Monday, April 19, 2010

The Rainbow Rule

A couple weeks ago Sam urged people to talk about little tips and tricks done in their classrooms.  Since I found THE CLAW so helpful, I thought it would be only fair if I shared a trick of mine.

The Rainbow rule, a Sweeney original, is my favorite as it's useful for all of my classes from Algebra 1 to Honors Calculus.

Whether my algebra students come across this...

or my calculus students come across this...

...they either don't seem to know how to do it, or are confident about doing it the wrong way.

 Enter the rainbow rule:
Since we don't all have the luxury of excess time and image editing software when working out problems, the actual version looks and works like this:
This rule has been very helpful for my students because it gives a name to this situation which is both easy to remember and helps to avoid the common mistake of crossing the two lines (rainbows don't do that, after all).  While not every students gets it totally right, it still has really improved my students' ability to deal with fractions, especially those who I've had for more than a year.


  1. I do this too! I don't call it rainbow, though. I like rainbow better! Thanks.

  2. Thanks for sharing. My students will be able to remember this easily!

  3. Wow! This is the first time that I have seen this technique. I'll remember this! Thanks!

  4. I think this will help my students so much more then the standard "keep change flip!" Thank you!

  5. I've been doing this for years as IP/OP (Outside Pair over Inside Pair). It's a great trick for getting questions right, but they have to remember to turn a traditional divide by question into a fraction over a fraction. Sometimes with students who are having trouble with math, the reason for that doesn't stick. I suspect that it may feel counterintuitive to students having trouble with fractions to make mega-fractions.