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  • Katrien Vance

    July 5, 2020 at 9:08 pm

    The idea that there are two types of subtraction, and that the numbers in the problem should determine one’s strategy blew my mind when I heard Jon and Kyle talking to Pam Harris on their podcast. It was a throw-away moment in a much larger conversation, but it made very clear how much I don’t know about fundamentals. I was like, “There are two kinds of subtraction?? What the heck else do I not know?”

    I believe that thinking about “difference” instead of “take-away” will make a big difference with my students when learning about subtracting integers. When I model subtraction of integers with manipulatives, I have to do this artificial thing of adding “zero pairs” to make it work. 6 – (-2) — I can’t take away -2, so I add two sets of positive 2 and negative 2, which is adding zero, and now I can physically take away -2, and that leaves me with 8 positive cubes. This often confuses kids more than it helps them because there is no point in writing down steps or in moving from the concrete to the abstract that we keep this step of adding zero pairs. So then kids just try to memorize without understanding.

    Imagine asking a kid, “What is the difference on the number line between 6 and -2?” Then the answer of 8 is easy. I’m less clear on how to model 6 – 8 as the difference between 6 and 8 — why is that -2 instead of 2? Again, a number line makes it clear, but perhaps this is just a good example of a time to use “take away” as opposed to “difference.”

    And, even as a fan of many paths and strategies, I have never in my life thought of adding the same number to the two numbers and making the problem friendlier, as you did with 1002 – 1000. Even when I think I know exactly what a lesson is going to say, you guys say something new to me!

    I am a HUGE fan of the idea of letting the numbers dictate the strategy, rather than relying on one algorithm to fit all cases.