Cuisenaire Rods Go Pythagorean!

I’ve been playing with the lovely Cuisenaire Rods for a few weeks now. I made the (fortunate) mistake of creating this flower in a past article about coordinate pairs.

The mistake was that I would eventually have to come up with the coordinates for this thing. Fortunate because it gives the MathFourTicians out there something else to teach with the rods!

The center of the flower is the place to start.

Since all the “petals” are attached to the center, that’s probably the best place to begin.

I converted to something I could see.

Since everything is tiny (1 cm), I went to a bigger setup. And some of the coordinates were easy to pick out. So I put those in the big grid, too:

And then I started to do some work…

Next I considered what I was really dealing with: a square. And each side was 1 cm.

According to those crazy Pythagoreans, the diagonal measures :

So half the diagonal is :

I went back to the big grid.

When I put this information on the big grid, it looks like this:

Doing some arithmetic and geometry, I get:

Using my very cool TI-30 calculator, I get that .

I can accurately name the points!

Knowing that each corner pokes out roughly 0.2, I can calculate the coordinates:

From this I can create the ordered quadruples as described here for the petals of the flower. But at this point I’m pretty much needing a break. So I’ll leave that for next time.

Whatcha think? Fun? Share your thoughts in the comments and on Twitter:

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2 Responses to Cuisenaire Rods Go Pythagorean!

melissa says:

September 22, 2011 at 9:59 am

Hi bon, I am really enjoying reading about the things you do with cuisinaire rods (i never thought of dooing fractions with them!). Im wondering how I can intuite if this will be too difficult for my kids? we love “playing” with the c.rods …but Id hate to pull this one out and then get overwhelme with them.

what do you think?
thanks, melissa in italy

- Bon says:
  
  September 23, 2011 at 4:03 am
  
  Thanks for your question, Melissa!
  
  You can ask them. Either right out or covertly.
  
  You could print it out and put it on the table so they’ll see it. If they ask for more information, or ask to do it, then do it. If they look at it and ignore it, then put it somewhere else (in plain site) to let them find it in their own time.
  
  Or you can hand it to them and say, “What do you think? Are you interested in this?” They might say no, so then put it aside (in plain site) and let their curiosity find it when they’re ready.
  
  You could also do it yourself. Sit down and make some exercises based on it. If they ask you what you’re doing tell them you’re making exercises for this and you’re not sure they’re ready for it. But you’ll have it handy when they are. This lack of pressure might get them interested in doing it now.
  
  Let me know how it goes – and if this is helpful.