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Pearson Mathematics 7 Student Book PDF

374 Pages·2016·270.276 MB·English
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w mathematics •••••••••••••••••••• PEARSON ••••••••••••••••••••• •••••••••••••••••••••• ••••••••••••••••••••••• ••••••••••••••••••••••• ••••••••••••••••••••••• •••••••••••••••••••••• •••••••••• •••••••••• •••••••••• •••••••••• •••••••••• 2ND EDITION ••••••••• •••••••• ••••••• •••• •• • w w w w Ptarson Australi.a Australian Footb.111 League CAFL): p. 5S8LI PEARSON Mathematics 7-10 (a division of Pea/SOil Australia G<oup Ply Ltd) BIS Schrapnel: p. 57.k. 707 Collins Stree4, Melbourne, Victoria 3008 Bureau of Meteorology (BOM): 0 Conwnoowealth of Australia, pp. S40b, 5431, 5S2, 5S41, 555c, PO Box 23360, Meibo1Jne, ViclOtia 8012 572b. www.pearson.com.au Casio Computer Co., Ltd.: Casio Cl.assP.ld CAS screenshots and elements. Writing and Development Team Copyright O 2017 Di1k Strass~ Geoff Phillips Pwlic.ations Trust, Nolan Consulting SeMces Dep,artment ol SusLainabilily & Environment: p. 538. Pty Ltd and Pe;uson Australia (a division of Pearson Australia Gloup Ply Ltd) Dreamstime: FilipHen:ig, p. 159c; Rookcreations. p. 62<»>. The Pearson Afdthematics 7-10 second edition series is an adaptation ol the Entomaf1: p. 335hr. Heinemann Mdthematics 7- IO series. Fololia: liaurinko, p. 110 (piu.a). Evelyn Ashcroft Tony Daws Cindy Hogan Catherine McKenzie Soumya Saini Firs! published 2017 by Pearson Australia Getty Images: BingoPiJ1:el, p. t 5 I b; ROOen Cianflone, p. 83; Michael Dodge/SI ringer, p. JS: Canberra Mathematical Contributing Author Author Content and Leaming Contributing Author 2020 2019 2018 2017 BradSey Kanaris• CA, p. 2431; Paul Kane/Stringe,, p. 558tr; lndtanil Mukherjee, p. 565c; Association President Teacher-Victoria (Homework Program) Specialist Teacher- Victoria 10 9 8 7 6 S 4 J 2 I Marwan Naamani, p. 330; Andreas Rentz, p. S14. Mathematics Consultant Pearson Australia lmagefolk (was Amana/Cotbis}: 2/Ed SnowshoeK>cean, p. 149 (girl with headphones); Reproduction .ind communication for educational purposes Teacher-ACT Kiran Dhot Damien Igoe Aimee Shackleton Antennalfs.lop, p. 10; John Camemolla, p. 234; Ron Chapple, p. 30r; Sieve Christo, p. 43; COC'bis, TheAuslralian Copyrighl Act 1968 (lhe Ad} allows a maximum of one chapter or 10% ol the pp. 3351r, 467cl; Jose. .H ioo;osa,Demo(ix, p. 2: Mango Productions, p. 149 (boy with earphones): Contributing Author Contributing Author John Mclaverty Contributing Author pages ol this \\Otk, whichever is the greater, to be reproduced and/o, communicated by any Joe i\1<:Bride, p. 87; Jared Milgrim, p. 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Reproduction and con-muniGltion for other purposes Contributing Author Teacher- Victoria Content Developer Teacher- Victoria Microsof1C cwpo<ation: Used wi1h permis.sion from Microsoft., pp. JOObr, JOier, 301d , 4161, 416r, Except as pe,mined under the Act (for example any fair dealing fOC' the purposes of study, 417bl, 417d, 417cr, 539hr, 539a. Bob Aus Teacher-Victoria (First Edition) research, criticism ot review), no pa.rt of this book may be repcoduced, stewed in a rettieval system, Newspix: Stuart i\1<:Evoy, p. I 78; Michael A:>tter, p. 560tl. Contributing Author Helen Keating Pearson Australia Neetu Sharma communicated or ttansmitted in any form or by any means without priOf written permission. All enquiries should be made 10 the publisher at the address above. Pearson Australia: Jon Batlow/Peats0n Education Ltd, p. 392; Alice i\1<:Bcoom, pp. 238tr, 371 er, 389t. Teacher-NSW Mark Dusting Consultant Contributing Author Shuuerstock: p. 170 <&:ts mask); p. 170 (man); aastock, p. 220t; Abdurahman, p. 315t; ban adce, Contributing Author John McMillan Teacher-Victoria n This book is n01 to be treated as a bladdine master; thar is, any p. 237bc: Helder Almeida, p. 171 (box): ampF010Studio, p. 1 (sandwich}; Andrey,JCuzmin, Rosetta Batsakis Teacher-Victoria Leah Kelly Contributing Author photocopying beyond fair dealing requires priot written permission. p. 354; Galyna Andrushko, p. 76tr, anetapics, p. 625; Marie Aplec, p. 467d; Ariwasahi, p. 26; Contributing Author Consultant Teacher- Victoria Nicola Silva axpitel, p. 447ft (pi1ch angle}; Baloncici, p. 20t Stacy Bamen. p. 134; Galina Barskaya, p. 171 Series Publishef: Tim Carruthen (girt); Joe Belanger, p. 418hr; Bigio, p. 4241 (badcground}; blessings, p. 509; Yehuda Boltshauser, Teacher- Victoria Sia Evans Contributing Author Conten1 and Learning Specialisrs.: Catherine McKenzie, Aynur BulUI p. 212h; BrunoSINNAH, p. 63t; CandyBox Images, p. 145; Ivan Chola.kov, p. 164:. dearviewstock, Contributing Author Ingrid Kemp Andrew Mentlikowski Teacher-Queensland Pro;e<:1M anagers.: Tamara O'Mello-Pirois, Etmla-Jane McCarrofl, Jennifer Boyce p. 169; doki, p. 236tc; Stephen Coburn, p. 100; Neale Cousland, p. 270; CreativeNature.nl, Deborah Bridge Teacher-Victoria Contributing Author Author Production Managets: Diane Leyman, Shahata Ahmed p. 348; cosma, p. 171 (rope ladder); zhu difeng, p. 228; On Davis. p. 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Justin Lim Robel'I Kneschke., p. 38; Kraska, p. "1151' (disco ball'r, Kudryashka, p. "11411( background); Leksele, Series Cower Design: Anne Donald p. 585t; Stephanie Urecte, pp. 42◄•5 (e)-es'r, J.Y. Loke, p. 532t; M;\(ffen, p. 62◄cc; mangos1ock, Teacher-NSW Patricia Fraser Literacy and ESL Consultant Consultant p. 293; J.-.cqui Mat1in, p. 233; Man-Studio, p. 3881x: mexrix, p. 624bc; mgl408, p. 20t; Consultant Jana Kohout Teacher-Victoria Printed in Malaysia MichaelJayBerfin, p. 1S2; Oatia Minaeva, p. 309cr, Monkey Business Images, pp. 40, 46, 547; Aynur Bulut Teacher-Victoria Contributing Author Jennifer Nolan monticello, p. 99; My ~rtfolio, p. 502; M.vina Nahatova, p. 258; nakamasa. p. 52; lnna Og.lndo, Content and Learning Teacher- Victoria Author Jena Sous or Nation.ii liJ>r.vy Australia Cal.iloguing,,in,Publicalion entry p. 314 (radar); Tyler Olson, p. 3811; BORTEL Pavel - Pavelmidi, p. 611t; Bnjan Pavlukcwic, p. 19; Specialist Belinda Frew Contributing Author Creator. Strasser, Dirk. author. Photohank, p. 20!; PHOTOCREO Michal Bednarek, p. 237hr; PhotoSky, p. 352d; Wessel du Title: Peal'SOO mathematics 7 student book/ Dirk Sttasser la.nd twenty-two Olhefsl Plooy, p. 2l6hr; paul presco!t, p. 222 (h.\Ckgmund); Ptessmastet, p. 616; pryzmat, p. 414 (disco Pearson Australia Contributing Author Richard Korbosky James O'Connor Teacher-Victoria ISBN: 9781◄88613982 (papcfhack) ball); R..1ia, p. 420t; Alexander Raths, p. S341t; Stephen Rees, p. 62◄bl; Sergej RaZ\'Odcwskij, Teacher-Victoria, NSW Mathematical Association Contributing Author Tatge' Audience! For secood.uy school age. p. 149 (mobile phone); Neda Sadreddin, pp. 4811; R. Gino Santa Maria, p. 170 (bonle); Terry Byers of WA President Teacher- Victoria, Professor Kaye Stacey Subjecls: Ma1hem.a1ics-Textbooks. Denis Selivanov, p. 2781; Kuchet Sethii, p. ◄621; Eugen Shevchenko, p. 202; Contributing Author Kelly Gallivan Edith Cowan University Western Australia University of Melbourne Ma1hem.a1ics-Prohlems.. exe..ciw, etc. ShufterPNPhotography, p. 74; sil63, p. 170 (lorch'r, sixninepixels, p. 42C>>; Ljupco Smokovski, p. 23611; Sp.1rkling Moments Phot(>g.laphy, p. 28; Cloudia Spinnet, p. 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Sl2b: Btuce Yeung. p. SIS; Feng Yu, 1:lfl• 20!, 172; Tim Carruthers Teacher- Victoria Mathematical Association Act 1968 nnd is owned by the Aus1u llan Curriculum, Assessment an<I Rcr10r1lng Aulhotlty 2017. Knygo,,ockw Yutiy, ll. 236tr; ihangyai,gl3576997233, ll. 432hr. lead Publisher (2nd Edition) Patricia Goss of Western Australia Dirk Strasser ACAR.A nclthc_it ('OdotSCS no, verifies 1hc ~racy of the lnfonn.,tlon 1:H'C)vidcd nnd accc1Ms no Snowy Hydro Umile<I! 1>. S46. Content and learning Consuhant Donna Lannan Teacher- Western Australia Author rcs1)()1'1sihility kw lnco,nplc.-te Ot ln:.cc~1,ntc lnforma1lon. In l'.Wlf1icular, AC.ARA does 001e ndoric TeltaS lns.trumcncs Aus.Italia Pty Lid: TI-Nspirc CAS SCtCCn~OIS and elemen1s. 0t verify that: Thlnk51ock: J)f). 127, 2241c, 27111; cbudlodlvlzla, p. 598hr; Comstock, p. S99d; Ctcatns, 1). 301; Specialist Contributing Author • The conccn1 descrlp1lons arc solely f0t n panic:ular yenr nnd sd>jcc:I; dal)()(liSt, p. 73; Olgll;il Vision, 1>. 620c: lbtahlm sual Emnn, p. 79; CoodshOOI, 1>. 430; C'.tilflsslmo, Pearson Australia Dr John Gough Teacher- Victoria Karen Perkins Sofia Thapa • All 1he contcm descriptions fo, 1hat yenr nnd s.J>jecl have bttn used; and p. S99bl; lm.'lnn.'lggla, p. I 19bt: ITSloc:k Free, p. S07c; J11fliletin,ages, pp. 37, 53, 63h, 224hl, 316, Deakin University Consultant Contributing Author • The aull'(>t\ nl.'ltetl.11 nlig1'S whh 1hc AuW;ill.1n Curr',c:~1lum contenl dcKtiplions 508, 59911: V1ac:hcsl11v Krisanov, p. 568: Alcksandr LychJgin, 1). 599hr; M.1nfrcdlnl Mauro. 11. 88c:r, Karen Chin Mathematics Education Antje Leigh-Lancaster Teacher-Victoria Teacher-Victoria Ry.1n McV.ty, p. 30911; JMd<: Miarka, p. 203c; moming,u.1gc, 1>. 26St: SvlllMa Nlcdlels:ka, p. 243b; lot 1he l'Clcv;in1 ye11r nnd s.J,jec:1, Contributing Author Consuhant Head of K-12 Leaming MJl'lin Poole, J)I), 22411, 2241r, 344cl; 1Umnef~tJ1>hlalnc, 1>, 29S; ~hn Wohlfeil, 2241:,r; Lal leo.g 'mu can find lhc unahcl'Cd nnd fl'lie»I u1>I O cL11e \'CNion of this tn.'l1crl.-l m Vl.,p, p. I I 6c; Hongqi Zhang. p. 18hr. Teacher-Victoria Services (Mathematie1) Trang Pham Arthur Tsingoidas lmfrJ/www.:.us;1r.1llnnc:utric:ulum,cdu.au/This m.'ltetkd Is reproduced whh 1hc Bozenna Graham Pearson Australia Contributing Author Contributing Author Victorian De1»nmeo1o f Educ.ition nnd Eafly O,ildhood Oe-vclq,mcn1( OEECO): LBOTE Census flctmis.sic>n ol ACAR.A, Augus1 2008 cl..1t.1, p, S361, David Coffey Contributing Author Teacher- Victoria Teacher-Victoria We 1hank the following b 1>ermiuion 10 re1)f(l(IUC:C copyrigh1 mmcrial. The loUowing W.uer Corpor.1tlon: p, S4Jc, Contributing Author & Technical Consultant Martin Lindsay abbrc.'\llations arc used In this list 1• IOI>, b • bonom, I• lef1, r • right, c: • centre. \\tor'ld HC.Jhh Og.10is.1tion (WHO): J>p. SS6b, SS6c. Teacher-Victoria Teacher-Victoria Contributing Author Geoff Phillips Peter Walsh Co\~ im.,ge: l23RF/Mak1im Shebeko. ~ B.,~: 11. 3S5. Teacher- Victoria Author Consultant 123RF: algte, p, 33S11; alhovik, 1>, 176br: Todd Atcn.1, 11. 200; avron;i, p, 135cr: bjul, 1>, S78b; 'I\Jr;ansky: p, 309br, Evan Curnow Joshua Harnwell Teacher-Victoria Mabym Bond;uchuk, p. 336br; O,ris Brigncfl, p. 220b; J.1cck 0,:1br~lcwskl, p. 2J7bl; enkl, 1>. 3851; l>;Jul Flec1, 1>, 931r; free.misc, p. ◄4b: g;try718, 1>1>, 618-9: Ramon E1t>cl1C 0tgozo, p. S6; Eve,y cffon h;1s ba-n made 10 ,race .ind ac;knowk-dgc co1,yriglu. HOwtM..'t, If nny inftingemt-nl hM Development Editor Contributing Author Julian Lumb Annette Psereckis occunec~ lhc publishers 1cndef 1hcir npologies and invite cq,yright owners to conCX'I 1hem. Joi> Herm.ins, p. 34c; Tim Ht'SICf, 1>, 4671r; P,lblo Hidalgo, J>, 163: hon~ludio, 1>. 3001; Denis (First Edition) Teacher- NSW Content and l earning Mathematics Consultant- Sahooda Walters l.ichimcwsc:hi, J>, 2IS; 0.1nny Kosm~. J>, 282t; Herbefl Kl'o1tky, J>p. 188, 19S; lanJk, 1>. l"19 (boy Oisclaimen Pearson Australia Specialist Tasmania Contributing Author wi1h guit,u): Karin Lau, 1>. 282b: Robyn M.tckcnz.ie, 1>. 80; Svi1l;ma MJnynova, p. 376cl; Nelson The .cfoction of intemt-c a<klt~ (URU) providt-d f0t this book w.u v,1lid a, 1ht, lime ol Daniel Hernandez Pearson Australia Teacher- Victoria M.in1uc..'J. p. I 76bl; mil,mthikov, ,,. 2 13; NejroN, 1>. S071; oscill, ,,. 2◄Sr; Androy ~•vlov, 1>. 38Sb: 1>ublic-.11ion nnd was chosen ;as being .1111,ropri.itc for~ ;as a K.oeond.,ry educ.,1k10 rescardl 1001. Raint'f Pk'f)(lt, ,,. S2Sc:r, Jozcf Pole, p. 29; radub85, 1>. 1771: Erik Em.,nuol Vioir-,1 R.cis, 1>. 564; rido, HOWO\'Cr, due 10 1ho dynJmic n.iturc of 1ho inl(_"l'O(.'t, k>mc addrt'SSCJ m.,y h.ivo c:hangt-d, m.,y h;wc Mark Darrell l ead Editor (Mathematics) Katherine Quane 1>. 385c; Andrt'5 R.odriguea:, 1>. SOO; Hellen Setg(!YOYa. p. 212c; Maksim Shcbcko, i; limpson33, CCilR'<I co exiM since 1>ublicalion, or may in.tdv1.'f1t'fllly link 10 ~it<.'5 wi1h con1cnc lha1 could be Mathematical Association Pearson Australia Amanda Marasco Consultant Terry White 1>. 4061r; H,,nn., Sl:winsk.,, p. 271b r; Yulia Sokolov.l, J>. 4 18bc; s1ockyim.ig~. I>• 76c:r, s.ungchul77, conskk'rod offensive or inaP1>t01>riaro. While lhc au1hors and 1>.J>lis.hcr r('g,'t't any incoovcntCncc of South Australia President Contributing Author Teacher-NSW Author l>P• 31"1-S (b.idground); lOm.lCCojc, I>• 314 (Sl)y►; Lily,1na Vynogr.ldova, p. 190. 1his may c.,usc rcadt-n. no rCJi>onsibility for any such chang<.'5 ot unf0fcsco.1blc t.-"l'rors c.rn be Assistant Principal- Kate Hillery Teacher- Victoria Age Focostock: Ct.'Orgo Doyle, I>• 7611. acC(.'plt'd by ci1he, 1hc au1hors or 1he publisher. Contributing Author Shanna Rankin Leanne Wilson South Australia Alamy Stock Phoco: Richard C. Bingh.am II, J>. 157: Marie Conlin. p. 337b; Mitch Oi.atnon(~ Some ol lho imag~ us...-d in PeJnoo M.ithematk:s 1 mighl have associ:a1ions wilh dcce.a.K-d Teacher-NSW, Victoria Anne Matheson Consultant Contributing Author 1>. 236bc: Oigifoto C..,mma, p. I 56: Dino Gt'IOlnell.a, p. 248; Ni.all Mc:Diarmid, p. J44ll: The Indigenous Austr.1li.ans. Please be .aware lhal 1hcse images might cause 5.ldnt'Ss or distr<.'55 in Phocol1btary Wales, I>· S60br; Rachel Torms, p. 386; uk mtail Alan King, I>· 249; VIEW Pictures Ltd, Aboriginal or Tor ms Str a ii lsbndt'f commu nhit'S. Noel Davies Contributing Author Teacher-Victoria 1>. 81l r, VisUo1ls Stock, p. 237ll. Author Gregory Hine Teacher- Victoria Li Richardson APN News & Media limitt-d: Photo MaJl Flccl / APN, I>· 9. Consultant Consultant Aus.lralian Bureau al SCalislics (ABS): 0 Commonwealth ot Amtralia, (Plus• Au!>llalian Bureau of Teacher-Western Australia Statislics (ABS) and source dec.1ils}, pp. S33b, S45, 5SSI, S72c; (l\>f:>Ul:alion Pro;ections. Australi.a, 2006 lo 210 I, cat. no. 3222.0), p. S4"1c. w w Challenge 3 169 Chapter 5 Algebra 258 C o n t e n t s Gamespace: Fractured ravine 170 Recall 5 260 Chapter review 3 172 Exploration Task: Areas of rectangles 260 Numeracy practice 3 175 5.1 Pronumerals and variables 261 Pearson Mathematics writing and development team Maths 4 Real: Prime numbers and encryption 74 111 5.2 Terms, expressions and equations 266 Series features vm 2.4 Introduction to integers 76 Exploration STEM: The secret message 176 Problen1 solving: We all want ice-cream! 270 Using Pearson Mathematics x Puzzle: Ten1perature tangle 82 Exploration STEM: Electric fonts 176 5.3 Using rules 271 Half-time 2 83 Exploration STEM: The best buys 177 Chapter 1 Whole numbers 2 Problen1 solving: Cutting string 277 Exploration Coding: Adding consecutive numbers 177 2.5 Adding and subtracting positive integers 84 Recall 1 4 5.4 Formulas and substitution 278 Problem solving: The slippery snail 88 Chapter 4 Decimals, Exploration Task: The root of the problem 4 Game: Dicey formulas 283 2.6 Adding and subtracting negative integers 89 percentage and ratio 178 1.1 Mental strategies 5 5.5 Patterns and rules 284 Investigation: Heat beads and ice blocks 94 Game: Greed 10 Recall 4 180 Puzzle: Puzzling tables 290 2.7 Sin1plifying addition and subtraction 96 1.2 Indices 11 Exploration Task: Which deal is best? 180 Half-time 5 291 Puzzle: Pattern sums 100 Problem solving: Teacher's age 18 4.1 Place value and comparing decimals 181 Investigation: Richie's Restaurant 292 Challenge 2 101 Investigation: How many squares on a chessboard? 19 Game: Duelling decimals 190 5.6 Sin1plifying expressions with addition Chapter review 2 102 Maths 4 Real: Numbers around the wor1d 20 4.2 Rounding decimals 191 and subtraction 294 Numeracy practice 2 105 1.3 More strategies for multiplication 4.3 Decimals and fractions 196 Puzzle: Latin squares 299 and division 22 Mixed review A 106 Puzzle: What are the neighbours having Exploration Spreadsheet: Age matters 300 Problem solving: Wizard maths 28 for dinner? 200 5.7 The Cartesian plane 302 Chapter 3 Fractions 108 Half-time 1 29 4.4 Decimal addition and subtraction 201 Game: Line up 307 Recall 3 110 1.4 Estimating and rounding 30 Game: Closer than you 204 Maths 4 Real: Maths meets art 308 Exploration Task: Sharing again and again ... Game: Estimation frustration 37 Game: Decimal zilch 204 5.8 Patterns and plotting points 310 makes more? 110 1.5 Order of operations 38 Investigation: Ten dollars and eighty-nine cents 205 Puzzle: Gridlock 313 3.1 Understanding fractions 111 Problem solving: Four 4s = 100? 42 4.5 Decimal multiplication 206 Gamespace: Spy vs spy 314 Puzzle: Fractionally funny fiction 119 1.6 Mixed whole number problems 43 Game: Multiplicity 214 5.9 Interpreting graphs 316 3.2 Working with fractions 120 Problem solving: Nine hundred Half-time 4 215 Puzzle: Solve the grid 322 Puzzle: What fractions are we? 128 and ninety-nine 46 4.6 Decimal division 216 Challenge 5 323 3.3 Estimating and comparing fractions 129 Challenge 1 4 7 Puzzle: Magic square 221 Chapter review 5 324 Game: Flatlining 137 Gamespace: The operation theatre 48 Maths 4 Real: Perplexing prices 222 Numeracy practice 5 328 3.4 Adding and subtracting fractions 138 Chapter review 1 50 4.7 Percentages, fractions and decimals 224 Game: Race to 10 146 Numeracy practice 1 53 4.8 Using percentages 230 Half-time 3 147 Problem solving: The great half-price sale 235 Chapter 2 Integers 54 Maths 4 Real: Musical fractions 148 Maths 4 Real: Our global village 236 Recall 2 56 Investigation: Tangram teaser 150 4.9 Ratio 238 Exploration Task: Is adding always more? 3.5 Multiplying fractions 152 4.10 Rates 245 Is subtracting always less? 56 Game: Fringo! 158 Problem solving: Numberrrrrrrrrs 250 2.1 Multiples, factors and divisibility 57 Problem solving: Fill in the blanks 158 Challenge 4 251 2.2 Primes and composites 65 3.6 Dividing fractions 159 Chapter review 4 252 Puzzle: Gold digger 67 3. 7 Mixed fraction problems 165 Numeracy practice 4 255 Gamespace: Factorpillar 68 Problem solving: Mega-equivalents 168 2.3 Prime factors 70 Mixed review B 256 mathematics 7 Contents PEARSON 2ND EDITION w w Chapter 6 Measurement 330 Maths 4 Real: Dance party dilemma 414 Chapter 9 Statistics Chapter 10 Transformation Exploration Spreadsheet: Algebra using and probability 500 and visualisation 576 Recall 6 332 a spreadsheet 416 Exploration Task: What size? 332 Recall 9 502 Recall 10 578 7.5 Solving problems with equations 418 6.1 Units of length 333 Exploration Task: Improving the odds 502 Exploration Task: Shape shifting 578 Problem solving: Algebraic puzzles 422 6.2 Perin1eter 340 9.1 Collecting data 503 10.1 Translations 579 Investigation: The great escape 423 Problen1 solving: Ram's rulers 343 Puzzle: Matchstick puzzles 510 Puzzle: Jigsaw paradox 584 Gamespace: The case of the confusing clues 424 6.3 Area 344 9.2 Measures of centre and spread 511 10.2 Reflections 585 Challenge 7 426 Game: Jungle pathways 351 Problem solving: Running the race 515 Problen1 solving: Mirror, mirror, on the wall, Chapter review 7 427 Investigation: Paddocks 352 Gamespace: Crack the code 516 does it matter where I stand at all? 591 Numeracy practice 7 429 Half-time 6 354 10.3 Rotations 592 9.3 Graphing univariate data 518 6.4 Area of a parallelogram 355 Chapter 8 Angles and shapes 430 Puzzle: Number puzzles 528 Problem solving: Tan gram magic 600 6.5 Area of triangles and composite shapes 359 9.4 Comparing parts of a whole with graphs 529 Investigation: Diamonds are forever! 601 Recall 8 432 6.6 Volume 367 Problem solving: Missing pieces of the pie 537 10.4 Combined transformations 603 Exploration Task: Are you sure they are parallel? 432 Problem solving: The red cube 371 Half-time 9 538 Game: Conway's soldiers 610 8.1 Measuring, estimating and drawing angles 433 Gamespace: City mission 372 Exploration Spreadsheet: Finding statistics Half-time 10 611 Game: Angle Master 439 Maths 4 Real: Landscape gardening 374 using technology 539 Exploration CAS: Transformations with CAS 612 8.2 Classifying and naming angles 440 Investigation: Blocks of chocolate 376 9.5 Graphing bivariate data 540 Maths 4 Real: Snow logo 616 Problem solving: Count the angles 445 Challenge 6 378 Problem solving: Add it up 547 Gamespace: Ambigrams and symmetry 618 Maths 4 Real: Constructing angles 446 Chapter review 6 379 Maths 4 Real: The 1-watt initiative 548 10.5 Symmetry 620 8.3 Calculating angles 448 ( .,;. Numeracy practice 6 382 9.6 Comparing data sets 550 Problem solving: Symmetry challenge 626 1 Problem solving: Ella's angles 452 Puzzle: Number puzzles 559 10.6 Drawing and visualising 3D shapes 627 8.4 Angles and transversals 453 Mixed review C 383 9.7 Probability and sample space 560 Problem solving: What comes next? 631 Exploration CAS: Investigating angles Exploration STEM: The grand architect 385 Game: Catch me if you can 567 10.7 Plan views and elevations 632 on parallel lines 458 Exploration STEM: SuNey and discovery 385 Investigation: Billiard ball bounces 462 Investigation: Experimental probability 568 Problem solving: Bird's eye squares 636 Exploration Coding: Creating geometric patterns 385 Half-time 8 464 Challenge 9 570 Challenge 1O 637 8.5 Polygons 465 Chapter review 9 _...... 571 Chapter review 10 638 Chapter 7 Linear equations 386 Problem solving: The hex is gone 468 Numeracy practice 9 J:;;-~ ~ 575 Numeracy practice 10 642 Recall 7 388 8.6 Triangles 469 Mixed review E 644 Exploration Task: Comparing mobile phone plans- .._, Puzzle: Eggs, spoons and turtles 477 which is better? 388 Answers 646 Investigation: Angle sum of polygons 478 7.1 Number sentences 389 Glossary and index 727 8.7 Quadrilaterals 480 Game: Star quest 393 Problem solving: Quadrilateral quandaries 485 7.2 Introduction to equations 394 Gamespace: Planet polygon 486 Puzzle: The great number mystery 398 8.8 Compass constructions 488 7.3 Solving equations using backtracking 399 Challenge 8 492 Puzzle: Gold digger returns! 406 Chapter review 8 493 Half-time 7 407 Numeracy practice 8 497 7.4 Solving equations using the balance method 408 Mixed review D 498 Problem solving: Paper mountain 413 mathematics 7 Contents PEARSON 2ND EDITION w w PEARSON Student Book Pearson Lightbook Starter Pearson Places is the gateway to digital learning material l'f.otJISOltmott. ., 101i:s ,Uoll$Clttmotr..1.olles -- 5.8. HP. for teachers and students across Australia. Access your The Second Edition Student Book includes updated Lightbook Starter is an innovative digital resource powered content at www.pearsonplaces.com.au. questions, activities and design, with full coverage of the by Pearson's award-winning Lightbook technology. It has li1 Pearson Digital Australian Curriculum: Mathematics as well as the Victorian been developed to help students learn key mathematical Curriculum: Mathematics. concepts, evaluate their understanding and track their Professional Learning, progress. 'Before you begin' sections assess learner It incorporates the latest research as well as feedback from Training and Development readiness before each chapter topic, while 'Check-in' teachers and learners across Australia. questions can be used to evaluate learner understanding Did you know that Pearson also offers teachers a diverse Content caters for students of all abilities, with improved and practice after every chapter section. Student Book Homework Program range of training and development product-linked learning differentiation of all exercise questions and more questions ,uJt,o,,, ,,10it.,101101 for students consolidating their skills. Auto-correcting questions are linked to the Progress programs? We are dedicated to supporting your IC. Tracker dashboard for easy analysis and viewing of results, implementation of Pearson Mathematics, but it doesn't Homework Program which are mapped to progression through the Student stop there. The Homework Program provides a collection of tear-out Book as well as to Australian Curriculum: Mathematics and Our courses align closely with Pearson Mathematics Second worksheets for students to practise and revise Victorian Curriculum: Mathematics content descriptions. Edition and offer an in-depth learning experience, mathematical concepts. combining both practical and theoretical elements, enabling Pearson eBook you to implement the resource effectively in your Teacher Companion Much more than just pages on a screen, Pearson eBook is classroom. The Teacher Companion makes lesson preparation easy an on line or offline version of your Student Book linked to Find out more about our product-linked learning, Teacher Companion 1 Teacher Companion 2 by combining full-colour Student Book pages with teacher interactive content, rich media resources and other useful workshops, courses and conferences at Pearson Academy [ s]I I support including improved contextual teaching suggestions content specifically developed for Mathematics. It supports LightbookStarter www.pearsonacademy.com.au. and strategies, class activities, extra questions, worked you with appropriate online resources and tools for every Lightbook Starter solutions and answers for every question in the section of the Student Book, including videos, eWorked Student Book Examples, interactive lessons, worksheets and more. Teacher resources include chapter tests, full teaching programs and curriculum mapping for the Australian Curriculum: Mathematics and for the Victorian Curriculum: Mathematics. eBook We believe in learning. All kinds of learning for all kinds of people, delivered in a personal style. Pearson Because wherever learning flourishes, so do people. w w Supporting all learners Differentiation Pearson Mathematics Second Edition has been written and designed for the needs of the full ability spectrum of students in Australian classrooms. Recall- Each chapter begins with a review of assumed and necessary knowledge for the chapter. For students Recall needing extra revision, Recall Worksheets are available for each Recall question, with explanations to refresh understanding and exercises to practise skills. Exercises-All Exercises include questions according The Australian Curriculum: Mathematics Pearson Mathematics Second Edition is a compelling g) to the Australian Curriculum Proficiency Strands: Expanding brackets aims to ensure that students: research-based series, written by experienced and Fluency, Understanding and Reasoning. They have practising Australian teachers with the support of • are confident, creative users and been carefully paced to help students build skills, Australia's leading mathematics education experts. develop deep conceptual understanding and apply communicators of mathematics, It has been specifically designed to scaffold students' learning. Every Exercise also has 'Open-ended' able to investigate, represent and fluency development, conceptual understanding, questions to encourage students' creative thinking interpret situations in their personal reasoning and problem-solving skills. and ability to communicate mathematics effectively. and work lives and as active citizens Navigator Navigator-Three optional graded pathways • develop an increasingly sophisticated ,. 2, 3, "· s.. a. 1. 10, 12. 13. 1a. 2ca, ~ "· s. a. 1, a.. 9, 10. 12, 13, 2 • · b), "(a).sea>. a (a). 1 <e>, a, through every Exercise, with every question rated 19, 22 14. 18.. 19, 20. 21, 22 9, 10, 11, 14, IS. 18.. 17, 18, 19, understanding of mathematical concepts 20, 21, 22, 23 as Foundation, Standard or Advanced level. and tluency with processes, and are able to pose and solve problems and reason Challenge-Every chapter includes a full page Challenge in number and algebra, measurement and section for early finishers and advanced students. geometry, and statistics and probability • recognise connections between the areas of mathematics and other disciplines and • • • appreciate mathematics as an accessible Regular revision and reinforcement and enjoyable discipline to study. Pearson Mathematics Second Edition has a broad range of cumulative and chapter-based revision. (0 Australian Curriculum, Assessment and Reporting Authority Half-time-A mid-chapter review of chapter I content so far. /A Australian '(ij1 CURRICULUM Chapter review Chapter review-An end-of-chapter thorough review of chapter content. Pearson Mathematics shares these aims. Mixed review Mixed review-Cumulative revision that mixes content from previous chapters. Using Pearson Mathematics PEARSON mothemotics 7 2ND EDITION w w Encouraging inquiry Real-life contexts and problem solving and engagement Investigation Exploration Spreadsheet Exploration Task and STEM Home Page dCAS These are scaffolded to be accessible to all learners Practical contexts provide useful learning Anticipate the 'Why learn this?' question and and structured following a Se+ format. opportunities and natural pathways into interesting, provide a motivating entry into every new Pearson Mathematics Second Edition relevant mathematics. chapter topic, including discussion-provoking understands the importance places of students Forum questions. Exploration tasks are rich tasks that encourage Investigation developing technological literacy. Explorations student engagement, questioning and creative with CAS technology and spreadsheet thinking. STEM activities allow students to explore software allow students to learn and practise topics related to Science, Technology, Engineering their technical proficiency, while also helping and Design with a Mathematics perspective. Integers to develop students' deeper understanding ---11 .. - - ··-'°'-'"--"-- - ..... i.-•-- of the mathematical concepts covered. Exploration Task Exploration Spreadsheet ---- Exploration STEM ·----- Exploration CAS ·=--=-=--~- =---= Pearson Mathematics Second Edition has been designed to capture students' interest, Exploration Coding with the incorporation of Maths 4 Real, Gamespace and more. Algorithmic thinking is an increasingly relevant component of mathematics education for the Maths 4 Real Gamespace These are located throughout every chapter 21 st century. Algorithmic thinking and coding tasks and give students fun opportunities to develop encourage learners to understand and develop Scenarios that help students make Skill consolidation and reinforcement wrapped up their problem-solving skills and logical reasoning. reasoning skills with computational procedures, connections with mathematics in the real world. in fun and quirky scenarios, including multi-player algorithms and logical problem-solving, exploring a maths board games and solve-the-riddle, coding environment within a mathematical context. find-the-clue tasks and games. Problem solving Exploration Coding -- ..... . ..... .' .•·.•..·.·. .'......... . ' ,- '····· .... .. • •·••• •W., -- ___ ··-- -- -----·-- -- ·..·.- .. =-.. -=-=-=-.-,--_=-_ = :-=.-:.--=-=-=-·---- ·- -·-·- =------=-.::-..--:--.:-... ·-~---=·-=--=-~':. ==--===--=.:. ===r-·--- ------- - Game ...,., mm- -----·-----··- ·--·- ---- --------·--------·-------· ·----~-·- -- 1-.-..-.-..-..-..."- -"m\ ---·--·-----·--· ·-~:-::: ... r .'.... .......... . ..,,, ... ...... ... .. ..,.._~ ---··•----.·------•--··-·--··---·-- r ......... ., ---··-··- =r:":"-·: --:::..-====- .' ..., .. ., .........•.. =:.:::. -- -- mothemotics 7 PEARSON 2ND EDITION w w e r s It's a Santa stampede! Another Guinness World Record, this time for 'the largest gathering of Santa Claus'. ( 18 112 of them!) For decades, Guinness World Records has resources we use. Every day, people need to been recording extreme and bizarre feats, find totals, work out dlfferences, divide Including 'the most cockroaches eaten In one quantities, and make estimates. To live In lhfs minute' (36), and 'the most consecutive world, you need to be able to work with skateboard fronts!de ollies off a half-pipe numbers! ramp' (348). The book itself holds the record for being the best-selling copyrighted series of all time. People are fascinated to know the Forum most, the biggest, the fastest and the tallest. Is It Important to keep 'world records'? To keep records, you need a system of If so, then what kinds of of achievements numbers to count, order, measure and should records be kept for? calculate with. People also need numbers for What other kinds of records are good our personal lives: how much money we to keep? spend, save and earn; how far and how often we travel; and how much of the Earth's Why learn this? You are buying two $18 T-shirts and a $65 pair of jeans. Will $100 be enough? If you swim 12 laps of a 50 metre pool 4 times a week, how many metres per week Is that? Working with numbers means more than just being able to add, subtract, multiply and divide. It means being able to choose which skill to use, to estimate and round numbers, and to have a range of mental skills so that you can work things out efficiently and accurately. After completing this chapter you will be able to: • choose and use a range of mental strategies for calculations • understand how the properties of numbers can be used to calculate efficiently • Interpret and work with numbers In Index form • estimate answers to problems using estimating and rounding strategies • apply the order of operations • solve problems Involving whole numbers. 1 Whole numbers w w Recall M e n t a l s t r a t e g i e s Prepare for this chapter by attempting the following questions. lf you have difficulty with a This section looks at some strategies that are useful for doing calculations in your question, you can download a Recall Worksheet from the eBook or the Pearson Places website. head. Try writing them out first, before you do them only in your head. You might find 1 What is the place value of the red digit shown? some methods easier than others, or you might have different strategies of your own. (a) 45 783 That's okay-people are different in the way they like to approach things. A eight B tens C eighty-three D hundreds Strategy 1-Make easy numbers (b) 1264184 This strategy uses these two properties of numbers: A two B hundreds C ten-thousands D hundred-thousands 1 The order in which you add or multiply any two numbers does not change the result. 2 (a) Rearrange the following numbers in ascending order (from smallest to largest). For example: 2 x 3 = 6 and 3 x 2 = 6 ------------------, o, 567, 4500, 74, 11100, 6008, 12,602 I \ 4 + 5 = 9 and 5 + 4 = 9 1 The word 'commutative' comes 1 : from the Latin word commuts/8, : (b) Rearrange the following numbers in descending order (from largest to smallest). This is known as the commutative law. : which means to : 1200, 204, 987, 2196, 240, 95, 2400, 1010 2 The order in which three or more numbers are added, or the order in 1 s_w_itc h or change! 1 \ .... ,-- I 3 Find: which they are multiplied, also does not change the result. ...... I .......... .' (a) 50 000 + 6000 + 800 + 90 + 5 (b) 7 000 000 + 20 000 + 5000 + 70 + 3 In the following examples, brackets are used to show which pair of numbers is added or multiplied first. 4 (a) Round 1245 to the nearest: Multiplication: (i) 10 (ii) 100 (iii) 1000 (2 X 3) X 5 and 2 X (3 X 5) (b) Round 8983 to the nearest: =6x5 =2X 15 (i) 10 (ii) 100 (iii) 1000 =30 =30 5 Find: Addition: (a) 3 X 2 X 3 (b) 5 X 3 X3 X 2 (C) 2 X 2 X 2 (d) lOxlOxlOxlO (6+ 7) +8 and 6 + (7 + 8) =13+8 =6+ 15 6 Set out these calculations in your preferred way and work out the answers. =21 =21 (a) 456 + 56 (b) 16 + 2047 (c) 90 + 1267 + 341 Th is is known as the associative law. 7 Set out these calculations in your preferred way and work out the answers. It is important to understand that the commutative and associative laws do not apply to (a) 298 - 123 (b) 854 - 227 (c) 1406 - 249 subtraction and division, which both need to be worked from left to right. 8 Set out these calculations in your preferred way and work out the answers. For example: (9 - 5) - 4 but 9 - (5 - 4) (a) 45 x 7 (b) 134 x 5 (c) 34 x 95 =4-4 =9-1 =0 =8 l_ _ 9 Set out these calculations in your preferred way and work out the answers. (40+10)+2 but 40 + (10 + 2) (a) 844 + 4 (b) 3708 + 9 (c) 897 + 7 =4+2 =40+5 =2 =8 The order in which you add numbers and the order in which you multiply numbers does Exploration Task not change the result. The order only changes the result for subtraction or division. .. You can use the commutative and associative laws to'shuffle' or rearrange the calculation to create multiples of 10, which are easier to add and multiply. You can download this activity from the eBook or the Pearson Places website. For example: The root of the problem 7 + 9 + 3 is the same as: 3 + 7 + 9 5 x 37 x 2 is the same as: 5 x 2 x 37 =10 + 9 = 10 37 X You can also split one number into two parts, then use the associative law to add one part to ln this activity, you will explore the relationship between square roots and the the other number to create a multiple of 10. geometric properties of squares. 4 PEARSON mathematics 7 2ND EDITION 1 Whole numbers

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