Teaching Number Facts and Tables

Every child leaving primary school needs to know their number facts at least up to 10 + 10, 20 – 10, 10 x 10, and 100 ÷ 10. This is often done by asking children to learn off tables such as
7 + 0 = 7
7 + 1 = 8
7 + 2 = 9
7 + 3 = 10
7 + 4 = 11 and so on.

Learning off number facts in such tables works well for some children, but not for all. Stanislas Dehaene, author of The Number sense: How the Mind Creates Mathematics compares excerpts from addition and multiplication tables to the following groups of sentences to show how similar some of the tables can sound and how difficult they can be to learn off.

“Charlie David lives on George Avenue
Charlie George lives on Albert Zoe Avenue
George Ernie lives on Albert Bruno Avenue”
and
“Charlie David works on Albert Bruno Avenue
Charlie George works on Bruno Albert Avenue
George Ernie works on Charlie Ernie Avenue.”

An alternative to learning off such tables, where every number fact is presented as if it’s equally difficult to learn, is to connect facts to one another, to teach facts that apply to all sets of numbers and to minimise those that need to be learned by rote.

First, children should learn their addition number facts. These can subsequently be used to learn the subtraction number facts once children learn the inverse relationship that exists between addition and subtraction. Thus, facts can be learn in groups of four as follows:
4 + 2 = 6
2 + 4 = 6
6 – 4 = 2
6 – 2 = 4

An overview of addition and multiplication number facts to be learned can be illustrated on an addition table and on a multiplication table respectively. Then the children can be taught facts in the following order (spending up to a school year on the addition facts and the same on the multiplication facts).

Addition Number Facts
Commutative pairs
Zero facts (0 + n = n)
Add one facts
Add two facts
The ten and facts
Doubles
Near Doubles (E.g. 4 + 5 = 4 + (4 + 1) = (4 + 4) + 1
Through ten facts (e.g. 7 + 4 = 7 + (3 + 1) = (7 + 3) + 1

Multiplication Number Facts
Commutative pairs
Zero facts (0 x n = 0)
Times one facts
Times ten facts (Digit(s) move(s) one place to left)
Times two facts
Times five facts
Times nine facts (Multiply by ten and subtract one set)
Times four facts

These can be illustrated on the addition table and the multiplication table.

When children are thoroughly familiar with the addition number facts, these can be used to work on the subtraction number facts. Similarly, when children know the multiplication number facts, these can be used as a basis for learning the division number facts.