Classifying Rational Numbers

I feel as though teaching classifying Rational Numbers to my 7th graders is probably not the most exciting lesson of their mathematics career.  There is no awesome Mathalicious lesson on it and most of the resources I have found are pretty dry and boring.  This is the story of how I developed an understanding of Rational Numbers without falling asleep.  If you have a suggestion on how to make it better I would love that!  I always struggle with this standard and making it come alive for kids.  I do however feel it is an important place to start in 7th grade.  Before we can really start to work with integers it seems logical to me that they must first understand different types of numbers and what integers really are.

The Hook

I always start the lesson with a blank venn diagram of the Real Number System on the board.  I have the kids call out numbers while I place them in the correct category.  The goal of the game is to get the students to figure out the characteristics of each group of numbers.  I provide rewards each time a student figures out a classification.  Generally the students repeatedly call out natural numbers and get frustrated when only the inner most circle is filled with numbers.  After a few minutes they usually branch out into the whole and integer categories but that elusive outer ring usually leaves them baffled.


It is always a major breakthrough when someone calls out that first rational numbers and then the kids start to pick up on the system more quickly.


And then once someone throws Pi into the mix if really starts to take shape:


Eventually after a lot of discussions the kids usually come up with descriptions for each category and I help add the vocabulary in.  




The Follow-Up

We followed this up with a sorting activity.  The students drew the Real Number System diagram on their tables and I provided cards with different numbers on them.  Students then worked in their groups to place each number in the correct category.  I provided feedback to groups as needed and asked guiding questions to help tables who were struggling.



As a separate follow-up activity we also completed the Is It Rational FAL activity found here.  What I love about that activity is that it really helps kids focus in on looking for the pattern in what really makes a number rational or irrational.  I feel like too many kids have the misconception that rational numbers = fractions when the definition is actually a ratio of two integers.  There are plenty of examples of things that look like fractions but are not actually rational numbers and it is important kids can recognize the differences.

Although the students really seemed to grasp on to the concepts of classifying numbers I am always looking for ways to improve.  How do you teach classifying rational numbers?



4 thoughts on “Classifying Rational Numbers

  1. This sounds like an awesome lesson — I’m introducing this topic tomorrow! I start by having students investigate by finding the decimal expansion for lots of numbers — fractions, pi, multiples of pi, square roots, cube roots. Then we sort the numbers based on their decimals to come to the idea of rational and irrational numbers. After that, I break down the rational side into subcategories.

    I found that starting with decimals that don’t terminate or repeat is a more concrete definition for kids than numbers that can be written as a fraction for rational numbers. Then we build off of that. But the lesson is far from perfect!

  2. Excited to do this today or tomorrow. I read this when you first posted and it’s been in the back of my mind ever since. Thanks for such a great idea 🙂

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