I got the idea for this activity from something I saw in a science classroom. It takes the Venn diagram most commonly used to represent the real number system and breaks it apart for the students to see how the subsets interact. It comes with a worksheet that hopefully leads the students to make some conclusions about the system on their own (or with a partner).
It takes a long time to make enough sets for half the class, but it's worth it. If you laminate the parts (even more time), it will last for years. I laminated mine before using them and have used it for at least 4 years. The black mats are fading from sun exposure (chose a bad spot to store my items), but everything else looks great.
This document includes the pages to copy and cut to create the activity, the worksheet that goes with it, a page with pictures for the construction of the activity, and an answer key.
If you want to see how I used it in my own classroom, visit my blog at designsbysunshine.weebly.com. Click on the teacher blog.