How to Teach the Commutative Law at Home

As a former math teacher (now a homeschool dad)... I’ve seen plenty of kids struggle with math rules that seem obvious to adults. The commutative law is one of those concepts that can trip kids up, even though it’s simple: the order of numbers doesn’t change the result when adding or multiplying. In my house, I make sure my kids not only understand this rule but also see why it matters.

The Basics of the Commutative Law

The commutative law applies to addition and multiplication:

• Addition: 3 + 4 = 7 is the same as 4 + 3 = 7
• Multiplication: 3 × 4 = 12 is the same as 4 × 3 = 12

Subtraction and division don’t follow this rule, which is something I make sure my kids know right away..If they try to swap numbers in 10 – 4 or 10 ÷ 2, they’ll get completely different answers.

Real-Life Examples That Work

I try not to waste time with textbook definitions. Instead, I show my kids how this rule works in everyday life:

• Stacking objects: If I have three apples and then add four more, it’s the same total as adding four first, then three.
• Grouping toys: Lining up two groups of blocks helps them see that no matter the order, the total is the same.
• Multiplication with items: If I arrange three rows of four pencils or four rows of three, there are still 12 pencils in total.

Multiplying More Than Two Numbers

When kids move beyond basic facts, they need to know the commutative law still applies. If we’re multiplying three numbers, it doesn’t matter which two we start with:

• Example 1: 2 × 4 × 6 = (2 × 4) × 6 = 8 × 6 = 48
• Example 2: 2 × 4 × 6 = 2 × (4 × 6) = 2 × 24 = 48

One super important tips I can share with you guys is to get your kids to experiment(!) I’ll give them different sets of numbers and have them try out different groupings to see for themselves that the answer stays the same.

Why This Rule Matters

In short, she commutative law is a shortcut that makes math easier in the long run. If my kids know they can switch numbers around, they don’t waste time doing problems the hard way.

Math doesn't have to be about memorizing rules, it’s more important that we understand why numbers work the way they do. The commutative law is one of those rules that, once it clicks, makes everything else a little easier.