Ever found yourself staring at the curriculum, wondering if the commutative, associative, and distributive laws are some kind of mysterious mathematical code? Trust me, you’re not alone. I vividly remember my early teaching days, grappling with these seemingly cryptic concepts. I’ll confess – back then, I might have skimmed over the content descriptor, hoping it wouldn’t come up too often in class simply because I didn’t quite get it myself.

But fast forward a decade, and now I LOVE teaching the number laws and I have seen first-hand students improve leaps and bounds in their mental computation all because… I took the time to understand it myself! 

Today I have a step-by-step lesson for how you too can teach the Three Laws of Number Computation.

Let’s start with Commutative Law!

This is the easiest and quickest for students to grasp so I always start here.

To gain students engagement I start with a sum on the board and ask students to EXPLAIN how they came to their answer. Students will always use different strategies to solve multiplication problems.

Use this as the introduction into learning a new strategy. Students will have already been taught the commutative law although they most likely would not have called it this.

Commutative law of multiplication means that when you multiply numbers, the order does not matter, the product (answer) will be the same.

Quite simply put – you can swap the numbers around and the answer will be the same! This is why I nickname it “The Swap It” Law.

To finish the lesson, I give the students an inquiry question – Does this law work for any of the other operations or only multiplication? I do a quick raise your hands if they think it applies to subtraction… addition… and division. Students then prove if does or not. Helpful hint: the law only applies to multiplication and addition!

I combine commutative and associative laws into the same lesson. Mainly because they are strategies that have been previously taught during the earlier years.

Associative law requires prior knowledge around factors and multiples, I like to do some warm ups around identifying factors of numbers! My favourite is the use of student whiteboards – simple, fun and low prep! Simply write a number on the board and ask students to write down two factors (numbers that when multiplied together will equal the number on the board) and chin show – student whiteboard under their chin so you don’t have 35 whiteboards being waved around the room!).

By changing the groupings of the numbers that are being multiplied together does not change the final sum.

By breaking up BIG numbers into their factors you can re-group number sentences to make it easier to manually calculate the answer! I nick name this law “Group Them!”

Use the associative law to solve this sum : 15 x 8

Let’s break it down into steps:

Now for the trickiest law but 100% the most fun!

I like to nickname this law Break it Up!

“The distributive law is used to simplify multiplication problems by breaking apart or distributing the factors of a sum into smaller amounts – tens and ones.”

See why I nickname it Break it Up?

Best explained through examples, so let’s go!

5 x 36

This will need to be practiced multiple times for students to understand the concept – I also like using the visual method to cater for our visual learners in the class! Check it out in the picture above!

If you have any questions, please reach out I’m always happy to help! Also, if you want to save some of your precious time – I have a PowerPoint that comes with a detailed lesson plan and the matching worksheets!