Math = Love: Ending Our Unit On Radicals

Monday, December 16, 2013

Ending Our Unit On Radicals

My Algebra 2 students have moved into logarithm territory, so I guess it's best time I post the rest of our interactive notebook pages regarding radicals.  We sort of got off to a bad start with logarithms.  I seriously blame it on the winter weather.  But, I think most of my students have finally caught on and realized that logarithms only look scary.  But, more about them in a future post.

Radicals.  Earlier, I posted pictures of the pages we made that dealt with prime factorization, parts of a radical, simplifying radicals, adding and subtracting radicals, and multiplying radicals.  The latter half of our unit covered dividing radicals, rationalizing the denominator, and converting between radical form and rational exponent form.

I shared with my students the reason why standardized tests require them to rationalize the denominator.  I gave them a long division problem to do by hand.  It was not pretty.  They cannot divide.  At all.  If I had more time, I would have had them write a persuasive paper over whether students should be required to rationalize the denominator in this day and age of technology.  I hate the fact that I have so much to cover in Algebra 2.  The majority of my students' Algebra 1 background is extremely lacking, however.  So, I've had to do some necessary reteaching.  Plus, I still have to make sure I teach all of the Algebra 2 standards.  It's a lot to do, but I'm doing the best that I can.

Multiplying and Dividing Radicals
Dividing Radicals Interactive Notebook Page

Rationalizing the Denominator and Converting Between Radical Form and Rational Exponent Form
Rationalizing the Denominator Interactive Notebook Page
Converting Between Rational Exponent Form and Radical Form INB Page
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.  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.  

PDF templates have been uploaded below.  You will need Flash/Shockwave to view.  If you cannot view these files, send me an e-mail, and I will be happy to send them to you in an attachment.

Dividing Radicals (PDF)

Rationalizing The Denominator (PDF)

Converting Between Rational Exponent Form and Radical Form (PDF)


  1. 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).

    1. 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!

    2. 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.

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

  2. 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.