### Transcription

Life of FredButterfliesStanley F. Schmidt, Ph.D.Polka Dot Publishing

2011 Stanley F. SchmidtAll rights reserved.ISBN: 978-0-9791072-5-2Library of Congress Catalog Number: 2011924327Printed and bound in the United States of AmericaPolka Dot PublishingReno, NevadaTo order copies of books in the Life of Fred series,visit our website PolkaDotPublishing.comQuestions or comments? Email Polka Dot Publishing at lifeoffred@yahoo.comFirst printingLife of Fred: Butterflies was illustrated by the author with additional clip art furnished underlicense from Nova Development Corporation, which holds the copyright to that art.

A Note Before We Beginthe Second Book in the SeriesWe all have dreams for our children. So quickly they grow up.We would like them to have more than we had when we wereyoung. Medicine is better nowadays. Dentistry is better.Even toys have improved a little bit.Boy looking at toys.Taken by G. G. Bain in1910Choices for your children’s math education have widened. In theold days, the math books all looked pretty much alike. A lesson would tellhow to do something and then give 40 problems. Then the next lessonwould tell how to do something else and give 40 more problems.But they never really told why your child should learn the stuff.Then came the colorful “new” math books. They were filled withphotographs of jet airplanes and four-color diagrams. They weresometimes called coffee table math books: heavy, pretty, and expensive.7

And each lesson would tell how to do something and give 40 problems.They were like the old math books except they had wore lipstick.Then came video math “education.” Someone stood at ablackboard and read the lesson to the child. They were even moreexpensive than the coffee table math books.Your child had even lessexperience in learning how to read.Since learning how to learn by readingis one of the most important skills forcollege and later life, video was a step inthe wrong direction.Each video lesson told how todo some piece of math and gave 40problems to do.And they never learned why theywere supposed to learn the math.Learning by videoIn the old math books,in the coffee table math books,in the video,math was sealed off from the rest of the world. Thepictures of jet airplanes or video of someone at the blackboard brought apredictable response from kids: “So what? Why am I learning this stuff?”. . . and then there is Fred. All of life is wrapped up in theadventures of this five-year-old.In this book your child will learn reasons to count by fives,will learn how to set a table,will learn about the giant star Betelgeuse, anda zillion other things.8

Mathematics is taught in the Life of Fred series in the context ofliving a full life. A real education—not just memorizing math facts.HOW THIS BOOK IS ORGANIZEDEach chapter is about six pages. Do a chapter a day.At the end of each chapter is a Your Turn to Play.Have a paper and pencil handy before you sit down to read.Each Your Turn to Play consists of about four or five questions.Have your child write out the answers.After all the questions are answered, then take a peek at myanswers that are given on the next page.Don’t just let your child read the questions and look at the answers.Your child won’t learn as much taking that shortcut.CALCULATORS?Not now. There will be plenty of time later (when students hitPre-Algebra). Right now in arithmetic, our job is to learn the addition andmultiplication facts by heart.9

ContentsChapter 1Kingie Dreams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13nine vending machines5 4 9one yard three feetfive o’clocknumber of members in a setChapter 2Drawing Butterflies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19–15 degrees 15 degrees below zerocounting by twosten minutes after five o’clockdays of the weekChapter 3A Bug Up Close. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25what caterpillars eatbutterflies do not use cocoonscounting by fivesmonths of the yearbraces, parentheses, and bracketsChapter 4Putting Kingie to Bed. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3110 – 9 15:25 on the clockthe poet Christina Rossettisheet music for “But Not Alone”exclamation pointsChapter 5At the Food Court. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37protein and calciumhalf pound 8 ounceshistory of the strawChapter 6The Hunter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Orion’s beltthe star Betelgeusetriangles10

Chapter 7For Later. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49squaresfive minutes to six 5:55all about book signingsdeliberate vs. inadvertentChapter 8First, Second. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55the three kinds of booksordinal numbersyurts4 5 92 7 9counting to 35 in nickelsChapter 9Campus Mail. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617–4 3counting the stars in Orion’s swordtranslating der Zehennagel from German to Englishhalf past six 6:30Chapter 10Orion Nebula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67light yearsAndromeda Galaxythousand, million, billion, trillionthe Alphabet gameChapter 11The Bell Tower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73find the second derivative of y arctan (x2 – 17)a night jobperpendicularright anglesdozenChapter 12Talking with Ned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79a.m. and p.m.eleven hours of television a dayorthogonalitysyncopeeight 5-pound watermelonssentences with a dozen words in them11

Chapter 13Who to Call?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85“The Crash of the Bell Tower” symphonyif tomorrow is Wednesday, what day was yesterday?history of a baker’s dozenChapter 14Quotes within Quotes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91a world’s record4–2 29–1 8Chapter 15Back to His Office. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97how to carry a very big doughnut0 0spines of booksone-tenth of 100words used on televisionChapter 16The Third Note. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103cardinal numberssetsmillion, billion, trillion, quadrillion, quintillionhow many whole numbers, {0, 1, 2, . . .}, are there?Alice in Wonderland, Moby Dick, Don QuixoteChapter 17Nighttime Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Donald Duck: Eine Ente Wie Du Und IchStates in the United States9–6 34 is not a numberChapter 18Letters from Brothers. . . . . . . . . . . . . . . . . . . . . . . . . . . . 115saying thank you for giftshistory of pizzathe next number after 4,000,000Chapter 19Mysteries of Life. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121the speed of campus mailcorrect place settingsIndex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12612

Chapter OneKingie Dreamsred had pulled out a book about butterfliesto read to his doll, Kingie. Fred sat in thecorner and put Kingie on his lap. It wasfive o’clock in the afternoon.FKingie was a doll thatliked to draw and paint. Hehad been working allday on oil paintings.5:00With his little five-year-old voice, Fred wasreading to Kingie about butterflies. There werepictures of all kinds of butterflies in the book.When Fred was about halfway through thebook, Kingie shut his eyes and fell asleep.Kingie was dreaming.13

Chapter OneKingie DreamsFred usually sang to Kingie each night tohelp Kingie go to sleep. Since he was alreadyasleep, Fred did not sing.He picked Kingie up and carried him to thespot under his desk where they slept each night.Fred wasn’t sleepy yet. He put a bookmarkin the butterfly book and put it back in its placeon the shelf.He turned out the light and headed out intothe hallway outside his office. Fred is a teacherat KITTENS University. He and Kingie live inhis office on the third floor of the math building.There were nine vending machines in thehallway. Five of them were on one side, andfour of them on the other side. Some were candymachines. One offered doughnuts. One offeredcrackers. One offered a soft drinkcalled Sluice.Sluice is a very, very, verysweet soda. It is mostly sugar witha little bit of water. Fred stood infront of the machine. He hadn’teaten anything all day.14

Chapter OneKingie DreamsHe decided not to get a Sluice. Itsometimes made him sick.Fred did not have parents to watch overhim.w No one had ever told Fred about eatingthe right foods.Fred was five years old, but he was onlyone yard tall. He was as tall as a yardstick.One yard is three feet.- - -- - - - - -- - - - - - - one yard ---------------------Because of his poor eating habits, Fred hadnot grown an inch in a long time.Fred started to head down the stairs.“Hi!” said Betty. She was coming up thestairs as Fred was heading down the stairs. “Iwas just going to your office to see you.”Betty was one of Fred’s students atKITTENS. She was one of the first people tomeet Fred when he came to the university toteach four years ago. She and her boyfriend,Alexander, have shared many adventures withFred over the years.wIt’s a sad story that is told in Life of Fred: Calculus. It may not be suitable for theprepubescent mind.15

Chapter OneKingie Dreams“Hi Betty,” Fred answered. “I was justgoing outside to get some fresh air. Kingie hasbeen doing oil painting all day in my office. Theroom smells a bit like oil paint.”Betty said, “That sounds like a good idea.May I join you?”When they got outside, Fred asked Bettywhy she had come to see him.She was about to tell him about a calculusproblemw that she was working on, when shelooked up at the building.“What’s that comingout of your window!” Bettyexclaimed. “It looks likelittle pieces of coloredpaper.”Fred could see betterthan Betty since his eyes were only five yearswShe had been trying to solveThe big long SII x³1 1 dx which is a problem from calculus.means “find the area under the curve.”It all looks very mysterious right now, but once you have studied arithmetic, algebra,1geometry, and trig, learning how to find the area under x³ 1 will be no harder thanwhat you are doing right now, which is learning about the numbers that add to 9.16

Chapter OneKingie Dreamsold. He said, “No, that is not colored paper.Those are butterflies.”Betty counted nine butterflies that cameout of Fred’s window. Five of them landed onthe flowers. The other four landedon Fred’s head.They tickled Fred.Please take out a piece ofpaper and write your answers.Afer you are all done, you can check your workon the next page.Your Turn to Play1. 5 4 ?2. 4 5 ?3. What time is it?4. Fred is one yard tall. How many feet is that? (Ifyou have forgotten, it is okay to look back two pages tofind the answer.)5. How many members does the set {1, 2, 3, 4, 5, 6}have? (This was in Life of Fred: Apples.)6. 2 5 ? (This was also in Apples.)17

Chapter OneKingie Dreams. . . . . . . ANSWERS . . . . . . .1. 5 4 92. 4 5 93. 5 o’clock or 5:004. One yard is three feet.5. The set {1, 2, 3, 4, 5, 6} has six members in it.Here are some other sets with six members:{A, B, C, D, E, F}{ , , , , , }{ , , , , , }and the set of the days of the week that don’t have anh in their spelling: {Sunday, Monday, Tuesday,Wednesday, Friday, Saturday}.6. 2 5 7In Apples we did all the numbers that add to 7:0 7 71 6 72 5 73 4 74 3 75 2 76 1 77 0 718

Chapter TwoDrawing Butterflieshe butterflies tickled Fred’s head. Hegiggled, and the butterflies all flew away.The four butterflies joined the five thatwere on the flowers.Betty and Fred sat very quietly on a benchto watch those nine butterflies.Betty took out a piece of paper and drewone of the butterflies.TShe gave Fred a piece of paper so that hecould also draw.Betty looked atFred’s drawing andsmiled. She said, “Idon’t think their feetlook like that.”19

Chapter TwoDrawing ButterfliesFred got another sheet of paper and drew anew picture.Fred thought that thispicture was much better.Now the butterfly had shoeson.Betty had forgotten about asking about theI1dx . Instead, she asked,calculus problemx³ 1“How did those nine butterflies fly out of youroffice window?”Fred said, “I left the window open.”Fred’s answer was true, but it was notwhat Betty was really asking. She tried again:“I mean how did those butterflies get into youroffice in the first place?”Fred wasn’t sure. He answered, “I guessthey flew in.”“But this is February in Kansas,” Bettysaid. “This morning it was –15 degrees, andwhen it is 15 degrees below zero, you don’t havebutterflies flying around.”They decided to go back to his office andfind out what was going on.20

Chapter TwoDrawing ButterfliesFred climbed the steps one-at-a-time:13 14 15 161211106 7 8 95431 2Betty’s legs were a lot longer than Fred’s.She took the stairs two-at-a-time:1612 14106 842When Fred was climbing the stairs, hetried to think of where the butterflies had comefrom.He had been reading a book aboutbutterflies to Kingie. Did the butterflies in thebook come alive and fly out the window? No,that would be silly.Kingie had been dreaming aboutbutterflies. Did his dream break open and thebutterflies fly out the window?No. That would also be silly.21

Chapter TwoDrawing ButterfliesWhen they got to Fred’s office, he told Bettythat Kingie was sleeping. He said that theyshould be quiet so they wouldn’t wake him up.He carefully opened his office door. Whenhe looked in, he got a surprise. Kingie wasawake and sitting on topof Fred’s desk.“What happened?”Fred asked.Now, as everyone knows, when dolls talk,sometimes only their owners can hear them. Sowhen Kingie told Fred what was happening,Betty didn’t hear anything Kingie said.Kingie told Fred, “First of5all, I didn’t go to sleep for the10whole night. It is only tenminutes after five o’clock right15now.20“Second, you forgot to singto me, so I knew it wasn’t time5:10for my nighttime sleep.“Third, what are those bugs on the top ofyour desk?”Fred ran over to his desk to look.22

Chapter TwoDrawing ButterfliesHe couldn’t see any bugs on the top of hisdesk.Please write your answers on a piece of paper before youlook at my answers on the next page.Your Turn to Play1. Why couldn’t Fred see the bugs?2. Kingie started his nap at5:00He ended his nap at5:10How long had Kingie slept?3. Betty went up the stairs two at a time.2, 4, 6, 8, 10, 12, 14, 16. Continue this series up to 40.Your answer will look like: 2, 4, 6, 8, 10, 12, 14, 16, 18,20, 22. . . .4. Here is the set of days of the week that have an s intheir names: {Sunday, Tuesday, Wednesday, Thursday,Saturday.} Write the set of the days of the week thathave an h in their names.23

Chapter TwoDrawing Butterflies. . . . . . . ANSWERS . . . . . . .1. I think Fred couldn’t see the bugs since he was tooshort to see the top of his desk.That’s not the only possible answer.Some people might have written that Fred couldn’tsee the bugs because Kingie was standing in the way.Some people might have written that Fred couldn’tsee the bugs because those things on the top of hisdesk were not bugs. They were pieces of string.Moral: There is not always just one right answer toa question.2. If Kingie started his nap at 5:00 and slept for 1minute, he would have woken up at 5:01.If he started at 5:00 and slept for 2 minutes, he would havewoken up at 5:02.If he started at 5:00 and slept for 3 minutes, he would havewoken up at 5:03.If he started at 5:00 and slept for 4 minutes, he would have woken up at5:04.If he started at 5:00 and slept for 5 minutes, he would have woken up at 5:05.If he started at 5:00 and slept for 6 m inutes, he w ould have w oken up at 5:06.If he started at 5:00 and slept for 7 minutes, he would have woken up at 5:07.If he started at 5:00 and slept for 8 minutes, he would have woken up at 5:08.I f h e s t a r t e d a t 5 :0 0 a n d s le p t f o r 9 m in u t e s , h e w o u ld h a v e w o k e n u p a t 5 :0 9 .If he started at 5:00 and slept for 10 minutes,he would have woken up at 5:10.3. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,34, 36, 38, 404. There is only one day of the week that has an h inits name. {Thursday}.24

Index–15 degrees. . . . . . . . . . . . . . . 20a.m. . . . . . . . . . . . . . . . . . . . . 79Aeneid by Virgil. . . . . . . . . . . 117aleph-null. . . . . . . . . . . . . . . . 105Alice’s Adventures inWonderland. . . . 106, 107Alphabet game. . . . . . . . . . 69-71Andromeda Galaxy. . . . . . . . . 69baker’s dozena history. . . . . . . . . . . . . . . 90Betelgeuse. . . . . . . . . . . . . . . . 45billion. . . . . . . . . . . . . . . . 69, 104book signing. . . . . . . . . . . 51-53braces. . . . . . . . . . . . . . . . . . . . 30brackets. . . . . . . . . . . . . . . . . . 30"But Not Alone"piano piece by Fred Gauss. . . . . . . . . . . . . . . . . . . 33butterfly eggs. . . . . . . . . . . 28, 31calcium. . . . . . . . . . . . . . . . . . 37campus mail. . . . . 61-63, 99, 115cardinal numbers. . 101-104, 112,119chrysalis. . . . . . . . . . . . . . . 29, 31cocoon. . . . . . . . . . . . . . . . . . . 29collinear. . . . . . . . . . . . . . . . . . 48"Consider the Lilies". . . . . . . . 33counting by fives. 29, 35, 41, 69,118counting by twos. 21, 23, 27, 29,35, 69, 108counting using nickels. . . 58, 59,65, 71126days of the week. 18, 23, 60, 71,84, 96deliberate vs. inadvertent. . . . . 54der Zehennagel. . . . . . . . . 55, 65Don Quixote. . . . . . . . . . 106, 107Donald Duck. . . . . . . . . . . . . 109dozen. . . . . . . . . . . . . . 77-79, 83exclamation points. . . . . . . . . . 35Goldilocks. . . . . . . . . . . . . . . . 26googol. . . . . . . . . . . . . . . . . . 108Great Orion Nebula. . . . . . . . . 67Harry's Burger Crumb. . . . . . . 39Hungary vs. hungry. . . . . . . . . 71infinite sets. . . . . . . . . . . . . . . 114inventing constellations. . 45, 46,52Jamestown . . . . . . . . . . . . . . 117lie, lay, and lain. . . . . . . . . . . 101light year. . . . . . . . . . . . . . 67, 68litterbug. . . . . . . . . . . . . . . . . . 34Marvin Stone. . . . . . . . . . . . . . 41members of a set. . . . . . . . 17, 18Messier 42. . . . . . . . . . . . . . . . 67million. . . . . . . . . . . . . . . 69, 104Moby Dick. . . . . . . . . . . 106, 107Muscle Shoals. . . . . . . . . . . . . 56Naissance of Numeration. . . 100Names for Toenail in 300Languages. . . . . . . . . . 55Nedrick A. Wistrom. . . . . 76, 86numbers that add to 7. . . 18, 95,96numbers that add to 9. . . . . . . 95

ordinal numbers. . . . . 56, 59, 65,101, 102, 112, 119Orion. . . . 43, 44, 46, 52, 64, 123Orion Nebula. . . . . . . . . . . 67, 68orthogonality. . . . . 80, 82, 86, 89Our sun is a star. . . . . . . . . . . 45p.m. . . . . . . . . . . . . . . . . . . . . 79P.M. . . . . . . . . . . . . . . . . . . . . 79parentheses. . . . . . . . . . . . . . . 30perpendicular . . . . . . . 77, 78, 83pizzaa history. . . . . . . . . . . . . . 117place settings. . . . . . . . . . . . . 122protein. . . . . . . . . . . . . . . . . . . 37quadrillion. . . . . . . . . . . . . . . 104quintillion. . . . . . . 104, 107, 108quotation marks. . . . . . . . . . . . 87Ralph L. Wistrom. . . . . . . . . . 89Renaissance . . . . . . . . . . . . . 100right angles. . . . . . . . . . . . . . . 77Rossetti, Christina. . . . . . . 32, 33"Consider the Lilies". . . . . 33single quote marks. . . . . . . 87, 88Sluice. . . . . . . . . . . . . . 14, 35, 79spines of books. . . . . . . . . . . . 98squares. . . . . . . . . . . . . . . . 49, 77states in the United States. . 111,113, 114straws. . . . . . . . . . . . . . . . . 39, 40a history. . . . . . . . . . . . . . . 41sugar might be related to . . . . 36syncope. . . . . . . . . . . . . . . . . . 81three kinds of books. . . . . . . . . 56"The Crash of the Bell Tower"symphony. . . . . . . . . . . . . . . . . 85triangles. . . . . . . . . . . . . . . 47, 48trillion. . . . . . . . . . . 69, 104, 107whole numbers. . . . . . . . 103, 107world’s record. . . . . . . . . . 91, 92yard three feet. . . . . 15, 17, 35,119yurt. . . . . . . . . . . . . . . . . . . . . . 56127

asleep, Fred did not sing. He picked Kingie up and carried him to the spot under his desk where they slept each night. Fred wasn't sleepy yet. He put a bookmark in the butterfly book and put it back in its place on the shelf. He turned out the light and headed out into the hallway outside his office. Fred is a teacher at KITTENS University.