#WTPW Simplifying Radical Expressions-Rationalizing Denominators #tlapmath


I am not sure how exciting this lesson is, but I believe the idea beats the run of the mill take notes-practice on a worksheet.  It gives students opportunities to notice patterns on their own, a chance to share and discuss those ideas as well as consider ideas from their classmates.

I appreicate Math Equals Love Walk the Plank Wednesday post and will definitely use some of her ideas with the “why” we do this.

My goal is for my students to be able to determine if expressions are equivalent, so I am beginning with a simple card matching task.  As students enter the room, they will receive a card with a radical expression either simplified or not (similar to set A).  As we begin class, they will be asked to find their match…without verbal communication…while I post attendance, etc.  They will come to me with their match and I will confirm if they are correct.  Yes, I will allow calculators.  I know, not too high level on the thinking scale.


I will have several sets of cards similar to those they matched.  Each group will then be asked to complete an open-card sort.  This simply means, I do not give them any direction on how to sort their cards.  The only stipulation is they are ready to explain why they chose to sort them as they did.  When the timer goes off, we will share sorts (both volunteers and any I find that are interesting to me).

Part C, I will have concept attainment cards placed around the room.  Each card will contain examples of radical expressions labeled simplified and expressions labeled not simplified.  Students will carousel to different cards, noticing patterns, trying to develop their own rules.  After a set time, they will do a quick pair-share to summarize their findings before we have a whole class discussion. 

Hopefully their ‘rules’ will encompass all we need to know, but if not, I can always use their ideas to lead us to our goal.

We will create a set of notes for our INBs.  Part of their HW will be a LHP assignment to give examples of expressions that are simplfied and not simplified from their earlier carousel work.  Ideally, they would create their own expressions.

If students need practice with skills, an idea from a workshop several years ago…on a page of say 30 problems, I pick 5 I want them to do, then they pick another 5 or 10, whatever I/they feel is necessary.  By giving them this option, I have more success getting them complete the practice.  I would much rather have 10 complete than 30 incomplete or not even attempted.

An idea for formative assessment…return to card sort from Part B.  They should sort into groups of simplified/not, even match up equivalent expressions.  One person stays with the sorts, while others go to different groups to peer assess.


Possible written assessment questions, a) give a bank of expressions to match equivalents, noting simplified terms; b) given a simplified expression, create an unsimplified, equivalence.

This is a very generic layout, but I can use the sequence with whatever level of Algebra I am working with.

I will post again when I have sets of cards completed. 

Feedback to move forward, ideas  for improvements are welcomed.

Pam Wilson, NBCT
Currently Reading
5 Practices for Orchestrating Productive Mathematical Discussions, Smith & Stein
Teach Like  a Pirate, Dave Burgess
From Ashes to Honor, Loree Lough

5 responses »

  1. I like the activity because, even though I don’t agree, students need to be aware of when some “powers that be” deem something simplified or not. I agree that it’s a good alternative to a worksheet and gets students looking at structure (PS #7) and creating viable arguments (PS #3).

    I’ve always had a problem with the idea of “simplified” or “not simplified”. The rules are arbitrary, especially for expressions with radicals. I don’t agree that [15 (sq rt 2)]/2 is simpler than 15/(sq rt 2). I do see a reason for students to notice when expressions are equivalent. However, sometimes an answer of 15/(sq rt 3) may describe a situation more intuitively than 5(sq rt 3). I suspect that rules were made so that assessments are easier to grade. My nature is to not be a rule follower, so I bristle at seeing points taken off for a fraction left as improper, or horrors, not fully reduced!

    I like that the CCSSM does not demand fully simplified answers or least common denominator. There are more important ideas to work with in mathematics than what form an answer is in. This is not to say that students don’t need the ability to be able to figure out when two very different looking expressions are equivalent. This is just to say that one is not better than another.

    • I agree with you, and continue to ask myself, when is it necessary? Thanks for your comments and hopefully I can tweak this to become a prodcutive task for student learning.

  2. Can you tell me where students are asked to simplify radicals in the CCSSM… a colleague and I could not find the requirement anywhere! Where do you insert this topic within your course?

    • In geometry, I do a side bar review unless more time is needed. I use a “go-fish” game to intro it after allowing students to develop their own understanding of rational exponents.

      I see using similar right triangles as a possibility, make connection between scalar and the simplified hypotenuse length, maybe?

      In Algebra 2, in a radical ezpressions.

      Just tutored someone in a College Algebra class the other day as well.

      In Algebra I, maybe exponents unit. It really depends, if you teach it as an inverse function..

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