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Classifying rational numbers is a rather boring topic, let’s make it engaging and meaningful for students!

Let’s face it, students are thrust into topics to which they have no interest and no practical reason for learning.  For me, classifying rational numbers used to fall into this category. Often we find ourselves, as educators, attempting to simulate a need or use for these lessons.  In fact, at times we simply push through the lesson ourselves without any reasoning aside from the fact that it’s covered in the standards, so it’s covered in my classroom.  Classifying rational numbers is the perfect topic that comes to mind when I think of a lesson that fulfills this requirement. 

It’s hard to provide a meaningful classifying rational numbers activity when as the teacher you cannot see its purpose.  This is how I felt with every classifying rational numbers worksheet or textbook example and explanation I found.  It’s difficult to get buy in from the students when you can’t seem to find importance yourself.  This is how I felt, that is, until I was able to think deeper and find use in my own mind for the necessity to be able to categorize rational numbers, integers, and whole numbers into a Venn diagram.

Hook, line and sinker for classifying rational numbers

Dan Meyer has a great intro to this topic with an entertaining game he calls the “$100 Bet” which can be viewed here. (The clip I am referring to starts at 42:50; however, he has some other great ideas in this video as well.)  To summarize, Dan provides students with ten attempts to guess a number he is thinking of (written down in an undisclosed location).  Better yet, after each guess he promises to tell the contestant if the number he is thinking of is higher or lower than the provided guess.  When the student has four guesses left and two numbers to choose from, he feels overexcited to win the ridiculous monetary prize.

 “What is your next guess?”
“thirty-two”
“lower”
his body completely filled with excitement, “thirty-one”
“higher” with perfect composure…
“you didn’t say it could be…”

As a math teacher who is in on the joke, this slightly corrupt and dishonest game makes an appearance every time I teach my lesson on rational numbers.  The hook!  Every great song has one and many exceptional lessons, presentations and bodies of writing have their own as well.  However, although the students have a sudden need for knowing what type of number you were referring to, they still don’t fully need to classify them or understand how the various categories overlap.

You have their attention, now create the need for this topic!

That’s why I play dumb.  Completely dumb.  After the game, I shift gears drastically like someone just waved the checkered flag to the start of the race.  I randomly (seemingly), take a survey or poll of my audience, my students.  “Has anyone ever seen an animal before in or around your house?”  Hands start to go up, some eager with excessive stories they would like to share about a particularly peculiar incident.  I quickly change directions again and ask “Okay, does anyone have a pet?”  Most of the hands still lingering from the last question remain erect with a groan from the class clown, “does my little brother count?”

“Oh, it looks like quite a few of you have pets, does anyone have a dog?”  While several hands go down, those proud owners of a man’s best friend remain with several waving enthusiastically because they have a story they must share.  Although story time is not on the horizon, the fun for me is just about to start.  At the beginning of the last paragraph I said play dumb.  This is where that comes in.  My final question is “does anyone have a golden retriever?”  Usually I get one or two students, if not I yell out another common type of dog until I get a response.  I then start asking the student about her golden retriever.  How old, name, etc. Then I ask, “So, Ember, you have a golden retriever and you have a dog too, how old is your dog?”  With slight confusion and disbelief, she responds something along the lines of “that is my dog” with a well-deserved roll of the eyes.  Play dumb a little more.  “Oh okay, I get it your golden retriever is a dog, how about your pet?  How old is your pet?” 

Sometimes I feel like I may be torturing these kids…

When she gives me a similar response, I turn to another student that clearly put his hand down after I asked if anyone has a pet, call him by name and ask “Griffen, how old is your golden retriever?”  “He looks at me at this point like I am a completely out of my mind and says, “I don’t have a golden retriever.  I don’t even have a dog!  I have a cat.”  I look back over to Ember with confusion and say you said golden retrievers are pets.  He has a pet, it’s a golden retriever.”

The torture leads to teaching and meaningful learning

 I let the shenanigans run on for a few minutes after playing completely dumb to the idea of the animal, pet, dog classification hierarchy.  Once the students are settled from the ridiculous discussion, I use this Venn diagram along with images of animals to help them understand how the Venn Diagram works.  We discuss how to classify the animals and where we can place them.  George – the golden retriever best fits in the innermost circle because he is a dog, which also happens to be a pet, which still fulfills the requirement for animal.  We categorize a few other animals like Gary the goldfish, Cindy the cat and Zed the zebra by dragging their images into the Venn diagram as well.   If you like this idea, download the freebie here!

 

Finally, a need for classifying rational numbers

From this activity, the students are fully committed to understanding the need for classification.  It isn’t until this need is observed that I feel students are in a place to be exposed to a Venn diagram with rational numbers.  Now that the students have an understanding of the Venn diagram and where to classify items or objects that fulfill multiple requirements, the categorization of numbers becomes much easier. 

Assess understanding

Once the students understand and practice the idea of classifying rational numbers, I provide students with a cute ice cream cone Venn diagram. This activity gets students thinking at a much higher level than your average rational numbers Venn diagram worksheet because students must provide their own numbers to be categorized.   The students enjoy the mini project because they get to take a little break from the normal routine of math class to color their cone.  Eating healthy and promoting healthy living is always a goal of mine; however, who doesn’t make a little exception for some ice cream with rational number sprinkles?

Conclusion

I hope you enjoyed this delicious post!  To recap, I start off the lesson with Dan Meyers number guessing game, roll right into animal categorization and finish up with some practice and examples.  Once my students fully grasp the idea and understand a need for classification, I assess their knowledge with this mini project.

Similar Ideas and Content

If your students need to learn how to classify real numbers, this lesson idea can be adapted accordingly. To asses their understanding, you can use this similar classifying real numbers project. Similarly, this number sprinkle idea can be applied to prime and composite numbers as well.

I love taking topics that seem abstract and making them more meaningful. I find a lesson that feels broken to me and I come up with a way to fix it. In my opinion, how many teachers teach the order of operations is broken. Check out how I fixed it.