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Times tables

Why do we teach children times tables in primary school?

Sometimes we have to go back to basics to remember the reason we’re teaching something. The answer here is not just so that they can pass their Year 4 multiplication tables check!

There are three overwhelming reasons we need children to prioritise their times tables skills at primary school.

 

1. Times tables are fundamental to many maths topics

Fractions is the most obvious area where learning times tables well is essential. However, all short multiplication and long multiplication methods and short division and long division methods require speed and instant recall of times tables while at primary school. At secondary school the needs become even greater.

Times Tables are central to KS2 Maths and need to be embedded by Year 4 in order that pupils can then start practising for the next two years. Otherwise, if you don’t teach times tables early and well in Key Stage 2, you’re just storing up problems for the Year 6 teacher trying to prepare pupils for KS2 SATs.

2. Freeing up working memory allows pupils to develop their reasoning skills

There are certain mental maths facts and operations children need to be able to carry out quickly and with a degree of automaticity in order to free up their working memory for newer, more challenging tasks at hand.

If we can ensure the transition of times tables facts to children’s long term memory and times tables can become an instantly recallable fact the working memory can be freed up for reasoning.

All children need to go through these cognitive steps in order to achieve this. Some will only need a light touch whilst some will need significantly longer on particular points.

3. Multiplication and division feature very highly in the KS2 SATs reasoning papers

Many of the end of Year 6 maths reasoning questions in the KS2 SATs seem to necessitate the use of multiplication facts and related division facts by the children in order for them to simplify complex questions.

 

Teaching times tables facts first

Children need to understand and know these facts about how times tables work before they start learning them.

1. Repeated addition

4 x 5 is the same as 5 + 5 + 5 + 5. 

Children need experience of using concrete maths manipulatives such as counters or multilink cubes and pictorial representations of objects, forming arrays.

Read more on the importance of concrete pictorial abstract here, and how to use it.

2. Multiplication is commutative

4 x 5 is the same as 5 x 4.

Children build on their existing understanding using arrays, turning the arrays around to show that you now have 5 groups of 4 and they will still total 20. This can then be linked to recalling multiplication facts, i.e. if they know their 5 times table as facts but not their 4 times table, they can use 4 x 5 to work out 5 x 4. This link needs to be made explicit.

3. Multiplication is the inverse of division

20 ÷ 5 = 4 can be worked out because 5 x 4 = 20.

Again, the use of arrays is key. Children need experience of pulling arrays apart into groups or sharing. After basic experience has been gained, the children should start to ‘see’ an array structure as 5 groups of 4 equal 20 and 20 can be split into 5 groups of 4.

A Third Space Learning Year 2 lesson on the relationships of multiplication and division facts

4. Number families

4 x 5 = 20, 5 x 4 = 20, 20 ÷ 5 = 4, 20 ÷ 4 = 5

Due to their commutative understanding, by now children should also be able to see whole number families. For many children this will need to be pointed out and discussed. Most children will be able to explore this in its abstract form but if in doubt, go back to arrays.

From here it is only a short jump to understanding that any missing number can be worked out through knowledge of number families, e.g. 4 x [ ] = 20 or [ ] ÷ 4 = 5. There are other methods children can use to work out missing numbers but our goal is to increase working memory in order to increase instant recall from long term memory. Being able to bounce around a number family will achieve that.

 

10 fun tips for teaching times tables effectively

1. Use times tables chanting

This is a simple yet effective way to drill multiplication knowledge into your pupils . It may not be the most glamorous and exciting way of teaching times tables, but it is a great place to start!

2. Make times tables fun with songs and multiplication games

Our favourite times tables song is Schoolhouse Rock’s ‘3 Is A Magic Number’ and we’ve got lots of fun times tables games in this blog post.

3. Make use of times tables grids

It might be a simple technique, but it is one that works! Hand out times tables grids to your class and get them to fill them in. Not only will they enjoy the challenge of filling in a times table grid but it will encourage them to practise, practise, practise!

4. Use concrete resources

It doesn’t matter whether it is pasta, counters or even coins, just having a concrete resources to help pupils work out times tables can be massively beneficial.

5. Get active outside the classroom

Our times tables pavement chalk activity above is just one of the outdoor maths ideas could use to make times tables learning more active and therefore memorable for your class.

6. Use pupil’s interests to engage them with times tables

Use the carious interests your class will have to help teach times tables. One of our favourite examples of this is the BBC, who have found a way to use football mascots to teach times tables.

7. Use tricks that may be common knowledge to us, but will be revolutionary to young minds

You are well aware by now that you can do the 9 times tables on your fingers, but your pupils may not be just yet!

8. Use quick fire times tables quizzes

Whilst you shouldn’t make quizzes regular feature, they can be a great way to help pupils get to grips with their times tables. Got 5 minutes spare when walking to swimming lessons? Get a quickfire times tables quiz in. There is always an opportunity to fit a quick times tables quiz in around school.

9. Ask short division based questions

Simple division questions such as “55 divided by 11” and “30 divided by 3” can help pupils realise that times tables and division are closely linked, and can be used in tandem when trying to solve a maths problem.

10. Use times tables worksheets and tests

Your class will rebel if you use these too often, but regular quizzing with times tables tests that children mark themselves can help you and they build up a picture of their overall strengths and gaps in their times tables.

And finally…reward pupil efforts regardless of the answer

Nobody is perfect when they are just beginning to learn about something, and this is definitely the case when it comes to times tables and primary school pupils. Don’t be afraid to hand out praise when you see that a child has been working hard in their times tables, even if they haven’t quite got the answer yet.

National Curriculum Breakdown of Expectations for year groups

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