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}

^{1}We’ve spent the past few days on “if-then” statements and counterexamples as a lead in to this.

^{2}I thought it was time to start sharing.

Image: popping colors via flickr under cc

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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

wasfun. 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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