Fourth Edition. Advanced. maths Harry O Brien SAMPLE

Transcription

1 Fourth Eition Avne mths Hrry O Brien 6

2 CONTENTS Unit 1 Mentl strtegies 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 Dot plot grphs... 1 Unit 4 Estimting multiplition Improper frtions n mixe numerls... 1 Super prolem solving Sle n iretion Millimetres/perimeter Unit Romn numerls Orer of opertions Super prolem solving Line grphs Squre entimetres n metres... 2 Unit 6 Division with frtionl reminers Geometri ptterns... 2 Super prolem solving Top, front n sie views Unit 7 Fining equivlent frtions Prime n omposite numers Super prolem solving... 0 Chne... 1 Unit 8 Diviing eimls... 2 Aing n sutrting like frtions... Super prolem solving... 4 Angles hour time/elpse time... 6 Unit 9 TERM1 TERM 2 Fining unit frtions... 7 Strtegies... 8 Super prolem solving... 9 Drwing 2D shpes Isometri rwing Unit 10 Sutrting eimls Clultor lulting... 4 Super prolem solving Sie-y-sie olumn grphs Unit 11 Aing n sutrting eimls Orering frtions 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 Unit 14 Expning numers Deiml ple vlue Super prolem solving... 6 Digonls hour timetle/elpse time... 6 Unit 1 Reuing frtions Flow hrts/rnhing Super prolem solving Squre numers Unit 16 Multiplition y 2 igits Grphing numer ptterns Super prolem solving Rottionl symmetry n tesselltion... 7 Unit 17 Diviing eimls...74 Strtegies... 7 Super prolem solving Chne tree igrm Cirumferene n length onversions Unit 18 Lrger itions Perentges Super prolem solving Investigting D ojets Sle squre metres... 8 DIAGNOSTIC Review DIAGNOSTIC Review

3 Unit 19 Multiplying frtions y whole numers Spresheets Super prolem solving Gri referenes Unit 20 Sutrtion Aing n sutrting mixe numerls Super prolem solving Angles... 9 Unit 21 Multiplition y 2 igits Tringulr numers/psl s tringle... 9 Super prolem solving Chne preitions Unit 22 Goos n Servies Tx (GST) Inverse opertions Super prolem solving Reflet, trnslte, rotte Cpity units Unit 2 Deiml reminers...10 Numer ptterns Super prolem solving...10 Negtive numers Grms Unit 24 Geometri ptterns Sle prolems Super prolem solving Two-wy tles Unit 2 Multiplitions Frtionl quntities...11 Super prolem solving Potentilly misleing t...11 Unit 26 Equl numer sentenes Purhsing Super prolem solving Negtive numers Meriins of longitue Unit 27 TERM TERM 4 Multiplition y 2 igits Numer ptterns Super prolem solving Enlrgements Cui metres CONTENTS Unit 28 Expning numers Multiplying frtions Super prolem solving Rnge n mein Unit 29 Multiplying n iviing eimls Dt vrition/posing questions... 1 Super prolem solving Hetres n squre kilometres... 1 Unit 0 Missing numers Resonle or unresonle Super prolem solving Misleing t Metri reltionships Unit 1 Multiplition y igits The Crtesin plne Super prolem solving The irle Rtes Unit 2 Division y 2 igits Desriing prolems Super prolem solving Clulting ngles Unit Pronumerls Estimtion Super prolem solving Men n moe... 1 Unit 4 Long ivision The Crtesin plne... 1 Super prolem solving Explining grphs Timelines Unit Fining perentges Diviing y frtions Super prolem solving Mking mps Are of tringles DIAGNOSTIC Review DIAGNOSTIC Review ANSWERS

4 UNIT1 Mentl strtegies 1 A these numers using the ompenstion strtegy = f = k = = g = l = = h = m = = i + 29 = n = e = j = o = Think minus = 9 2 A these numers using the jump strtegy = f = k = = g = l = = h = m = = i = n = e = j = o = A these numers using the split strtegy = f = k = = g = l = = h = m = = i = n = e = j = o = 4 Give n estimte for eh question y rouning eh numer to 100. The first one hs een one for you = 600 g = m = = h = n = = i = o = = j = p = e = k = q = f = l = r = Solve the prolems Think = = Think = = = 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)

5 6-igit sutrtion UNIT 1 6 Complete eh lgorithm e f g h i j k l m n o e 7 Bill s house renovtions. Bill ought house t Mngerton for $ n sol it for $4 00. How muh profit i he mke? Bill ought house t Corriml for $ n sol it for $ How muh profit i he mke? Bill ought house t Dpto for $ n sol it for $ 0. How muh profit i he mke? Bill ought house t Kim for $17 40 n sol it for $ How muh profit i he mke? Bill ought house t Mt Keir for $12 20 n sol it for $ 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/ / / / e 24/ 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)

6 UNIT1 Super prolem solving 9 Complete the ition stks. 10 Solve the prolems spettors ttene the show on Stury n 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 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 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)

7 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)

8 DIAGNOSTIC Review 1 PART 1 Write the ple vlue of the igit in ol print 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 e f g h 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 = = 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 = l Fin the frtions. m of 20 sheep = n o PART 4 of 96 gots = of 600 stmps = 1 = 6 17 = = = Complete the numer sentenes. 7 + = = (7 + ) = = e Cirle the numers tht re prime: Complete. f = g = h = 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 Lines Rule: 42

9 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 Drw the top, front n sie views. PART 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 mm e Are = m 2 Are = m 2 PART 12 Temperture C m Noon 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