Tailgating and Solving Radical Equations

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Objective

SWBAT evaluate radical expressions and solve radical equations using order of operations and inverse operations.

Big Idea

The purpose of this lesson is for students to solve radical equations of index 2 by taking the square root and understanding extraneous solutions.

Warm Up

10 minutes

The purpose of this lesson is for students to identify the difference between evaluating a radical expression and solving a radical equation.  I allow students about five minutes to complete the Tailgaiting-Warm up. I will have them hand it in when they are done. 

After completing the Warm Up, students will take notes on how to solve a radical equation. Later in the lesson, they will be given an opportunity to correct their Warm Up in the Closure Activity.  I provide two samples below of student work in the reflection where I talk about some of the challenges provided by today's Warmup tasks.

Guided Notes

15 minutes

After the Warm Up, I will focus on teaching students how to solve radical equations conceptually, algebraically, and graphically.  I begin today's Guided Notes session by questioning students about the domain of the graph of the square root of x function.  I ask, "What can x not be in the domain?" Most of my students recognize that the expression under the radical may be equal to zero, but it cannot be less than zero.  

I plan to graph the first problem with the class as we complete the Guided Notes. I want to make sure that all of my students can visually see the solutions for x.  We enter each expression on each side of the equation as a function, and we graph both of them.  As a class, we discuss the guiding points in solving a radical equation, and students write them down.  The key points that I emphasize are listed below:

  1. Are there restrictions on x in the equation?
  2. Isolate the radical before solving?
  3. Are the solution(s) real or extraneous?

Next, I will ask my students to solve several radical equations algebraically.  My students have previously learned that taking the square root, and squaring, are inverse operations. Therefore, to eliminate the radical, they will be aware that squaring is a possible solution.  I will make sure that they idea of squaring both sides of the equation is discussed.  

I model reviewing Examples 5 and  6 in this TI-Nspire Solving Radical Equations video in which we compare the algebraic method to the graphing method.

Independent practice

20 minutes

The Independent Practice should take my students about 20 minutes to complete.  Afterward, students should have a better understanding of how the inverse operations of squaring and taking the square root work to undo each other to solve equations.

After the Guided Practice, my students generally work diligently on the Independent Practice. I walk around the room to assist students, and to monitor their progress while they are working.  Some students will need help with their Calculator. I am also relatively forward about checking their algebraic work.  As usual, I plan to require my students to do a check either graphically or algebraically. 

I will collect today's Independent Practice in order to check student understanding of solving radical equations.

Closure

5 minutes

The Closure Activity only take the students about five minutes to complete.  In this activity, I hand out a sticky note to each student, and they are to correct Problem 1 or 2 (or both) from the Warm up for today's lesson.