A number is a number is a number

It's been years since I had to think about classifying numbers, and to be honest, I really don't think that I understood what the teachers meant about rational numbers, real numbers... I knew that an integer was a number that could be expressed in either a positive or negative form, but that's about it. I don't think I was alone in my ignorance. If you can get maturing generation x'er like myself to understand these concepts after years of misconception; how come it's so difficult to teach this to middle schoolers and high school kids. Okay, there are numerous reasons, but still... if I can get this, most people can with the right help.

Here's an image I made to show the relationships of the following types of numbers (are they called types?):

• Real Numbers
• Algebraic Numbers
• Rational Numbers
• Integers
• Whole Numbers

Rational numbers are algebraic real numbers. Rational numbers include integers. Integers include both whole numbers and their negatives. All integers can be presented or expressed in their rational form. For example:

• 3 can equal 3/1 or 30/10 or 9/3
• 2.5 can equal 3/2,
• -5 can equal -5/1, etc

It makes sense that kids, when then get into Middle School, they have difficulties understanding the other types of numbers outside of "whole numbers." They spent all of elementary school only focusing on how whole numbers function and are used. Honestly, I think it's because that's all that most elementary school teachers have been trained to teach (and feel comfortable with).