We're doing a little unit on the properties of addition, since it's one of the categories in the Splash Math 3rd Grade app that Will's trying to zoom through and finish up before I download the fourth grade app for her.
I would like the girls to be able to define and understand each property of addition, so I downloaded and printed these properties of addition flash cards for the girls to memorize, and we're also doing several hands-on activities to demonstrate each property, such as this one, in which the girls used Cuisenaire rods to "prove" the commutative property of addition:
Using centimeter-gridded graph paper and our Cuisenaire rods (which are also counted in centimeters, so they match!), each kid illustrated and wrote one addition equation--
--and then illustrated and wrote its commutation right above or below it:
Using the graph paper and Cuisenaire rods, it's easy to see that each equation is equivalent.
This wasn't a surprise to the girls, of course, but rather something that they perhaps hadn't necessarily spent time thinking out for themselves, so they were happy enough to write out a few examples. I've got a couple more hands-on activities to demonstrate the property, and then we'll add the flash card to our Memory Work Binder, to be quizzed on and recited from a couple of times a week until it's old, old news.