## Objectives

- To practice completing whole number patterns.
- To explore different representations of patterns.

## Materials

- Compass
- Ruler
- Pencil
- Construction paper (a variety of colors)
- Scissors
- Glue

## Pre Investigation Questions:

- Examine the following pattern of dots and explain in words what the rule is for the pattern.
- Express the pattern in numbers and continue it up until the 10th entry.
- Is this an increasing pattern or a decreasing pattern?
- Can you think of a way to represent the 100th entry in this pattern?
- Compare with a friend! Did they represent the 100th entry in a different way? Compare and contrast your representations.

## Investigate!

- The pattern you have just discovered is very similar to a famous sequence known as the Fibonacci Sequence.
- Look up the mathematical definition of a sequence. How is it similar to a number pattern?
- Use this website to look up the number(s) that are missing from the pattern above to make it the Fibonacci Sequence.

## Create a Visual Representation of the Fibonacci Sequence

In this investigation you will create circles each with a diameter of the Fibonacci Sequence. There will be one circle for each number in the Fibonacci Sequence up to the 6th term.

- Use your ruler to set the compass so that it will create the desired radius. For example, if I want to create a circle with a diameter of 1, I will set the distance between the compass legs, which indicate the radius, to be 0.5.
- When your compass is set, use it to draw a circle on a piece of construction paper. Try to use a different colored piece of construction paper for each circle.
- Cut out the circle you have just drawn with your scissors.
- Repeat this until you have 6 circles- one for each of the first six terms in the Fibonacci Sequence. The radii of each of the circles will be: 0.5, 0.5, 1, 1.5, 2.5, and 4. Or if you want a slightly bigger one you could start with 1, and your sequence of radii would be 1,1,2,3,5,8.
- Glue the 6 circles you have cut out to a piece of paper in any design that you would like.

## Post Investigation Questions

- Work on the following questions with a friend.
- Compare and contrast the way you and your partner chose to arrange the circles on the piece of paper. Does it help you see the pattern in different ways?
- Can you see the general pattern of the Fibonacci Sequence? Explain.
- Together, use the internet to investigate where Fibonacci Numbers can be found in nature.