Thinking in Threes

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The more I learn about the exquisite connections between shape, number and nature, the more convinced I am that combining numbers and shapes is a win-win situation for building number sense in young children.  For example, consider the benefits of exploring the basic, but charming, triangle.  This mesmerizing video provides some exquisite, thought provoking examples of three-ness:


What three-ness did you notice?  I noticed three colors, triangles with three sides and three corners, many different types of triangles and, best of all, a lovely waltz rhythm (1-2-3, 1-2-3)!  The video is also a demonstration of the power of doubling – double 3 is 6 (a hexagon or a snowflake) and double 6 is 12 (a dodecagon).  My seven-year-old watched the video all the way to the end the second time (the first time she was waltzing along to the music) and said: “T. [a friend] and I saw a big snowflake once – it looked like that!”

Back in November I read a Moebius Noodles post that mentioned ‘iconic numbers’  — numbers that are so ubiquitous in our daily lives that we don’t really notice them but are perfect for building number sense.  One iconic number object is the clover.

clover tri

















I, for one, had never given its ‘three-ness’ much thought until the day my daughter brought me one with a clear triangle scribed on its leaves.  As soon as I saw it I knew exactly what to do with it.

We picked more clovers, flattened and dried them in a sketchbook, and finally found some time (and a glue stick) to paste them down. Although my daughter sometimes eschews direct participation in the projects I think up, she is generally always around as I’m making something.  In this particular case, I chatted with her about what I was doing while I glued and pasted, and she made a lot of observations, which is good enough for me.

clover tri 1















Isn’t it cool?!?  It’s a Sierpinski triangle fractal made out of clovers, a true monument to three-ness!

Prior to this we had constructed other Sierpinksi triangles out of candies, with a straight edge and ruler, with colored pencils, and with money.  Now that’s what I call ‘thinking in threes’.

It is fun to find math wherever we go and it’s even more fun to make math out of the things we find. What other three-ness will you find today? Here are a few ideas to get you started: tricycles; three little kittens who lost their mittens; morning, noon and night; a triple junction created when three bubbles come together and, as a final adieu…

…perhaps my favorite example of three-ness so far: This one I made out of a little circular piece of cookie divider paper.  Presenting the teeny, tiny, translucent tetrahedron!


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