Grade Level: 10 - 12
Subject: Mathematics and Music
Learner Outcomes:
Duration of Lesson: 4 - 5 class periods (approximately 200
minutes)
Materials:
Student activity worksheets:
Items needed for Activity #6:Who is Fibonacci...(needed for Activity #1) Creating the Fibonacci Series (needed for Activity #2) Fibonacci and a Pair of Rabbits Activity (needed for Activity #3) The Golden Ratio (needed for Activity #4) Pascal's Triangle Form Worksheet (need for Activity #5) Pascal's Triangle (needed for Activity #5) Fibonacci and Nature (needed for Activity #6) Dominoes to Fibonacci (needed for Activity #7)
Items needed for Activity
#7
Technology Tools/Courseware:
Teacher Notes:
Each of the activities
described can be extended or abbreviated according
to individual student needs and levels.
Procedures:
Activity 1: "Who is Fibonacci..."
Students are to access the website, "Leonardo Pisano Fibonacci" or use
the
information found in AIMS Foundation's book, Historical Connections
in
Mathematics,
Volume III to learn about the life of Fibonacci. Then using
a word
processor, they are to create a fact sheet of highlights of his life/career.
Activity 2: "Creating the Fibonacci Series"
Following the steps outlined on the activity worksheet, students are to
calculate and
describe algebraically the first 20 numbers of the series.
Activity 3: "Fibonacci and a Pair of Rabbits"
Let students work in teams of 3 to 4 members. Each team is to determine
the number
of rabbits generated at the end of 12 months. They will discover
that the number of
rabbits in each successive month reflects the numbers in the Fibonacci
Series.
Activity 4: "The Golden Ratio"
Students are to access the website, "The Golden Ratio" in order to
learn about a connection of the Fibonacci Series to music. Students
will read
about the Golden Ratio, how it is found, and how it has been used by musicians.
They will also try some Fibonacci puzzles related to this ratio.
Activity 5: "Pascal's Triangle"
Students are to fill out a blank Pascal's Triangle
form. Once the numbers of the
form have been filled in, the students are to lightly draw diagonal lines
from the
left side of the triangle to the right side. They are to find the
sum of the values
of each diagonal. They will discover that this results in the Fibonacci
Series.
Students can access the website, "How
Pascal's Triangle is Constructed" to
check the calculations made to see if they were correct.
Activity 6: "Fibonacci and Nature"
Using the food, fruit, and nature items listed above in the materials list
for this
activity, teams of 3 to 4 students are to use an item to count the item
sections.
They will discover that the sections are arranged in the Fibonacci Series
values.
Either before, or after, looking at the items, the students may access
the following
website, "Fibonacci Numbers and the Golden Section". This site allows
the
students to read about the Fibonacci Series and nature.
Activity 7: "Dominoes to Fibonacci"
Let students work in teams of 2 to 3 members. Give each team of students
a set
of dominoes. Following the illustrations shown on the worksheet for
this activity,
the students are to build with the dominoes the rectangles described for
'n' number
of dominoes. Each team is to construct a chart which illustrates
the solutions they
found. After a pre-set amount of time set by the instructor, a group
discussion is
to be held in which the students compare solutions. In this group
discussion, the
students will discover that the Fibonacci Series is generated.
Modifications:
Activities #1, #2, #3 and #5 can be used with average and below students.
Enrichment Activities:
Activities #4 and #6 can be used for extension activities.
National Conference of Teachers of Mathematics Standards:
References:
"Historical Connections in Mathematics, Volume III", AIMS Foundation, pages 9 - 11
Authors:
Kathleen G. Corbett
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me mail
Barbara S. Lockhart
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me mail
Judith C. Shew
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me mail
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