Fourth Eition Avne mths Hrry O Brien 6
CONTENTS Unit 1 Mentl strtegies... 2 6-igit sutrtion... Super prolem solving... 4 Tringles... Unit 2 6-igit ition... 6 Equivlent frtions... 7 Super prolem solving/elpse time... 8 Nets of D ojets... 9 Unit Reing n orering numers...10 Mentl multiplying...11 Super prolem solving... 12 Dot plot grphs... 1 Unit 4 Estimting multiplition... 14 Improper frtions n mixe numerls... 1 Super prolem solving... 16 Sle n iretion... 17 Millimetres/perimeter... 18 Unit Romn numerls... 19 Orer of opertions... 20 Super prolem solving... 21 Line grphs... 22 Squre entimetres n metres... 2 Unit 6 Division with frtionl reminers... 24 Geometri ptterns... 2 Super prolem solving... 26 Top, front n sie views... 27 Unit 7 Fining equivlent frtions... 28 Prime n omposite numers... 29 Super prolem solving... 0 Chne... 1 Unit 8 Diviing eimls... 2 Aing n sutrting like frtions... Super prolem solving... 4 Angles... 24-hour time/elpse time... 6 Unit 9 TERM1 TERM 2 Fining unit frtions... 7 Strtegies... 8 Super prolem solving... 9 Drwing 2D shpes... 40 Isometri rwing... 41 Unit 10 Sutrting eimls... 44 Clultor lulting... 4 Super prolem solving... 46 Sie-y-sie olumn grphs... 47 Unit 11 Aing n sutrting eimls... 48 Orering frtions... 49 Super prolem solving... 0 Drwing D ojets... 1 Unit 12 Multiplying eimls... 2 Clultor perentges... Super prolem solving... 4 Chne experiment/posing questions... Unit 1 Division to 6 igits... 6 Ftors n multiples... 7 Super prolem solving... 8 Mpping... 9 Tonnes... 60 Unit 14 Expning numers... 61 Deiml ple vlue... 62 Super prolem solving... 6 Digonls... 64 24-hour timetle/elpse time... 6 Unit 1 Reuing frtions... 66 Flow hrts/rnhing... 67 Super prolem solving... 68 Squre numers... 69 Unit 16 Multiplition y 2 igits... 70 Grphing numer ptterns... 71 Super prolem solving... 72 Rottionl symmetry n tesselltion... 7 Unit 17 Diviing eimls...74 Strtegies... 7 Super prolem solving... 76 Chne tree igrm... 77 Cirumferene n length onversions... 78 Unit 18 Lrger itions... 79 Perentges... 80 Super prolem solving... 81 Investigting D ojets... 82 Sle squre metres... 8 DIAGNOSTIC Review 1... 42 DIAGNOSTIC Review 2... 84
Unit 19 Multiplying frtions y whole numers... 86 Spresheets... 87 Super prolem solving... 88 Gri referenes... 89 Unit 20 Sutrtion... 90 Aing n sutrting mixe numerls... 91 Super prolem solving... 92 Angles... 9 Unit 21 Multiplition y 2 igits... 94 Tringulr numers/psl s tringle... 9 Super prolem solving... 96 Chne preitions... 97 Unit 22 Goos n Servies Tx (GST)... 98 Inverse opertions... 99 Super prolem solving...100 Reflet, trnslte, rotte...101 Cpity units...102 Unit 2 Deiml reminers...10 Numer ptterns...104 Super prolem solving...10 Negtive numers...106 Grms...107 Unit 24 Geometri ptterns...108 Sle prolems...109 Super prolem solving...110 Two-wy tles... 111 Unit 2 Multiplitions...112 Frtionl quntities...11 Super prolem solving...114 Potentilly misleing t...11 Unit 26 Equl numer sentenes...116 Purhsing...117 Super prolem solving...118 Negtive numers...119 Meriins of longitue... 120 Unit 27 TERM TERM 4 Multiplition y 2 igits... 121 Numer ptterns... 122 Super prolem solving... 12 Enlrgements... 124 Cui metres... 12 CONTENTS Unit 28 Expning numers... 128 Multiplying frtions... 129 Super prolem solving... 10 Rnge n mein... 11 Unit 29 Multiplying n iviing eimls... 12 Dt vrition/posing questions... 1 Super prolem solving... 14 Hetres n squre kilometres... 1 Unit 0 Missing numers... 16 Resonle or unresonle... 17 Super prolem solving... 18 Misleing t... 19 Metri reltionships... 140 Unit 1 Multiplition y igits... 141 The Crtesin plne... 142 Super prolem solving... 14 The irle... 144 Rtes... 14 Unit 2 Division y 2 igits... 146 Desriing prolems... 147 Super prolem solving... 148 Clulting ngles... 149 Unit Pronumerls... 10 Estimtion... 11 Super prolem solving... 12 Men n moe... 1 Unit 4 Long ivision... 14 The Crtesin plne... 1 Super prolem solving... 16 Explining grphs... 17 Timelines... 18 Unit Fining perentges... 19 Diviing y frtions... 160 Super prolem solving... 161 Mking mps... 162 Are of tringles... 16 DIAGNOSTIC Review 4... 164 DIAGNOSTIC Review... 126 ANSWERS... 166
UNIT1 Mentl strtegies 1 A these numers using the ompenstion strtegy. 64 + 29 = f 16 + 19 = k 2128 + 67 = 1 + 8 = g 127 + 7 = l 47 + 47 = 16 + 29 = h 229 + 48 = m 467 + 29 = 1 + 28 = i + 29 = n 876 + 7 = e 27 + 49 = j 247 + 8 = o 629 + 8 = 67 + 28 Think 67 + 0 minus 2 97 2 = 9 2 A these numers using the jump strtegy. 7 + 29 = f 19 + 149 = k 2128 + 28 = 687 + 48 = g 6292 + 18 = l 297 + 27 = 79 + 49 = h 716 + 227 = m 46 + 49 = 887 + 8 = i 4194 + 29 = n 27 + 17 = e 486 + 7 = j 8176 + 49 = o 6196 + 829 = A these numers using the split strtegy. 164 + 229 = f 16 + 19 = k 128 + 767 = 1 + 18 = g 127 + 47 = l 47 + 447 = 16 + 229 = h 229 + 48 = m 67 + 229 = 1 + 28 = i + 229 = n 876 + 17 = e 27 + 449 = j 247 + 68 = o 29 + 8 = 4 Give n estimte for eh question y rouning eh numer to 100. The first one hs een one for you. 212 + 97 = 600 g 4 + 146 = m 179 + 1222 = 16 + 484 = h 424 + 60 = n 1498 + 107 = 09 + 201 = i 479 + = o 1689 + 2221 = 678 + 20 = j 47 + 6 = p 26 + 47 = e 476 + 281 = k 797 + 707 = q 290 + 61 = f 979 + 219 = l 469 + 42 = r 409 + 288 = Solve the prolems. 27 + 8 Think 27 + 0 = 287 287 + 8 = 29 164 + 229 Think 100 + 200 = 00 60 + 20 = 80 4 + 9 = 1 Totl = 9 Trent flew 12 4 km on Mony n 746 km on Tuesy. Wht ws the totl length of his flight? Jim s mother ought new r for $24 4 n spent nother $2449 on extrs. Wht ws the totl ost of the r? 2 Selet n pply effiient mentl n written strtegies n pproprite igitl tehnologies to solve prolems involving ll four opertions with whole numers (ACMNA12)
6-igit sutrtion UNIT 1 6 Complete eh lgorithm. 4 7 0 6 7 8 0 4 6 8 6 6 6 7 7 0 e 6 7 7 7 7 2 0 0 4 7 0 0 0 8 6 8 2 6 9 8 6 9 4 4 6 0 0 f 4 6 0 7 g 6 8 7 0 h 7 6 7 4 0 0 i 8 7 8 0 0 j 9 8 7 0 0 0 4 6 7 2 4 0 6 4 8 6 7 0 0 4 4 8 6 0 8 k 2 6 7 8 9 l 7 4 0 6 m 2 6 7 0 9 n 7 6 2 0 8 o 7 4 0 0 8 9 6 2 7 4 8 0 6 9 8 7 2 6 7 0 8 6 6 4 9 e 7 Bill s house renovtions. Bill ought house t Mngerton for $297 000 n sol it for $4 00. How muh profit i he mke? Bill ought house t Corriml for $289 00 n sol it for $47 20. How muh profit i he mke? Bill ought house t Dpto for $277 980 n sol it for $ 0. How muh profit i he mke? Bill ought house t Kim for $17 40 n sol it for $77 90. How muh profit i he mke? Bill ought house t Mt Keir for $12 20 n sol it for $90 00. How muh profit i he mke? SUPER QUESTION 8 To lim trvelling expenses on her tx return, Christin keeps log ook whih shows her r s oometer reing t the eginning n t the en of eh trip. Help her lulte the istnes overe n the mounts she n lim lulte t 1 per kilometre. Dte Beginning of trip En of trip Kilometres trvelle Amount lime 18/9 8 42 9 461 19/10 4 814 44 002 4/11 44 629 44 91 29/ 2 414 2 79 e 24/4 029 216 f Totl Selet n pply effiient mentl n written strtegies n pproprite igitl tehnologies to solve prolems involving ll four opertions with whole numers (ACMNA12)
UNIT1 Super prolem solving 9 Complete the ition stks. 10 Solve the prolems. 21 8 1 19 7 24 18 16 19 27 4 27 6 4 62 spettors ttene the show on Stury n 40 67 ttene on Suny. How mny ttene in totl? The monoril runs every 10 minutes, 18 hours y, every y of the week. How mny times woul it run in 26 weeks? A lrge kyr fish pon hs pity of 00 L. If it is 4 full, how muh more wter woul nee to e e to mke it full? WEEKLY TESTER 11 Jill is times oler thn Jk who is 1 2 the ge of Josh. Slly is 4 times oler thn Jk n Kim is 7 8 the ge of Slly. Clulte the ges given vrious ges for Jill. 24 27 18 42 Jill Jk Josh Slly Kim OPEN-ENDED CHALLENGER 12 The teher wrote this numer sentene on the lkor.. = She lso si tht the numers in the missing oxes were 4, 7, 9,. Wht oul some of the multiplitions n their nswers e?...... e f Mr Jones ought 6 new sell ts for his sell lu. If the ts ost $174.0 eh, how muh woul he hve spent? Five uses rrying 48 hilren eh trnsporte them to the sports rnivl. If eh hil pi $4.0, how muh woul e ollete? Jk h g of 4 000 ens. If he lost 1 10 of them n sol of them, how mny ens woul Jk hve left? 4 Selet n pply effiient mentl n written strtegies n pproprite igitl tehnologies to solve prolems involving ll four opertions with whole numers (ACMNA12)
Tringles UNIT1 Equilterl tringle Right-ngle tringle Isoseles tringle Slene tringle 1 Answer the questions. Whih tringle hs sies the sme length n ngles the sme size? Whih tringle hs 2 sies the sme length n 2 ngles the sme size? Whih tringle hs no sies the sme length n no ngles the sme size? Whih tringle ontins right ngle? 14 Nme these shpes, inluing the full nmes for the tringles. e i m f j n g k o h l p 1 Wht shpe m I? I hve stright sies. My sie lengths re 7 m, 4 m n m. I hve 8 ngles the sme size n 8 stright sies the sme length. I hve 6 stright sies. I hve 10 stright sies the sme length n 10 ngles the sme size. Investigte, with n without igitl tehnologies, ngles on stright line, ngles t point, n vertilly opposite ngles. Use the results to fin unknown ngles (ACMMG141)
DIAGNOSTIC Review 1 PART 1 Write the ple vlue of the igit in ol print. 216 84 49 27 786 08 Write these numers in Romn numerls. 7 e 66 f 129 g 8 Write Hinu Ari numers for these. h i j k XXXVIII LXIX CCCLXIV DCCCLXXXVIII PART 2 9 6 7 7 8 8 4 0 6 7 + 6 4 4 7 + 4 6 8 4 6 9 6 6 4 7 4 4 8 e 8 8 0 9 8 7 f 2 6 2 g 1 4 7 4 h 4 6 4 7 6 i If Tim s verge for 9 riket gmes ws 67 runs, wht ws his totl sore? runs PART Write equivlent frtions for. 1 2 = 10 1 4 = 8 = 10 8 = 24 Write mixe numerl for eh improper frtion. e 7 4 = f 9 g = h A the frtions. i + 2 = 8 8 j k + 4 = 10 10 l Fin the frtions. m of 20 sheep = n o 6 7 12 PART 4 of 96 gots = of 600 stmps = 1 = 6 17 = 6 + 2 = 4 4 + 8 = 10 10 Complete the numer sentenes. 7 + = 100 9 + 8 = (7 + ) = + 47 9 = e Cirle the numers tht re prime: 74 89 167 21 96 77 19 Complete. f 27 100 = g 27 1000 = h 27 10 000 = PART j k 80 people ttene y one of the riket mth ut only 276 ttene y two. How mny more people ttene on y one? John sve $24 in Jnury, $47 in Ferury n $67 in Mrh. How muh more oes he nee to sve to uy omputer worth $199? $ Exten the numer pttern se on the shpes, then write rule for it. Shpes 1 2 4 6 7 8 Lines Rule: 42
DIAGNOSTIC Review 1 PART 6 Drw this shpe on the isometri ot pper. The k lok hs een rwn for you. PART 7 PART 8 If 0 is impossile n 1 is ertin, wht is the proility of this spinner lning on re? Put ross on the sle to show your nswer. 0 0.2 0.4 0.6 0.8 1.0 Drw the top, front n sie views. PART 9 0.1 0. 0. 0.7 0.9 Top Front Sie Nme n mesure these ngles. F PART 10 Mesure the length of eh line in mm. Mesure n reor the perimeters of these shpes in millimetres. 2 mm 20 mm PART 11 e 27 mm Clulte the res in m 2. 16 mm e Are = m 2 Are = m 2 PART 12 Temperture C 40 0 2 20 1 10 0 9 m 10 11 Noon 1 2 4 pm Time The temperture t 11:00 m ws: At wht time ws it C? The iggest hnge in one hour in temperture took ple etween: 4