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