The number one reason give up on maths so early is they can not do sums quick enough. That feeling when someone asks “what is 8 times 7?” or “what numbers go into 323?” can fill someone with dread when it 100% doesn’t need to. The reason – we have aids to answer these questions (64 and, 19 and 17 for the questions above).

The reason why we can feel stupid when faced with mental arithmetic is the expectation that you should know the answer instantly as we learnt arithmetic in school possibly through chanting out the numbers in line .. “1 times 3 is 3, 2 times 3 is 6, 3 times 3 is 9, …”) in the hope that the answers would stick. For the vast majority of people this doesn’t work. What does work is using numbers in a real situation where you get a reward for getting is right. To prove this ask any one that works with mental arithmetic everyday and they will know how much change you need, how much concrete is needed, or how long it will take to travel.

Learning Numbers – more than 12

When I was as school for some reason that I still can’t work out we learnt our times tables up to 12 through the repetitive number method I mentioned earlier. Below is a list of multiplications from 2 to 20 we will use to illustrate what you already know and how a few hints can help you remember some key numbers.

Hint 1: Everyone knows their 10 times table. We can cross out out the 10 times table as we just add a zero the number we are multiplying.

Hint 2: 5 times tables are half the number being multiplied then multiply by 10. For example 7 times 5 can be worked out as half of 7 (3.5) times 10 = 35. Try 18 times 5 … Half of 18 is 9 then multiple by 10 = 90.

Hint 3: Simplify to a small number. 4 times and 8 times are bigger versions of the 2 times table. The same with 6, 9, with 3. Although there looks like there are lots of numbers to remember if you can simplify the bigger numbers to small ones. For example 16 times 4 can be reorganised into 32 times 2 by doubling one half and halving the other – 32 times 2 is 64.

Hint 4: Take the 10 out. When faced with a big number look to take the 10 if possible. For example 20 x 21 (not on the grid below) is the same as 2 times 10 times 21 (you could simply 21 to 3 times 9 but it’s not necessary). 2 x 21 is 42 then times 10 is 420.

Hint 5: Learn the squares: There are common multiplication that are really handy to spot – a number times by itself or it’s square. These have been highlighted in grey. As a bonus if you can spot the squares you will know the roots of these numbers as well.

Hint 6: Multiples of 9 add up to 9 expect for 99. Weirdly when a number is multiplied by 9 the answer adds up to 9. This combined with knowing the answers first number is 1 less than the first number which changes to 2 less after 99. For example 7 times 9 is 63 as 6 is one less than 7 and 6 plus 3 make 9. 19 times 9 is 17 for the first 2 numbers (as 2 less after 11 times) then 2 as 1+7+2 = 9, 172. (it’s fancy if you can do your 19 times table!)

Hint 7: Just 6, 7,8 it. Just learn these 4 multiplications to memory: 6 x 6 = 36 7 x 6 = 42, 7 x 7 = 49, 8 x7 = 56, 8 x 8 = 64. The reason to learn these is they fall into the didn’t learn zone. Before the 6,7,8 times table you can work it out as the numbers are small. After its 9,10, 11 which are quite easy.

Hint 8: Take your time and have a go. The big reason anyone doesn’t know something is they never knew or don’t remember. It’s very easy to grab a calculator on a phone these days but when you have a chance do use paper and pen to work through it. This is especially helpful as you will recognise the numbers rather so will spot errors you may miss if you trust your calcualator.

Bonus Hint: Learning to Divide

None does their division table (the opposite of the times or multiplication tables). The reason being you have to start with a big number and then go down and learn what the answer would be. In hint 5: learn the squares I said if you know the square numbers then you know the root. Try learning the factors of the numbers above and it will super charge your mental arithmetic.

A related topic to know about are numerical factors – the numbers multiplied together to make a bigger number.