Kiss those Math Headaches GOODBYE!

We all know that one of the trickiest subject for many students is the subject of combining integers.

I’ve hit on a new way to help students with this topic, a way that involves using color.

Using different colors helps students relate similar concepts and separate different concepts. Color works faster than underlining or drawing rings around numbers, it’s more attractive, and it makes a student’s page fun to look at, too.

Here’s just one example of how using color can help students make sense of those oft-bewildering positive and negative numbers.

Take a problem like:   + 3 – 7 + 6 – 9

Many students get confused by a problem like this because they don’t have the least idea of what to do first.

But when you use color, tell students that the first step is an easy step:  just re-write the problem, making the positive numbers red, and the negative numbers blue, like this:

The next step is equally easy … group the positives on the left and the negatives on the right. I use my handy-dandy “double-slash” divider to show the separation, like this:

After that, use the rule for combining integers with the same sign (here you can say “with the same color!”), like this:

At this point you depart from color, as you combine the integers with different signs, and you get the answer, like this:

All together, it looks like this:


I have found this approach extremely helpful for those students — and you know the ones I’m talking about — who just struggle endlessly with these rules. 

By the way, if you’d like to see the chapter of my Algebra Survival Guide, which explains the “Same-Sign” Rule and the “Mixed-Sign” Rule, just go to this page and scroll down about half-way down till you come to the link for downloading chapters:

Please try this out yourself and feel free to let me know how it goes. I’m always open to feedback.


Comments on: "Color Your Way to Integer Success" (2)

  1. Annette Tiff said:

    Josh, Thank you very much for writing Algebra Survival Guide. I am a High School Special Education Teacher and love your book. It has helped me to teach Algebra to my students. I also love your idea of using color to teach Algebra. It would be great if you wrote a book on using color to teach the concepts of Algebra. Most of my students are on the Autism Spectrum and learn best with visual instruction. I would love to see your examples in the above example of Color Your Way to Integer Success. For some reason, I am not able to see your pictures. Thank you Annette


  2. Tanara Block said:

    I am just wondering, I find all this very interesting and also possibly quite helpful for my remedial math students that I tutor. In this particular post, I was unable to pull up any of the pictures that correspond, would I be able to get an email copy of them or something so I could visualize what you are saying? I really appreciate it, thanks!


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