"The Golden Rectangle"

Edwina R. Justice              Gunsaulus Academy
10641 South Lowe Ave.          4420 South Sacramento Ave.
Chicago IL  60628              Chicago IL  60632
(312)468-3376                  (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.

Materials:

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 
     side.

     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.