the whole.
• Verbalize the thinking and ask the class to verbalize the thinking.
• Then ask the class to use counting on 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 on. 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 start at 3 and count on 8 and compare it to starting at 8 and counting on 3. Reinforce the efficiency of starting with the larger number and counting on the smaller number.
• Discuss when counting on can be used efficiently, that is, when one of the parts being added is small.
• After the students can count on, a few minutes of practice on a regular basis for two or three weeks will enable them to solve counting on problems in about 3 seconds. If they also know the zero generalization, they will be able to solve 64 of the 100 basic addition facts quickly.

Alternative procedures can also be used. One teaching strategy is to use counters to show addition problems, but keep the large set hidden. Then add the small part, one counter at a time. The following are examples of situations that can be created.

Show 6 bear counters on the overhead projector. Cover them with your hand as you tell the students that 6 bears went into a cave. Now tell them that 2 more bears went into the cave as you show two more bear counters being moved under your hand. Move them under your hand one at a time. Then ask how many bears are in the cave? Have the students explain how you can count on two more by saying 7, 8. Then uncover the bears to check your answer. Ask what addition problem you just solved. You may want to write an equation to show it, then repeat how counting on can help solve that equation. Repeat with other numbers.

Put 8 counters into a plastic cup. Tell the students how many are there. Now ask them to listen as you drop some more counters into the cup. Drop 1, 2, or 3 more into the cup one at a time. Then ask how many counters are in the cup? Have the students explain how you can count on to solve the problem. Ask the students what addition problem you just solved. You may want to write an equation to show it, then repeat how counting on can help you solve that equation. Repeat with other numbers. To create more mystique, turn your back to the students and tell them you are not going to tell how many more you added. Drop 1, 2, or 3 more counters into the cup one at a time. Act surprised when they can still solve the problem.

Similar situations can be created by saying a number or rolling a number cube, then rolling a dot cube (1, 2, or 3 dots on each side) to create situations where counting on can easily be used. Ask how many there are in all. Have the students verbalize counting on to show how it can be used to solve the problem. Ask them what addition problem they just solved and write that equation. Repeat with other numbers.

Create other situations where the large part is hidden and children can easily count on the small part being added to it. These can be done with dot cards, rolling dot cubes, putting pennies into a piggy bank or your pocket, having some children join another group that can not be seen, etc.

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