Multiplication Table Generator
Times table chart, filled or blank to complete.
The shaded diagonal is where a number multiplies itself. Everything above it mirrors everything below, which halves the number of facts there are actually to learn.
Multiplication Table
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
How the Multiplication Table Generator works
A filled chart to pin up and a blank grid to fill in are the same table doing two different jobs, so both come off the same settings here. The squares down the diagonal are shaded, because that diagonal is the line the whole table mirrors around and seeing it is what turns a hundred and forty-four facts into far fewer.
Also known as: printable times table chart · blank multiplication grid · times tables to 12 chart · multiplication square
What the shaded diagonal is telling you
The diagonal marks the square numbers: one, four, nine, sixteen, twenty-five and so on, the cells where a number multiplies itself. It is shaded because it is the most useful line on the chart, and most children are never shown why.
The table is symmetric about that diagonal. Seven times eight sits in one half and eight times seven in the other, and they hold the same number. That means the hundred and forty-four cells of a twelve by twelve table contain only seventy-eight distinct facts, and once the commutative property genuinely lands, a child's memorisation workload halves overnight.
The squares themselves are also the anchors people navigate by. Someone who has forgotten seven times eight but knows seven times seven is forty-nine can get there by adding seven. That strategy only exists if the squares are known cold, which is a strong argument for learning them as a set rather than table by table.
Filled chart or blank grid
They do different jobs and it is worth having both. The filled chart is a reference: pin it up, let a child look up a fact they are stuck on, and gradually they stop needing to look. Its value is that it removes the anxiety of being stuck, which is what stops a child engaging at all.
The blank grid is the practice. Filling it in is recall, and recall is what actually builds durable memory. Testing yourself on material is substantially more effective than re-reading it, an effect robust enough to have its own name in the literature, and a blank multiplication grid is about the cleanest example of it in primary maths.
A useful routine is to time the blank grid weekly and record the time on the sheet. The number falls quickly at first and then plateaus, and both the fall and the plateau are informative. The plateau usually sits exactly where the unlearned facts are.
A sensible order to learn them in
One to twelve in sequence is the order they are printed in and a poor order to learn them in, because it puts two of the hardest tables in the middle of the run just as motivation is flagging.
Twos, fives and tens come nearly free: they are counting patterns a child already has. Elevens up to nine are a visible pattern. Nines have the finger trick and the digit-sum property, where the digits of every answer add to nine. Those five tables account for a large fraction of the grid before any real memorisation has happened.
Then threes, fours, sixes and eights, each of which has a doubling relationship to something already known: fours are double twos, eights are double fours, sixes are double threes. Sevens go last, which is why seven times eight is the fact adults still hesitate over. It is the one cell with no easy pattern and no earlier table to lean on.
Reading the patterns off the chart
A printed chart is worth more than a list because the patterns are spatial. The five column ends alternately in five and zero all the way down. The nine column has tens digits counting up while units count down. The two column is every even number in order. None of this is visible in a list of facts recited aloud.
The ten column and the ten row are worth pointing at explicitly, because they make the place value idea concrete: multiplying by ten shifts the digits, it does not add a zero, and the chart shows the shift happening.
Children who find the table overwhelming often respond well to being shown how much of it they already know. Shade in the twos, fives and tens on a blank grid and most of the page is already covered. What remains looks manageable in a way that a hundred and forty-four empty cells never does.
Fitting it on paper
Up to about fifteen by fifteen fits comfortably on A4 portrait with cells large enough to write a two-digit number in. Beyond that, switch the print dialogue to landscape, which buys enough width for a twenty by twenty grid at the cost of a shorter page.
For a wall chart, print at the largest size your printer takes and consider printing the filled version in a lighter colour, since a chart that is easy to read from across a room is also easy to read from a desk during a test, which may or may not be what you want.
If you are printing blank grids repeatedly for timed practice, print one master and photocopy. The lines survive copying well, and it saves a great deal of ink over a term.
Frequently asked questions
How far should the table go?
Twelve by twelve is the traditional range in the UK and the one the national curriculum expects by the end of Year 4. Ten by ten is the American norm. Going to twenty is useful for older children working on mental strategies, though it is well past what anyone needs to memorise.
What is the diagonal for?
It marks the square numbers, where a number multiplies itself. Everything above the diagonal is a mirror of everything below it, because 7 × 8 and 8 × 7 give the same answer. Noticing that halves the number of separate facts a child has to hold.
Is the blank grid better than the filled chart?
For learning, considerably. Reading a chart is recognition; filling one in is recall, and recall is what builds the memory. Print the filled version for the wall and the blank version for practice.
What order should tables be learned in?
Not one to twelve in sequence. Twos, fives and tens come almost free from counting. Then elevens and nines, both of which have patterns a child can see. Threes, fours, sixes and eights next, and sevens last, which is why seven times eight is the fact everyone hesitates on.
Can I print it on one page?
Up to about fifteen by fifteen fits comfortably on A4 portrait. Beyond that, switch your print dialogue to landscape or the cells get too narrow to write in.