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Rational Exponents Graphic Organizer

We ended our unit on radicals in Algebra 2 with rational exponents and converting between radical form and rational exponent form. I created a visual summary of the process for my students to glue in their interactive notebooks as a sort of rational exponents graphic organizer.

I gave this page to my students, and I instructed them to choose a variable of their choice for the index of their radical and for the exponent of their radicand.  One of my students thought it would make sense to use the variable e for the exponent and the variable i for the index.  When you convert to rational exponent form, the exponent goes over the index in the fraction that forms the exponent.  Exponent Over Index.  EOI.  

converting radicals and rational exponents graphic organizer notes.

The standardized tests that Oklahoma high school students take at the end of the year are known as End-Of-Instruction (EOI) tests.  So, this mnemonic device really only has special meaning to Oklahoma high school students.  But, I was so proud of my student for creating something to help her remember something she deemed important and sharing it with the class.  I was so impressed, I shared the idea with my other Algebra 2 period.  They didn’t seem too thrilled or impressed, but I saw some students writing “EOI” on their quizzes.  So, I think it helped.  

I’m thinking that you could maybe find a way to relate it to Old MacDonald???  “Old MacDonald Had a Farm.  E I E I O.”  Okay, maybe that’s stretching it.  

Want to give your students some practice converting between radical form and rational exponent form? I created a rational exponents square puzzle activity to do just that!

Kristy Cho Jones

Saturday 12th of December 2020

Your situation is EXACTLY my current situation right now with my 8th and 9th graders. The textbook we are using cover radicals and rational exponents with and without variables. I have been struggling with them to help them grasp everything; especially my 9th graders. Thank you for these! I plan to actually print them out and send them to my students with their package of things from me! Thank you!


Tuesday 28th of June 2016

Hi Sarah

I haven't been able to download the pdfs as it says that the server closed unexpectedly. I would be grateful if you could email them to me at. Also what package do you use to make your sheets? I am struggling to get Office to make the symbols I want. Yours are ideal, but I would like to be able to make my own, too.


Wednesday 8th of January 2014

Hi Sarah -- I remember exponents by using "Hats and Boots"...

IN exponent form, think of the base as the person. Now think of the exponent, the part on top is the hat (because that is what you wear on TOP on your body), and the base of the fraction are the boots (because you wear them on the bottom of your body.) When you get home and are about to walk into your house (the square root sign), you take off your boots and leave them outside the door, then hang up your hat!

I never forget now!!

feet (or boots). Whenever you enter a house, you “hang your hat and leave your boots at the door”. So the 3 becomes an exponent (hanging on the number) and the 2 becomes the index (out front and at the door).

Sarah Carter (@mathequalslove)

Friday 20th of February 2015

I haven't made one for the reverse. Hopefully this summer I will revamp things and find the time to make one!


Sunday 16th of November 2014

I like this analogy as well. The only thing I would suggest is showing the students that the arrows go both ways in your visual. I know my honors students would over analyze the uni-directional arrow and say I didn't say it could go both ways. Just a thought.

What I'd really like to know is, how did you explain simplifying radicals to the students with the Hat's and Boots analogy? I typically use the factorization tree and explain it using circles, squares and X's. The things in squares get multiplied back together and go back under the radical. The things in circles get multiplied back together and come out of the radical. Not sure how I would incorporate that with the Hat's and brain keeps thinking of Dora the Explorer and Boots...I love my boots, yeah my boots and me...I'll probably end up singing that for them.

Also, did you do the reverse as a PDF as well?

BTW, thanks for all the great stuff you do, it has made my second year of teaching much easier and wish I'd found your blog before my first year.

Sarah Carter (@mathequalslove)

Friday 10th of January 2014

Jana, thank you so much for your comment! This week, I had my students convert an expression from rational exponent form to radical form as review/bellwork. I used this as an opportunity to share your hats and boots analogy with them.

My 2nd hour Algebra 2 class loved it. I heard multiple students say that there was no way they could ever forget it with that analogy. My 5th hour class hated it. But, then again, they hate every single thing I do.

I absolutely love learning new ways to explain things. Thanks so much for sharing!

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