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Day 93: Proving Triangles Congruent

This section of Unit 6 was a major focus of mine while I wrote this curriculum last summer. I hate teaching proofs in the traditional style presented by most textbooks because of how formal it's presumed that proofs need to be. I just want students to be able to justify their reasoning and think sequentially, which has been the underlying focus of this entire venture.

My school's geometry textbook introduces proofs in Chapter 3, which would be fine if it relied on them heavily throughout the remainder of the book. Instead, they're introduced at a very basic level (which is necessitated by starting them so early) and basically abandoned after that.

My thoughts are along the lines of "let's not deal with proofs until we're well equipped" (read: 2nd semester). Once the students have the basic skills down pat (such as types of angles), we can attack proofs that have more substance. And maybe we could even use proofs to test/discover new ideas.

So to start out, I made "bundles" which consisted of 3 pieces of drinking straw and 3 pipe cleaners. Each bundle has the same 4 inch, 5 inch, and 6 inch piece of drinking straw, so students can use the pipe cleaners as angles (inserted in the straws) to make triangles. Even though the supplies were cheap, I only made enough to have students work in pairs and simply asked each group to build a triangle, trace its outline onto paper, then measure all three angles and sides. We collected the data and the hope was to show that everyone's triangle was the same, thus demonstrating the SSS postulate.

The major snag is that too many students cannot use a ruler or protractor reliably, so there's a much larger spread in the data that you'd like. I still think it was a useful activity though.
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