In math explorations all week, we have focusing on the sequence of numbers known as the Fibonacci series. This is a sequence of numbers named after Leonado of Pisa, known as Fibonacci, who studied them in 1202.
Quite simply, the sequence is generated by, after the starting numbers, adding each number to the one that preceded it.
0,1,1,2,3,5,8,13,21,34,55....
One of the most intriguing aspects of this sequence is it's relationship to the Golden Rectangle and Golden Ratio that we studied earlier in the week (see Monday's blog entry). If you divide one of the Fibonacci numbers by it's predececor, e.g. 21/13 you end up with a number that gets increasingly closer to the Golden Ratio. The Golden Ratio is close to 1.618. 21 divided by 13 equals 1.6153846 but interestingly, the further you travel down the Fibonacci trail, the closer these divisions bring you to the Golden Ratio. There's a high level math explanation of what is going on here for those of you who want to pursue it is. Just Google Fibonacci numbers and you'll find endless explanations of this.
In the Elmquoia classrooms, we looked at this and other patterns and then proceded to explore the fantastic and mysterious appearance of the Fibonacci sequence in other places. Did you know that the fibonacci patern can be found in pine cones, sea shells, sunflowers, trees to name but a few examples.
After introducing the sequence, we cut the children loose to engage in their own explorations. The students dicovered patterns, explored Fibonacci spirals and drew their own Fibonacci trees. (The preceding link is a YouTube video showing a Fibonacci tree.) Today, we had a great conversation about the purpose of this type of math workshop. Michelle and I believe that children can be, and should be, as excited about math as any other subject. This passion grows with the opportunity to see the awe and wonder that number can inspire. In discussion about their learning during this exploration, the students highlighted other habits of mind they employed. These included: persistance (creating that Fibonacci tree or spiral can be tricky initially), 
striving for accuracy (careful addition as the sequence grows), creating and imagining (finding different ways to display the sequence beyond pencil and paper (making a spiral with tape on the gym floor or using colored tiles 
to show the pattern of golden rectangles generated by Fibonacci numbers) and applying past knowledge ("hey, that tree over there has branches that follow the Fibonacci pattern). It was a wonderful reflection on the beauty and mystery of math.
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