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Rational and Irrational Numbers Exploration Activity

This is a picture of a foldable that I created for my students to use as they walked through a rational and irrational numbers exploration activity.  This activity did not go as planned.  I thought it would take one class period.  After one class period, we had only started to scratch the surface.  I ended up never finishing this activity with my students because I felt a need to move on.  

compass and map in background with text "rational & irrational numbers exploration activity."

Still, I want to share this activity with you in the hopes that someone might be inspired to take this and make it better or at least give me insight on why it didn’t quite work.

rational and irrational numbers exploration activity algebra math foldable interactive notebook

This activity was created with N-RN.3 in mind.  

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

I had some blank sticker name badges in my desk.  So, I took a Sharpie and wrote various rational and irrational numbers on each name badge.  As students came in the classroom, they got to pick a random number from the pile.  

After a brief introduction to the TI-30 Scientific Calculator, students were instructed to partner up and fill out the first line of this chart.  They would fill in their number, the classification of their number (rational or irrational), their partner’s number, their partner’s number’s classification, and the operation of addition.  

Using the scientific calculator, students would add the two numbers together, record the result, and then determine whether the result was rational or irrational.  Find a new partner.  Repeat until the first five lines have been filled in.

rational and irrational numbers exploration activity algebra math foldable interactive notebook

After completing five addition operations, we would have a class discussion.  I was hoping that students would arrive at the fact (on their own) that a rational plus a rational is always rational, an irrational plus a rational is always irrational, etc.  This went semi-well.  Some of my classes struggled with this way more than others.  None of my classes made it to division.  One class barely made it through subtraction.

rational and irrational numbers exploration activity algebra math foldable interactive notebook

What I didn’t account for was the sheer amount of time that it took for my students to partner up, do the calculations, and fill out this chart.  This ended up feeling like an entire waste of a class period because it was a lot of work with very little to show for it.  I ended up doing most of the talking and discovering during our discovery period which was frustrating.

We wrote our “discoveries” on the front of the foldable.

I still want to put this idea out there, though.  I think it’s good to blog about the lessons that go well, the lessons that are just mediocre, and the lessons that don’t go as planned.

And, yes, I’m the crazy teacher who wore a sticker around ALL DAY that read 3/8.  I put it on during first hour because I had an odd number of students.  So, I actually went through the activity with my students.  I didn’t take off my sticker because I figured I would just have to make another one to wear for third hour and sixth hour.  Third hour, we had a fire drill.  

Of course, I got asked by everyone I saw why I was wearing a number on my shirt.  The math teacher definitely came out in my answer as I explained that I wasn’t just wearing any number, but a rational number.  Conversation ensued about what a rational number was.  Yes, I’m that teacher who takes every opportunity possible to teach my kiddos something mathematical!

rational and irrational numbers exploration activity algebra math foldable interactive notebook

Later that morning, we had our tornado drill.  As the students huddled in the stairwell, the teachers stood in the hall.  The history teacher looked at me and said, “So, you’re less than half?”  Confused, I asked her to repeat the question.  “So, you’re less than half?”  Still confused, I decided that I would just agree with the history teacher and go on down the road even though I had no idea what she was talking about.  Luckily, she motioned toward my sticker, and I realized that she was referring to the fraction I was proudly wearing.  The other teachers in my building are used to my crazy methods that I use to teach math by now, so they weren’t that surprised.

What did surprise me was my statistics students.  I have a class of 5 juniors who are taking statistics as their upper level math elective.  Statistics is the only class that we offer our students above Algebra 2.  These are our best and brightest math students who have chosen to take their math class at our school instead of our local Career Tech center.  

Of course, they had to ask about my lovely sticker that I was wearing.  I explained why I was wearing it, and I told them about all the crazy conversations I had had that morning as a result.  What do my students decide to do?  They decide that they want to make their own stickers with numbers on them to wear around the school for the rest of the day.  There are kids who love math, and I’m so thankful that I get the chance to teach them!  

Anne K.

Sunday 4th of August 2019

Hi! I realize I'm coming to this late, but this will be my first year teaching Algebra in public school and I am finding your stuff really helpful. I like the idea of each unit having its own table of contents, rather than a long list at the beginning of the notebook...especially if it's combined with tabs for the start of each unit. Do you have a file of your table of contents page that you would be willing to share? Thank you!


Sunday 1st of July 2018

Some of your files do not show on my browser. Will you please email me your files for Algebra I and Geometry. Thank you! lprocks05[at]


Monday 24th of July 2017

Some of your files do not show on my browser :( Will you please email your INB files for Algebra I and Geometry (if you have any!) Thank you! jacque0716[at]


Thursday 1st of September 2016

Hey, I love this activity! I did something similar to lead into properties of real numbers. I did "speed dating" and at each spot they had to answer 8 questions (2 minutes was more than enough time, even without a calculator.) Here's the setup. |my#|+|their#|=|Answer| then |their#|+|my#|=|Answer|

we did this for all four operations. Each student did 70+ questions, depending on how many students were in the class. I gave out "hello my name is" name tags from -12 to 12. The students loved it and it is a great way for them to see patterns.

Jackie Edmonds

Monday 15th of August 2016

Hi Sara, I have been enjoying your blogs for the past year and think that you are a wonderful and honest teacher. I teach Algebra I and have been somewhat traditional in my teaching. I really want to try to do Interactive Notebooks with my students this year. Do you complete an INB of your own before you present it to the students? I'm somewhat nervous, but want to give it a try. I also could not get the files. Could you email them to ??? I really appreciate you sharing your material and teaching strategies. Pray for me. :)

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