Fibonacci Sequence Board shops Mindful Math

The Fibonacci Sequence and Spiral is a mathematical phenomenon that we find reoccurring in nature, art and architecture.

If you look at the array of seeds in the center of a sunflower and you'll notice what looks like spiral patterns curving left and right. If you count these spirals, your total will be a Fibonacci number. Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. You can decipher spiral patterns in pinecones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner. ­

A number plants express the Fibonacci sequence in their growth points, the places where tree branches form or split. One trunk grows until it produces a branch, resulting in two growth points. The main trunk then produces another branch, resulting in three growth points. Then the trunk and the first branch produce two more growth points, bringing the total to five. This pattern continues, following the Fibonacci numbers. Additionally, if you count the number of petals on a flower, you'll often find the total to be one of the numbers in the Fibonacci sequence. For example, lilies and irises have three petals, buttercups and wild roses have five, delphiniums have eight petals and so on.

This Fibonacci Sequence can also be found in

Shells: Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral.

Spiral galaxies: The Milky Way has a number of spiral arms, each of which has a logarithmic spiral of roughly 12 degrees. The shape of the spiral is identical to the Golden spiral, and the Golden rectangle can be drawn over any spiral galaxy.

Hurricanes: Much like shells, hurricanes often display the Golden spiral.

Fingers: The length of our fingers, each section from the tip of the base to the wrist is larger than the preceding one by roughly the ratio of phi.

Animal bodies: The measurement of the human navel to the floor and the top of the head to the navel is the Golden ratio. But we are not the only examples of the Golden ratio in the animal kingdom; dolphins, starfish, sand dollars, sea urchins, ants and honeybees also exhibit the proportion.

DNA molecules: A DNA molecule measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral. In the Fibonacci series, 34 and 21 are successive numbers.

While this concept may seem complex the math is actually quite simple. The Fibonacci sequence is

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 ...

The next number is found by adding up the two numbers before it.

The 2 is found by adding the two numbers before it (1+1)
The 3 is found by adding the two numbers before it (1+2),
And the 5 is (2+3),
and so on!

In this work children can learn how shops create the Fibonacci Sequence, discover the the simple addition patterns used to create the sequence, and then use 1 cm wool balls to actually map out the math and create and beautiful Fibonacci Spiral. Beginning learners can use our mini 10 frames allowing another visual representation of how the sequence grows while developing an understanding and number sense within 10.

When working with my youngest daughter we began by sequencing the numbers least to greatest, and then matched the addition problem to the sum. She quickly caught on that to find the next equation she simply had to look at the bottom number of the addition problem and its sum. Then we used wool balls to map out the sequence in the spiral.

The wooden spiral holds the pattern until it reaches 21. However, I have included addition cards through 55, demonstrating that the pattern continues indefinitely.

In the full collection you will receive the wooden Fibonacci Spiral, wool balls to map out the sequence, and laminated addition cards, Fibonacci Description/Reference Card, 7 pictures of the Fibonacci Spiral in nature.

The sum will come attached to the problem. However, you may decide to detach them in order to extend the learning!