The Map is Not the Territory

My seven year old daughter and I are really quite a team.  One of us will share an idea or an observation and all of a sudden the other of us will be inspired into action.  For example, she found a triangle in this clover last week and I immediately knew what we could do with it.



And, although she sometimes eschews direct participation in projects I think up, my kid 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.

Isn't it cool?!?






















It's a (dried) clover Sierpinski triangle!  We picked clovers, flattened and dried them in a sketchbook, and finally found some time (and a glue stick) to paste them down.  I don't know about my kid, but I am really enjoying all the different types of Sierpinksi triangles we've made over the last few weeks: out of candies, with our straight edge and ruler, with our colored pencils, with money, and now this!

It's fun to find math, wherever we go and it's even more fun to make math out of the things we find. 

Day One
Me:  I'm going to make a triangle out of three candies.  Can you copy it? Good! Now I'm going to make this triangle bigger by adding two more triangles.  Let's see if you can make the same as me.

Kid:  Look, Mama!  This side is red, yellow, red, yellow.  And the other side is yellow, orange, yellow, orange, and the third side is...

























Me:  Great!  So let's see if we can make another triangle just like our first two, except with different patterns. [Kid starts right in...]

[I've been thinking lately about the importance of modeling inquiry, especially in the math we do.  I want her to not just identify patterns, which she's good at, but also consider those patterns malleable to the whims of her own curiosity.  Also, if I ask a question that leads to my desired result it's generally a lot more successful than giving her a direction.]

Me: What would happen if we added on two more triangles the same size but with different patterns?

[With these sized candies it was easier to build the fractal structure if we made each 3-candy triangle out of three of the same color.  I also had to point out that the right and left sides of the top triangle had to be extended diagonally to make this work, which was a bit challenging for her to see and do.]

























Kid:  Oh look!  There's a triangle in the middle!

Me:  Let's take this big one apart and see how many different colored candies we used. These three columns each have six candies and the orange row has how many...?  How many candies is that all together?

























Me: I wonder if we could make another big triangle using the same candies, but different color patterns?














































Day Two
I have been waiting for months and months to use this sheet I found here.  It's meant for older kids, I think, but we adapted it just fine for the candy approach.