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Learning Times Tables

CraigsMaths
Mathematics Teaching for Learning
Number
October 6th, 2009 by Craig Rose
Permalink: http://www.craigsmaths.com/number/learning-times-tables/

Number
October 6th, 2009 by Craig Rose
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Once you know your times tables by rote a lot of what we do in maths becomes much easier. As with memorising anything, the trick is to do a little at time. Practice a few tables each day. This article includes some tricks you can use and some references to online resources I have found.

OK … so you want to learn your times tables. But the task seems so huge, “How can I possibly remember the 100 multiplication facts in the 10 times tables let alone the 144 facts in the 12 times tables?”

The answer is you don’t have to learn them all at once! If you practice for a short time on a regular basis you will soon find that you just know the answers to many of them and the rest you have to think for a short while. Then if you keep going you’ll eventually know the answers to them all.

Here are a few tricks to help you on your way.

Pairs of numbers

$4 \times 9 = 36$ will give you the same answer as $9 \times 4 = 36$ . It doesn’t matter what order the numbers are in, the answer is the same.

This means that you only have to remember 78 facts not 144.

1 times table

$1 \times 5 = 5$ and $1 \times 7 = 7$ . The answer is always the number you are multiplying by.

With this we only have to remember 66 facts.

10 times table

$10 \times 3 = 30$ and $10 \times 12 = 120$ . Just add a zero to the number you are multiplying by.

Now we are down to 55 facts to remember.

2 times table

$2 \times 7 = 14$ and $2 \times 4 = 8$ . The 2 times table is just the number you are multiplying by added to itself.

If you are good with addition then you now have just 45 facts to remember.

11 times table

$11 \times 5 = 55$ and $11 \times 3 = 33$ . If you are multiplying by numbers up to 9 then it’s just the number repeated.

Now we have only 38 facts.

9 times table

$9 \times 7 = 63$ and $9 \times 3 = 27$ . For the 9 times table first multiply by 10 then subtract the number you are multiplying by.

If you are good with subtraction then you now have only 30 facts to remember.

5 times table

$5 \times 4 = 20$ and $5 \times 7 = 35$ . This one is a little more tricky but there a couple of things that can help. First, all 5 times tables end in 0 or 5 so make sure your answer does. You can halve the number you are multiplying and multiply this by 10. For example:

$5 \times 4$ becomes $10 \times 2$ which equals 20.

This is fairly easy if the number you are multiplying by is even. If it is odd then you end up with:

$5 \times 7$ becomes $10 \times 3\frac{1}{2}$ . A bit messy! To avoid this I just take half of one less than the number I am multiplying by then, multiply this by 10 and add 5. Not the best - but it helps.

$5 \times 7$ becomes $10 \times 3 = 30$ . Then adding 5 you get $30 + 5 = 35$ .

I’ll admit that this is not so simple at first but now we have only 23 facts to remember.

12 times table

$12 \times 7$ is $10 \times 7$ plus $2 \times 7$ :

$(10 \times 7) + (2 \times 7) = 84$

The rule here is to multiply by 10 then multiply by 2 and add.

Now there are 16 facts left.

11 times 11

$11 \times 11$ is $10 \times 11$ plus $1 \times 11$ :

$(10 \times 11) + (1 \times 11)$

This is similar to the 12 times table and leaves you with 15 facts to learn.

Learn the squares

After learning all the above rules now have a go at memorising the squares. That’s a number multiplied by itself. $4 \times 4 = 16$ .

Once you have memorised these there will only be 10 facts left.

Another trick

If the two numbers you want to multiply are seperated by 2 then square the middle number and subtract 1.

For example:

For $6 \times 4$ the middle number is 5 and $5 \times 5 = 25$ . Subtract 1 and you have $25 - 1 = 24$ .

Now there are 8 facts left.

Using squares again

If the two numbers you want to multiply are seperated by 1 then square the smaller number and add it to the result.

For example:

For $6 \times 7$ the smaller number is 6 and $6 \times 6 = 36$ . Add 6 and you have $36 + 6 = 42$ .

Now there are 5 facts left.

These are:

$3 \times 6 = 18$

$3 \times 7 = 21$

$3 \times 8 = 24$

$4 \times 7 = 28$

$4 \times 8 = 32$

For the remaining 4 times table facts you can double the number you are multiplying by then double again. The remaining 3 times table facts I just have memorised.

A method for multiplying any two numbers

There is a fairly simple method that allows you to multiply any two numbers (including the times tables) quickly and easily. But I’ll save that for another article.

Let me know in the comments if there are any tricks I’m missing.

Commiting to memory

The tricks above are a great help when starting out with times tables. But you will want to develop the skill of remember all the times tables instantly. To do this you need to practice them. I recommend 15 or 20 minutes each day recalling the answers to randomly asked questions. You can have a friend fire the questions at you, use a stack of flash cards or computer software.

Computer software is the best because it can time your responses and track your improvements in a record. Here’s a few you might want to try:

This one is online and you can’t save your progress. Questions are categorised in 6 groups of times tables.

http://www.mathsisfun.com/numbers/math-trainer-multiply.html

This is a freeware that you can install on your computer. It let’s you save your results so you can keep track of progress. In some exercises questions are random across all the 12 times tables.

http://timestables.darrenyates.com.au/

Here are some flash cards you can download and print:

http://www.multiplication.com/flashcards.htm

Tuesday, October 6th, 2009 at 12:38 pm
Category: Number.
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