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Real Number System Activities

Looking for a fun hands-on real number system activity to help students learn the difference between integers and irrational numbers?

Activities for Visualizing the Real Numbers

Real Number System Nesting Boxes

three colorful boxes stacked one on top of the other with text "real number system nesting boxes"

Build a set of DIY nesting boxes to help illustrate the real number system to students. When the integer box fits inside the rational number box, students will be able to visually see why every integer is a rational number but every rational number is not an integer.

Real Number System Graphic Organizer

graphic organizer of the real number system

This graphic organizer attempts to capture the same illustration of the real number system as the nesting boxes with a 2D diagram.

Real Number System Projects

Real Number Line Project

real number line project

Students must construct a number line with a specified number of natural numbers, integers that are not whole numbers,, irrational numbers, and rational numbers that are not integers.

Activities for Classifying Real Numbers

Real Number System Card Activity

real number symbol on top of index card on orange background

I created this set of real number system cards several years ago to give my students much-needed practice determining which subsets of the real number system a number belongs to.

Always Sometimes Never Dice Activity for Real Number System

photograph of colorful dice with text "always? sometimes? never? real number system dice activity."

I created this always sometimes never dice activity for classifying numbers according to the real number system. We completed this after sorting numbers using our Real Number System Nesting Boxes. I always hated Always, Sometimes, Never questions when I did them as a geometry student in high school. But, I decided to give it a try with my students.

Subsets of the Real Numbers Graphic Organizer

subsets of the real number system graphic organizer.

Use this subsets of the real numbers graphic organizer to help students keep the definitions for natural numbers, whole numbers, integers, rational numbers, and irrational numbers organized.