Saturday, July 28, 2012

Gang Violence and Adding Integers

This is my borderline inappropriate way to teach integer addition to students. It was inspired by a presentation I saw by Dr Kadhir Rajagopal on solving equations (NCTM 2009, DC). Check out his website here.

Algebra tiles are a great way to teach integer addition. But I like to represent positives and negatives as members of two rival gangs.
The yellow gang member is basically the same as a yellow algebra tile (+1) and the red gang member is the same as a red algebra tile (-1). Yellow gang members get along with other yellow gang members. Same goes for the reds. But when a yellow and red meet up, bad things happen.
To a 13 year old child, this explanation is much more satisfying than some nonsense about "zero-pairs". And when one of my students is confused about an addition problem, all I have to say is "gang violence", and they know exactly what to do.

Say a student is presented with a problem like this: -4 + 7. I have to ask two questions: Which gang will win? (the positives) How many will be left? (three)

To me, this is much better than some silly rule that students have to memorize. They are visualizing the numbers. And they are seeing positives and negatives as opposites that cancel one another out. And best of all, they remember it.

Credits: Graphics are from the Smart Notebook software. I'm sure the people at Smart Technologies appreciate that I've found this use for them.

Nathan Kraft


  1. Fun analogy. MS kids are a blood-thirsty lot, aren't they? Question: is there a way to extend your analogy to subtraction of integers? That seemed to be the sticking point when I taught that topic a few years back.

  2. Thanks for the question Anna. Personally, I'm not crazy about using algebra tiles (or gang violence) to demonstrate subtraction. I tried bringing in the zero-pair idea using "gang zombies", but that didn't make a whole lot of sense. I'm sad to say that after all of the explanation, I teach the kids KFC (Keep the first number the same, Fix the minus to a plus, Change the last number to its opposite). Not only is it easy to remember, but they like it because it is also one of their favorite fast food restaurants.
    I think the most important thing about subtraction is that students understand that it is the same as adding the opposite of a number.

    1. Yup, I wanted to tattoo "change subtraction to adding the opposite" on my forehead at one point, I seem to recall. Have you seen the "cold cubes/hot cubes" analogy from the IMP series? It's not nearly as fun as warring gangs, but works for both adding and subtracting integers.

  3. At my school -- but I'm sure we stole it from somewhere else -- we do something similar for adding integers, but the violence is a bit more cartoonish: "ninjas" for negatives and "pirates" for positives.

  4. Ah....Mr. Kraft I saw your post on I Speak Math about your techniques for explaining integer subtraction. You inspired to add your blog to my google blog reader, and now you say you resort to the dreaded KFC or folks down here say KEEP, CHANGE, CHANGE method, and you just made me cuss out loud! Lol...I HATE that way. I totally dig the gang violence technique so rest assured I'm going to use that. I just hate using additive inverse because I feel it takes away from kids seeing addition as addition and subtraction as subtraction. I hate zero pairs too, so kudos to you for thinking it's nonsense as well.

    1. I completely understand what you're saying, but for some kids, they just don't get some things conceptually. At the end of the day they need to be able to subtract, and tricks are what usually get them there.
      I think there are a lot of things I've learned initially as a rule/trick and was able to understand it on a more conceptual level later. And I don't think there's anything wrong with that. I think it's important that we show students both sides (procedure/concept) with the hope that someday they'll understand both.
      The real problem is that too many teachers only focus on the procedures. These are the same people that complain that students don't think when it comes to problem-solving. Well, duh.