"The Golden Rectangle"

Edwina R. Justice Gunsaulus Scholastic Academy
4420 South Sacramento Ave.
Chicago IL 60632
(312) 535-7215

Objectives (Staff):

Demonstrate a phenomenological approach to teaching mathematics.

Inspire others to use the approach.

Present new (to most participants) concepts.

Reinforce skills.

Objectives (Grades 6-8):

Measure using metric units.

Calculate averages.

Compare and round decimals.

Use calculators.

Examine Fibonacci Sequence and Golden Ratio relationship.

Relate mathematics to real-life situations.


Measure in advance and select items whose sides are in the approximate
ratio of 1:1.6.

file cards (assorted sizes) envelopes charge plates photos
greeting cards (assorted sizes) invitations pamphlets books
graph paper

Recommended Strategy:

Measure items and calculate the ratio of longer side divided by shorter

List quotients on the chalkboard and discuss similarities.

Calculate average.

Measure height and the distance from the top of the head to the middle
finger tip with arm extended to one side and calculate the ratio of the
two measurements.

Calculate group average.

Compare the ratio of body measurements to the ratio of measured items.

Determine a pattern and complete the sequence:

1, 1, 2, 3, 5, 8, 13, 21, ...
(Additional numbers are optional.)

Calculate the ratio of two successive numbers:

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

(The ratio 21/13 equals 1.6154 rounded to the nearest ten-thousandth and
represents the ratio of the sides of a golden rectangle.)

Compare the ratio of a golden rectangle to ratios of body proportions and
selected items.

Measure sections of layouts in magazines and newspapers and relate to
golden rectangle.

Make spirals.

Look for golden rectangles at school, home, and other places.

Performance Assessment:

Groups should look for five pictures or sections of magazines whose
dimensions appear to represent the sides of a golden rectangle. Measure and
record length and width and calculate the ratio of the sides (to the nearest
hundredth). Determine the average for the five items. The teacher should
compare the groups' results to the golden rectangle ratio.

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