Add and Subtract Radical Expressions

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SWBAT add or subtract radical expressions by combining like terms.

Big Idea

To introduce like terms using Radicals from student's prior knowledge of like terms in Polynomials.

Warm Up

10 minutes

The goal of this lesson is adding and subtracting radical expressions.  Again, even though I know it is review from previous grades, I want students to have a deep understanding of the term like radicals or like terms. Therefore, I introduce like radicals by building from student's prior knowledge of like terms in polynomials. 

I intend for this Warm Up to take about 10 minutes for the students to complete and for me to review with the class.   In the Warm Up Questions 1 and 2 are adding and subtracting polynomials. Then, I have students add or subtract radicals in Questions 3 and 4.  I relate the two concepts as I review the Warm Up in the video below.

Independent Practice

15 minutes

I will probably work a few additional examples with my students before handing them the Independent Practice worksheet.  The Warm Up introduced students to like radicals, but students need more practice creating like radicals by simplifying.  I model the examples below in the video:

My goal for the Independent Practice is to allow students more of an opportunity to practice on their own.  I expect my students to have the most difficulty with rewriting some of the radicals to create like radicals. When students are unable to simplify correctly first, the answers are not simplified completely, and therefore not fully correct.


Exit Slip

10 minutes

The Exit Slip takes about 10 minutes at the end of class.  I allow students about five minutes to work on it individually.  Then, I ask the students to work with their elbow partners. I encourage the students to critique each other's work.

In this Exit Slip:

  1. Students find the exact total length of all the line segments in the irregular shape provided first, leaving the sum in radical form.  
  2. In Question 2, students change the answer to approximate form.
  3. In step three, elbow partners critique each other's work in one of two ways:
  • Partners agree on the two answers and discuss methods used 
  • Partners disagree and look for the mistakes made, and how to correct them (MP3)

I plan to collect the Exit Slip to check for student understanding of simplifying, adding , and subtracting radicals.  I anticipate that some of my students will struggle with simplifying the radicals to create like radicals.