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The order of addends doesn't change the sum: 3 + 5 = 5 + 3 = 8. Recognizing this property reduces the number of facts to learn (if you know 3 + 5, you automatically know 5 + 3) and supports mental math strategies.
You already know how to add numbers within 20. Now here is a big insight: it doesn't matter which number you start with. If you have 3 red apples and 5 green apples, you have 8 apples total. But if you count the green ones first and then the red ones — 5 and then 3 more — you still get 8. The commutative property of addition says that switching the order of the two numbers you're adding never changes the answer.
Think about it with objects. Put 4 blocks on the left and 2 blocks on the right. Count them all: 6. Now move the groups — 2 on the left and 4 on the right. Count again: still 6. The blocks didn't disappear or multiply — you just looked at them from a different direction. The total is always 8 (or whatever the sum is), no matter which group you count first. This is what "commutative" means: you can commute (swap) the addends back and forth.
Here is why this is a superpower for learning addition facts. Suppose you already know that 7 + 3 = 10. The commutative property tells you, for free, that 3 + 7 = 10 too. You didn't have to memorize a separate fact — you got it automatically. This cuts the number of addition facts you need to memorize roughly in half. Every fact you learn comes with a partner: 6 + 4 gives you 4 + 6 as a bonus. When you see a new addition problem, always ask yourself: do I already know this one in the other order?
This property also helps you pick the easier path when adding mentally. If someone asks you to solve 2 + 9, you might not immediately know that one. But if you flip it to 9 + 2 — starting from 9 and counting up 2 — it becomes easy: 9, 10, 11. The commutative property lets you rearrange the problem to match your strongest strategies. You will keep using this idea all the way through school; it applies to bigger numbers and eventually to variables in algebra too. But the core idea is already here: order doesn't matter when you add.