Solving a variety of radical equations and engaging with conceptual questions, students come to understand why extraneous solutions arise.

Many examples help students to see how the structure of an equation indicates whether extraneous solutions will arise.

5 minutes

Class may begin with a brief recap of the previous lesson. Student responses should be elicited with questions like: What is a radical function? What does its graph look like? Didn’t we say something about an extraneous solution? The point here is to simply call all of this to mind again.

35 minutes

5 minutes

In 35 minutes, I generally expect students to complete about the first third of the worksheet. There will have been plenty of misconceptions to clear up with questions and conversation, but by the end of the period everyone should be confidently moving ahead. Things will have been complicated as the students find that these radical equations may have 0, 1, or 2 solutions, and it is not necessary that any of them be extraneous. Graphing both sides of the equation as separate functions and observing their intersections will be very helpful. Class ends with a very brief opportunity for questions, and the direction to attempt one more problem for homework.