# Turning the tables

### by Di Hillage.

Learning their tables is one of the most commonly mentioned problems amongst those who find numeracy difficult.

Previous generations learned their tables by rote, usually relying on some sort of chanting, making use of auditory memory. This can be particularly inefficient for those with memory difficulties associated with dyslexia, where sequencing is often a problem. Also you are more likely to need to access an individual fact rather than a whole list.

So what can you do to learn times tables up to 10? (Many years ago the 11 and 12 times tables were included, but since we now have decimal currency and metric measures the 12 times values are not so important. The 11 times were just there to fill the gap. If your child’s teacher persists with these, please challenge them.)

### Concept of multiplication.

Firstly, it is essential to understand the concept of multiplication. For example, 2 x 5 in symbols and two fives in words means ‘two lots of five’ or 5 + 5. The use of concrete materials such as Cuisenaire rods is perfect to explain this.

It is also necessary to realise that the results for 2 x 5 and 5 x 2 will be the same. Understanding that division is the reverse of multiplication is also necessary. So if you know that 2 x 5 =10, you also know that 5 x 2 = 10,
10 ÷ 5 = 2 and 10 ÷ 2 = 5. There are many similar connected triples in maths and science. A useful device for remembering and using them is a triangle like this…

### Tables squares. A tables’ square is a very useful tool, providing the learner understands how to use it.

It should be printed out as a square to reinforce the symmetry i.e. not as a rectangle.

Learners who enjoy the challenge of using computers may also enjoy generating a tables’ square using a spreadsheet.

To find the result of 6 x 7 (six lots of seven) choose the row with the 6 on the left hand edge and move along until you reach the column under the 7 where you should find 42.

To find the answer to 30 ÷ 6 (How many sixes in 30?) chose the 6 row and move along it until you find 30. Then look for the number at the top of this column, which should be 5.

Practice at using the table to solve similar problems is very useful. It may also mean that some of the results become very familiar. Saying the complete statement out loud each time can help to fix it in your memory.

I expect that many readers, at this stage, are saying that this idea will be no good in exams and tests as candidates are not allowed to take tables squares into the room. However, they are allowed to ask for a piece of squared paper. I found that my pupils who had difficulty in learning their tables were nevertheless able to learn to complete a tables square in around five minutes. Start by outlining a square 10 by 10 squares, preferably on centimetre squared paper so that the squares are big enough to write in. Leave room around the edges to label the rows and columns. Label the top and left hand side with the numbers from 1 to 10.

You should be able to fill in the 1x, 10x and 2x values quite quickly and probably the 5x as well. Don’t forget to fill in the columns as well as the rows for each number.

You may be surprised to know that you have already filled in 64 of the 100 squares. The 9x make a simple pattern. The units figure starts at 9 and goes down to 0, while the tens figure starts at 0 (if you think of 9 as 09) and goes up to 9.

Depending on which results you already know, you may have to do some counting on to fill in the rest of the squares. It is very useful to know the square numbers i.e. 3 x 3, 4 x 4 etc., which go diagonally down the square. Every unknown fact will then only be one step away from one in the table.

If you are good at doubling then you can get the 4s and 8s by this method starting from the 2s.

Add the 5s and 1s to get the 6s or double the 3s.

Add the 5s and 2s or the 4s and 3s to get the 7s.

Perhaps you know some tricks for remembering some of the missing facts, such as:

I ate and I ate and was sick on the floor!

(eight eights are sixty-four).

Other memory tricks will help like these:

56 = 7 x 8                  12 = 3 x 4

The best method is to invent your own memory tricks for the facts you find the most difficult to remember.

Whatever method you use it is very helpful to be able to recall or find the result you want reliably. Practice will obviously help.

### Useful programs.

There are loads of useful computer programs available such as:

Numbershark from White Space as on the Numeracy page.
Number Gym as on the Numeracy page.
Mathbase as on the Numeracy page.
with games and activities focused on tables facts.

You might like to try some of the free resources available at sites such as: