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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 + 214 + 1 = 13 + 219 + 4 = 19 + 34 + 4 + 4 = 4 + 4 + 3 + 14 + 4 + 4 = 8 + 423 + 5 = 25 + 347 + 62 = 62 + 4710 + 10 + 1 = 1 + 205 + 5 = 5 + 5 - 230 - 2 = 20 - 210 - 9 = 9 - 8We
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.