Times Tables That Actually Stick
There are not 144 facts to learn. Once you know that order does not matter, there are far fewer, and only a handful of them are genuinely hard.
A times table is a picture
Three times eight means three rows of eight.
That sentence is doing more work than it looks. A child who only ever meets multiplication as a chant has no way to rebuild a fact they have forgotten, and forgetting one under pressure is guaranteed. A child who can picture three rows of eight can count them, or work out three rows of ten and take away three rows of two, or notice they already know four eights and double it. The picture gives them a way back.
Order does not matter
Now turn the same counters a quarter turn.
The rule this gives you
a x b is always the same as b x a. Three eights and eight threes are one fact wearing two hats.
This is not a shortcut or a trick. It is a fact about rectangles, and turning the page proves it.
The consequence is worth spelling out. A child who has learned their three times table has, without doing anything extra, also learned the three in every other table. Every "something times three" is already done.
How few facts there really are
The full grid up to twelve looks like 144 separate things to memorise, which is a genuinely discouraging number to put in front of a nine year old. It is also wrong.
- The 1 times table is not a fact, it is the definition of one.
- The 10 times table is place value, which is why it is the first one everybody gets.
- The 2, 4 and 8 tables are doubling, then doubling again, then again.
- The 5 table is half of the 10 table.
- The 9 table has the digit trick, and the digits of every answer add to nine.
- And every fact you learn one way round, you get free the other way round.
Strip all of that out and what is left is a short list.
The genuinely hard ones
Once the patterns above are taken away, the facts that children actually get wrong are these: 6x7, 6x8, 7x8, 7x9, 6x9 and 8x9. That is six facts. Six is a list you can put on the fridge, and it is a very different proposition from 144.
7 x 8, the one everybody misses
Say it as "five, six, seven, eight": 56 = 7 x 8. The digits run in order. It is a silly memory hook and it works on almost every child who meets it.
A child cannot remember 6 x 7. What can they do about it?
- They almost certainly know 6 x 6 = 36, because square facts stick better than the rest.
- 6 x 7 is one more row of six than 6 x 6.
- 36 + 6 = 42.
- The same works from above: 6 x 10 is 60, minus three sixes is 60 - 18 = 42.
6 x 7 = 42, and there were two routes to it
Common mistakes
1. Chanting from the start every time
Being asked 7 x 8 and beginning "seven, fourteen, twenty one". It gets there, and in a timed test it does not get there fast enough, and by question four the child has run out of time rather than out of knowledge. Chanting is how a table is learned, not how a fact is recalled.
2. Treating 8 x 3 and 3 x 8 as separate homework
Doubling the work for no reason. If a child hesitates on 8 x 3, ask them for 3 x 8 instead and watch the answer arrive. Then show them the turned array, because the point is not the trick, it is that they already knew it.
3. Multiplying by 10 by adding a zero
It works for whole numbers and it breaks the moment decimals arrive, when 3.5 x 10 gets written as 3.50. The digits move one column left. The zero turns up to hold the ones column, which is a consequence, not the rule.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
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What to learn next
Times tables are the engine that long multiplication and division run on. They are also what makes factors and primes possible to think about at all.
For parents
Test out of order, never in order. A child who can recite the seven times table perfectly can often still not answer "seven eights" cold, because they have learned a sequence rather than a set of facts. Ask three random ones a day in the car. Two minutes a day beats an hour on Sunday.
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