## Negative Subtraction

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I compose this blog while stretched out on a dorm bed at Yale University. I’m midway through my time at the Yale National Initiative’s Intensive Session as a College Faculty Member given my involvement with the Charlotte Teachers Institute. My time has been inspiring and thought-provoking.

Today, I visited the seminar Great Ideas of Primary Mathematics led by Roger E. Howe and Amanda Folsom. Michael Pillsbury, the seminar coordinator for the CTI seminar Math through Pop Culture that I lead, is a national fellow and creating a curriculum unit from the ideas of Howe and Folsom’s seminar. This week has afforded us wonderful opportunities to discuss mathematics and innovative ways to encourage students to delve deeper or broader into their knowledge of content.

Yesterday, Mike showed me an interesting variation on subtraction that connects to discussions that subtraction is the addition of positive and negative numbers. Let’s consider subtracting 359 from 746. First, we line the numbers up as we probably did in grammar school:

$begin{array}{lrrr} & 7 & 4 & 6 \ -& 3 & 5 & 9 \ hline ~ & ~ & ~ & \ end{array}$

With the standard algorithm, we would borrow to get:

$begin{array}{lrrr} & 6 & ^13 & ^16 \ -& 3 & 5 & 9 \ hline & 3 & 8 & 7 end{array}$

Such a method calls for an understanding or at least makes mechanical use of place value as we “borrow”. Consider Mike’s approach that calls for the use of negative numbers. This technique caught my eye and had me thinking about subtraction in a way that pulled me from my usual mechanical response to a problem.

$begin{array}{lrrr} & 7 & 4 & 6 \ -& 3 & 5 & 9 \ hline & 400 & -10 & -3 end{array}$

Now, simply add the numbers along the bottom row to get 400 + (-10) + (-3) = 390 – 3 = 387. Such a method sheds a different light on the method of subtraction and depending on your student’s outlook and mathematical preferences, might be most helpful.

Thanks to Mike Pillsbury of Randolph IB Middle School. If only I could infuse this blog post with the laughter and joy that comes naturally when learning it with him!

## 4 Comments

•   Jim Muller

I have always found it easier to “add” negative numbers when subtracting.

What I learned from your post is that I could use the Distributive Property to make it even easier. Thank you

746+ (-359) = 387 = 700 + (-300) + (-50) +40 + (-9)+6