Learn your number facts efficiently and with the minimum of fuss. The quicker you can command total mastery of your number facts, the quicker you can stop having to learn them, and the more time you can spend on the more creative and interesting aspects of maths.
Play games
Many games, online and offline, help you practise and learn your number facts. Games are a really useful way of learning anything at all, because they take the chore element out of learning and turn it into something a bit more fun. Playing a number-facts game with cards or on the computer is much less like hard work than writing down endless lists of sums.
Flash cards
Flash cards aren’t very common in the UK, but in America pretty much every successful student spends hours of their revision time writing down the key facts they want to remember on index cards and repeatedly testing themselves until they have all their facts down pat. Using flash cards like this is a bit tedious but very effective.
Stickies
Put five key things you want to remember on sticky notes and put the notes somewhere you’re bound to see them – say, on the bottom of your computer screen, the microwave or the bathroom mirror – anything you look at more than once a day and is a suitable surface for sticky notes is a great choice.
When you can remember the info on the sticky note without even trying, replace the sticky with a new note covering something else you need to learn.
Count on your fingers
Fingers are the reason for counting things in tens, so using your digits to figure out questions is perfectly natural. The disadvantage is that counting on your fingers can be a lot slower than just remembering the facts – and especially in an exam, time isn’t something you have a lot of.
Trick out the nines
Here’s one way to do nine times anything (up to ten):
Take one away from the number you’re timesing by.
Write down the answer.
Take your answer to Step 1 away from nine.
Write this new answer to the right of your first answer – and there’s your answer. For example, to do 7 x 9, take 1 away from 7 and write down 6. Now take 6 from 9 to get 3, and write that to the right – you get 63, which is 7 x 9.
A good way to check your answer to a nine times table (up to ten) question is to notice that the two numbers in the answer always add up to nine.
For example, 7 x 9 is 63, and 6 + 3 is 9. After ten, things get a bit trickier: for example, 11 x 9 = 99, and 9 + 9 is 18 . . . but if you add 1 + 8, you then get 9. You just have to keep going until you get to a single digit.
Tricking out the other big numbers
Here are some clever tricks you can use to figure out your five, six, seven and eight times tables.
To times a number by six:
Times the number by three.
Double the answer.
For example, to work out 9 x 6, do 9 x 3 = 27, and then double your answer to get 54. It doesn’t matter which way around you do the doubling and trebling, as long as you do them both.
To times a number by eight:
Double the number.
Double the answer (this is now four times the original number).
Double the answer again.
For example, to do 7 x 8, double 7 to get 14. Double 14 to get 28. Then double 28 to get 56.
To times a number by seven using the sixes:
Work out six times your number.
Add the original number to that.
For example, to work out 7 x 7, do 7 x 6 = 42, and add 7 to get 49.
Alternatively, you can times a number by seven using the eights:
Work out eight times your number.
Take away the original number.
So, to work out 7 x 7, do 7 x 8 = 56 and take away 7 to get 49.
The five times table also has an easy trick: you can times the number by ten and then divide the answer by two, or halve the number first and then times by ten.
Break down and build up
Division tricks are pretty much the opposite of the multiplication tricks.
If you want to divide by eight, but doing ‘proper’ division bothers you, try the following method:
Divide the number by two.
Divide by two again (you’ve now divided by 2 x 2 = 4).
Now divide by two again (you’ve now divided by 4 x 2 = 8).
So, to do 72 ÷ 8, halve 72 to get 36, halve again to get 18, and halve one more time to get 9. And that’s right: 72 ÷ 8 = 9.
Here's another way to divide by six:
Divide by three.
Then divide your answer by two.
You can do these steps in either order. For example, to do 42 ÷ 6, you can halve 42 to get 21 and then divide by 3 to get 7. Or you can do 42 ÷ 3 = 14 first and then halve the answer to get 7.
Dividing by nine is just as simple:
Divide by three.
Divide by three again.
So, faced with 81 ÷ 9, you can work out 81 ÷ 3 = 27, and then 27 ÷ 3 = 9, which is the right answer.
For the five times table, you can double and then divide by ten, or you can divide by ten and then double.
Learn from your mistakes
Whenever you make a mistake in doing a sum, take a moment to note down what you should’ve done. Then add this to your list of things to learn.
Work from what you know
You can split up any times sum into smaller times sums. You can also split up many divide sums into smaller, easier ones.
Train yourself with treats
If you reward yourself with a treat after you learn to perform a task well, you do better at repeating your feat at a later time.