This article is a follow-up to the article “Times Tables – What Are They And Why Do They Matter?”. As explained in the previous article, “Times Tables” is the traditional term used for many generations to refer to multiplication facts. In this article, I argue for the alternative term, “Number Facts”.
The biggest drawback to the term “times” in “times tables” is that it really refers to just the one operation. While multiplication facts are a vital part of a student’s mathematical education, the other three operations of addition, subtraction and division are just as important, and yet are not included in the term “times tables”. And while the facts for these other three operations may be written in a tabular form, it makes little sense to call them “addition tables”, and so on. Instead, mathematics educators like me use the preferred terms “addition number facts”, “subtraction number facts”, and so on.
Basic Number Facts
Number facts may be divided into two different, yet related, groups. The first set is the “basic facts”. These include the facts involving addition or multiplication of pairs of single digits, and the inverse facts for subtraction and division. In other words, number facts for the four operations are as follows:
- Addition – all facts from 0+0 to 9+9
- Subtraction – inverses of all addition facts from 0-0 to 18-9
- Multiplication – all facts from 0x0 to 10×10 or 0x0 to 12×12
- Division – inverses of all multiplication facts from 1÷1 to 81÷9 or 1÷1 to 144÷12 (we can’t divide by 0, of course)
Side note about 11x and 12x facts: In countries where the metric, SI system of measurement units is used exclusively, the need for knowing multiplication facts beyond 10×10 is much reduced. However, as long as American students need to convert inches into feet and inches, knowing the 12x facts is still useful.
What Should Students Know?
As I have argued in previous articles, I believe it is obvious that students of mathematics must know all their basic number facts “by heart”. This includes all four operations, and the standard to aim for is “instant recall”. While working towards that goal, students will need strategies to figure basic facts from known facts, without a calculator. Once those strategies are in place, the teacher should provide students with frequent opportunities to practise recalling the facts as quickly as they can.
A follow-up article in this series will explain the extended number facts and how they may be used to extend students’ mental computation abilities.