Fibonacci Fun

A note for parents, teachers, and other caring adults:

This activity can be as simple as counting practice or pattern detection for young learners (1st grade and up!). Make it more complicated by practicing finding the area of the rectangles (3rd grade and up) and by calculating further into the sequence as larger numbers emerge. For older grades (7th grade and up), this can be an opportunity to talk about ratio (specifically the golden ratio) and to explore the logarithmic spiral pattern embedded in the growth factor of the golden ratio.

Was that a lot of gibberish? Don’t worry about it — just enjoy exploring and the more complex implications of this activity will come through exploration and exposure.

This activity is meant purely as a playful introduction and a vehicle for skill-building.

What do DNA sequences, computer data storage, hurricane patterns, the number of petals on a flower, or the number of seeds in a fruit have in common?

They all follow a pattern that was famously observed and written about by the Italian mathematician Leonardo Fibonacci.

The pattern of counting that he noticed is one in which each number is the sum of the previous two numbers: 1, 1, 2, 3, 5, 8, 13, ... and on and on and on!

Fibonacci’s sequence leads to what is called the “Golden Rectangle”. What is that? How do these numbers make rectangles?

Let’s explore for ourselves!

You’ll need:

• Colored pencils (to keep the squares visually separate)
• Our FREE printable graph paper (or create your own, making sure it is at least 34 squares high and 55 squares wide.

Printable Grid and Instructions (PDF)

Using a colored pencil, start by coloring in the highlighted, single square. We’ll call this square a 1x1 square, because each side has a length of one square.

Next, color in a second square that is 1x1 and that shares one side with the first square.

Add a 2x2 square (a square that measures two lengths on each side) that shares a side with both 1x1 squares.

Now add a 3x3 square that shares a side with two other squares.

Add a 5x5 square that shares a side with the other squares.

Do you see a pattern yet? How would you describe it? What should come next? Add it on!

Here are some bonus challenges:

Can you fill the whole page, following Fibonacci’s sequence? It may take a few tries of repositioning your rectangles!

When you’ve filled the page, how many squares would you need to make the next number? How many squares would there need to be on that graph paper?

You’ll see Fibonacci’s sequence again as you progress down your math career, but enjoy this introduction and exploration!

Remember to celebrate Fibonacci Day every November 23 (11/23, the first numbers of the sequence)!

• math games
• student
• grades 1 - 8