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Larry Lesser “Math Song Sing-Along: Formula for a Hit!” join me on the choruses & become a choral-Larry! UTEP’s Bhutanese architecture was ‘Math Lens’ in Sept. 2008 Mathematics Teacher!

for lots of math & music resources, lyrics, MP 3 s, etc. , just Google me!

calculus co-inventor Gottfried Wilhelm von Leibniz “Music is the pleasure the human soul experiences from counting without being aware that it is counting. ”

Connections with structure of music: demos with acoustics, music theory, etc. (CCSSM Mathematical Practice standard #7: “look for and make use of structure”) e. g. , see Sept. 2009 Mathematics Teacher for how group theory and geometric transformations connect to music

MATH MUSIC Ordinal numbers naming intervals (e. g. , fifths) Least common multiple rhythm patterns; harmony (from pitches w/ low LCM) Fractions time signature; interval is a ratio of frequencies Geometric shapes instrument shapes (e. g. , triangle) Arithmetic sequence overtones (f, 2 f, 3 f, 4 f, …) Geometric sequence chromatic scale (in equal temperament) Sine function graph of (pure tone) sound wave Graph (pitch over time) musical notes on a staff Geometric transformations melodic transformations Permutations, Probability “change ringing” of bells; Mozart’s “Musical dice game” (1793) Statistics DATA SOUND: sonification SOUND DATA: traits of hit songs Group theory, modular arithmetic analyze the set of pitches in a scale Fourier series, partial differential equations musical sound, acoustics

math in lyrics of “regular songs”… • “One is the loneliest number” – Three Dog Night • “if I could count infinity” – Christine Kane • “ 100% chance of rain” – Gary Morris • “reduce me to the mean” – Richard Shindell • “random sample, hold the one you need” – Rush • “at the edges of the bell-shaped curve” – David Wilcox • “it’s like a Möbius strip” – Nelly Furtado

…and of Math Songs! Sometimes, the title is already a math word, like Taylor Swift’s “Mean”! Other times, I have to change it: Don Mc. Lean’s “American Pie” became “American Pi” 3 Dog Night’s “One is the Loneliest Number” became “One is the Likeliest Number” (HW: look up “Benford’s Law”)

Okay, let’s start singing with a song that helps students recall the 2 main circle formulas using the tune that helped us all learn the alphabet!

“Circle Song” lyric © 2004 L. Lesser Take your finger ‘round a jar -Circumf’rence equals 2 pi ___; For area, you multiply R squared by that number ___. Twinkle, twinkle, you’re a star Knowing math will take you___!

to recall (6 sig. figures of) Chorus of “American Pi” (lyric © L. Lesser): Find, find the value of pi, starts 3 point 1 4 1 5 9 A good ol’ fraction you may hope to define But the decimal never dies, The decimal never dies….

(1 st verse of) “American Pi” lyric L. Lesser In the Bible we do see the circle ratio appears as 3, or a little more. . That genius Archimedes found with polygons, an upper bound Of 22 / 7 for sure! The Chinese got it really keen: 355 over 113! More joined the action with series and continued fractions. In the 1700’s, my oh my, the English coined the symbol π, Then Lambert showed it was a lie to look for rational pi. He started singing . .

Chorus of “American ” lyric © L. Lesser SING ALONG! Find, find the value of pi, starts 3 point 1 4 1 5 9 A good ol’ fraction you may hope to define But the decimal never dies, The decimal never dies…. find this song on Google. Video, You. Tube, and my webpage for “Pi Day”(3/14)!

Just like history teachers use “we didn’t start the fire…” In preparation for PI DAY, I share the lyrics of “American Pi” with my Algebra 1 students who spend part of a week researching topics & making a Power. Point, book or short story. -- email from Melissa S. , HS teacher in Nokomis, IL

Math club (from Shaker Heights, OH) wrote a song from first 50 digits of pi: B middle C D E F G A B C D 0 1 3 4 5 6 7 8 9 2 (see April 1987 Mathematics Teacher)

Capo followup When we shorten the string length that’s free to vibrate, the note’s pitch (frequency) goes: a) up b) down String length L is _______ proportional to frequency F. a) directly b) inversely L = k F L = k / F

Wait! My guitar’s 6 strings have same length but different notes! Mersenne’s Laws include length L, weight W, force F: Frequency =

a more concrete way to perceive frequency(pitch) (thanks, Leon Harkleroad!) As turning blades of “siren whistle” speed up, then slow down, do you hear frequency (cycles/second) rise, then fall?

pick a frequency to graph and play

possible benefits of M&M: Multidisciplinary connections, Memory aid, Multiple intelligences, Motivation, Making community, Math anxiety reduction, Mashing stereotypes (content, class, teacher), Modelling stretching, etc.

a classroom study (Van. Voorhis, 2002) 2 equal-GPA sections of stats Section R read 3 definitions aloud; Section S sang 3 stat jingles (for same concepts) S did better than R on relevant test items p <. 05 S had high correlation between test score and self-rated jingle knowledge p <. 05

“What p-Value Means” lyric © 2005 L. Lesser tune: “Row, Row Your Boat” It is key to know What p-value means – It’s the chance (with the null) you obtain data that’s At least that extreme!

QUIZ: a “work problem” I sang that song by myself in 10 seconds, so how long would it take for a group of 5 singers?

Georgia’s gift when I became a dad after 90 s “Mozart effect” studies

lotta lottery outreach • adult ed. courses • media coverage (newspapers, radio/TV from local to CNN) • features in teacher-friendly journals (e. g. , Sept. 2012 Mathematics Teacher) • Lottery Literacy webpage; You. Tube video • a song: #1 country song whose title begged to be made into a lottery education song!

1 / / On a | warm summer’s evenin’ on a| 4 / 1 / | train bound for nowhere, I | / / / | met up with a gambler-- we were| 5 / / / | both too tired to sleep, so| example of “Nashville numbering system” for chord charts

“The Gambler” © 2001, 2009 L. Lesser On a warm summer’s evenin’, on a train bound for nowhere, I met up with a gambler -- we were both too tired to sleep. So he told me how he planned winnin’ lottery prizes ‘Til, as a math teacher, I just had to speak: “Son, you track those draws, you say ya got a system– You call some numbers “hot”, you deem others “due”; But I insist, they each have the same chance– If you’re gonna play the game, boy, Ya gotta know what’s true!”

“The Gambler” © 2001, 2009 L. Lesser SING ALONG: You gotta Know when you pick ‘em, What’s superstition, Know what is strategy And know when there’s none! You never try to learn this At the 7 -11: Take the time right now for learnin’ When the singin’s done! [now, watch my capo do a math-&-music “translation”…]

“The Gambler” © 2001, 2009 L. Lesser Now all sets of numbers are equally unlikely, More rare than death by lightning, still there’s somethin’ you should know; If you should happen to win that big jackpot, You’ll win more money if you picked it all alone! So avoid those numbers that more folks are playin’: Like 7’s and birthdays and sequences, too. ‘Til this song gets famous, you’ll have the advantage– Maybe you’ll thank me with a share of your loot!”

“The Gambler” © 2001, 2009 L. Lesser SING ALONG : You gotta Know when you pick ‘em, What’s superstition, Know what is strategy And know when there’s none! You never try to learn this At the 7 -11: Take the time right now for learnin’ When the singin’s done! [now, watch my brief ‘steel guitar solo’…. ]

‘harmonics’ in my ‘steel guitar solo’ I didn’t press any strings all the way down, just touched some at their midpoint, making those strings vibrate in halves Halving wavelength doubles frequency since wavelength = (speed of sound)/frequency

from the 2001 play PROOF (that won Tony & Pulitzer Awards), here’s a song about -1

QUIZ what happens if you give this hotel sign a quarter-turn?

the “Hilbert Hotel” David Hilbert is no Hilton Hotel: infinite # of rooms always full, but always room for more guests!

lyric © 2000 -2012 L. Lesser On a dark desert highway – not much scenery Except this long hotel stretchin’ far as I could see. Neon sign in front read But it was late and I was tired, so I went inside to plea. The clerk said, “No problem. 1 2 3 4 5 6 …. Here’s what can be done– We’ll move those in a room 1 2 3 4 5 6 …. to the next higher one. That will free up the first room and that’s where you can stay. ” I tried understanding that as I heard him say:

“Hotel (Called) Infinity” lyric © 2000 -2012 L. Lesser CHORUS (sing along!) “Welcome to the Hotel called Infinity Where every room is full (every room is full) Yet there’s room for more. Plenty of room at the HOTEL called Infinity Move ‘em down the floor (move em’ down the floor) To make room for more. ”

“Hotel (Called) Infinity” © 2000 -2012 L. Lesser My mind got more twisted when I saw a bus without end 1 2 3 4 5 6 …. With an infinite number of riders coming up to check in! 1 2 3 4 5 6 …. “Relax, ” said the nightman. “Each one will move to the double of their room number to free the odd-numbered rooms. ” Last thing I remember at the end of my stay– It was time to pay the bill, but I had no means to pay. The man in room #3 smiled, “Your bill is on me. #4 pays mine, and so on, so you get yours for free!

“Hotel (Called) Infinity” lyric © 2000 -2012 L. Lesser CHORUS (sing along!) “Welcome to the Hotel called Infinity Where every room is full (every room is full) Yet there’s room for more. Plenty of room at the HOTEL called Infinity Move ‘em down the floor (move em’ down the floor) To make room for more. ”

QUIZ Speaking of infinity, what’s the world’s longest math song? Hint: it uses “aleph null” ( , )0 א which is the cardinality of {1, 2, 3, …}

“World’s Longest Math Song” (author unknown) 0 א bottles of beer on the wall 0 א bottles of beer Take one down, Pass it around…. 0 א bottles of beer on the wall! (repeat over & …. ) (see Sept. 2010 Math Horizons for more variations!)

World’s Longest Math Song: “all-ages version” 0 א bottles of beer on the wall 0 א bottles of beer Take one down, Pass it around…. 0 א bottles of beer on the wall

QUIZ TRUE or FALSE? Fractions are challenging not only for students, but also for 5 out of 4 adults!

math & music connection: Cuisenaire rods named for conservatory composer Georges Cuisenaire who became an ES principal seeking fresh ways to teach math! ¾ = ¼+1/8+¼ = ½ + ¼

songs can help make connections to: language and culture

On Top of a Fraction lyric © 2004, 2006 L. Lesser (tune: “On Top of Old Smokey”) On top of a fraction is the numerator-It is the number of pieces you store. But we call the bottom denominator-It is the kind of each piece, señor.

“On Top of a Fraction” lyric © 2004, 2006 L. Lesser Like denomination of money or faith, Like 3 rds or 7 ths or halves or 8 ths. So denominators can be explained Because in Spanish, nombre means name!

“On Top of a Fraction” lyric © 2004, 2006 L. Lesser While on top of a fraction, we enumerate! That means to count up those of the same trait. & when we add fractions, make bottoms the same. Add apples to apples; add 8 ths to 8 ths.

“On Top of a Fraction” © 2004, 2006 L. Lesser Think about music: the time signature Is really a fraction – you can be sure That fraction for this tune is three-quarter time – So in each measure, 3 quarter-notes we find!

from PBS-TV kids show “Blast Beyond” (episode 29 of season 1 archived at kcostv. org)

Speaking of fractions, do ratios of “nice” numbers sound “nice”? Compare sound of 2: 1 to √ 2: 1 using a guitar …. or a monochord (buy one or make one (see 3/82 MT) like the first Mathemusician, Pythagoras!

QUIZ: Which radio wave is FM? (hint: FM stands for “_______ modulation”) (another hint: same answer for “vibrato”)

Classroom demo with a tuning fork, blowing across soda bottle, etc. (mike CBL GC)

if not yet ready to try melody…. Give rap a chants chance -Rap still has rhythm ‘n’ rhyme (shortest example: SOH-CAH-TO-A) Try this (algo)rhythm: Stomp-stomp-clap-(rest) 1 2 3 4

For graphing y = m x+b: L. Lesser adaptation of 1998 version by former IL teacher-of-the-year & NCTM Board member John A. Carter Buddy you’re tryin’ to draw the line For the m and b we’re assigned: Ain’t hard you see, put your pencil on the b, One more point will guarantee that….

“We Will Graph You!” © 1998 Carter/Lesser sing-along: We will, we will Graph you!

“We Will Graph You!” © 1998 Carter/Lesser So now you know the y-intercept; Here’s how we find the rest of it: Up with rise, across for run, Plot another point & when they’re strung, sing:

“We Will Graph You!” © 1998 Carter/Lesser sing-along: We will, we will Graph you!

3/31/02 [Melbourne] Herald Sun

QUIZ: Which tune(s) has/have been used for the quadratic formula? a) Pop Goes the Weasel b) Frère Jacques c) Battle Hymn of the Republic d) Amazing Grace e) ‘Gilligan’s Island’ theme f) Macarena g) A school ‘fight song’ h) All of the above

song traits are basis of music recommendations (Pandora, Mufin, etc. ); is there a “formula” for a hit? (e. g. , scoreahit. com; uplaya. com)

“but Larry, I have no talent!” • “Hey, it didn’t stop me!” • “If you can walk, you can dance. If you can talk, you can sing. ” – Zimbabwean proverb • Do we let students with ‘fear of no talent’ give up on math class? • Good to recall what it’s like to learn new things. • There’s a continuum of options! Spotlight student talent, collaborate with school’s music teacher, press “play” for a soundfile from singaboutscience. org, etc.

“but Larry, I have no class time to spare!” • Some raps/songs are as short as 10 seconds • Song can help retention more than saying things, and that saves time! • A little does a lot: if a minute of fun halves anxiety and doubles attention the rest of the hour, isn’t it worth it?

in the big picture… • Song is just 1 of 20 ways to make class “fun” (Lesser & Pearl, Nov. 2008 Journal of Statistics Education) • “Fun” is just one of many ways that may increase student engagement, learning, attitude, or motivation (I also incorporate “serious” contexts such as equity) • Fun is FUNdable: Dennis Pearl (Ohio State), John Weber (Georgia Perimeter College), and I got a 2012 -14 NSF grant on use of fun items

some thank-you’s before my last* song • GMC conference team: Carole, Denise, etc. • my AASU friends (Jane Barnard, etc. ) • Art Benjamin, Dane Camp, Dennis Pearl, etc. • Mom & Dad for the first guitar & lessons! • Pete at (Conyers) * barring an “encore”

what if things were run by math teachers, not politicians?

The Day Math Teachers Took Over the World! (© 2008, 2012 L. M. Lesser) No one got lost in Boston again: The teachers mapped the streets into a nice Cartesian grid, And the road-coloring theorem was known by every kid The day math teachers took over the world!

The Day Math Teachers Took Over the World! (© 2008, 2012 L. M. Lesser) All the politicians had to clean up their stats And forgo call-in polls and misleading graphs, And approval voting kept elections on track The day math teachers took over the world!

The Day Math Teachers Took Over the World! (© 2008, 2012 L. M. Lesser) Yeah, math teachers fin’ly decided to uprise— ‘Cause their functions were underutilized! They divided-and-conquered, got radical, too: They brought integration to every school! ∑ ∫ ∆ =

The Day Math Teachers Took Over the World! (© 2008, 2012 L. M. Lesser) NUMB 3 RS was the TV show on top of the list, And the math that’s in music gave everyone bliss And consumer scams all took hits The day math teachers took over the world!

The Day Math Teachers Took Over the World! (© 2008, 2012 L. M. Lesser) That day brought peace – no axes to grind: Everyone spoke rationally, with a logical mind, And fair division solved disputes for all time The day math teachers took over the world!

have a great conference & enjoy Rock Eagle! Professor Lesser Mathemusician of UT-El Paso

my version of “Mean”, 2012 Grammy-winning country song of the year

“Mean” (lyric © 2011 L. Lesser) But it can get pulled off by just one single point, And you don’t know what you don’t know…

“Mean” (lyric © 2011 L. Lesser) Sometimes, data have a real asymmetry Or values that are really quite extreme. In those cases, better use the median If what’s typical is what you need – That’s not gonna be the mean! That won’t be the mean with outliers, just forget it, do you see just what I mean & mean….

“Mean” (lyric © 2011 L. Lesser) Sometimes, data have a real asymmetry Or values that are really quite extreme. Yeah, yeah! In those cases, better use the median If the middle is what you need – Not gonna be the mean!

my followup song to “We Will Graph You!” (lyric © 2005 L. Lesser) The math that I knew – I’d memorize To get me through what teachers devised! And mistakes, we’ve all made a few But I learned the reasons behind the math that we do And I went on & on…. .

“We Are the MATHLETES!” © 2005 L. Lesser SING ALONG! We are the MATHLETES, my friend, and we’ll keep deriving ‘til the end We are the MATHLETES, No time to sell fries, ‘Cause we are the MATHLETES of the world!

thanks, ya’ll ! Professor Lesser Mathemusician of UT-El Paso

That’s Odd! (© L. Lesser 2000 -2012) 1, 3, 5, 7, or 9 Is the end of a number of what kind? THAT’S ODD! When there’s no Olympics, winter or summer, That year is what kind of number? THAT’S ODD!

That’s Odd! (© L. Lesser 2000 -2012) If you pick a book and open wide, What page number’s on the right-hand side? THAT’S ODD! An interstate goin’ north and south Has what kind of number for the route? THAT’S ODD!

That’s Odd! (© L. Lesser 2000 -2012) Do a cascade so nothin’ falls Takes what number of juggling balls? THAT’S ODD!

Stayin’ with 5 lyric © 2006, 2007 Larry Lesser Well you can tell by the way I use my chalk That I teach math & I love to talk With my class usin’ rhyme About a number that is prime! Now it’s all right, it’s okay-Use 5 senses every day. We can try to understand The Roman “V” on my hand… CHORUS: Whether it’s a wonder, this Fibonacci number, I’m stayin’ with 5, stayin’ with 5. Symmetry flows in an apple or a rose: Stayin’ with 5, stayin’ with 5. Ah, ha, ha, ha, stayin’ with 5…….

Stayin’ with 5 lyric © 2006, 2007 Larry Lesser Platonic solids – there are 5, Like the vowels – not countin’ y. Starfish arms, Olympic rings, Playin’ hoops on a team: You know it’s all right, it’s okay Muslims pray 5 times a day. We can try to understand Patterns in a pentagram… CHORUS: Whether it’s a wonder, this Fibonacci number, I’m stayin’ with 5, stayin’ with 5. Symmetry flows in an apple or a rose: Stayin’ with 5, stayin’ with 5. Ah, ha, ha, ha, stayin’ with 5……. Gonna celebrate Cinco de Mayo: we’re gonna “take 5”! 5 is everywhere, somebody give me, somebody give me a “high 5”!

QUIZ Before Caesar added July(“Julius”) and August(“Augustus”) to the calendar, October was the _____th month.

“ 8 is so neat!” lyric © 2007 by L. Lesser Oh I really love 8, that Fibonacci cube! 8 scale notes make octaves I need for a tune. Spider, scorpion, pints in a gallon: I just can’t help but love 8 -- 8 is so neat!

“ 8 is so neat!” lyric © 2007 by L. Lesser Love to play some ‘ 8 ball’: always I'm behind, Thinking of umbrellas and big red stop signs. Octopus, tug-of-war, cylinders in a big car: I just can’t help but love 8 -- 8 is so neat!

“ 8 is so neat!” lyric © 2007 by L. Lesser 8, you're so neat -- I love you! Pieces of 8 are not enough to show I care Ooh, I feel like countin’ corners of a cube— It’s a fast boat’s number & name of its crew. Chessboard, jellyfish, a byte is 8 bits: Ancient Greeks and Romans had 8 days a week, ‘cause 8 is so neat!

QUIZ: What’s the title of Paul Simon’s only #1 hit as a solo artist? hint: there’s a number in it

the “Lesser-known” origin of ‘ 50 Ways…’ 1 st verse begins: “The problem is all inside your head, ” she said to me. “The answer is easy if you take it logically…” Chorus begins: “Just work from slip out the back, Jack. Make a new plan, Stan…”

50 Ways to Work a Problem (lyric 1998 L. Lesser) Just say what’s known, Joan, And what’s to find, Caroline. What rings a bell, Nell, To what we’ve done? Make a plan, Stan, Follow it through, Sue, Try to extend, Ken, And we’ll be done!

Simon says… "the more you are familiar with problem solving, you recognize variations on problems that you've solved before. . The typical problems, everyone learns to solve in the early years of your songwriting. But with the atypical problems, experience and technique become invaluable. " -- Paul Simon, interviewed in Sept. /Oct. 2006 Performing Songwriter

parallels: doing math & songwriting • “Flashes of inspiration” may come anytime, but are usually preceded by much reflection, false starts, and prior effort of developing a toolkit and repertoire • Essence comes fast, details take longer • Versions can have same “content” but differ greatly aesthetically • Some are steps toward something “bigger” • Useful to try varying structures or starting points • Peer feedback/collaboration helpful! • Cultivate “whole-brain”, not just left or right-brain

QUIZ When working a problem, what do your students most often forget to do when they think they’re done?

“Check Your Work” © 2001 L. Lesser I’ve been workin’ on a problem seems like all the day! Now I fin’ly got a number, so I’ll put my book away— But then I hear my teacher calling: “Don’t rise up so soon! You need to check your work for errors – No one is immune!”

“Check Your Work” © 2001 L. Lesser [ (Dinah won’t you check)3 x your work? ] 2 x Somethin’ went wrong for NASA Near Mars in ’ 99: They lost a pricey spacecraft From units not aligned!

“Check Your Work” © 2001 L. Lesser So check your units now and the answer’s magnitude Does good reasoning back what you conclude?

QUIZ Are we 100% sure there’s a birthday match (of month & day) among all the people in this room?

QUIZ So how many people are needed to be 50% sure of at least one ?

“Birthday Song” lyric © 2001 L. Lesser Happy birthday to you— Bring another 22: Then we’ll have even chances Of a match in this room…. Or many more! to learn why, see my article in May 1999 Mathematics Teacher