How do you explain to a student new to algebra the importance of the commutative property? Giving an example of the opposite of course! Putting on shoes and socks are an example of a non-commutative operation. Putting socks on bare feet and shoes over the stocking feet is a completely different outcome than putting shoes on bare feet and socks over shod feet. The commutative property is very much dependent upon whether the order of doing something matters or not. To help a student with new mathematical concepts, do your darnedest (heh sock humor) to tie the concepts to something concrete, tangible, and memorable/ridiculous. Paying for an item in cash is an example of a commutative operation. If an item costs $21, the vendor will not care if you pay with a twenty dollar bill and then a one dollar bill, or a one dollar bill and then a twenty dollar bill. Finally a simple addition problem like 199 + 198 + 202 + 201 will hammer home that choice of order of addition can make a problem much easier.