We’ve been exploring the ideas of similarity and congruence in my freshmen classes. Today the students developed congruence by SSS – with straws.
Supplies needed: drinking Straws (1-2 per student), string (dental floss was too slippery), and scissors.
Question 1: Are all quadrilaterals with congruent corresponding sides necessarily congruent?1
Students began by cutting a drinking straw into four pieces, threading the string through, and tying it off to form a quadrilateral. They quickly realized that they could “move” the angles, so nope, this is not true. Unexpected bonus: discussion of concave/convex.
Question 2: Are all polygons with more than four sides that have congruent corresponding sides necessarily congruent?
Repeat the bit with the straws. Some of them realized they could easily create this by carefully cutting one of the straws from their quadrilaterals. Conclusion, nope, more “moving” angles.
Question 3: Are all triangles with corresponding sides congruent necessarily congruent?
Make the triangle with straws… conclusion, yep, this does guarantee congruent triangles as the angles are “locked”.
We spent the rest of the period trying to explain why this is the case (and formalize the language after a bit). We also discussed whether of not this constituted a proof.
On the way out, one student thanked me for the lesson. He said it was fun to really understand why it worked. Wow. I was thanked. For a math lesson. Wow.
Up next: SAS congruence with straws and pipe cleaners.2
1We’ve spent the past few days on “if-then” statements and counterexamples as a lead in to this.
2I thought it was time to start sharing.
Image: popping colors via flickr under cc
Continuities 
Nice! I was reading, assimilating, thinking about my next year teaching congruency, without realizing I was reading a lesson plan. That’s the way.
You *had* to wait till I was done with the polygon unit to bring this up? š Very cool. I’ll be using this next year, for sure. Thanks!
What a great way to teach this! Almost makes me hope to have a grade 9 math class next year; almost, but not quite!
Nice to hear that someone may get some use out of this. It was fun. I was also amazed at the number of kids who couldn’t tie a knot – darn velcro!
Can’t tie a knot? They’ll never become topologists at that rate!
Hmm.. I wonder if it would be possible to give a one-off knot theory presentation to a grade-school/high-school class. Could it be stripped down so they’d follow? Would they care?
John your welcome to use my classes as a test case!
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Hmmm. We do a similar lesson using twist ties inside straws to connect with our 3rd graders. String is so much better for keeping it together. Great questions, which can be used with a few modifications with little guys. Thanks!
3rd grade huh? Good for you (and for them). I’d be interested in hearing how you modify the questions for that grade. Sadly I know very little about the mathematical topics covered in elementary school.
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