Counting on is valuable preparation for the “counting up to” model for subtraction. For example, 13 – 8 may be worked by saying “eight” and counting 9-10-11-12-13 while keeping track of the number of counts, five in this case. This way of viewing subtraction is regarded by some researchers (Fuson 1984; Fuson and Secada 1986; Fuson and Willis 1988) as a much-needed supplement to the standard approach of teaching only the take-away model for subtraction.

The counting up to model is sometimes called shopkeeper’s math because of its use in making change. For example, if a \$7 purchase is made with a \$10 bill, a shopkeeper might count 8-9-10 to check their arithmetic for how much change to return. Before cash registers did the arithmetic for shopkeepers, almost all of them returned change this way!

Tap & Tally™ Lessons 41-48

Figuring Out the Addition Facts Fast (Counting On)

Prerequisites: The Tap & Tally™ numerals and knowing how to count on, that is, being able to start with any number between 1 and 9 and count to 18 (for example, to start with 5 and count 6-7-8- . . . -18). Elementary school students who have difficulty with counting on should be allowed to continue to count all the tap points.

Procedure: Say the top or first number and count from there on the tap points of the bottom or second number. The last number said is the answer.

For 5 + 4, say “five” and count 6-7-8-9, with 9 being the answer.

For 7 + 8, say “seven” and count 8-9, 10-11, 12-13, 14-15, with 15 being the answer.