Number facts Graphic

Help your child learn number facts

by Matthew Leitch, 5 October 2012, expanded 3 January 2013

If your child struggles to learn number facts, such as times tables facts and number bonds, then it may be that he or she will find it easier with a better way to practise them. That's what this article is about.

You may have noticed that number facts don't sink in. Alternatively, you may have noticed that number facts seem to go in, but a few days later they've gone again. Hours of practice seem to make no difference. Progress feels agonizingly slow. If any of this is familiar, then read on.

What children need to learn

Between the ages of about 4 years old and 10 years old most children learn number facts for mental arithmetic that include addition and subtraction of small numbers and multiplication facts from 1 × 1 up to 12 × 12. Some children learn much more than this.

It is sometimes said that maths is logical, and that you can work everything out if you need to. That's true, but you can't work it out quickly enough for that to be a workable approach. In reality, memory is vital to mathematicians, which is why they lose so much skill in just a few months of not practising.

To be specific, your child needs to be able to recall number facts within a second or two, with no working out, given problems like ‘5 × 7 =’ and ‘3 + 7 =’, in any order, with no other clues.

Being able to count up in 5s or chant a times table in order is useless. Furthermore, it is not enough to be able to work out times tables by adding or other strategies, or to work out addition and subtraction by counting on a ruler or with fingers. All those are temporary strategies that should be used for as short a time as possible, if at all.

If your child has to do calculations to work out simple number facts then doing bigger calculations will be exhausting and probably impossible. Your child will suffer fatigue, confusion, and failure. Mastering those number facts properly is by far the easiest and least painful way forward.

If progress is slow then you may find that your child's school keeps him/her using ‘scaffolding’ methods, like using number lines and fingers, instead of getting on to the practical methods that are required for competence. This can lead to a child starting to believe that the number line and finger methods are the proper methods to use and that nothing else is needed. They may stop improving altogether.

How long should it take?

Although we are used to the idea that learning multiplication facts (the ‘times tables’) takes place over years of schooling and requires endless grind, I have seen cases where the whole lot has been learned in a few days. Admittedly, that is not normal, but how long should it take to learn all the number facts (not just times tables), if there are no problems? Nobody seems to know.

Here's an estimate. There are 328 facts to learn, in 91 groups, (see appendix below) so if it took 2 minutes per fact (30 seconds initial study to build three chunks, and the rest for 30 tests to build speed) then that would be 656 minutes, which is just under 11 hours of concentrated study. If a student can do 10 minutes of concentrated study per school day then that means 66 days of study, which is about 13 weeks, or 3 months. A student who can focus for half an hour a day would do it in a month.

This is pure guesstimation, but surely if the number facts have not been learned within, say, a year then something is going wrong.

Stop wasting time

As a first step, cut out the activities that take up time but don't help, or actually make things worse:

Why number facts are hard to memorize

There are several reasons why number facts are inherently hard to memorize. They are abstract, often unfamiliar, and there are lots of superficially similar ones. However, the most important point is that they seem arbitrary at first. Of course all the number facts can be worked out, and they are not arbitrary at all. Two plus two is always equal to four, and there is a good reason for that. However, number facts seem arbitrary unless you work them out and working them out from first principles is too slow in most practical situations. So, in practice, they feel arbitrary and so very hard to remember unless you do something to make them less arbitrary.

What your child needs to get started is ways to link questions to answers so that the answers seem less arbitrary. There are two types of link that can be used:

  1. Very short calculation rules that can be used within 1 or 2 seconds until automatic recall develops. For example, ‘10 times any whole number is the whole number with an extra zero on the end’.

  2. Rules that help you pick one answer from the possibilities that pop into your mind. For example, ‘an even number of sixes gives an answer ending with the even number e.g. 2 × 6 = 12, 4 × 6 = 24’, and ‘adding two small numbers gives a larger but still smallish number’.

Guidelines for efficient practice

Here are some good things to do:

If you've been reading critically you will have noticed that there is a difficult compromise between introducing new number facts and making sure your child notices each part of the question. For example, if you introduce three new facts then your learner knows that the answer must be one of the three just introduced. They don't necessarily have to attend to all parts of the question to know which.

A certain amount of this is unavoidable, but you can minimize it by making sure all elements of the question are noticed on first study, and moving to a larger set of number facts for testing purposes as quickly as possible.

How to study a new number fact

To an adult, many numbers are recognizable, special chunks with their own familiar properties. For example, think of the significance of 16, 21, 50, 7, and so on. We are particularly familiar with smaller numbers and with numbers we learned number facts about at school. Prime numbers, like 37, 41, and 59, seem less familiar and memorable.

However, to a child who has little or no knowledge of numbers they have less character and uniqueness. If you say ‘21 16 7 50’ it just sounds like ‘blah blah blah’ to them.

So, take the time to build each number into a familiar unit. For example, in ‘3 × 5 = 15’ it may be that 15 is a new number to your child but 3 and 5 are familiar. Before 15 can be linked to ‘3 × 5’ using ‘=’, the ‘15’ needs to become familiar, so get him/her to take a few seconds to look at the number, say it a few times, and see where it lies on the number line. You could even think of some things that are famous about the number outside the world of mathematics, such as that 15 is the number of players in a rugby union team.

Numbers are not the only chunks a child needs to notice and get familiar with. Each ‘question’ is different and the student needs to recognize each one. For example, ‘2 + 3’ is different from ‘2 × 3’ and each needs to become familiar and recognizable. So, take a few seconds to look at each of the three elements of each question, then get used to seeing them together and recognizing that familiar chunk. When the question and the answer are familiar it is time to learn to put them together.

Understand that a fact like ‘4 × 7 = 28’ is a lot to take in when all you know is ‘4’, ‘×’, ‘7’, ‘=’, ‘2’, and ‘8’. To be precise, it's 6 things to take in and that's too much in one step. However, combining ‘4’, ‘×’, and ‘7’ to make ‘4 × 7’ is an easier step, combining ‘2’ and ‘8’ to make ‘28’ isn't hard either, and finally putting ‘4 × 7’ together with ‘=’ and ‘28’ to make ‘4 × 7 = 28’ is just lumping together three elements.

These details, though they seem trivial, all need careful, patient attention. By studying the details before the first test of memory, and whenever a recall mistake occurs, your child can make better progress.

Useful rules

Here are some rules you can use for addition and subtraction facts:

Here are some rules you can use for multiplication and division facts:

However, with all but the simplest of rules (e.g. times by 1 or 10) the real goal is to be able to recall the answers immediately with no working out. So, be especially careful not to mistake memory for working out with a rule, and keep on pushing for speed until memory takes over and is doing the work.

Using practice software – Maths Accelerator

Maths Accelerator is a simple web page program, free for anyone to use, that provides tests following these principles. Don't be fooled by the lack of ‘fun’ graphics or the detailed performance statistics. Children love being able to see how they are improving and, just like in a computer game, they study those stats intently. Even young children seem to be more motivated by progress than by shooting frogs, or any other irrelevant sugar coating.

One important limitation of Maths Accelerator is that it does not provide ideal support for the very earliest stages of learning number facts. However, as soon as you know enough to tackle one of the tests it is an excellent way to practise.


I hope this helps you and your children. Learning number facts is another of those big hurdles for young students.

Appendix: the number facts list

First, the add and subtract facts needed for primary school arithmetic. Adding or subtracting 0 or 1 can be done by very simple rules, so no number facts are included in the list for them. This leaves 128 number facts in 36 groups.


Next, the multiply and divide facts needed for primary school arithmetic. Multiplying by 0, 1, or 10 can be done by a simple rule, so no number facts are included in the list for them. This leaves 200 number facts in 55 groups.


About the author: Matthew Leitch has been studying the applied psychology of learning and memory since about 1979 and holds a BSc in psychology from University College London.