We learn tables at school because we have to, it’s part of the curriculum.

Our success or lack of it may affect our esteem and how we are judged by teachers and others. Ultimately it may affect our lives by contributing to our choice of career, whether we go to university or not, whether we succeed in business or investment.

Curiously, considering how much importance is put on learning tables, it’s not that difficult.

It is also something that people are much happier to do in everyday life, perhaps they just get put off by the school setting.

When was the last time you saw a darts match held up because no one could work out the score. Or snooker, pool or scrabble for that matter.

James Martin, the TV chef, says from time to time that he never passed an exam in his life but he doesn’t seem to have trouble with his recipes whens scaling them up or down for more or less people.

Plumbers, builders, decorators, carpenters all get by. Have you ever had any say

“I’d have like to give you a quote but I couldn’t do the multiplication”

Anyway getting back to tables. When I was at primary school we learned from 1 x 1 to 12 x 12. Nowadays the tendency is to stop at 10 x 10 as it’s easier. But I prefer to stick with 12 x 12, if only to get practice with answers over 100.

In addition I like to include the 0x table, as it makes for some easy answers!

So we have a table like this, 169 different answers.

Let’s discount the 0x and 1x tables as they are so easy.

Also when multiplying any pair of numbers the answer is the same which ever way you multiply them. So

Or more generally, for any two numbers i and j

This cuts the number of answers down it is necessary to learn to 66. So in the table below we are cutting out the numbers shaded in blue and ignoring the 0x and 1x tables.

I printed 11 copies of this for my children, one for each of 2 through 12.

and got them to step through in steps of 2 to 12 circling each number they step on. Then write the step number by the circle.

Here is an easy example, stepping forward in 10s

For each of the page they circled I gave them one of the following templates for them to copy the results to, and they wrote out the times tables for themselves.

Download your free copy of the appendices from my report Starting Arithmetic

which contain these templates and much more.

I recommend you give your children blank templates and let them circle as they step through, then copy the results to the tables template. However Starting Arithmetic appendices contain the results of stepping forward in steps of size 2 to 12. It is instructive to page through the pdf file watching how the patterns change as you do so.

It is common to start with the 2 times table as it is ‘easiest’. But in many ways 10, 11 and 5 times tables are easier. You have seen the circle template for 10s here are 11s. From 11 x 1 to 11 x 9 is easy, 11 x 10 is in the 10 times table.

There is a simple pattern to the 9 times table from 9 x 1 to 9 x 9. The units get one smaller and the tens get one bigger. 9 x 10 is in the 10s and 9 x 11 is in the 11s.

Just these 4 tables contain 35 of the 66 answers. Over 1/2 way already!

You may have seen you children playing “Dizzy Dinosaurs”, where they put there arms out and spin round and round, often chanting as they do so. 5s and 10s are great for this as they are so regular that they can just go on and on, until they fall down!

In the following table I’ve broken down learning tables into groups. It seems easiest to me to start with 10x, 11x, 5x and then 9x which covers over 1/2 the 66 answers.

At school children will probably be learning 2x 3x and 4x tables and there is no reason why you can’t or shouldn’t help with these too.

Table | To Learn At This Stage | Number To Learn | Total So Far | Number Left |
---|---|---|---|---|

10 | x2 to x12 | 11 | 11 | 55 |

11 | x2 to x9 | 8 | 19 | 47 |

5 | x2 to x9, x12 | 9 | 28 | 38 |

9 | x2 to x4 x6 to x9 |
7 | 35 | 31 |

2 | x2, x3, x4 | 3 | 38 | 28 |

3 | x3, x4 | 2 | 40 | 26 |

4 | x4 | 1 | 41 | 25 |

2 | x6 x7 x8 | 3 | 44 | 22 |

3 | x6 x7 x8 | 3 | 47 | 19 |

4 | x6 x7 x8 | 3 | 50 | 16 |

9 | x12 | 1 | 51 | 15 |

11 | x11 | 1 | 52 | 14 |

12 | x11 x12 | 2 | 54 | 12 |

12 | x2 x3 x4 x6 x7 x8 |
6 | 60 | 6 |

6 | x6 x7 x8 | 3 | 63 | 3 |

7 | x7 x8 | 2 | 65 | 1 |

8 | x8 | 1 | 66 | 0 |

Once your children have learned 2x 3x 4x by 6,7,8 they’re nearly 2/3 done.

There are the 4 numbers above 100

It helps if you have a little story to tell, for example

- 12 x 12 is 144 which is the largest number in the times tables
- 9 x 12 is 108 which is like 18 only with a 0 in the middle

11×11 and 11×12 can be worked out by stepping forward in steps of 11 from 11×10.

Next the parts of the 12x table not yet learned. One way of working out the 12x tables is to find the answer for 11x then add on, for example

11 x 3 = 33

33 + 3 = 36

Finally the 6 answers some children find the hardest of all.

These can be worked out by counting on from x5, once 5x table has been learned.

So that’s it then – it’s all easy?

There has to be a catch.

Well yes there is, in fact there are two.

The first is we tend to forget what we have learned, anyone who has ever crammed for an exam knows that. To really learn facts you have to revise over and over again. But the good news is it doesn’t take much. Just a few minutes regularly is enough.

You can help you children learn by asking them questions about tables. In this way you relieve them of the burden of what to learn and revise. The downside is you take up this load. But the good news is you only need a few minutes a day.

Think of it this way, how good would your children’s speaking be if you never spoke with them at home, as that was something schools did?

It’s ridiculous isn’t it.

Why should maths and tables be any different.

To start with choose one table, say the 10x, let your children have the sheets they circled. Then ask them some questions. After a bit ask them questions without the sheets and if they can’t answer immediately encourage them to step through the tables (10 20 30 40 …).

Answering questions helps build and strengthen the associations (between questions and answers), which are the basis of learning. Short sessions means it should never get too much. Regular sessions help ensure what has been learned is not forgotten, but rather is consolidated.

Once your children have learned one table move on to the next, but keep asking questions about the tables they have already learned in case they become forgotten.

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Learning Times Tables