## Reflection: Connection to Prior Knowledge Extraneous Solutions - Section 3: Share and Summarize

I taught this lesson twice to both of my Precalculus classes and it was interesting to me how completely different these lessons turned out. In one class, students did not have previous knowledge about how you can get extraneous solutions. After we graphed and decided that one of our algebraic solutions did not work, they were stumped as to why. There was an electric mixture of confusion, engagement, bewilderment, and excitement in the room - these are my favorite teaching moments! Students knew something was awry and they were determined to figure it out!

In my other Precalculus class, a few students instantly knew that squaring an equation could lead to extraneous results. I am glad that they had that prior knowledge, but it definitely impacted the lesson.

My takeaway from this is that I want to create these high-engagement moments and much as possible. The key in this case was the disconnect between two concepts that students know well - a graphical and an algebraic method of solving equations. I try to "set up" students as much as possible in order to get them thinking deeply about important mathematical concepts instead of merely scratching the surface.

Two Classes - Two Different Lessons
Connection to Prior Knowledge: Two Classes - Two Different Lessons

# Extraneous Solutions

Unit 5: Trigonometric Relationships
Lesson 11 of 15

## Big Idea: Checking the answers after squaring both sides leads to an unexpected result.

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Standards:
50 minutes

### Tim Marley

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