Math Concept Reader MCR g5 halfpipe

Math Concept Reader

Halfpipe Halfpipe Math Concept Reader ca54os_lay_070107xad_cp.indd 3 1/8/07 11:28:02 PM DIGITAL FINAL PROOF Expedition: Antarctica by Aenea Mickelsen ca62xs_lay_061207ad_am.indd 4 1/9/07 9:09:15 AM DIGITAL FINAL PROOF Halfpipe by Ilse Ortabasi Math Concept Reader Copyright © Gareth Stevens, Inc. All rights reserved. Developed for Harcourt, Inc., by Gareth Stevens, Inc. This edition published by Harcourt, Inc., by agreement with Gareth Stevens, Inc. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the copyright holder. Requests for permission to make copies of any part of the work should be addressed to Permissions Department, Gareth Stevens, Inc., 330 West Olive Street, Suite 100, Milwaukee, Wisconsin 53212. Fax: 414-332-3567. 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Printed in the United States of America ISBN 13: 978-0-15-360198-9 ISBN 10: 0-15-360198-1 1 2 3 4 5 6 7 8 9 10 179 16 15 14 13 12 11 10 09 08 07 ca54os_lay_070107xad_cp.indd 1 1/8/07 11:28:04 PM DIGITAL FINAL PROOF Chapter 1: Halfpipe Dreams   ItisearlySeptemberandMr.Dunbar’sstudentsareinscienceclass. Outside,theweatherisstillwarm,butthepublicswimmingpoolsinBoise, Idaho,arealreadyclosedfortheseason.Thecrowdsdisappearshortlyafterthe LaborDayholiday.Thelifeguardsreturntoschoolortotheirwinterjobs.  Mr.Dunbarstandsbeforetheclassasheintroducestherstscienceunit. HesaysthattheclasswillstudyNewton’sLawsofMotion.Heasksifanyof thestudentshaveeverheardoftheselawsofphysics.Whennobodyanswers,he askstheclasswhetheranyofthemhavesnowboardedbefore.Onlyafewofthe studentsraisetheirhands.Then,heaskshowmanyofthemhavewatchedthe WinterOlympicssnowboardingcompetitions.  Itturnsoutthatquiteafewofthestudentshavewatchedsnowboardingon television.Thestudentsdon’thavemuchexperiencesnowboarding,buttheydo havesomeknowledgeaboutthesportandthetricksthattheathletesdo.  Everybodyintheclasswonderswhatsnowboardingcouldpossiblyhaveto dowithNewton’slaws. ca54os_lay_070107xad_cp.indd 2 1/8/07 11:28:05 PM DIGITAL FINAL PROOF This is a diagram of a halfpipe.   Melanietellstheclassthatshelovestowatchsnowboardersridedownthe halfpipeanduptheotherside.Melaniemakestheshapeofatroughwithher handstoshowtheotherstudentswhatthehalfpipelookslike.Thehalfpipeis dugrightintothesnowandthewallscanbeasmuchas18metersacross. Eduardosaysthathelikestowatchsnowboardersdotrickslikearodeoip. Heexplainsthatarodeoipisa720-degreesidewayssomersault.  Mr.DunbarexplainsthatNewton’sLawsofMotionhelpthesnowboarder maneuveranddotricks.HesaysthatNewton’srstlawstatesthatanobjectat restremainsatrest.Thislawalsostatesthatanobjectinmotioncontinuesat aconstantspeedandinastraightlineunlessactedonbyanoutsideforce.Mr. Dunbartellstheclassthatthisisthereasonthatsnowboarderscansoarsohigh intheair.Becausetheyareinmotionwhentheyreachthetopofthepipe,they stayinmotion.Next,heexplainsthatNewton’ssecondlawofmotionstatesthat theEarth’sforceofgravitypullsthesnowboarderbackdowntotheground! 10 to 18 meters 1.5 to 3 meters Entry Ramp Flat Lip Vertical Platform Transition Wall 10 to 30 centimeters 50 to 100 meters ca54os_lay_070107xad_cp.indd 3 1/8/07 11:28:08 PM DIGITAL FINAL PROOF When class is over, the students continue to talk about snowboarding.   Melanieandherfriendscontinuetotalkaboutsnowboardingwhenclassis over.Theythinkabouthowgreatitwouldbeiftheycouldgosnowboardingthis winter.Manyofthemknowhowtorideskateboards,butMelanieandherfriends havenevertriedsnowboarding.  Cathypicturesherselfonasnowboard,yingdownthemountainatfull speed.Eduardohasgonesnowboardingbefore,andhetellshisfriendsallabout it.Heexplainsthatwhencarving,asnowboardermustturnwithoutanyskidding, makingasingle,thinlineinthesnow.Itisaskillthatisverydifculttolearn. Eduardopretendstocarveupthehalfpipeandperformatrickintheair.Helands withathumponthegrassontheplayground.Hegetsup,anddeclaresthatthis yearhewantstogosnowboardingagain.  Michaelwalksoverandjoinsthegroupoffriends.HetellsEduardoand theothersthattheMogulValleyResortnearbyrunssnowboardinglessonsfor schools.Hesawanarticleabouttheresortinthesportssectionofthelocal newspaper. ca54os_lay_070107xad_cp.indd 4 1/8/07 11:28:12 PM DIGITAL FINAL PROOF This snowboarder wears the proper safety equipment as he enjoys his run through the halfpipe.   Melanieisexcitedabouttheideaoftakinglessons.Sheremindsherfriends thatitwillbeexpensiveforthewholeclasstogo.Michaelsaysthecostforone dayis$25.00aperson.Thiscostincludesthelessonaswellastheuseofa snowboardandboots.  “Thepriceevenincludesallthesafetyequipment,”Michaelsays.“Because snowboardingisanextremesport,weshouldwearwristguards,kneepads,and hippads.Hippadsareusedtocushionyourfallsandkeepyourseatwarmand dry.Theyarestretchyandpullonlikebikeshorts.Youhavetoweara snowboardhelmetwhilesnowboarding,too.”  “Youalsoneedasafetyleash,”addsEduardo.“Theleashisdesignedto keepyourboardattachedtoyourleg.Thatway,iftheboardcomesloosefrom yourboots,theleashwillstopitfromslidingawaydownthehill.”  Cathywondershowthestudentswouldtraveltotheslopes.Michaelexplains thateventhebustransportationandliftticketsareincludedinthecostofthe lesson.Now,thestudentsbelievethattheycanraisethemoneysotheycanall gosnowboardingtogetherthiswinter. ca54os_lay_070107xad_cp.indd 5 1/8/07 11:28:15 PM DIGITAL FINAL PROOF Mr. Dunbar explains how Newton’s laws affect snowboarding.   Michaelbringsthenewspaperarticleaboutthesnowboardinglessonsto schoolthenextday.Mr.Dunbaraskshimuptoreadthearticletotheclass.The articlesays,“Theprogramisdesignedtoteachwintersports.Itfocusesonthe safeenjoymentofsnowboardingasalifetimesport.Qualiedinstructorshelp studentsdeveloptheirsnowboardingskills.Level1classesareforthosestudents whohaveneversnowboardedbefore.”  Theclasscriesout,“That’sus!”  Michaellooksathisteacher.Mr.Dunbarhasalreadydecidedthatthe experienceofsnowboardingwouldworkverywellwithhislessononNewton’s lawsofmotion.Hecannotthinkofabetterwayforhisstudentstolearnand understandNewton’slawsthanexperiencingthemrsthandontheslopes.Onthe slipperysnow,hisstudentswillseeforthemselveswhatitmeansforobjectsto stayinmotion!  Mr.Dunbarletstheclassknowthathewillhelpthemraisethefunds.He willalsohelporganizetheclasstriptoMogulValleyResort.Thestudentsareso excitedaboutthetripthattheyallclapandcheer. ca54os_lay_070107xad_cp.indd 6 1/8/07 11:28:18 PM DIGITAL FINAL PROOF $25.00 × 27 = $675.00 , The students decide that the first step they need to take is to calculate how much money they need for the trip. The class includes a total of 27 students. Michael multiplies 27 by $25.00, which is the cost for each student. The product is $675.00. Thatʼs how much money the class needs to pay for the trip. Cathy suggests they raise the funds for the trip by selling popcorn. A friend of hers in another class raised funds that way last year, and the school can purchase cases of popcorn for students to sell. Mr. Dunbar talks to the schoolʼs principal. She thinks the popcorn fundraiser is a good idea and agrees to help the class. Mr. Dunbar orders the popcorn for the fundraiser. Half of the money the students collect will pay for the popcorn, while the other half will be the profit for the trip. The popcorn arrives in October. Each student in Mr. Dunbarʼs class agrees to sell at least one case of popcorn. Some students hope to sell even more than that. Students work hard to sell popcorn right away because the date of the December trip is not far away.  Melanie’smothervolunteerstohelpwiththefundraiser.Shecomestoschool oftentocollectmoneyfromthepopcornsales.MelanieandMichaelhelpheradd upthemoney.  Theclassmeetstheirgoalforsellingpopcorn.Theymade$1,470.00!First, thestudentsneedtopayforallofthepopcorn.Theschoolpaid$735.00forthe popcorn.  M rs.Petty,theprincipal’sassistant,subtractsthisamountofmoneyfromthe amountcollectedbythestudents.Sheusesthatmoneytopayforthepopcorn.  $1,470.00−$735.00=$735.00  Thestudentshave$735.00leftover.Thatamountismorethanenoughtopay forthetrip.Thetripcosts$675.00.  Theydidit!Thefundraiserwassuccessful.Everyoneintheclasswillgoon thesnowboardingtrip.Mr.Dunbarandthestudentscelebratetheirsuccesswitha fewbagsofpopcorn. $ 1,470.00 − $ 735.00 $ 735.00 ca54os_lay_070107xad_cp.indd 8 1/8/07 11:28:25 PM DIGITAL FINAL PROOF [...]... knowledgeable about snowboarding Mr Dunbar asks him to explain to the class what the halfpipe snowboarding event is all about Eduardo describes the halfpipe as a half-cylindrical field about 145 meters long that is dug into the snow Snowboarders enter the halfpipe from a ramp at the top Eduardo explains how the snowboarders must cross the halfpipe from side to side six to eight times during a competition They... The students watch as an advanced snowboarder does tricks in the halfpipe Riding the halfpipe is definitely not for new snowboarders! Eduardo remarks, “Now I can see Newton’s Laws of Motion at work That’s amazing!” The instructor takes the class to the beginner’s area She tells the students that it takes years of practice to be a good halfpipe rider New snowboarders need to start on the beginner’s slope,... the whole class is busy figuring out who won the men’s halfpipe competition Eduardo reminds the class that the run with the highest score is the one that counts for each snowboarder He doesn’t know if that scoring rule is the same for all Olympic winter sports, though Eduardo, Roy, and Angela work together They finish adding the scores for the men’s halfpipe snowboarding competition 11 ca54os_lay_070107xad_cp.indd... The class meets in groups to review their computations Angela and the other students in her group made a table of the results for the second final run in the women’s halfpipe snowboarding competition Results from 2nd Final Run Women’s Halfpipe Competition Athlete’s Bib Number Jump 1 Jump 2 1 3 4 22 8.0 8.2 8.9 7.7 Jump 3 Jump 4 Jump 5 8.0 8.3 8.9 7.9 8.4 8.7 8.9 8.6 8.2 7.6 8.9 8.4 8.5 8.7 9.0...DIGITAL FINAL PROOF Chapter 2: Results: Men’s and Women’s Snowboard Halfpipe Mr Dunbar prepares his math lesson with his students’ interest about snowboarding in mind He always likes to make connections to the real world in his lessons Today’s lesson is called “Fascinating Facts about... on the snowboard final forming or occurring at the end halfpipe a smooth-surfaced structure shaped like a trough and used for stunts in sports such as in-line skating and snowboarding lifetime sport sports performed by people on a regular basis even after they are no longer young maneuver a movement that requires skill and ability Newton English mathematician and physicist Sir Isaac Newton, who lived... range, which is the difference between the greatest number and the least number, for this set of data Results from Women’s Halfpipe Competition Athlete’s Bib Number Score 14 38 58 67 70 89 50.12 52.09 52.93 55.29 51.02 53.91 4 Is it possible for a competitor in the snowboarding halfpipe event to win the event if his or her first run gets a low score? Explain your answer ... highest total score from two jumps Unlike in snowboarding, the worst score isn’t thrown out Eduardo wonders whether that different method of scoring would have changed the results of the snowboarding halfpipe competition Melanie raises her hand and tells the class that she has already done the computations in her notebook She added up scores from the first and second final runs for each snowboarder,... compute the scores for each snowboarder in the competition, and rank the top four To find the score for each athlete in both runs, they need to add up the points for all jumps Results from Final Men’s Halfpipe Competition Jump 3 Jump 4 Jump 5 1st Final Run Athlete’s Bib Number Jump 1 Jump 2 31 25 19 8 8.58 8.1 4.4 9.56 8.03 7.6 4.06 9.4 8.1 8.47 4.23 9.6 8.5 8.4 4.04 9.02 8.48 7.8 4.2 9.5 31 25... 6.7 5.2 8.63 5.5 7.67 6.82 8.7 6.5 7.01 5.7 8.6 4.5 8.03 6.8 9.1 4.62 2nd Final Run 10 ca54os_lay_070107xad_cp.indd 10 1/8/07 11:28:27 PM DIGITAL FINAL PROOF A snowboarder completes a maneuver on the halfpipe “You know how to add whole numbers, so you already know how to add numbers with decimals,” Mr Dunbar says “You just need to line up the decimal points You can give your decimals the same number . Eduardoseemstobeveryknowledgeableaboutsnowboarding.Mr. Dunbaraskshimtoexplaintotheclasswhatthe halfpipe snowboardingevent isallabout.Eduardodescribesthe halfpipe asahalf-cylindricaleldabout145 meterslongthatisdugintothesnow.Snowboardersenterthe halfpipe froma rampatthetop. . 11:28:05 PM DIGITAL FINAL PROOF This is a diagram of a halfpipe.   Melanietellstheclassthatshelovestowatchsnowboardersridedownthe halfpipe anduptheotherside.Melaniemakestheshapeofatroughwithher handstoshowtheotherstudentswhatthe halfpipe lookslike.The halfpipe is dugrightintothesnowandthewallscanbeasmuchas18metersacross. Eduardosaysthathelikestowatchsnowboardersdotrickslikearodeoip. Heexplainsthatarodeoipisa720-degreesidewayssomersault. . Melanietellstheclassthatshelovestowatchsnowboardersridedownthe halfpipe anduptheotherside.Melaniemakestheshapeofatroughwithher handstoshowtheotherstudentswhatthe halfpipe lookslike.The halfpipe is dugrightintothesnowandthewallscanbeasmuchas18metersacross. Eduardosaysthathelikestowatchsnowboardersdotrickslikearodeoip. Heexplainsthatarodeoipisa720-degreesidewayssomersault. 