Tuesday, January 23, 2018

Fibonacci discovered!

Last week, we went on a math quest to see if we could discover what the famed Fibonacci sequence is all about. There were items like the ones below placed all around Mrs. Towne's room -- plants, pineapples, cauliflowers, books with pictures of the galaxy, several different types of shells, and a big bin full of different sized pone cones. We started with a question: What "common denominator" do you notice about all these things?

Armed with clipboards, paper and pencils, the Dragons and Navigators spent time observing the different items. They touched, talked, and thought about what they were noticing.  They turned things upside down and looked at them from different angles. What WAS the same about a pine cone, a galaxy, a whelk shell?

We sketched and labeled what we were seeing and noticing...

Were they all spiky? Did they all have tentacles? Then words like "circle" and "swirls" started to rise above the others, and suddenly "SPIRALS!" We looked more closely at the galaxy, the big pine cone, the shell - and everyone agreed - yes, they all had spirals!

We stopped and read the book Blockhead: The Life of Fibonacci by Joseph D'Agnese, and when we got to the part where he talks about his famous rabbit riddle: "There was a man who put two baby rabbits in a field. It takes rabbits one month to grow up and be ready to have babies. And it takes them one more month to give birth to a pair of baby rabbits. Every month a pair of grown-up rabbits gives birth to a new pair of baby rabbits. How many pairs of rabbits will the man have at the end of the year?" We wrote down the numbers in the riddles' solution...
1, 1, 2, 3, 5, 8...
and we asked: how can you continue the sequence? It did not take these mathematical thinkers long to figure out that the two previous numbers add together to create the next number in the sequence.
Then we looked at what happens when you graph these squares with the dimensions in a spiraling pattern on graph paper:

and there it was - the Fibonacci sequence and the beautiful golden spiral!

Those who were interested went on to explore this some more, some creating pages and pages of numbers following the sequence well into the thousands using calculators and other math tools. Some carefully taped pages and pages of graph paper together and continued to expand the spiral (see picture at the top). All of us will learn more about the Fibonacci sequence and the golden ratio as we delve into the Renaissance and Renaissance art in the months to come (did you know you can even find this ratio in the Mona Lisa?) I can hardly wait, and many of the kids can't either!

If you are as fascinated by the Fibonacci sequence as we are, check out this wonderful series of videos by Vi Hart at Khan Academy (this is one of 3 - they are all worth a look!):

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An exciting week of learning culminated in a visit from the education department from the Slater Museum of Natural History at the University...