Figuring Out the Subtraction Facts

Prerequisites: The Tap & Tally™ numerals and knowing how to count backward from 18 to 0 beginning with any number. Counting backward is easily and delightfully taught to elementary school students with the games, activities, songs, rhymes, and children’s books listed on pages 213-219.

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

Tap & Tally™ Lessons 41-48

Remarks: Carpenter and Moser (1984) list three types of counting procedures for subtraction:

Counting up to a given number

For 8 – 5 = ?, start with 5 and count 6-7-8 for an answer of 3. The answer is the number of counts.

Counting down to a given number

For 8 – 5 = ?, start with 8 and count 7-6-5 for an answer of 3. The answer is the number of counts.

Counting down from a given number

For 8 – 5 = ?, start with 8 and count 7-6-5-4-3 for an answer of 3. The answer is the last number said.

According to Carpenter and Moser, the last procedure is easiest for young children to learn. This is the procedure used in saying the top or first number and counting backward. Fuson (1984) notes that for any form of subtraction, children must keep track of the number words that are said and that they typically do so with their fingers. With Tap & Tally™, this is unnecessary. Their fingers, so to speak, are the tap points on the numerals.

For 5 – 4, say “five” and count 4-3-2-1, with 1 being the answer.

For 9 – 7, say “nine” and count 8-7, 6-5, 4-3, 2, with 2 being the answer.