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3-4-5 Triangles

This weekend Bruce(6.5) and I had fun building real life triangles. I was inspired to try this activity after reading Keith Devlin’s thought provoking book, The Language of Mathematics. Unlike The Math Instinct, The Language of Mathematics focuses more on the history of mathematics rather than best practices in teaching mathematics.

Dr. Devlin wrote The Language of Mathematics for the general reader, but I found it quite challenging even though I was an A- student in mathematics all the way through college level Calculus. I wish I had read this book back in high school, because it might have helped me knock off those minuses!  On page 44, he discusses 3-4-5 triangles and ancient builders.

A 3-4-5 triangle is also mentioned in a children’s book Bruce and I read recently by Avi called The Barn. That too, was an excellent book although I would not recommend it for children under ten (oops) because it dealt with a really depressing storyline. In The Barn, the children use 3-4-5 triangles to create the right angle of the barn they are building for their father who is dying after suffering from a stroke. Here is how we built our own 3-4-5 triangle:

First, Bruce measured out 12 segments on masking tape that was folded on itself so it wasn’t sticky. He used Legos as his nonstandard unit of measurement. It would have been better to tie knots in rope or yarn at 12 equal lengths, but I knew that tying knots with a six year old would have added about ten minutes of utter frustration to the activity, and fine motor skill improvement was not my learning objective. Plus, I couldn’t find any rope. 🙂

At the 3 and 7 marks, we pulled the triangle tight. This picture doesn’t do the triangle justice, because I was also trying to hold the camera, but we did end up forming a right triangle with sides that were equal to 3-4-5 Legos. This triangle was also scalene because all three sides were different lengths.

After building our right triangle, we built a giant Isosolese triangle on the ground for fun. We also got out our protractor and measured angles, but as you can probably tell from the picture, since we had built our triangle with masking tape instead of rope, the angles were off by a few degrees. Bruce had previously had trouble remembering what an Isosclese triangle was, so hopefully this helps him remember. You can fit an “I” in an Isosceles triangle. Hopefully he also remembers what a right triangle is too.


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