Classifying real numbers is a topic that seems so simple, but can be so confusing for students at the same time. I mean, math is about numbers, right? Why do we have to give them names? It is important for students to be able to understand the difference between rational and irrational numbers as it will help them with further calculations. My students often struggle initially with being able to determine what numbers make up rational numbers. We did a lot – played games, used a graphic organizer, did vocabulary activities, etc. After a few days, it still seemed to be a difficult thing to grasp. I wanted to find a way to be able to provide another visual representation to help with their overall understanding of what numbers make up a rational number. I finally thought of something that worked! Here’s what I did…

First I gathered some materials. I got a few plastic cups (5 cups, to be exact), scissors, a permanent marker, and a pingpong ball (not pictured).

I cut the bottom off from three cups to create an opening in the cup. Then, I labeled each cup with the following words:

* Irrational Numbers (closed bottom cup)

* Rational Numbers (closed bottom cup)

* Integers (opened bottom cup)

* Whole Numbers (opened bottom cup)

* Natural Numbers (opened bottom cup)

I also included a few examples of each of those numbers on the cups.

When I got to school, I taped the cups on my whiteboard in the order that is shown below:

When the students came in, their warm-up was to classify a few numbers. We went over this using the cups. For example, I asked them what the first subset of real numbers the number six belonged to. When they told me ‘natural numbers,’ I used the ping pong ball and dropped it into the natural numbers cup. Then, the ping pong ball made its way down to the rational numbers cup. We talked about how it traveled through the whole numbers, integers, and rational numbers cups; which shows how six is classified as all of those subsets of real numbers.

We also discussed what we saw with the visual. We had a very good conversation about how rational numbers and irrational numbers are in two separate places. Students were able to really differentiate between a rational and irrational number after this activity. They also had a lot of fun dropping the ping pong ball through the cups!