How to teach addition is commutative

Try this hands-on arithmetic investigation to show your children that addition is commutative and teach them that you can add up numbers in and order.

How to show kids you can add up in any order

This activity, from our Fun Math curriculum, will allow your child to discover that addition is commutative: it can be done in any order.

2 + 3 is the same as 3 + 2.

This concept is very important to understand, for your child’s current addition learning, quick mental totalling, and when your child moves into more complex arithmetic and algebra.

In this activity, your children can:

:: practice counting

:: practice addition

:: learn that addition is commutative: it can be done in any order. 2 + 3 is the same as 3 + 2

Materials needed

:: various small items in distinct groups (for example, green leaves and brown leaves or red blocks and yellow blocks or toy cars and toy dinosaurs)

:: chalk or pen and paper or hula hoops

How to introduce the lesson

Draw two circles on the floor using chalk, or on two sheets of paper using pen, or set out two hula hoops in the floor.

Explain that you’re going to put some of your items in each circle and add them up.

Have your child put, for example, three toy dinosaurs in one circle and two toy cars in the other. How many toys are there altogether?

Three plus two equals five.

Write down the sum to show it in digits: 3 + 2 = 5.

What about if you flipped over the toys in the circles? Would you still have the same answer?

If you counted the cars before the dinosaurs would you still end up with five in total? Try it and see.

Two plus three equals five.

Write down the sum to show it in digits: 2 + 3 = 5.

Exploring the commutative nature of addition

Does this work with all numbers? Empty and refill the circles with various numbers of toys and add them up.

Flip them and add them again.

Write down the two pairs of sums each time, to show them in digits and to re-inforce the flipping of the numbers making no difference to the total.

You can add up in an order!

Addition is commutative.

Extending the activity to add three amounts

You can extend this by using three circles and mixing up the order in which you add them.

You can go big and have as many circles as you like!

Whatever order you add them up in, doesn’t matter.

Comparing addition with subtraction

It is also important to understand that subtraction isn’t commutative. It IS important to keep the numbers in order when taking away.

You can use your toys to illustrate this too (as part of this activity, if your child is ready, or later when you are focussed on subtraction skills.)

Try the experiment with 5 – 3. Have your child make a pile of five toys, then give you three.

How many left? 5 – 3 = 2.

Can you flip them and get the same answer?

Have your child make a pile of three toys and then give you five. Uh-oh! You don’t have enough!

3 – 5 doesn’t leave you with two toys – you don’t have enough to do the sum.

Subtraction isn’t commutative: you can’t flip the numbers.

It will be very important to keep this in mind when working on more complex subtraction, especially when working with word problems where you need to work out the correct calculation to use to solves the problem.