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Showing posts with label fractals. Show all posts
Showing posts with label fractals. Show all posts
Friday, December 7, 2012
Tuesday, September 18, 2012
Sweetly Sierpinski
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.
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.
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