55

Harry O’Brien

Fourth Edition

mathsAdvanced

9 780190 310738

ISBN 978-0-19-031073-8

visit us at: oup.com.au or contact customer service: cs.au@oup.com

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Harry O

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ISBN 9780190310714 ISBN 9780190310721 ISBN 9780190310738 ISBN 9780190310745

title: Advanced Primary Maths 5 format: 210mm x 280 mm spine: 12 mm colours used: CMYK

www.oxfordowl.com.au

Oxford Owl — the online destination for Oxford maths resources.

Advanced Primary Maths provides interesting and challenging activities that work towards the achievement standards of the Australian Curriculum, the Victorian Curriculum and the NSW Mathematics Syllabus for the Australian Curriculum.

The series can be used as part of any maths program or in any classroom where students’ maths abilities need to be challenged or extended.

Thirty-� ve units of work provide students with:• advanced activities with challenging algorithms and problems• problem-solving activities in relevant and interesting contexts• Super Questions for students ready to explore mathematical concepts at

a higher level• Weekly Testers for students to measure their progress• Open-Ended Challenger questions that elicit multiple solutions to problems• Super Problem-solving pages to encourage and develop the Australian

Curriculum Pro� ciency Strands (Fluency, Understanding, Problem-solvingand Reasoning) and NSW Syllabus Working Mathematically processes.

The series supports teachers’ classroom planning with:• Term Planners following a graded and spiralled approach• Find the Topic pages to select speci� c topics• curriculum cross-reference charts to identify related content descriptions

and outcomes• end-of-term Diagnostic Reviews to check students’ understandings• a comprehensive answer section at the back of each book to provide support for

teaching and learning.

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SAMPLE

CONTENTS

Unit 10 5-digit subtraction ................................................................... 44Adding fractions ...................................................................... 45Super problem solving ............................................................ 46Databases ............................................................................... 47

Unit 11 4-digit multiplication ................................................................ 48Rates ...................................................................................... 49Super problem solving ............................................................ 50Sector graphs ......................................................................... 51

Unit 12 3-digit division ......................................................................... 52Subtracting fractions ............................................................... 53Super problem solving ............................................................ 54Chance .................................................................................... 55

Unit 13 6-digit addition ........................................................................ 56Decimal place value ................................................................ 57Super problem solving ............................................................ 58Describing shapes .................................................................. 59Area and perimeter ................................................................. 60

Unit 14 Multiplying by tens ................................................................. 61Missing numbers .................................................................... 62Super problem solving ............................................................ 63Coordinates ............................................................................ 64Grams ..................................................................................... 65

Unit 15 Remainders as fractions ......................................................... 66Percentages ............................................................................ 67Super problem solving ............................................................ 68Chance 0 to 1 ......................................................................... 69

Unit 16 Subtraction to 6 digits ............................................................. 70Shopping ................................................................................. 71Super problem solving ............................................................ 72Tree diagrams ......................................................................... 73

Unit 17 Multiples ..................................................................................74Financial plan / budget .............................................................. 75Super problem solving ............................................................ 76Dot plots ................................................................................. 77am and pm notation ............................................................... 78

Unit 18 Averages ................................................................................. 79Fractions of a collection .......................................................... 80Super problem solving ............................................................ 81Grid references, direction, scale ............................................. 82Volume .................................................................................... 83

DIAGNOSTIC Review 2 ................................................. 84

Unit 1 Addition and subtraction strategies .......................................... 2Place value to 7 digits ............................................................... 3Super problem solving .............................................................. 4Recognising angles ................................................................... 5

Unit 2 Addition to 5 digits .................................................................... 6Financial plans .......................................................................... 7Super problem solving .............................................................. 8Symmetry/polygons and diagonals ........................................... 9

Unit 3 Mental multiplying ...................................................................10Thirds, sixths and twelfths .......................................................11Super problem solving ............................................................ 12Faces, vertices and edges ...................................................... 13

Unit 4 Order of operations ................................................................ 14Mixed numerals and improper fractions ................................. 15Super problem solving ............................................................ 16Measuring angles ................................................................... 17Kilometres .............................................................................. 18

Unit 5 Calculator memory ................................................................. 19Recording decimals ................................................................ 20Super problem solving ............................................................ 21Line graphs ............................................................................. 22Calculating area ...................................................................... 23

Unit 6 Subtraction to 5 digits ............................................................. 24Geometric patterns ................................................................. 25Super problem solving ............................................................ 26Enlargements ......................................................................... 27

Unit 7 Revising 3-digit multiplication ................................................. 28Equivalent fractions ................................................................ 29Super problem solving ............................................................ 30Picture graphs ......................................................................... 31

Unit 8 3-digit division ......................................................................... 32Real-life problems ................................................................... 33Super problem solving ............................................................ 34Triangles .................................................................................. 35Length .................................................................................... 36

Unit 9 Calculator memory ................................................................. 37Prime and composite .............................................................. 38Super problem solving ............................................................ 39Drawing 3D objects ................................................................ 40Perimeter ................................................................................ 41

DIAGNOSTIC Review 1 ................................................. 42

TERM1 TERM 2

SAMPLE

CONTENTS

Unit 28 Calculator division ................................................................. 128Substitution .......................................................................... 129Super problem solving .......................................................... 130Dot plot graphs ..................................................................... 131

Unit 29 Order of operations .............................................................. 132Reviewing fractions .............................................................. 133Super problem solving .......................................................... 134Rotational symmetry ............................................................ 135

Unit 30 Lattice multiplication ............................................................. 136Estimation strategies ............................................................ 137Super problem solving .......................................................... 138Mode and mean ................................................................... 13924-hour timetable ................................................................. 140

Unit 31 Dividing decimals .................................................................. 141Negative numbers ................................................................ 142Super problem solving .......................................................... 143Column graphs ..................................................................... 144Cubic centimetres and metres ............................................. 145

Unit 32 Long multiplication ............................................................... 146Strategies ............................................................................. 147Super problem solving .......................................................... 148Median and range ................................................................. 149

Unit 33 Place value to tens of millions .............................................. 150Decimals on a number line ................................................... 151Super problem solving .......................................................... 152Perspective ........................................................................... 153

Unit 34 Long multiplication ............................................................... 154Negative numbers ................................................................ 155Super problem solving .......................................................... 156Surveys/graphs ..................................................................... 157Time zones and timelines ..................................................... 158

Unit 35 5-digit division ....................................................................... 159Inverse operations ................................................................ 160Super problem solving .......................................................... 161Collecting data/questionnaires ............................................. 162Millilitres ............................................................................... 163

DIAGNOSTIC Review 4 ............................................... 164

ANSWERS ........................................................................ 166

Unit 19 Long multiplication ................................................................. 86Geometric patterns ................................................................. 87Super problem solving ............................................................ 88Drawing shapes ...................................................................... 89

Unit 20 Subtracting decimals .............................................................. 90Real-life problems ................................................................... 91Super problem solving ............................................................ 92Top, front and side views ........................................................ 93

Unit 21 4-digit multiplication ................................................................ 94Percentages ............................................................................ 95Super problem solving ............................................................ 96Chance .................................................................................... 97

Unit 22 Number patterns..................................................................... 98Describing problems ............................................................... 99Super problem solving ...........................................................100Scale ......................................................................................10124-hour time ..........................................................................102

Unit 23 4-digit division ........................................................................103Multiply decimals mentally ....................................................104Super problem solving ...........................................................105Nets .......................................................................................106Hectares and square kilometres ............................................107

Unit 24 Adding decimals ....................................................................108Roman numerals ...................................................................109Super problem solving ...........................................................110Enlargements and reductions ................................................ 111

Unit 25 Multiplying decimals ..............................................................112Count in decimals ..................................................................113Super problem solving ...........................................................114Adding mixed numerals .........................................................115

Unit 26 4-digit division ........................................................................116Mobile phone plans ...............................................................117Super problem solving ...........................................................118Construct objects from views................................................119Areas of triangles .................................................................. 120

Unit 27 Highest common factor (HCF) .............................................. 121Number patterns................................................................... 122Super problem solving .......................................................... 123Street directory ..................................................................... 124Tonnes, kilograms and grams ............................................... 125

DIAGNOSTIC Review 3 ............................................... 126

TERM 3 TERM 4

SAMPLE

2 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

1UNIT Addition and subtraction strategies

1 Use the split strategy to add and subtract these numbers.

a 42 + 35 = h 57 + 28 = o 427 + 132 =

b 31 + 54 = i 23 + 35 = p 534 + 354 =

c 62 – 32 = j 24 + 67 = q 627 + 252 =

d 23 + 45 = k 68 – 47 = r 309 + 490 =

e 42 + 54 = l 75 + 36 = s 3378 + 1267 =

f 48 + 26 = m 325 + 133 = t 2784 + 1141 =

g 66 – 34 = n 372 + 125 = u 1356 + 1277 =

2 Use the jump strategy to add and subtract these numbers.

a 26 + 15 = g 157 – 26 = m 448 + 24 =

b 35 + 27 = h 368 + 29 = n 137 – 36 =

c 46 + 42 = i 278 + 36 = o 346 + 125 =

d 35 + 23 = j 427 – 25 = p 757 – 326 =

e 48 – 25 = k 132 + 37 = q 485 – 224 =

f 58 – 37 = l 356 + 23 = r 297 + 133 =

3 Add the numbers mentally using the compensation strategy.

a 24 + 39 = f 27 + 42 = k 336 + 38 =

b 36 + 28 = g 53 + 38 = l 242 + 49 =

c 54 + 27 = h 36 + 37 = m 1137 + 57 =

d 47 + 49 = i 47 + 36 = n 2545 + 27 =

e 47 + 39 = j 126 + 57 = o 3276 + 89 =

4 Subtract the numbers mentally using the compensation strategy.

a 65 – 29 = f 83 – 49 = k 496 – 37 =

b 72 – 39 = g 92 – 78 = l 285 – 57 =

c 85 – 38 = h 64 – 37 = m 2174 – 36 =

d 73 – 49 = i 672 – 37 = n 2283 – 58 =

e 86 – 48 = j 569 – 28 = o 3684 – 69 =

SUPER QUESTION5 On the first day of a special interstate delivery

Sam drove 568 km and on the second day he drove 632 km. How much did he charge to do his delivery if his rate was 50c per kilometre? $

Add the hundreds, tens and ones

separately. 325 + 133?

Think 300 + 100 plus 20 + 30 plus 5 + 3

equals 458.

38 + 43?Think

38 + 40 + 3 = 81

35 + 48?Think

35 + 50 minus 2

64 – 29?Think

64 – 30 + 1SAMPLE

3Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

1UNITPlace value to 7 digits

6 Write the numbers on the place value chart. The first one has been done for you.

Number Millions Hundred thousands

Ten thousands Thousands Hundreds Tens Ones

a 37 685 3 7 6 8 5

b 127 903

c 2 291 376

d 3 754 264

e 4 390 235

f 5 437 294

7 Order the numbers from smallest to largest.

a 1234 4321 3241 4231

b 23 485 21 099 27 305 35 674

c 37 296 22 899 45 809 42 013

d 126 354 154 876 119 999 149 887

e 1 251 362 1 255 999 1 212 898 1 221 889

f 3 112 553 3 112 335 4 121 553 4 121 335

g 5 135 762 5 153 767 5 513 762 5 351 762

8 Arrange the cards to make the largest number then the smallest number using all 6 digits.

Cards Largest number Smallest number

a 3 5 7 2 4 6

b 8 4 1 5 7 9

c 4 2 9 6 8 3

9 Write the numbers in words.

a 4287

b 24 370

c 3 125 307

d 4 236 000

5 4 3 2 1 ?SAMPLE

Super problem solving

4 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

1UNIT

13 Three consecutive whole numbers add to give a total between 180 and 210. What are all the possible answers?

14 Three consecutive numbers add to give 252. What are they?

OPEN-ENDED CHALLENGER

12 Mr Bean wanted a new car priced at $35 267 but he couldn’t afford it as he only had $30 967. He took the following options off the car and its price to see if he could afford the same car.

• Cruise control $1260 • CD player $ 767 • Mag wheels $ 970 • Leather upholstery $1450

Could Mr Bean now purchase the car?

WEEKLY TESTER

10 Complete the magic squares.a b c d

14 12

15

16

18 23 16

19

23

26 19 24

24

25

28 26

11 Solve the problems.

a Ji’s cricket team scored 379 runs in the first innings and 256 runs in the second innings. What was its total score for the game?

e James saved $36 per week for 8 weeks. How much more does he need to buy a bike worth $400?

b A farmer planted 78 trees in 6 paddocks. If the trees were shared equally, how many would there be in each paddock?

f Mr Kent planted 96 flowers in a large garden bed but only 3

4 of them sprouted. How many flowers sprouted?

c Jackie’s team scored 189 goals this year and Lauren’s team scored 139. How many goals did they score altogether?

g There are 113 children in the 4 classes of Year 5. How many are there in 5T if 5K has 30, 5S has 27 and 5R has 29?

d Mr Harris bought 7 tins of beans at $0.95 per can. How much change did he get from $10.00?

h Trent had $1000 but spent $376 on a TV and $247 on a bike. How much money does Trent have left?

SAMPLE

5Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)

1UNITRecognising angles

Right angle Obtuse angle Acute angle Straight angle Reflex anglea

b

c

d

e

Square corner— 90°

Larger than a right angle— Greater than 90° but less than 180°

Smaller than a right angle— Less than 90°

Can be made from 2 right angles—180°

Larger than a straight angle— Greater than 180°

15 Label the angles either right angle, obtuse, acute, reflex or straight.a d g j

b e h k

c f i l

16 Answer the questions about the irregular nonagon.

a Which angles are right angles?

b Which angles are acute angles?

c Which angles are obtuse angles?

d Which angles are reflex angles?

e Which angle is the smallest acute angle?

f Which angle is the largest reflex angle?

17 Find an example of each angle in your school.

Acute

Obtuse

Angles are classified according to the amount of turn between the 2 arms.

F

G H

I

E

D

C

BA

SAMPLE

DIAGNOSTIC Review 1

42

PART 1 a Make the largest number you

can from the digits 4, 2, 5, 6, 3, 1

b Write 367 206 in words.

c Arrange the following numbers in order of size from the smallest to largest.

359 726 45 265 359 276 359 266

What is the place value of the bold numeral in each number?

d 37 806

e 35 264

f 49 321

PART 2 Record a decimal for each hundredths grid.

Ones Tenths Hundredths

a

0b

Write true or false:

c 12 = 3

6 f 14 = 2

8

d 14 > 1

8 g 26 = 1

3

e 12 > 7

8 h 13 > 7

12

Change to mixed numerals.

i 54 = l 9

8 =

j 43 = m 13

8 =

k 53 = n 17

6 =

PART 3 Write prime or composite after each number.

a 49

b 53

c 51

PART 4

a 2 1 7 b 3 4 2 c 3 8 7

× 3 × 6 × 8

d 2 3 4 2 4 e 3 7 5 4 5 9

+ 5 4 8 3 7 + 1 6 3 6 1 5

f 8 8 2 3 g 6 8 5 8 4

– 6 5 4 7 – 7 8 0 6

h 7 8 8 i 7 9 9 9 j 6 7 9 2

k 4384 tickets were sold for the concert. If 3272 people have already arrived, how many more are still expected to arrive?

people still to arrive

l Bread costs $1.75, milk $1.15, butter $1.95 and eggs $1.65. If you purchased all 4 items, how much change would you get from $10.00? $

m Samuel had 1374 marbles in his marble bag which had a hole in it. If 236 fell out, and he gave away 109, how many marbles were left?

n John saved $9.55 per month for 6 months and his mother gave him $9.70. How much more does he need to buy a game worth $100? $

•

• SAMPLE

DIAGNOSTIC Review 1

43

PART 5 Use the words acute, obtuse, right, reflex or straight to name the angles.a b c

d e f

Measure these angles.g h

PART 6 Draw a line to name the triangles.

isosceles equilateral scalene right angle

PART 7 a Name this object.

b How many faces?

c How many vertices?

d How many edges?

PART 8 Sketch these objects, showing dotted lines for hidden edges.

triangular prism square pyramid

PART 9 Trucks leaving depot

March Key = 400

April

May

June

a How many trucks left the depot in April?

b Complete the graph by adding 1400 trucks leaving the depot in June.

PART 10 Measure the perimeter in millimetres.

Perimeter = mm

PART 11 Calculate the area of these shapes.

PART 12 a How many centimetres in 2.5 m?

b How many millimetres in 312 cm?

c How many metres in 4.5 km?

Use decimal notation to record these measurements in kilometres.d 3746 m = kme 8079 m = kmf 27 359 m = km

a b

Area = cm2

7 cm

4 cm

Area = cm2

7 cm

6 cm

c

Area = cm2

14 cm

5 cmSAMPLE