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We love math and all of its patterns and sequences! The Fibonacci sequence might just be our favorite – it’s an amazing mathematical pattern that can be found throughout nature.

To make the Fibonacci sequence, you begin with zero and one, and take their sum to arrive at the next number. In other words, the sum of the two preceding values equals the next value. So the first numbers are:

0, 1, 1, 2, 3, 5, 8, 13 and so on.

When you use the numbers in the Fibonacci sequence as a guide to drawing squares, the result is a mathematical spiral that can be found everywhere – from the petals of flowers to the ways galaxies are formed!

Want to map the Fibonacci sequence at home or in your classroom? Watch the video for an overview, gather the materials listed at the right, and follow the instructions below!

Required Materials

  • 1 large sheet of paper
  • marker
  • ruler

Step-By-Step Instructions

Step 1

Draw two 1×1 inch squares next to each other. Draw a number one in each one.

Step 2

On top of the 1×1 inch squares, draw a 2×2 inch box. The bottom of the rectangle formed by your first two squares equals one side of the new square as together, they are two inches in length. Write a number two in this box.

Step 3

Next to the 2×2 inch square and the 1×1 inch squares, draw a 3×3 inch square. The side of the rectangle formed by your first three boxes forms one side of the new square as together, they are three inches in length. Write a number 3 in this box.

Step 4

Below these boxes, draw a 5×5 inch square. In this case, the bottom of the rectangle formed by box 3 and the first two boxes forms one side of the new square as together, they are 5 inches in length. Write a number 5 in this box. Note we are following a counterclockwise direction.

Step 5

Finally draw an 8×8 inch square next to these boxes. Note that the sides of box 5, box 2, and box 1 form the side of the new box as together, they are eight inches in length. Write a number 8 in this box. Together, all the boxes form a large rectangle. When you draw a spiral outward from the first square (see the video), you’ll arrive at the golden spiral! Feel free to keep going and adding onto this drawing. The Fibonacci sequence is infinite – how far can you go?