- by Blaine Helwig

# Subtraction Facts – Elementary Students’ Math Fact Nemesis

God created the Earth in six days and rested on the seventh. While God was resting, the devil created subtraction facts. And, to most elementary students, basic subtraction facts are indeed the original sin of arithmetic mathematics.

Kids learn single-digit addition and multiplication facts quickly. Why? Simple: the commutative property of mathematics (i.e. 2 + 3 = 3 + 2 and 4 x 5 = 5 x 4). If the addition or multiplication of 1’s (i.e. 1 + 3 or 4 x 1) are not counted, there are only 36 discrete single-digit addition and multiplication facts to memorize. These facts are easy to memorize with a little bit of work.

This isn’t the case with subtraction facts. 8 – 5 = 3 and 8 – 3 = 5 appear as two separate subtraction facts, and they are to a young kid. It may be the same fact family, but students must memorize both of these subtraction facts—there’s no such thing as a commutative property of subtraction. To complicate matters, students must also memorize double-digit facts subtracting a single digit (i.e. 13 – 8 = 5 and 13 – 5 = 8).

Ask any elementary math teacher, and the vast majority will agree. Subtraction facts are kids’ main adversary when compared to memorizing any of the four math fact operations.

Is there a method to help kids to quickly learn many of their subtraction facts? Yes. There is.

Students still need to memorize single-digit from single-digit subtraction facts (i.e. 5 – 3 = 2 and 9 – 6 = 3), but those facts are much easier than the memorization of single-digit numbers subtracted from a double-digit number (i.e. 17 – 9 = 8). So, there is a method that is very helpful in the latter case and simultaneously adds numeracy skills of number sense and base 10 mathematics. This subtraction technique also relies on student proficiency of the addition of two single-digit numbers – a skill that has been previously mastered or the student would not be working on their subtraction facts.

The method is shown below using the math fact 15 – 7 = 8 with a typical subtraction fact format.

The method of subtracting a single-digit number from a two-digit number may appear complicated, but it is not. After students are able to ‘Make 10’ quickly, they become very adept at the process – and subtraction facts are quickly mastered. The math skill of ‘Making 10’ should be taught to mastery prior to using this subtraction technique. Skill practice sheets for ‘Making 10’ are available in the Formative Loop Numeracy Resources Library.

Teachers should show this simple subtraction math fact process on a number line so kids visually understand the physical nature of the mathematics and why this subtraction process ONLY works for 2-digit numbers subtracting 1-digit numbers – that pass through the number 10.

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