How children learn their multiplication facts, and how to help at home

Children learn multiplication best when the facts are built on each other and practised a little every day, not crammed the night before a test.

Schools follow a clear order, and knowing it helps you support the right table at the right time. This guide sets out what children are expected to know and when, in England and in the United States, the strategies that turn a long list into a handful of hard facts, how fact families link multiplication to division, and the short games that keep practice at home friendly.

Which multiplication and division facts children learn, and when

In England, the national curriculum programmes of study for mathematics spread the times tables over three school years. In Year 2, pupils recall and use the multiplication and division facts for the 2, 5 and 10 tables. In Year 3 they add the 3, 4 and 8 tables. In Year 4 they recall multiplication and division facts for all the tables up to 12 × 12, and use factor pairs and commutativity in mental calculations.

In the United States, the Common Core standards for grade 3 ask children to multiply and divide fluently within 100, and state that by the end of grade 3 they should know from memory all products of two one-digit numbers.

In England, Year 4 pupils also take the statutory multiplication tables check. Our guide to the Year 4 multiplication tables check explains how it works and how to prepare without stress.

How children learn each multiplication table

The order in the English curriculum is not random. The 2, 5 and 10 tables come first because their patterns are easy to see: even numbers, numbers ending in 0 or 5, numbers ending in 0. The 3, 4 and 8 tables come together because 4 is double 2 and 8 is double 4, so a child who can double can rebuild them.

Two properties then cut the work dramatically. Turning a fact round gives a second fact for free: the Common Core standards give the example that if 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. And splitting a fact into easier ones rebuilds anything forgotten: 8 × 7 can be found as 8 × 5 + 8 × 2 = 40 + 16 = 56, another example from the same standards.

Once the 1, 2, 5, 10 and 11 tables are secure and every fact is counted only once in either order, the products that are left among 3, 4, 6, 7, 8, 9 and 12 come to just 28 facts. That is a much less daunting list to work on, and our multiplication tables from 2 to 12 give each table on its own page with practice.

Fact families: one fact, four number sentences

A fact family groups the multiplication and division sentences built from the same three numbers. From 8, 5 and 40 come four of them: 8 × 5 = 40, 5 × 8 = 40, 40 ÷ 5 = 8 and 40 ÷ 8 = 5. The Common Core standards make the same link, noting that knowing 8 × 5 = 40 means knowing 40 ÷ 5 = 8, and they describe division as an unknown-factor problem: 32 ÷ 8 is the number that makes 32 when multiplied by 8.

The English curriculum says the same thing from Year 2 onwards, since it always pairs each multiplication fact with the matching division fact. For your child, this means division is not a new set of facts to learn. A quick way to practise at home is to say one fact and ask for the other three, or to give the three numbers and ask which sentences can be made.

Fact families also help with checking. If a child writes 7 × 8 = 54, asking what 54 ÷ 8 gives shows that the answer does not work, without you having to say "wrong".

Multiplication practice that takes ten minutes a day

Short and frequent beats long and rare. Ten minutes a day, five days a week, gives almost an hour of practice without any session feeling like a punishment. Work on a few facts at a time, mix them with ones your child already knows, and stop while it is still going well.

It helps to keep a visible list of the facts that are secure, and to add to it every week. Children like to see the list grow, and you can see at a glance which table needs attention. A gentle timer works for some children, as long as the race is against their own previous score and not against a brother, a sister or a classmate.

When a fact will not stick, go back to the strategy rather than repeating the answer. Seven eights becomes "double 7 three times", and after a few rebuilds the answer starts to come straight away. An app such as Kalc can provide those ten minutes of practice, as long as your child does the calculating rather than guessing.

Times tables at home without tears

Games make repetition feel like play. With a pack of cards, each player turns over two cards and multiplies them; the higher product wins both cards. With two dice, children multiply the numbers they roll and race to cover the answers on a grid. In the car, a child can count up in sevens or eights between two lamp posts, or multiply the last two digits of a number plate.

Patterns are worth pointing out too. The Common Core standards suggest noticing, for instance, that four times a number is always even, and explaining why: four times a number is two equal halves, each of them double the number. Spotting these patterns turns the multiplication table into something to explore rather than something to recite.

Above all, keep the tone light. A child who is tired or upset will not remember much, and a battle over one fact can spoil the whole week. Our article on helping with maths homework without giving the answers has more ideas for staying on the right side of that line.

Frequently asked questions

What order should children learn the times tables in?

In England, the 2, 5 and 10 tables in Year 2, then the 3, 4 and 8 tables in Year 3, then all tables up to 12 × 12 in Year 4.

When should children know all their times tables?

By the end of Year 4 in England, and by the end of grade 3 in the US, where the Common Core asks for all products of two one-digit numbers from memory.

What is a fact family?

The four sentences built from the same three numbers, such as 8 × 5 = 40, 5 × 8 = 40, 40 ÷ 5 = 8 and 40 ÷ 8 = 5.

How many facts does a child need to learn up to 12 × 12?

Once the 1, 2, 5, 10 and 11 tables are known and each fact counts only once in either order, 28 facts remain among the 3, 4, 6, 7, 8, 9 and 12 tables.

How long should times tables practice last?

About ten minutes a day works well: short enough to stay friendly, frequent enough for the facts to stick.