**"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.

**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.

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