Transcript Logarithms and Music

Logarithms and Music
Christina Colangelo
Lesson Plan
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Introduction
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Justification for Lesson
Description of Population
Prerequisite Knowledge
Major Math Content
NCTM Standards
Length of Time
Lesson Goals
Instructional Aids
Lesson Plan
Evaluation
◦ Positives/Negatives/Effectiveness
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Personal Response
Lesson Plan
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Students tested vaguely remember
learning anything about logs
◦ Couldn’t recall why logs were used or what
they were used for
This is lesson is a great way for students
to conceptualize logs and see them used
in a real life situation
 3 day lesson, each class 60 minutes
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Lesson Plan
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Major Math Content Covered
◦ Functions
 Linear, Exponential, Logarithmic, Sine/Cosine,
Bounded, Damping
 Graphing & Manipulations
◦ Ratios
Lesson Goals
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Understand a real life application of
logarithmic functions
Learn the basics of notes, how they are
arranged on a piano, and their frequencies
Understand how pitch and frequency are
related to logarithmic functions
Learn what damping functions are and how
they are applicable to music
Realize how mathematics fits into the real
world and possibly inspire someone to
explore the field of math and music
Part 1: 3-5 Songs
What did you notice about how the song ended?
What was different between each song’s ending, if
anything?
 How did the song end? Fade out? Abrupt stop?
Other?
 Think about the functions we have discussed
throughout Algebra I and II (linear, exponential,
polynomial, rational, logarithm, periodic). If you
were to pick one of those functions to describe
the way in which the music ends, what function
would you choose? Why?
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Brief Topics
Frequency/Pitch & their relationship
 Damping functions
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◦ Bound functions
◦ Sound waves = Sine waves
◦ Use damping function to bound the end of
the sound wave
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Listen to sound clips that have damping
functions applied to them (the will fade
out the sound)
◦ Linearly, Exponentially, Logarithmically
Conclusion
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Students start to hear the logarithmic
fade sounds the best and most natural
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We also find out that music programs
adjust the base of a logarithmic to
determine how fast or slow a song fades
out
Conclusion
After the lesson, students will listen to
the 5 songs again
 Students get to reevaluate what they said
and write a short composition on how
each song fades out and why they think
that
 New Found Glory – “On My Mind”
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◦ Computerized linear fade with extremely
small slope
Negatives
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Timing for questions or confusion (originally
underestimated so I had to readjust time)
Math journal for opening questions or other
exercises
5 songs were too many for part 1, maybe cut
it down to 3
Some students thought thinking of functions
off the top of their head were too hard
when relating them to the songs…draw
them on the board?
Negatives
I never allocated time to go over
homework during class
 I never had a closing for each day
 Could students figure out frequency or
pitch equations themselves?
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◦ Not enough time or knowledge
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Frequency/Decibel parts a bit confusing
for some student
Positives
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Opening with music clips: “real attention
grabber”
Connection I was drawing between
functions and music was great, although in
the beginning they didn’t see how it was
possible
The use of the piano was a big hit!
Tissue box demonstration was thrilling
◦ Different size rubber bands stretched across
opening to show students the differences in
pitches
Positives
Continuously recapping
 Use of technology (music, sound clips,
sound wave examples, piano, graphing
calculator projections, etc)
 “Autumn Fell” example was great!
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◦ Sound Clip: faded out linearly, exponentially,
logarithmically
Reference Sheet & Handout
 Composition was a great conclusion
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Effectiveness
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Extremely interesting to students
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Students able to connect with material
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Although some students didn’t completely
understand all the music material they
enjoyed learning about it
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Students said they learned a lot