## Reflection: Backwards Planning Prove Triangle Midsegment Theorem using Analytic Geometry - Section 2: Part 1: School of Hard Knocks

When I sat down to design this lesson, one of my broader goals was to have students appreciate the major impact that choosing coordinates and position/orientation has when doing coordinate proofs. So as I thought of this end goal, I thought to myself, students will never appreciate the good life if they haven't first had a taste of what it's like to struggle through adversity.

Also, while doing things "the hard way" is not the smartest way to approach life, it does build muscles, so to speak. Doing these problems the hard way, for example, forces students to really master the algebra involved as it is not at all neat.

With all of this in mind, I decided that I should let students experience what it is like when we choose coordinates and position/orientation haphazardly. I decided to give them to get a taste of this struggle. This horrific experience, I planned, would make them truly appreciate the impact of choosing coordinates and position/orientation more strategically.

I have adopted this philosophy of letting students experience the hard way so that they can appreciate the easy way generally in my teaching. Nowadays there are so many aids that make things easier for students. High-tech calculators, algorithms and formulas, software applications, etc. spare students many of the arduous tasks that their predecessors had to endure. I like to still have my students go through these arduous ordeals so that they will truly appreciate the advancements that have been made.

And even though they whine and complain when I finally give them the "easy way" ("Why didn't you just tell us that in the first place?"), I think they know deep inside that they're better off for having gone through a little adversity.

Getting students to put some skin in the game
Backwards Planning: Getting students to put some skin in the game

# Prove Triangle Midsegment Theorem using Analytic Geometry

Unit 9: Analytic Geometry
Lesson 7 of 7

## Big Idea: As they say in real estate..."Location, Location, Location." In this lesson, students experience the impact of positioning when writing coordinate proofs.

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80 minutes

### Anthony Carruthers

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