Q&A: How to Explain Commutativity of Addition to a Kid

Cross-posted from here.

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Question

In primary school, it’s extremely easy to show that $a \times b = b \times a$ because the area of a rectange does not change when you flip it. But how can you show that $a + b = b + a?$

Answer

Suppose you have $a$ crayons in your left hand and $b$ crayons in your right hand. All together, you have $a+b$ crayons.

Now you switch hands. You now have $b$ crayons in your left hand and $a$ crayons in your right hand. All together, you have $b+a$ crayons.

You haven’t put any of the crayons down, so the number of crayons you have hasn’t changed.

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