Commutativity

Hello!

Today's top tip: Times Tables are Commutative!

Although a daunting word, the concept of commutativity is simple:

It means changing the order, doesn't change the result.

This is true for multiplication and addition.

Whichever way you write the multiplication (or times table), you'll get the same result:

4 x 8 = 8 x 4

4 x 8 = 32 and 8 x 4 = 32

This is really helpful to remember when children are learning their times tables!

Often, they find some times tables trickier than others.

For example: 7 x 3

The 7s are tricky! But if they remember that multiplication is commutative, then it becomes much easier. 7 x 3 = 3 x 7

This can really help as they will probably be more confident in their 3s.

And therefore know that both answers equal 21!

It is a vital step in children's understanding of number and calculations, to be able to independently spot patterns and make associations, such as commutativity.

Commutativity is also true for addition: 6 + 5 = 11 = 5 + 6

However it does not work for subtraction or division!

This is important to remember when children are asked to complete Fact Families.

This is when you're given three numbers and need to find all the associated number facts, in this instance two multiplication and two division facts. It's useful in understanding the inverse (opposite operation).

For example: Find all the facts for the fact family: 4, 6, 24

Knowing commutativity means they can easily spot the two multiplication facts:

6 x 4 = 24 4 x 6 = 24

They should also be able to spot a division fact:

24 ÷ 4 = 6

Then they need to be careful, because division is not commutative. We cannot just change the order:

4 ÷ 24 ... does not equal 6!

They need to remember for division, to always start with the Whole (the biggest number).

24 ÷ 6 = 4

So, all four facts in the fact family 4, 6, 24 are:

6 x 4 = 24 4 x 6 = 24      24 ÷ 4 = 6      24 ÷ 6 = 4

A fun way to remember what commutative means:

It's like commuting to and from work or school. You go and you come back!

Have a look at my other blogs for specific Times Tables tips, and some fun games and activities to support your child's practise.

Feel free to drop me an email or book a free call for any specific help you might want or if you'd be interested in booking tutoring or home-education lessons for your child.

I look forward to starting our learning journey together!

Alice

TT - Commutativity.pdf

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