Multiplication Table
The diagonal is the square numbers.
There are far fewer facts than it looks
A 12×12 grid has 144 cells, which sounds like 144 things to learn. It is not, and saying so out loud helps children enormously.
- Order does not matter. 7×8 and 8×7 are the same fact. That halves the grid immediately.
- The 1s, 2s, 5s and 10s are nearly free.
- The 11s up to 9 are just the digit doubled.
- The 9s have the neatest pattern of all: the digits of every answer add to 9, and the tens digit is one less than the number you multiplied by. 9×7 = 63, and 6 + 3 = 9.
Strip those out and there are only a handful of genuinely hard facts left — mostly 6, 7 and 8 multiplied by each other. 7×8 = 56 is the one that defeats everybody, and it has a mnemonic: 5, 6, 7, 8 — 56 is 7×8.
The diagonal
The highlighted diagonal is the square numbers: 1, 4, 9, 16, 25 and on. They are worth knowing separately because they anchor everything nearby.
Once you know 7×7 = 49, you can get 7×8 by adding another 7. The squares are stepping stones, and the gaps between consecutive squares are the odd numbers — 1, 3, 5, 7 — which is a pattern children usually enjoy spotting.
Useful tricks
- ×4 — double twice.
- ×8 — double three times.
- ×9 — multiply by 10 and subtract the number.
- ×5 — halve, then multiply by 10.
- ×15 — multiply by 10, then add half again.
Why they are still worth learning
Every calculator can multiply. The value is not the answer; it is having the facts available without thinking, so attention can go to the actual problem. A child who has to work out 7×8 mid-way through a division has lost the thread of the division.
It is the same reason musicians practise scales.
Common uses
- Homework and revision.
- Printing a reference for a wall or a desk.
- Spotting patterns, which is the part children enjoy.
- Checking a mental calculation.
Questions people ask
What is the easiest way to learn times tables?
Strip out what is nearly free — the 1s, 2s, 5s, 10s and 11s — and remember that order does not matter. Very few genuinely hard facts remain.
What is the trick for the nine times table?
The digits of every answer add to 9, and the tens digit is one less than the multiplier. 9 × 7 = 63, and 6 + 3 = 9.
Which fact do children find hardest?
7 × 8. The mnemonic is 5, 6, 7, 8 — 56 is 7 × 8.
What is the highlighted diagonal?
The square numbers. The gaps between consecutive squares are the odd numbers, which is a pattern worth spotting.
Are times tables still worth learning?
Yes. The value is having the facts available instantly so attention can go to the problem itself, not to the multiplication.
Built into the page
The whole chart is part of the page, so it works with no connection and nothing is requested while you use it.