logarithms and music
TRANSCRIPT
Logarithms and MusicLogarithms and MusicChristina Colangelo
Lesson PlanLesson PlanIntroduction
◦ Justification for Lesson◦ Description of Population ◦ Prerequisite Knowledge◦ Major Math Content◦ NCTM Standards◦ Length of Time
Lesson GoalsInstructional AidsLesson PlanEvaluation
◦ Positives/Negatives/EffectivenessPersonal Response
Lesson PlanLesson PlanStudents tested vaguely remember
learning anything about logs◦Couldn’t recall why logs were used or
what they were used forThis 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
Lesson PlanLesson PlanMajor Math Content Covered
◦Functions Linear, Exponential, Logarithmic,
Sine/Cosine, Bounded, Damping Graphing & Manipulations
◦Ratios
Lesson GoalsLesson GoalsUnderstand 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 SongsPart 1: 3-5 SongsWhat 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?
Brief TopicsBrief TopicsFrequency/Pitch & their relationshipDamping functions
◦Bound functions◦Sound waves = Sine waves◦Use damping function to bound the end
of the sound waveListen to sound clips that have
damping functions applied to them (the will fade out the sound)◦Linearly, Exponentially, Logarithmically
ConclusionConclusionStudents start to hear the
logarithmic fade sounds the best and most natural
We also find out that music programs adjust the base of a logarithmic to determine how fast or slow a song fades out
ConclusionConclusionAfter the lesson, students will
listen to the 5 songs againStudents 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”◦Computerized linear fade with
extremely small slope
NegativesNegativesTiming 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?
NegativesNegativesI never allocated time to go over
homework during classI never had a closing for each dayCould students figure out
frequency or pitch equations themselves? ◦Not enough time or knowledge
Frequency/Decibel parts a bit confusing for some student
PositivesPositivesOpening 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
PositivesPositivesContinuously recapping Use of technology (music, sound
clips, sound wave examples, piano, graphing calculator projections, etc)
“Autumn Fell” example was great!◦Sound Clip: faded out linearly,
exponentially, logarithmicallyReference Sheet & HandoutComposition was a great conclusion
EffectivenessEffectivenessExtremely interesting to students
Students able to connect with material
Although some students didn’t completely understand all the music material they enjoyed learning about it
Students said they learned a lot