The commutative property for Addition states that “it makes no difference in which order two numbers are added.” (Van De Walle, 2007). The sum remains the same. Therefore, 2 + 4 = 4 + 2. There are fun ways to teach this to six-year-olds. We used two-part mats and blocks to start. They put some blocks on one side and some on the other side then they stated their number sentences. Then they turned the mats around and stated the new number sentence, reading from the left. We did this for a while and they enjoyed testing the theory with several different number combinations. Some of them wanted to try it with three numbers and even four!The lesson progressed throughout the week and we moved on to using the symbols. So, I presented addition stories to them and they wrote the number sentences to match, observing the commutative property in action. Many realized that once they solved one addition problem, they didn’t have to count for the other one. They matched pairs of sentences and created their own stories and number sentences to match.
Some refer to this property as the ‘turn around’ method because these are the words children usually use to describe what they are doing. So, after all the exploration I presented a number sentence to my class and asked them to tell me the corresponding number sentence. “Just turn it around,” I said. One dear child proceeded to turn his entire exercise book around.
I calmly explained to him that there is a difference between literally turning a mat with blocks around and turning a book with numbers around. The numbers would be upside-down and you will not be able to read it. On and on went the calm explanation about what we mean when we say “turn around” the numbers. There was eventually some enlightenment in his eyes.
Yet another lesson: taught by the student; learnt by the teacher.