Double sided counters are my all-time favorite way to teach adding and subtracting integers. I love it because I teach it as a game, which I call integers war. But unlike the version of integer war that uses red and black playing cards to review integer operations, this game actually teaches the concept of adding integers. In fact, all I have to do is quickly review the concept of zero pairs, and then I let my students figure out the rules for adding integers on their own.
First off, you’re going to need some two-colored counters. I have students title a page “Integers War” in their notebook and make three columns, labeling the columns as Positives, Negatives, and Score. Students play the game in partners. Each pair of students will need around 10 counters total.
To play the game, when it is your turn, you pick up all ten counters, shake them, and drop them on the desk. You find your ‘score’ by eliminating all of the zero pairs. If the chips left over are negative, then the score is negative; if the leftovers are positive, then the score is positive. The student whose score is closest to zero wins the round. I always model the whole process on my document camera before I set students loose. It really drives students crazy if they have to play with an odd number of chips, so the sadistic part of me makes them do this every now and then just to watch them get annoyed. Ha!
I set a timer for 5 minutes and students play as many rounds as they can. I wander and check work. I’m very picky about making sure that they put negative signs next to all of the numbers in the negative column and I also am picky about them labeling their scores as either positive or negative.
After the five minutes is up, we pull it together by talking about adding negative numbers I give them a problem or two and ask questions like this:
- Are there more positives or negatives? Why is it important to know that?
- How many more positives/negatives are there?
- What would -2 + (-5) look like? How many zero pairs are there? How many negatives are there in all?
I repeat those questions all year long, whenever adding integers comes up in a problem. Pure magic. Most of them are able to come up with the ‘rules’ on their own from here, which is great! If they develop their own rules or algorithms as a result of this activity, then I know that the rules are based on solid conceptual understanding of integers and zero pairs, and not just random procedures that they were told to memorize.
My favorite part of this game is that is the perfect set-up for solving one-step equations with Hands on Equations. First thing I did when I got my Hands on Equations sets was to ditch the dice in the sets and replace them with double sided counters. That way students can actually see what it looks like to make a zero. Love it!