Fibonacci randomly came up in our house this week. It is one of my favorite math related things to talk about with my kids, because it is so connected with the beauty of nature.
Fibonacci (also known as Leonardo de Pisa) was an Italian mathematician that introduced the decimal system to the Latin speaking world and is famous for a series of numbers that describe exponential growth and are often seen in nature. It's commonly explained as what would happen if you had a pair of rabbits. First you have 1, then 1 more (2), then 3, then 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, and so on. You can get these by adding the last two numbers each time.
My all-time favorite resource concerning this is a video you can find on Youtube called "Nature by Numbers" by Cristobal Vila. It's a gorgeous video showing the various ways Fibonacci numbers and the golden mean are found in nature.
I really think it can be a nice break from the usual basic mathematics to delve into these other mathematical concepts. I am a patently unmathematical person, but this is a fun concept to look at, and it helps for kids to be able to see that math is more than just arithmetic, can be found everywhere, and can, in fact, be beautiful.
A couple of fun kids books that deal with Fibonacci numbers are:
Rabbits Everywhere: A Fibonacci Tale
This cute little story recounts the tale of a mean wizard who wants to teach some villagers a lesson by planting a couple of ever reproducing rabbits in their gardens. The rabbits, of course, increase in a Fibonacci way.
This one merely counts up the Fibonacci sequence using animals, so maybe not the first I would recommend, but it's fun to look at the drawings.
Another one I do not have, but looks lovely, is Growing Patterns: Fibonacci Numbers in Nature.
If you know of some other good resources, please do share!