To encourage students to look for and identify patterns
To assist students in making connections between mathematics and natural
science
To facilitate the use of technology in organizing information
Student Objectives:
To explore Fibonacci numbers as natural patterns as well as mathematical
patterns
To use a chart to organize data
To gather data and draw conclusions based on that data
To communicate findings in an organized manner
Teaching Strategies:
Lecture/Discussion
Demonstration
Individual/Group work
Manipulatives
Pencil/Paper
Computer spreadsheet
Prerequisite Information:
In previous lessons, students will have done the Fibonacci Rabbit
Problem to determine the numbers contained in the sequence. 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,
a golden rectangle, and a golden triangle. It may be assumed that students
would have a good recognition of the numbers in the Fibonacci sequence.
Anticipatory Set:
Discuss Fibonacci
patterns in nature. Show some examples. (Pine cone/ pineapple spirals,
fruit/vegetable sections, etc.) Show poster.
Materials:
Flowers (real/silk/pictures) with labels
Data sheets
Computer station (with spreadsheet program)
(Optional: other natural items such as artichokes, pine cones, pineapples,
seed pods, leaves, stems, branches, apples, green peppers, other fruits
and vegetables with sections, etc.)
Procedure:
1. Model activity using 1-2 flowers. (Have students record on their
data sheets.)
2. Distribute materials. (Or, set up several stations for access to
materials.)
3. Have students count petals (or spirals, sections, branching patterns,
etc.).
4. Students record name of flower (or object) and number of petals
(sections, spirals, etc.) on data sheet.
5. Collect data on "master" computer spreadsheet. (Students
may "report" data to recorder, or if time and logistics allow,
may enter their own data.)
Assessment:
1. Students should be able to identify preponderance of Fibonacci numbers
in items from class activity.
2. Students will locate at least 5 additional natural occurrences of
Fibonacci numbers as a homework extension of the lesson. (These may be
added to the data sheet later.)
Enrichment:
Students may choose to elaborate on, describe, draw or otherwise depict
Fibonacci numbers in nature as an individual final project for this unit.
A generic mailer GCI could be set up for collection of a broad base
of data from other classes.
Math 8: Use algebraic and analytical methods to identify and
describe patterns and relationships in data, solve problems and predict
results.
Math 10.A.3a: Construct, read and interpret tables, graphs and
charts as a means to organize and represent data.
Math 10.B.3: Formulate questions, devise and conduct experiments
or simulations, gather data, draw conclusions and communicate results to
an audience, using traditional methods and contemporary technologies.
Language Arts 5.C.3a: Plan, write, edit and revise documents
(e.g., databases, graphics, spreadsheets) using multiple sources.