### Look for and Express Regularity in Repeated Reasoning… in Math!

My class was working on coming up with the "rules" for multiplying integers. First, they used what they know about repeated addition (and rules for adding integers) to answer these problems.

Next, they cut apart the cards and sorted them into 3 categories… those that resulted in a positive answer, negative answer, and answer of 0. Then I had them look at each category (one at a time) and report out anything they noticed in the problem that they could use to predict if the answer would be positive, negative, or zero. My goal was to have them discover the rules that I used to just tell them:

positive x positive = positive

negative x negative = positive

negative x positive = negative

positive x negative = positive

anything x 0 = 0

0 x anything = 0

In the past, I might have just wrote this on the board, talked a lot, and expected student to apply the rules. Having students do this "card sort" and come up with the rules themselves really helped them to make sense of the r…

Next, they cut apart the cards and sorted them into 3 categories… those that resulted in a positive answer, negative answer, and answer of 0. Then I had them look at each category (one at a time) and report out anything they noticed in the problem that they could use to predict if the answer would be positive, negative, or zero. My goal was to have them discover the rules that I used to just tell them:

positive x positive = positive

negative x negative = positive

negative x positive = negative

positive x negative = positive

anything x 0 = 0

0 x anything = 0

In the past, I might have just wrote this on the board, talked a lot, and expected student to apply the rules. Having students do this "card sort" and come up with the rules themselves really helped them to make sense of the r…