Two-Column Proofs and Logical Reasoning

The second unit in Geometry for me is Logical Reasoning. I do three things: 

  1. Inductive and Deductive Reasoning
  2. Conditional Statements
  3. Two-Column Proofs

Monty Python

I have fun teaching inductive and deductive reasoning. I usually start the lesson by having students watch a YouTube clip of Monty Python and the Holy Grail. It’s a pretty hilarious demonstration of how drawing conclusions based on patterns can lead you to the wrong conclusion. This would be a great place to talk about stereotyping if you would like to go a little deeper into how people base information sometimes from the media or gossip. This lesson has 12 task cards to practice reasoning and knowing the difference between the two types. 

Conditional statements is also fun to teach. I love it when kids say that it doesn’t seem like we are learning math. We discuss where the hypothesis and conclusions are in the conditional statement so the students can write the converse, inverse and contrapositive. We also discuss counterexamples and biconditionals. This lesson has some hands-on activities where students create if/then statements and the related statements and tape them into their journals. 


The last part of this unit is spent on two-column proofs. This usually happens for me in October, sometimes earlier but close enough that I can show them a silly Halloween proof that I created. I made this up a long time ago after watching “It’s the Great Pumpkin, Charlie Brown.”  It’s got all the elements of a real proof. I’ve used this as a bulletin board in past years. Feel free to use this in your classroom.geometric-proofs-b

One thing that is in this lesson that helps my students is a set of matching cards. Students will match the property or definition with its name. I do this as a collaborative activity. Students enjoy this and it helps them to have some tools to use going into writing proofs. This is a beginning proof lesson. I only practice two-column proofs. In lessons that follow this one, I introduce the other types of proofs like paragraph and flowchart proofs. 

If you are teaching online, no problem. I’m in the process of making these lessons more online friendly. Teachers Pay Teachers has a new tool that can take a PDF and transform it into an interactive worksheet. Look for the “Use as a Digital Activity” button on products that are available for this. You as a teacher can modify it as you see fit then assign it to your students. 

I love this part of Geometry. It’s different from the norm in math. It’s always a fun time of year. If you’d like to use my lessons, then the best way to get them and save a little money is to purchase the Unit 2 Bundle

Good Luck and I hope you have a successful year!

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Math teacher dedicated to sharing teacher tips, ideas and resources.

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