Times Tables: Memorising, Understanding, and the Order That Works

17 August 2026 · by Larry

A child gets the 2s, the 5s and the 10s quickly, and then everything slows down. The 7s in particular seem to sit there for months. Somewhere around this point most parents get told one of two things: that tables must simply be memorised, or that memorising is old-fashioned and the child needs to understand instead.

Both pieces of advice are half right, and the half that is missing is the order. Understanding comes first, but it is not the destination — a child who understands multiplication perfectly and still has to work out 7 × 8 every time will run out of attention in the middle of a longer problem. The goal is that these facts arrive without effort, so the thinking can be spent on the actual question.

The grid is much smaller than it looks

A 12 × 12 table looks like 144 things to learn, and that is genuinely daunting for a nine-year-old. It is not 144.

The first cut is that 7 × 8 and 8 × 7 are the same fact. Once you stop counting each one twice, the grid holds 78 different facts rather than 144. That single realisation is worth saying out loud to a child, because it halves the mountain in one sentence, and because it is a real mathematical idea rather than a trick.

The second cut is that some of it is already done. Take out everything involving 1, 2, 5 and 10 — the tables nearly every child gets early — and 36 facts remain. Stop at 10 × 10 rather than 12 × 12 for now, and use the 9s pattern, and what is genuinely left is about fifteen facts.

Fifteen. That is the honest size of the problem, and it is a very different conversation from "learn your tables".

Understanding first, but briefly

Before any drilling, a child should be able to say what multiplication is doing. Not a definition — a picture. Four rows of seven. Seven groups of four. If they can lay out counters or draw dots in rows and see that turning the array sideways does not change how many there are, they have understood why 4 × 7 and 7 × 4 give the same answer, and they will trust the halving above instead of taking your word for it.

This part does not take weeks. It takes an afternoon with something to count. What takes time is the automaticity afterwards, and that is a different kind of work.

The order that makes it easier

The tables are usually taught roughly in numerical order, which is not the order that makes them easiest to learn. What works better is to build each one on the one before:

2, 10, 5 — nearly always already there. The 5s follow the 10s: half of the 10s answer.
4 — double the 2s. If they know 6 × 2 = 12, then 6 × 4 is 12 doubled.
8 — double the 4s, so double twice from the 2s.
3 — the first one with no shortcut, so it needs real practice. Keep it short and frequent.
6 — double the 3s.
9 — the digits of every answer add up to 9, and the tens digit is one less than the number you multiplied by. Children enjoy this one and it sticks.
7 — last, because it has the fewest patterns to lean on. By the time you get here, most of the 7s have already been learned from the other side: 7 × 4 came free with the 4s, 7 × 8 with the 8s. What is actually new is a small handful.

The squares — 3 × 3, 4 × 4, 6 × 6, 7 × 7, 8 × 8 — are worth learning as their own set. They act as anchors: a child who knows 7 × 7 = 49 can get to 7 × 8 by adding one more seven, which is far better than starting from nothing.

Chanting a table is not knowing it

This is the one that surprises parents most. A child can recite "seven, fourteen, twenty-one, twenty-eight…" fluently and still be unable to answer "what is 7 × 6?" without starting the chant from the beginning.

The chant is a sequence, and it is only recallable from the front. What is needed in a real question is instant access to one specific fact, in any order, in both directions — including "what times 6 gives 42?", which is the same knowledge and the one that division will later depend on.

So practise in mixed order, not in sequence. Ask individual facts, out of order, and include the reverse question. If a child answers a shuffled set as quickly as they answer a chanted one, it is genuinely learned.

Short and daily beats long and weekly

Five minutes a day does more for recall than half an hour on Sunday, and that is not a motivational slogan — it is how memory for facts behaves. Little and often, with a gap in between, is what moves something from "I can work it out" to "I know it".

Keep the sessions small enough that they end while the child is still fine. A round that finishes on a success is one they will come back to; a round that ends in frustration teaches them something about themselves that is much harder to undo than a times table.

Our free maths practice has a fluency drill you can point at specific tables, so a child working on the 7s and 8s gets those rather than a random mix. There is also a times tables guide with the same ground covered from the practice side.

Do not put a clock on it too early

Speed matters eventually — that is what automaticity means. But timing a child while they are still working the facts out turns practice into a test, and an anxious child gets slower, not faster.

The order is: understand it, get it right reliably, then get it fast. Bringing the clock in at stage three is useful. Bringing it in at stage one is where a child decides they are bad at maths. Larry wrote about that on the Forum in Why I stopped timing her.

How to tell where they actually are

Ask ten facts in mixed order and watch, rather than mark.

Answers straight away — that fact is learned. Stop practising it and spend the time on the others.
A pause of a few seconds, then correct — they are deriving it, probably by counting up or from a nearby fact. This is good progress and not a problem. It just is not finished.
Counts on fingers from the start — the underlying idea is there but nothing is stored yet. Keep it to a very small set of facts at a time.
Guesses, or gets the wrong table entirely — go back to the array and the picture before any more practice, because drilling something unanchored just makes a wrong answer fluent.

Write down which facts fall into which group. It usually turns out to be five or six specific facts causing most of the trouble, not "the times tables" — and five or six is something you can fix in a fortnight.

What to do this week

Show them the grid is 78 facts, not 144, and that most are already done.
Test ten in mixed order and sort them into knows / derives / counts / guesses.
Pick the five that are actually hard and work only on those.
Ask the reverse question too — "what times 8 makes 56?"
Five minutes a day, ending while it is still going well.
Leave the stopwatch alone until the answers are reliably right.