## Luke & Brad Discover a New Subtraction Algorithm!!!!

19 Feb

Yesterday I put this problem on the board and asked the students to solve it with mental math:

72 – 9=

I was hoping to get a strategy like using 10:

72 – 10 = 6 2+ 1 = 63

An some students did come up with that.  But Luke came up with the following, and it was an accident.  He accidentally did what many students do and he subtracted the minuend from the subtrahend instead of the reverse – but it worked!

This image will explain the terms for subtractions numbers:

At first I couldn’t figure out what he had done but Bradley understood it.  We tried some different equations to see if they worked and they did!  We still couldn’t really explain it though so I brought it to the staff room where five of us looked at it and tried it out with different numbers (and we tried double digit numbers which also worked!).  We figured out that they were subtracting in stages or using algebraic methods.  Watch the videos to see what I mean.

and this is their explanation

The explanation that makes the most sense to me is the algebraic way:

(72-2) – (9-2) =

70 – 7 = 63

Because the 2 was subtracted from both the minuend and the subtrahend, the difference is the same.  Or you could look at it like this:

9-2 = 7

70-7 = 63

Subtracting the 9 in stages, first 2, then the remaining 7.

Super Cool!!!!  It’s so true that when students come up with their own ways to solve problems their understanding is so much deeper.  These two are examples of that constructivist theory.  If we had more time for math, imagine the possibilities for all students!

Has anyone else seen a student solve a subtraction equation this way?  I’d love you comments please.