To encourage students to look for and identify patterns
To assist students in making connections between numbers and ratios
To demonstrate to students how to measure and cut paper into squares
and rectangles
To facilitate the use of calculators in finding information
Student Objectives:
To measure and cut rectangles and squares
To record the measurements and find the ratios of the measurements
To graph the ratios found
To discover the similarities of the ratios of the rectangles
To understand that these similarities are called the Golden Ratio
Teaching Strategies:
Lecture/Discussion
Demonstration
Individual/Group work
Pencil/Paper
Manipulatives
Calculator Work
Prerequisite Information:
Previously, students will have completed Fibonacci's Rabbit
Problem, and completed the Fibonacci Numbers in Nature lesson applied
to a spreadsheet. Both lessons work with the Fibonacci pattern, 1, 1, 2,
3, 5, 8, 13, 21...They will have viewed a Square One video in which
this sequence of numbers helps solve a mystery, and they will have constructed
an equiangular spiral using Fibonacci squares and graph paper. It may be
assumed that students would have some recognition of the numbers in the
Fibonacci sequence.
Anticipatory Set:
Review Fibonacci sequence and the Golden Rectangle. Demonstrate what
makes the Golden Rectangle so ubiquitous in architecture. Have students
find the following URLs for examples of the Golden
Rectangle in architecture:
The Golden Rectangle in the Parthenon
The Golden Rectangle in the UN Building
LeCorbusier (architect)
The Golden Section in King Tut's Tomb
Materials:
Newspaper sheets
Scissors
Tape
Pencil
Calculators
Worksheet/Graph
Procedure:
1. Demonstrate the measuring and cutting of a newspaper sheet that
measures 89 cm by 55 cm (In order to do that, 2 newspaper sheets need to
be taped together and then measured and cut.)
2. Discuss the properties of the Golden Rectangle: any rectangle using
the Fibonacci numbers, i.e. 8" by 5"
3. Distribute materials to the groups
4. Have students measure and cut the first Golden Rectangle (89 cm
by 55 cm)
5. Students determine the ratio of the measurements by dividing the
larger number by the smaller and getting 1.618 (the Golden Ratio)
6. Students cut a square 55cm by 55cm off of the Golden Rectangle and
record the remaining rectangle's measurements (55cm by 34cm), and ratio
(1.6176)
7. Students continue to measure, cut, record and calculate the Fibonacci
numbers
Assessment:
1. Students should be able to measure and cut( Select and use appropriate
technology, instruments, and formulas to solve problems, interpret results
and communicate findings.
2. Students should be able to calclulate the ratio of those numbers,
and know that ratio as the Golden Ratio.