Times tables: memorising and understanding, in that order?

"Should my child learn the times tables by heart, or understand what multiplication is?" It is one of the most common questions parents ask about primary mathematics, and it is often asked as though the two were rivals. In practice they work together, and the order in which they arrive makes a big difference. This article suggests a path that starts with meaning, builds up to recall, and keeps both alive, with ideas you can use at home.

Written for children aged 7 to 10.

Why the tables matter

Knowing the multiplication facts fluently frees a child's mind. Long division, fractions, equivalent ratios, area, and later algebra all rely on multiplication facts being available without effort. A child who has to work out 7 × 8 each time has less attention left for the new idea in front of them. That is why teachers care about fluency, and why parents are right to want it.

But fluency built on nothing is fragile. A child who has memorised 7 × 8 = 56 as a sound, like a rhyme, has no way to recover if the memory slips, and no way to check whether an answer is reasonable. Understanding provides that safety net.

Start with what multiplication means

Multiplication begins as repeated addition: 4 × 3 means four groups of three, or 3 + 3 + 3 + 3. Children meet this idea long before formal tables, in everyday life: four plates with three biscuits each, five hands with five fingers each, six eggs in each of two rows.

It is worth showing the same multiplication in several forms, because each one gives a different insight:

• Equal groups: four bags with three apples in each.
• Arrays: three rows of four dots, which shows that 3 × 4 and 4 × 3 give the same total, since turning the array on its side does not change how many dots there are.
• Number-line jumps: four jumps of three, landing on 12.
• Area: a rectangle that is 3 units by 4 units covers 12 squares.

The array is especially powerful. Children who see multiplication as an array discover for themselves that the order of the factors does not change the product, which halves the number of facts they need to learn.

Build the tables through patterns

Once multiplication makes sense, the tables stop looking like 100 unrelated facts and begin to look like families with patterns. A sensible order, used in many classrooms, goes like this.

Twos, fives and tens first. Doubling and skip-counting by twos, fives and tens are easy and satisfying. Tens have a clean place-value pattern, fives end in 0 or 5, twos are the even numbers.

Then fours and eights as doubles. Four times a number is double double that number, and eight times is double that again. A child who knows 6 × 2 = 12 can find 6 × 4 by doubling to 24 and 6 × 8 by doubling again to 48. These links turn a memory task into a reasoning task.

Threes, and then sixes as doubles of threes. Once threes are secure, sixes follow by doubling: 7 × 3 = 21, so 7 × 6 = 42.

Nines through a pattern. The nine times table has a famous trick: the digits of each answer add up to nine (18, 27, 36, 45...), and finger methods exist as well. A nicer route to understanding is that 9 × n is 10 × n minus n. So 9 × 7 is 70 − 7 = 63.

Sevens last. By sevens, nearly every fact has already appeared in an earlier table (7 × 2, 7 × 3, 7 × 4, 7 × 5, 7 × 6, 7 × 8 and 7 × 10 all live in tables met before, thanks to commutativity). The ones that still tend to stick are 7 × 7 and 7 × 8 = 56 (a rhyme "5, 6, 7, 8: 56 = 7 × 8" helps many families).

Which tables, by when? The order above is one common classroom order, not the only one. As a rough guide: the 2, 5 and 10 tables by the end of Grade 2 (about age 8); the 3, 4 and 8 tables during Grade 3; the 6, 7 and 9 tables and then all the facts up to 10 × 10 by the end of Grade 3 (about age 9); and the tables to 12 × 12 in Grade 4, where your school teaches them.

Moving from working it out to knowing it

Understanding gives children a way to find a fact; practice turns finding into knowing. Short, frequent practice, without pressure, works best.

Little and often. Five minutes a day beats an hour on Sunday. The brain consolidates memory over time, and spacing practice across days is more effective than cramming.

Mix it up. Practising one table at a time is a fine start, but real fluency means being able to pull any fact out of a mixed set. Once a few tables are secure, mix them.

Say the whole fact. "Seven eights are fifty-six" is more useful than just "fifty-six", because it ties the question to the answer.

Use games, not just cards. Dice games, card games ("multiplication war": each player flips two cards and the first to say the product wins), board games with multiplication moves, and quick-fire car-ride questions all provide practice that does not feel like practice.

Track the tricky ones. Most children have a handful of facts that refuse to stick. Keep a short personal list, and give those extra attention in small doses, rather than drilling everything equally.

Link to division. 56 ÷ 8 = 7 is the same fact turned around. Practising the "family" of four related statements (7 × 8, 8 × 7, 56 ÷ 7, 56 ÷ 8) quadruples the value of every fact learned.

What not to do

Don't skip the meaning. A child who only chants the tables may do well on a speed test and then fall apart on a word problem, because they do not know when to use multiplication.

Don't rely on pressure or shame. Timed tests can motivate some children, but for others they create anxiety that actually makes recall harder. If your child dreads practice, step back and play instead.

Don't expect all the facts at once. Mastery develops over about two or three years, which is why the tables are spread across several grades. Individual children vary a great deal.

A balanced answer

So, memorise or understand? Both, and in an order that respects how children learn: begin with what multiplication means, build the facts through patterns and relationships, and then practise until recall is quick and secure. Understanding makes memorising easier and more durable; memorising makes understanding usable. A child who has both will meet fractions, division and algebra with calm confidence.

Try it in the app

Practise this at the screen too: Times tables 2, 5 and 10, Times tables 3, 4 and 8, Times tables 6, 7 and 9. You may also like our articles on word problems and mental maths strategies.