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Real Number System Graphic Organizer

While looking for inspiration, I found a lot of creative illustrations of the real number system.  But, I was looking for something a little different.  I wanted my students to add the information. 

And, for my older students, I wanted them to even discover some of the information themselves before we added it to the graphic organizer as a class. 

So, I created my own real number system graphic organizer that would meet all my needs.

graphic organizer of the real number system

For my Algebra 2 students, I plan to give my students strips of numbers.  Each strip will correspond to one of the subsets of the real numbers.  It will not be labeled however.  I want them to take these numbers and try to figure out how they nest on to the graphic organizer. 

I’m hoping that they will discover for themselves that every natural number is a whole number, every whole number is an integer, etc. 

I ran across this in a pile of math resources I was given.  Something to think about:

Quote: "there was once an old teacher my grandfather knew who used to say... prepare your lessons so that your kids will discover the concepts you wish to present - then it will be their mathematics, and not yours. But my grandfather shortened this to - FINDERS KEEPERS. Both men were saying the same thing - the most fundamental maxim in teaching school mathematics."

I am using interactive notebooks with my Algebra 1 and Algebra 2 students.  So, I plan to have students glue the real number system graphic organizer in their INBs.

Real Number System Graphic Organizer for Math Interactive Notebooks
Real Number System Graphic Organizer in Algebra 1 Interactive Notebook.
Real Number System Graphic Organizer in Algebra 1 Interactive Notebook

I want the students to outline the boxes with colored pencils to emphasize the fact that everything inside the red box is an integer, even the whole numbers and natural numbers. 

Frayer Models for Definitions of Real Number System

So far, I just have definitions (Frayer Model) and a few examples.  Obviously, my final draft and sample notebook will be neater.  And, the rational numbers and irrational numbers are only a different color because I already had some printed on colored paper

In real life, they would either be all white or all different colors.  Trying to overcome my perfectionism here…

In 2013, I used the same graphic organizer for the real number system, but we filled it out slightly differently. It felt good to be able to reuse something from last year instead of creating something entirely new from scratch!

real number system graphic organizer

I ended up creating another version of the real number system graphic organizer.

blank real number system graphic organizer.

Free Download of Frayer Models (6 to a Page)

Frayer Model 6 to a Page (PDF) (4018 downloads )

You might also be interested in a graphic organizer I created for the subsets of the real numbers.


Wednesday 2nd of August 2017

You are inspiring. I

Sarah Carter (@mathequalslove)

Sunday 10th of September 2017



Tuesday 6th of September 2016

I absolutely love you! Thank you so much for sharing all your great resources.

Sarah Carter (@mathequalslove)

Tuesday 6th of September 2016

You're very welcome, Kelly!


Monday 10th of August 2015

I so love this thank you!!!

Sarah Carter (@mathequalslove)

Wednesday 9th of September 2015

You're welcome!


Wednesday 21st of January 2015

Great visuals. I teach 6th and have had some trouble using the Frayer models. The kids always have a really hard time with the Facts & Characteristics box. (And honestly, I do too...should I be admitting that?) Anyway, I wondered if you would share a pic of the inside of any of these models. Thanks!


Tuesday 19th of August 2014

So would I... :)

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