Last week, we had a great time exploring Pascal's Triangle. Initially, we simply tried to figure out how to construct the next row of the triangle. Then we looked for patterns (you can find the powers of 2, natural numbers, triangular numbers and even the fibonacci series.) We created new Pascal triangles using bases (or "Dinosaur Math" as the Elms have taken to calling it) and looking at the fractal patterns by coloring in the multiples of two, three, and five. We learned about Pascal's Petals and prime factorizations. Finally, we looked at how Pascal's Triangle could predict probability for coin flips (we ran the "quincunx" machine) and we looked at using Pascal's Triangle to work on combinatrix problems. Regularly during our explorations and discussions, the students were amazed, "NO WAY! That's so cool!"

I was pleased to find a

great article about math problem solving in the paper the other day. It talks about "Fermi Problems" which have long been a favorite of mine for math explorations. It's a math game of sorts that's played by mathematicians when they get together at conferences. My husband and his friends introduced me to the idea years ago, unaware that there were other people playing the same game. They called it "Guesses by Crackpots." Basically, you take an unusual question, say, how much ice cream would you have to buy to make an ice cream sundae the size of Prairie Creek's gym? Then, you talk through together how you would get the answer. Along the way, you make certain assumptions and estimations (like, well, a half gallon of ice cream is about seven inches long, four inches tall, and four inches wide.) It's like the Problem of the Week grown large and hairy -- and kids (and adults) have to do an amazing amount of math to find answers to such a problem. I highly recommend it for your family entertainment during long car trips!

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