Times Tables | TO BEcome proficient, or NOT TO BEcome proficient

Should you learn your times tables? If you can, the answer is, "YES, YES, YES."

Why do we suggest, and schools usually demand, that you store a bank of multiplication facts in your head? It’s not really about being able to recall that 6 x 8 is 48, so much as knowing that the factors of 48 include 6 and 8. And that 48 also appears in the 2, 3, 4, and 12 times tables; while we don’t usually recite our times tables up to 16 x 3 = 48, we can recognise that 48 is 30 + 18, and hence recall that this is (10 x 3) + (6 x 3). Worded another way: in 48 we have 10 lots of 3 and 6 lots of 3, and so 16 lots of 3 altogether.

For some of us, chanting our times tables until we know them by heart is a fun challenge and not overly taxing. But everyone’s different and at Gill Learning we have taught enough students – particularly our 1:1 tutees, in whose every struggle we’ve shared – to know that some brains outright refuse to file information this way.

Can your calculator help? In a word: yes. Typically, calculators used for GCSE Maths can give you the prime factors of a number, which can also be combined to produce all the factor pairs of that number. However, this is a slower, more methodical approach to “spotting” factors and can get frustrating when manipulating equations that require multiple steps of expansion and factorisation.

So, if learning your times tables by rote isn’t for you, what are your other options?

Our go-to suggestion is based on "pattern recognition", and we’ve seen students who struggled with rote learning go on to have huge success with it. Rather than completing multiplication questions formatted as 6 x 4 = ?, flip the question around and challenge yourself to find the factors of 24 using a multiplication grid like the one pictured below. Colour in the squares, or circle the numbers, or cross them through, or obliterate them with a rubber stamp… whatever means you choose, try to imprint those spatial patterns onto your brain. Note the diagonal line of symmetry, too: thanks to the commutative property of multiplication, if you know 5 x 7, you also know 7 x 5 for free!

A picture worth a thousand words: this 12x12 Times Tables Grid graphically highlights the spatial patterns that underpin the "traditional" Times Tables.

If spatial patterns aren’t your cup of tea either, though, try considering each times table from its own unique perspective:

• 2 times table – double it

• 10 times table – add a zero on the end (since we count in base-10)

• 5 times table – x10 and half it

• 9 times table – I suspect that you’re already familiar with the technique for this one!

• 11 times table – is all repeated digits

• 12 times table – grid method multiplication in your head, 8 x 12 = 80 + 16 = 96

If we eliminate the above from our multiplication grid, as well as the duplicates due to the commutative property of multiplication (i.e., 4 x 3 = 3 x 4), then we have just five square numbers (in orange) and 10 multiplication facts (unshaded) left to learn:

Only five square numbers and ten multiplication facts remain to be learned! That's barely more than the equivalent of just ONE "traditional" Times Table.

You can also spot patterns in each individual case: for all the even-numbered times tables, for example, the digit in the units column repeat,

The digits in the UNITS column repeat.

Multiplication can, of course, always be viewed as simple repeated addition, or even as subtraction. You may not know what 7 x 9 equals, but you do know that 70 is 7 x 10, and so 7 x 9 must be 70 – 7 = 63. We can see from this example the importance of knowing your number bonds to 10!