## Lesson
Plan Guide

## Georgia
Learning Connections

**Creating Fibonacci’s Golden
Rectangle**

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This
is an extension of an existing unit on Fibonacci. Students will have already seen examples of
art and architecture that employs the Golden Rectangle. Students will have the opportunity to make a
Golden Triangle and “see” for themselves how the ratio of the sides approaches
0.618 and is formed by: __width __ = __length_______

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length (width +
length)

This lesson is designed for
gifted 6^{th} grade math students.

The Primary Learning Outcome,
other than simply creating an example of a Golden Rectangle will be that
students can construct a rectangle with Golden Rectangle proportions and
understand how ratios are used to determine its proportions.

**Assessed QCC: **Strand Problem Solving # 2 Topic Vocabulary:
Describes orally and in writing, using the appropriate mathematical
vocabulary, mathematical concepts and procedures, such as the reasoning
involved in solving problems or computing
AND Strand Number Sense & Numeration; Fractions
& Decimals # 37 Topic: Equivalence, Equivalent Representations Standard:
Expresses equivalent ratios as a proportion

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## Standards:
Local and/or National: Gwinnett
County AKS # 14 Use a ratio to compare two quantities #15 use proportions to
solve problems

**Total Duration:**
This component of the lesson should take 60 minutes

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## Materials and
Equipment: Photos of examples of Golden Rectangles in art and
architecture

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## Technology
Connection: __Geometer’s Sketchpad__

**Procedure: **

This construction activity
comes from __Geometry Activities for Middle
School Students with The Geometer’s Sketchpad__
by Karen Windham Wyatt, Ann Lawrence and Gina M. Foletta.

**Steps:**

1.
Construct a
square using the GSP features for construction.

2.
Construct a
midpoint and connect it to the point at the top of the right adjacent
side.

3.
Use that segment
as a radius and construct a circle.

4.
Extend the
original line segment to a point on the circle.

5.
Construct a
perpendicular segment to the side of the square with a point on the circle.

6.
Extend the top
side of the original square to the previously constructed segment.

7.
Hide all points and
lines leaving only the newly constructed rectangle.

8.
Measure base and
height of new rectangle.

9.
Substitute these
measurements into the ratio that defines a Golden Rectangle. (see above formula)

10. Have students
“stretch” the rectangle and note that the ratio always remains the same.

**Example:**

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**Assessment: **Students will print their work showing the ratios
after measuring the sides. They will
write a paragraph explaining what they did and what they learned.

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