Wednesday, March 14, 2012

Relational thinking about numbers

Today I asked three kindergarteners to figure out whether a bunch of number sentences were true or false. I was partially inspired by an excellent book called Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School by Carpenter, Franke and Levi.

Here is what I gave them:

11 + 3 = 12 + 2

14 + 1 = 13 + 2

19 + 4 = 19 + 3

4 + 4 + 4 = 4 + 4 + 3 + 1

4 + 4 + 4 = 8 + 4

23 + 5 = 25 + 3

47 + 62 = 62 + 47

10 + 10 + 1 = 1 + 20

5 + 5 = 5 + 5 - 2

30 - 2 = 20 - 2

10 - 9 = 9 - 8

We didn’t get to the last 3 on the list yet, but not because of a lack of enthusiasm. The kindergarteners loved this activity and can’t wait to have a chance to finish it. They worked independently to decide whether they thought each one was true or false. Then I simply asked them “How did you know?”. If they decided very quickly - quicker than they could have done a calculation for each side of the equal sign - I asked in amazement if they would explain their thinking. I also asked them to prove their answer was correct. This work really got them thinking, not only about the meaning of the equal sign but also about relationships between numbers and properties of addition and subtraction.