6) fibonacci spiral (2)

4th February 2010

Objective: to create a Fibonacci spiral

Skills: Making Links and Questioning

By the end of the lesson:All: will be able to generate terms in the Fibonacci sequence.

Most: will be able to complete the Fibonacci spiral.

Some: will colour their Fibonacci spiral.

Starter

• How far can you get with the Fibonacci sequence?• You have 3 minutes to get as far as you can.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946,

17711, 28657, 46368, 75025....

Fibonacci Spiral

Fibonacci Sequence

• Here are the first terms of the sequence that we will be using to create our spiral.

1, 1, 2, 3, 5, 8, 13, 21, 34

• Step 1• Draw a rectangle 34 squares long and 21

squares high• DOUBLE CHECK AFTER YOU HAVE DONE IT

Fibonacci Spiral

• Step One

21 squares

34 squares

Fibonacci Spiral

• Step Two• Turn the page clockwise, count in 21 squares and draw a line

from one side to the other.

Step TwoTurn the page clockwise, count in 21 squares and draw a line from one side to the other

21 squares

34 squares

13 squares

21 squares

Fibonacci Spiral

• Step Three• Turn the page clockwise and count in 13 squares and do a line

across until you meet the previous line.

21 squares

34 squares

21 squares 13 squares

13 squares

8 squares

Fibonacci Spiral

• Step Four• Turn the page clockwise, count in 8 squares and draw a line

across.

8 squares

5 squares

Fibonacci Spirals

• Step Five• Turn the page clockwise and count in 5 square and draw a

line.

5 squares

3 squares

Fibonacci Spiral

• Step Six• Count in 3 squares, draw a line. Turn again and count in 2 squares and draw a line. Finally turn and count in 1 square and draw a line.

Fibonacci Spiral

• Now you need to use a compass to draw the curves.

• Set them as wide as they need to be to draw a quarter circle.

• You will need to adjust them for every section.

Fibonacci Spiral

Put your compass point on this point.

Put your pencil on this point

Fibonacci Spiral

• When you have completed it, colour it in.