Discovery Page 1

At the conclusion of this page the student will have constructed a geometric figure and be able to compare the dimensions of it to the Fibonacci numbers.

Directions:

Each group will get the following materials:

1. Sheet of graph paper

2. Protractor

3. Straight edge

1. Data form

As a group, look at the following sequence of numbers.

1, 1, 2, 3, 5, 8, 13 21, 34 …

(These numbers were first studied by a man known as Fibonacci. They are now called the fibonacci numbers.)

Get out the Data Page and, as a group, answer the first 4 questions.

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Get out the graph paper. Now the navigator will read the following directions; the geometer will draw each square on the graph paper, and label one side with its length; the recorder will write the data on the Data Page.

1. Draw a unit square at points A, B, C, and D. Each side is 1 unit long. Label the length of one side of this square "1".
2. Draw another unit square, adjacent to and directly above the first. ("adjacent" means next to) This square will include points E and F. Label the length of one side of this square.
3. Draw a larger square adjacent to and to the right of the first two squares. Each side of this square will be 2 units long. (That is, twice as long as the side of the first square.) This square will include points G and H. Label the length of one side of this square.
4. Draw a similar larger square below the first three squares. It should be large enough to fit evenly against the squares you have already drawn. Label the length of one side of this square.
5. In the same way, draw a another square to the left of the first four squares. Label the length of one side.
6. In the same way, draw another square above the first five. Label the length of one side.
7. In the same way, draw another square to the right of the first six. Label the length of one side.

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