Primary Mathematics - Back to Basics: Book F - Ages 10-11 by Teacher Superstore

RIC-6061 4.6/178

Additional titles available in this series:

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Primary mathematics: Back to basics (Book A) Primary mathematics: Back to basics (Book B) Primary mathematics: Back to basics (Book C) Primary mathematics: Back to basics (Book D) Primary mathematics: Back to basics (Book E) Primary mathematics: Back to basics (Book G)

This master may only be reproduced by the original purchaser for use with their class(es). The publisher prohibits the loaning or onselling of this master for the purposes of reproduction.

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Internet websites

In some cases, websites or specific URLs may be recommended. While these are checked and rechecked at the time of publication, the publisher has no control over any subsequent changes which may be made to webpages. It is strongly recommended that the class teacher checks all URLs before allowing students to access them.

View all pages online PO Box 332 Greenwood Western Australia 6924

Website: www.ricpublications.com.au Email: mail@ricgroup.com.au

FOREWORD Primary mathematics: Back to basics is a series of books with a back-to-basics approach designed to support the foundations of the maths curriculum. It is a clear and comprehensive resource that covers number, measurement, space, and chance and data concepts for each year level. This series is ideal for: • • • • •

teaching a new concept consolidation homework assessment revision.

Titles in the series are:

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Primary mathematics: Back to basics – Book B Primary mathematics: Back to basics – Book D Primary mathematics: Back to basics – Book F

Contents

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Primary mathematics: Back to basics – Book A Primary mathematics: Back to basics – Book C Primary mathematics: Back to basics – Book E Primary mathematics: Back to basics – Book G

Teachers notes .........................................................................................................................................................................................iv Curriculum links .........................................................................................................................................................................................v

Number

Space

Writing numbers................................................................. 2–3 Place value......................................................................... 4–5 Rounding............................................................................. 6–7 Addition............................................................................... 8–9 Addition problems.......................................................... 10–11 Mental addition.............................................................. 12–13 Subtraction..................................................................... 14–15 Subtraction problems.................................................... 16–17 Mental subtraction........................................................ 18–19 Multiplication.................................................................. 20–21 Multiplication problems................................................ 22–23 Mental multiplication.................................................... 24–25 Division............................................................................ 26–27 Mental division............................................................... 28–29 Fractions.......................................................................... 30–31 Decimals.......................................................................... 32–33 Percentages................................................................... 34–35 Money.............................................................................. 36–37 Mixed problems............................................................. 38–39 Mixed mental.................................................................. 40–41 Number sequences and patterns............................... 42–43 Number sentences........................................................ 44–45

Lines and angles........................................................... 46–47 2-D shapes..................................................................... 48–49 3-D shapes..................................................................... 50–51 Perspective and transformations............................... 52–53 Symmetry....................................................................... 54–55 Directions....................................................................... 56–57 Map features and scales............................................. 58–59

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Length............................................................................. 60–61 Perimeter........................................................................ 62–63 Area................................................................................. 64–65 Volume and capacity.................................................... 66–67 Mass............................................................................... 68–69 Temperature................................................................... 70–71 Angles............................................................................. 72–73 Time................................................................................. 74–75 Calendars and timetables............................................ 76–77

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Chance and data Chance............................................................................ 78–79 Data................................................................................. 80–81 Diagrams and tables.................................................... 82–83 Graphs............................................................................ 84–85 Averages........................................................................ 86–87

iii

Primary mathematics: Back to basics

TEACHERS NOTES The format of the book Each book contains teachers notes and curriculum links. Four sections are included in each book: • Number

• Space

• Measurement

• Chance and data

Each section covers a variety of concepts. The number of concepts covered varies from section to section. Each student page in the book provides teachers with activities that relate solely to one mathematical concept. The student pages are graded, with activities that provide a progressive degree of difficulty. In this way, teachers can use the page to introduce a new concept and then reinforce knowledge and skills.

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The student pages are supported by a corresponding teachers page which includes the following information:

The name of the concept is given.

Indicators show the specific desired outcomes when completing the worksheet.

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Teachers notes page

The concepts required for students to complete each page are provided.

The name of the related strand is given.

Answers are given for all questions on the student page.

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The name of the concept is given.

Space is provided for each student to write his/her name on each worksheet.

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Student page

The name of the related strand is given.

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Questions or activities relating to each concept are given with sufficient space provided for students to write answers.

Since this series of books follows a set format, teachers may find it useful to use a preceding title to review a corresponding concept before new skills are introduced. Students who need extra assistance may also find this a helpful way to revise material previously taught. Primary mathematics: Back to basics

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curriculum links Western Australia Working mathematically

WM3.4, WM4.4, WM5.4

Number

N6a.4, N6b.4, N7.4, N8.4

Measurement

M9a.4, M9b.4, M10a.4, M10b.4, M11.4

Chance and data

C&D12.4, C&D13a.4, C&D13b.4, C&D14.4

Space

S15a.4, S15b.4, S15c.4, S16.4

Algebra

PA17a.4, PA19.4

New South Wales

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Working mathematically

WMS3.1, WMS3.2, WMS3.4, WM3.5

Number

NS3.1, NS3.2, NS3.3, NS3.4

Measurement Chance and data Space

Algebra

DS3.1

SGS3.1, SGS3.2a, SGS3.2b, SGS3.3 PAS3.1a, PAS3.1b

Victoria

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MS3.1, MS3.2, MS3.3, MS3.4, MS3.5

Working mathematically

MARSR401, MARSS401, MARSS402, MARSS403

Number

MANUN401, MANUN402, MANUN403, MANUM401, MANUM402, MANUC402, MANUC404, MANUP401, MANUP402, MANUP403

Measurement

MAMEM401, MAMEM403, MAMEU401, MAMEU403

Chance and data

MACDC401, MACDP402, MACDS401, MACDS402, MACDS403, MACDI401, MACDI402,

Space

MASPS401, MASPS402, MASPS403, MASPS404, MASPS405, MASPS406, MASPS407,MASPL401, MASPL402, MASPL404, MASPL405

Algebra

MACDP402, MACDS401, MACDS402, MACDS403

3.1, 3.2

Number

3.6, 3.7, 3.8

Measurement

3,4, 3.5, 3.9

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Working mathematically

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Chance and data

3.1, 3.2, 3.3

Space

3.9, 3.12, 3.13, 3.14

Algebra

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3.10

Queensland Working mathematically

—

Number

N 4.1, N 4.2, N 4.3

Measurement

M 4.1, M 4.2

Chance and data

CD 4.2

Space

S 4.1, S 4.2

Algebra

PA 4.1, PA 4.2

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Primary mathematics: Back to basics

WRITING NUMBERS NUMBER

TEACHER INFORMATION Indicator Reads and writes whole numbers to six digits.

Concepts required

r o e t s Bo r e p ok u S Knowledge of numbers to six digits Ordering numbers Understanding of terms:

Answers

1. (a) 2435 (d) 600 011

(b) 14 874 (e) 502 502

2. (a) 3848, 3850 (c) 49 098, 49 100 (e) 106 000, 106 002

(b) 21 049, 21 051 (d) 69 999, 70 001 (f) 249 999, 250 001

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before, after, less than, more than.

(b) 98 432 (d) 984 210 (f) 886 644

4. (a) 1235 (d) 99 000

(b) 10 020 (e) 121 499

5. (a) 2740 (d) 52 006

(b) 5050 (e) 172 898

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6. Teacher check – answers depend on current date.

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WRITING NUMBERS NUMBER

1. Write each amount as a numeral. (a) two thousand, four hundred and thirty-five (b) fourteen thousand, eight hundred and seventy-four (c) three hundred and twenty-five thousand, two hundred and fifty

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(d) six hundred thousand and eleven

(e) five hundred and two thousand, five hundred and two

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2. Write the number that comes before and after each amount.

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(a)

3849

(b)

21 050

(c)

49 099

(d)

70 000

(e)

106 001

(f)

250 000

3. With each set of numbers, rearrange them to write the largest possible number. C (b) . 2,3,8,4,9 (c) 5,4,8,3,6,1 © R. I . Publ i cat i o ns (d) 2,0,9,4,1,8 (e) 8,4,6,9,7,9 (f) 4,6,4,6,8,8 •f orr evi e w pur poses onl y• (a) 4,9,2,7,6

4. Write the number that is 10 more than the written amount. (a) 1225

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(d) 98 990

(b) 10 010

(e) 121 489

(f) 500 000

5. Write the number that is 100 less than the written amount.

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(a) 2840

(d) 52 106

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(f) half a million

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(e) 172 998

(f) 500 000

6. Write down today’s date using six numerals; e.g. 19 01 09 (19 January 2009). (a)

(b) Write the number as an amount.

and after.

(e) Make the smallest possible number from the numerals. (f) Make the largest possible number from the numerals. R.I.C. Publications®

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Primary mathematics: Back to basics

PLACE VALUE NUMBER

TEACHER INFORMATION Indicators Recognises and demonstrates place value. Identifies and represents different forms of the same number.

r o e t s Bo r e p ok u S Place value to hundred thousands Expanded notation Ordering numbers Representing numbers as an addition sum

Materials needed Calculator

Answers

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Concepts required

tens thousands ones ten thousands thousands hundred thousands hundreds ten thousands

(a) (c) (e) (f)

400, 3 (b) 6000, 20, 8 5454 (d) 10 000, 2000, 20, 1 100 000, 20 000, 200, 50, 7 300 000, 70 000, 5000, 900, 40, 6

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(a) (b) (c) (d) (e) (f) (g) (h)

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(a) (c) (e) (g)

40 400 4000 40 000

6 x 10 7 x 1000 4 x 1 2 x 10 000 9 x 1000 3 x 100 000 0 x 100 5 x 10 000

(b) (d) (f) (h)

4 400 000 40 000 400

60 7000 4 20 000 9000 300 000 0 50 000

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4. (a) Teacher check setting out (b) Teacher check setting out (c) 2 6 5 4 7, 6 6 5 3 1 3

Primary mathematics: Back to basics

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PLACE VALUE NUMBER

1. Complete the table. Number

8461

(b)

7025

(c)

4114

(d)

24 500

(e)

169 869

(f)

382 406

(g)

250 000

(h)

555 555

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(a)

Expanded form

Meaning

hundreds

3 x 100

300

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2. Write the missing numbers. (a) 2403 = 2000 + (c)

= 5000 + 400 + 50 + 4

(b) 6928 = (d) 12 121 =

+ 900 + +

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+ 100 +

(e) 125 257 =

3. Write the value of the four (4) in these numbers. (a) 241

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(e) 4560

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(b) 314

(f) 41 231

(g) 541 000

(d) 421 112

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2387

Place value

(h) 123 456

4. Set out each set of numbers as an addition sum. Use a calculator to find each total.

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(a) 92 + 2941 + 108 + 6 + 23 400 (b) 42 307 + 59 + 1050 + 497 + 621 400

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Primary mathematics: Back to basics

ROUNDING NUMBER

TEACHER INFORMATION Indicators Demonstrates rounding whole numbers to the nearest 10, 100, 1000. Demonstrates rounding to the nearest whole number.

r o e t s Bo r e p ok u S Demonstrates rounding to one decimal place.

(a) (d) (g) (j)

Numbers ending in 5, 50, 500 are rounded up. Estimations are approximate answers.

Answers 50 50 320 8110

(b) 40 (e) 70 (h) 1450

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Concepts required

(a) (d) (g) (j)

200 1400 6600 10 100

3. (a) 1000 (d) 6000 (g) 46 000

(b) 6000 (e) 10 000 (h) 215 000

(a) (d) (g) (j)

3 23 121 556

(b) 9 (e) 40 (h) 421

(a) (d) (g) (j)

2.4 8.0 10.7 25.6

(b) 9.6 (e) 3.8 (h) 15.6

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(b) 300 (e) 2100 (h) 5500

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6. (a) 100 + 200 = 300 (c) 200 + 800 = 1000

(b) 200 + 200 = 400 (d) 1400 + 2500 = 3900

7. (a) 12 + 8 = 20 (c) 100 + 10 = 110

(b) 20 + 25 = 45 (d) 150 + 151 = 301

Primary mathematics: Back to basics

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ROUNDING NUMBER

1. Round these numbers to the nearest 10. (a) 51

(b) 39

(d) 54

(e) 65

(f) 208

(g) 317

(h) 1451

(i) 2075

(j) 8105

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2. Round these numbers to the nearest 100. (a) 184

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(d) 1401

(f) 7850

(g) 6555

(h) 5490

(j) 10 050

3. Round these numbers to the nearest 1000.

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(a) 1203

(b) 6050

(d) 5550

(e) 9909

(f) 10 001

(g) 45 500

(h) 215 005

4. Round these numbers to the nearest whole number.

(b) 8.9 (c) 7.5 (d) 22.9 © R . I . C.Pub l i cat i ons (e) 39.5 (f) 90.9 (g) 121.2 (h) 420.9 •f orr e vi ew pu r poseson l y• (a) 3.1

(i) 405.5

(j) 555.5

5. Round these numbers to one decimal place.

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(a) 2.41

(b) 9.58

(e) 3.75

(f) 10.07

(g) 10.71

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(i) 20.09

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(e) 2050

(b) 341

(d) 8.01

(h) 15.55

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6. Round each number to the nearest 100 to find the approximate answer; for example

141 + 172,

(a) 129 + 168,

100 + 200 =

300

(b) 191 + 198,

(d) 1404 + 2505,

= =

7. Round each number to the nearest whole number to find the approximate answer. (a) 12.1 + 7.9,

(b) 19.5 + 24.8,

(d) 150.2 + 150.7,

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= = Primary mathematics: Back to basics

ADDITION NUMBER

TEACHER INFORMATION Indicators Understands the role of place value when adding numbers. Calculates addition problems with numbers up to five digits.

r o e t s Bo r e p ok u S Concepts required

Answers

1. (a) 73 (d) 73

(b) 93 (e) 93

2. (a) 568 (d) 906

(b) 520 (e) 900

3. (a) 663 (d) 906

(b) 725 (e) 863

4. (a) 3803 (d) 10 211

(b) 4521 (e) 16 017

5. (a) 690 (d) 1497

(b) 715 (e) 1149

6. (a) 3386 (d) 64 620

(b) 6774 (e) 71 969

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Place value Trading Problem solving

(b) 677 + 189 866

(d) 4599 + 3421 8020

(e) 15 42 + 35 92

(f) 408 212 + 165 785

(g) 3602 1111 + 2406 7119

(h) 5999 1060 + 2051 9110

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7. (a) 646 + 247 893

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ADDITION NUMBER

1. (a)

39 (b) + 34

2. (a)

6. (a)

476 (c) + 249

799 (d) + 168

508 (e) + 398

3064 (c) + 1457

4234 (d) + 2878

465 + 398

5699 (e) + 4512

8048 + 7969

404 (b) 162 + 124

295 (c) 205 + 215

628 (d) 155 + 175

599 (e) 499 + 399

684 209 + 256

1206 (b) 1044 + 1136

2158 (c) 2258 + 2358

2409 (d) 3078 + 4980

30 450 (e) 21 271 + 12 899

31 045 12 125 + 28 799

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608 + 292

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2408 (b) + 1395

517 (e) + 389

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4. (a)

56 + 37

426 (d) + 347

384 (b) + 279

49 (e) + 24

205 (c) + 315

3. (a)

33 (d) + 28

321 (b) + 247

5. (a)

68 (c) + 25

7. Find the missing numbers to complete each sum.

(a)

2 8

(e)

4 9

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(b)

(f)

4 +

5 9

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(c)

(g)

(d)

(h)

9 4

1 +

Primary mathematics: Back to basics

ADDITION PROBLEMS NUMBER

TEACHER INFORMATION Indicators Calculates and solves addition word problems. Uses place value knowledge to solve addition problems.

r o e t s Bo r e p ok u S Concepts required

Materials needed Calculator

Answers

1. Teacher check correct setting (a) 544 (b) 1731

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Place value Trading Problem solving

4. 615 tickets

5. 1348 books 6. 4542 students

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7. 7593 votes 8. 15 343 people 9. 64 609 people

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10. (a)10 453

(b) 6135

11. (a) Teacher check word problem 249 + 251 + 205 = 705 (b) Teacher check word problem 2095 + 8099 = 10 194

Primary mathematics: Back to basics

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ADDITION PROBLEMS NUMBER

1. Correctly set out the following numbers before adding. (b) 299, 308, 76, 1040, 8

(c)

912, 88, 1000, 265, 2401

r o e t s Bo r e p ok u S 3. Mitchell travelled 348 km one day and 459 km the next. How far did he travel?

4. A movie screened three times on Tuesday with ticket sales of 242, 154 and 219. How many tickets were sold?

5. A bookshop sold 385 books in May, 465 in June and 498 in July. How many books were sold altogether?

6. A total of 3457 students attend one high school and 1085 attend another. How many students are there altogether?

7. In a phone poll, 4685 voted ‘Yes’ and 2908 voted ‘No’. How many votes were registered?

8. There was an attendance of 8058 at a football match on Saturday and 7285 on Sunday. What was the total?

9. A total of 26 510 people attended a semifinal match and 38 099 attended the grand final. What was the total?

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2. Australia scored 325 runs and India scored 244. How many runs were scored altogether?

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10. Use a calculator to complete the addition problems.

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(a) 20, 107, 9, 360, 48

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(a) 43 + 546 + 409 + 6821 + 2634 =

(b) 1688 + 3689 + 499 + 233 + 26 =

11. Write your own word problems using the numbers given. Set out and solve each problem. (a) 249 + 251 + 205

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(b) 2095 + 8099

Primary mathematics: Back to basics

MENTAL ADDITION NUMBER

TEACHER INFORMATION Indicator Shows proficiency with mental addition facts.

Concept required

r o e t s Bo r e p ok u S Mentally adding one and two digits.

Answers

(a)

100

18 21 24 25 26 28

101

17 20 23 24 25 27

14 17 20 21 22 24

13 16 19 20 21 23

16 19 22 23 24 26 15 18 21 22 23 25

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(b)

120

83 89 90 93 95 99

102

73 79 80 83 85 89

100

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140

100

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Primary mathematics: Back to basics

63 69 70 73 75 79 53 59 60 63 65 69

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16 65 14 48 © R . I . C . P ubl i cat i ons 13 30 50 28 32 103 109 110 113 115 119 18 51 20 94 24 •f o rr ev i ew pu93r p e105 s109onl y• 99 o 100s 103 16 23 90 0 70

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MENTAL ADDITION NUMBER

10 + 10 =

15 + 15 =

4 + 12 =

3 + 18 =

90 + 10 =

5+6=

8+6=

11 + 20 =

100 + 1 =

8+9=

71 + 4 =

70 + 10 =

12 + 13 =

10 + 30 =

32 + 8 =

13 + 7 =

22 + 4 =

30 + 30 =

2 + 51 =

15 + 10 =

9+9=

r o e t s Bo r e p ok u S 5+8=

19 + 6 =

13 + 7 =

11 + 10 =

41 + 9 =

32 + 7 =

61 + 16 =

3 + 15 =

17 + 10 =

20 + 9 =

3 + 47 =

15 + 1 =

55 + 10 =

7+7=

41 + 7 =

10 + 20 =

4 + 46 =

14 + 14 =

12 + 20 =

6 + 12 =

50 + 1 =

15 + 5 =

93 + 1 =

15 + 1 =

19 + 4 =

80 + 10 =

0+0=

4+6=

41 + 4 =

2 + 23 =

60 + 60 =

11 + 11 =

5+7=

40 + 1 =

27 + 4 =

40 + 40 =

14 + 6 =

3 + 37 =

4 + 16 =

7 + 11 =

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20 + 4 = 13 + 0 =

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6+6=

12 + 12 =

16 + 8 =

4 + 66 =

55 + 15 =

1 + 101 =

19 + 7 =

20 + 80 =

31 + 32 =

2 + 17 =

32 + 6 =

13 + 6 =

16 + 6 =

17 + 13 =

8+4=

70 + 70 =

19 + 5 =

41 + 8 =

10 + 50 =

60 + 10 =

4 + 36 =

14 + 7 =

15 + 55 =

1+4=

23 + 6 =

50 + 9 =

99 + 1 =

11 + 40 =

93 + 7 =

3 + 12 =

17 + 3 =

8+7=

5+9=

32 + 4 =

90 + 1 =

41 + 21 =

23 + 5 =

3 + 57 =

7 + 14 =

20 + 6 =

17 + 20 =

17 + 2 =

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55 + 5 =

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32 + 5 = 99 + 1 = 15 + 20 =

o c . che e r o t r s super 41 + 6 =

11 + 30 =

72 + 0 =

19 + 8 =

99 + 0 =

2 + 88 =

10 + 40 =

80 + 1 =

15 + 25 =

(b)

50 5

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4 + 20 =

100 90

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16 + 14 =

15 + 12 =

2 + 49 =

7 + 23 =

Complete the addition tables. (a) 16

3 + 21 =

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Primary mathematics: Back to basics

SUBTRACTION NUMBER

TEACHER INFORMATION Indicators Understands the role of place value when subtracting numbers. Calculates subtraction problems with numbers up to five digits.

r o e t s Bo r e p ok u S Concepts required

Answers

1. (a) 32 (d) 301

(b) 33 (e) 2122

2. (a) 47 (d) 47

(b) 26 (e) 44

3. (a) 124 (d) 504

(b) 323 (e) 368

4. (a) 368 (d) 267

(b) 256 (e) 253

5. (a) 2027 (d) 4341

(b) 2252 (e) 3189

6. (a) 118 (d) 1264

(b) 635 (e) 1424

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Place value Trading Problem solving

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7. (a)

65 (b) 78 (c) 81 – 23 – 49 – 35 42 29 46

(d) 740 (e) 535 (f) 4284 – 336 – 145 – 1162 404 390 3122

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(g) 5240 (h) 8000 –2039 – 2999 3201 5001

Primary mathematics: Back to basics

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SUBTRACTION NUMBER

1. (a)

78 (b) – 46

2. (a)

72 (b) – 25

95 (e) – 48

80 (f) – 36

732 (c) – 409

542 (d) – 228

534 (c) – 278

861 (d) – 598

3156 (b) – 1129

4841 (c) – 2589

840 (e) – 336

5703 (d) – 2485

777 (f) – 409

744 (e) – 477

953 – 207

631 (f) – 378

704 – 499

7430 (e) – 3089

70 – 47

6041 – 2852

7. Find the missing numbers to complete each problem. (a)

w ww

–

. te 2

–

(g)

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8 –

(d)

–

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–

2 –

(c)

8 –

2 4

(e)

(b)

m . u

STUDENT NAME

Teac he r 6. (a)

5. (a)

86 (d) – 28

4685 – 2563

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624 (b) – 256

63 (c) – 37

4. (a)

509 (e) – 208

r o e t s Bo r e p ok u S

251 (b) – 127

425 (d) – 214

3. (a)

69 (c) – 36

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(h)

8 –

0 9 0

9 0

Primary mathematics: Back to basics

SUBTRACTION PROBLEMS NUMBER

TEACHER INFORMATION Indicators Calculates and solves subtraction problems. Uses place value knowledge to solve subtraction problems.

r o e t s Bo r e p ok u S Concepts required

Materials needed Calculator

Answers

1. (a) 508 (b) – 192 316

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Place value Trading Problem solving

5. 322 words 6. 2217 adults

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m . u

7. 376 votes 8. 756 people 9. 28 418 tickets

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10. (a) 76 049

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(b) 1 102 538

11. (a) Teacher check word problem 352 – 178 = 174 (b) Teacher check word problem 9000 – 2463 = 6537

Primary mathematics: Back to basics

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SUBTRACTION PROBLEMS NUMBER

1. Correctly set out the following numbers before subtracting. (b) 893, 87

(d) 8239, 6041

r o e t s Bo r e p ok u S

3. There are 815 DVD covers on the shelf. Of them, 279 have already been rented. How many are still available?

4. From a total of 601 students, 364 are girls. How many boys attend the school?

5. Jake has written 678 words of a 1000 word essay. How many words does he still have to write?

6. A total of 3286 people registered for a fun run. If 1069 were children, how many were adults?

7. One reality show contestant received 4001 votes and a second received 3625. What was the difference?

8. There was an attendance of 3947 people at one match and 4703 at another. What was the difference?

9. There are 98 000 tickets available for the Grand Final. How many are left if 69 582 have already been sold?

Teac he r

2. A total of 352 people went to a family fun day. If there were 108 adults, how many children attended?

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m . u

STUDENT NAME

(a) 508, 192

10. Use a calculator to complete each problem.

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(a) 500 000 – 423 951 =

(b) Subtract 897 462 from 2 million =

11. Write your own word problems using the numbers given. Set out and solve each problem. (a) 352 – 178

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(b) 9000 – 2463

Primary mathematics: Back to basics

MENTAL SUBTRACTION NUMBER

TEACHER INFORMATION Indicator Shows proficiency with mental subtraction facts.

Concept required

r o e t s Bo r e p ok u S Mentally subtracting one and two digits with answers less than 100.

(a)

17 13 11 10

16 12 10

15 11

14 10

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Teac he r

Answers

©5 R40. I . C P bl i cat i ons 1. 11 u 17 40 12 20 14 85 o 79s 75 70 65 •f o r r e v i e w pu88r p es onl y• 0 8 30 52 90 90

(b)

78 75 69 65 60 55

68 65 59 55 50 45

58 55 49 45 40 35

. te

w ww

Primary mathematics: Back to basics

48 45 39 35 30 25 38 35 29 25 20 15

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o c . che e r o t r s super

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R.I.C. Publications®

MENTAL SUBTRACTION NUMBER

10 – 1 =

77 – 7 =

20 – 10 =

44 – 4 =

10 – 10 =

55 – 5 =

8–4=

13 – 7 =

100 – 60 =

22 – 2 =

13 – 9 =

50 – 10 =

66 – 33 =

12 – 10 =

48 – 24 =

20 – 20 =

19 – 3 =

100 – 20 =

35 – 5 =

100 – 2 =

33 – 23 =

r o e t s Bo r e p ok u S 10 – 3 =

19 – 5 =

21 – 8 =

14 – 7 =

90 – 9 =

53 – 23 =

85 – 5 =

100 – 5 =

7–7=

41 – 0 =

97 – 2 =

13 – 8 =

45 – 5 =

10 – 9 =

20 – 9 =

55 – 15 =

21 – 9 =

35 – 15 =

28 – 14 =

12 – 12 =

10 – 2 =

50 – 20 =

56 – 4 =

30 – 15 =

22 – 11 =

36 – 0 =

13 – 6 =

81 – 2 =

73 – 2 =

12 – 6 =

44 – 22 =

50 – 25 =

50 – 1 =

20 – 15 =

21 – 20 =

6–6=

43 – 23 =

100 – 70 =

75 – 15 =

24 – 12 =

Teac he r

100 – 10 = 17 – 0 =

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95 – 5 =

19 – 2 =

99 – 9 = 20 – 1 =

65 – 15 =

100 – 1 =

66 – 6 =

12 – 11 =

85 – 2 =

19 – 10 =

20 – 5 =

80 – 9 =

77 – 0 =

75 – 5 =

50 – 30 =

57 – 4 =

55 – 5 =

19 – 4 =

26 – 13 =

19 – 6 =

71 – 11 =

24 – 0 =

10 – 7 =

30 – 9 =

12 – 8 =

21 – 3 =

16 – 8 =

85 – 15 =

25 – 19 =

58 – 0 =

65 – 5 =

27 – 2 =

19 – 9 =

50 – 49 =

13 – 4 =

w ww

33 – 3 =

12 – 7 =

13 – 3 =

88 – 8 =

100 – 40 =

100 – 80 =

100 – 30 =

25 – 5 =

62 – 0 =

19 – 8 =

50 – 40 = 70 – 9 =

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60 – 9 =

12 – 9 =

45 – 15 =

24 – 12 =

10 – 4 =

10 – 6 =

100 – 90 =

19 – 7 =

Complete the subtraction tables. (a)

(b)

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40 – 9 =

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–

63 – 2 =

100 – 50 = 15 – 5 =

–

20 – 19 =

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20 – 3 =

10 – 5 =

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STUDENT NAME

Primary mathematics: Back to basics

MULTIPLICATION NUMBER

TEACHER INFORMATION Indicators Understands the role of place value when multiplying numbers. Calculates multiplication problems with one and two digits.

r o e t s Bo r e p ok u S Concepts required

Answers

1. (a) 84 (d) 153

(b) 66 (e) 164

2. (a) 78 (d) 116

(b) 85 (e) 74

3. (a) 105 (d) 380

(b) 230 (e) 414

4. (a) 484 (d) 729

(b) 969 (e) 700

5. (a) 264 (d) 442

(b) 726 (e) 520

6. (a) 1484 (d) 1464

(b) 2511 (e) 5082

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Place value Trading Problem solving

125 (c) x 3 375

38 x4 152

(d) 45 (e) 246 (f) x 3 x 4 135 984

62 x 14 248 620 868

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7. (a)

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206 (b) x 4 824

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MULTIPLICATION NUMBER

1. (a)

42 (b) x 2

26 (b) x 3

17 (c) x 5

28 (d) x 3

46 (c) x 5

58 (d) x 4

323 (c) x 3

135 (d) x 2

33 (c) x 22

42 (d) x 21

3. (a)

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242 (b) x 2

41 (f) x 4

29 (e) x 4

37 (f) x 2

76 (e) x 5

69 (f) x 6

22 (b) x 12

243 (e) x 3

350 (f) x 2

34 (e) x 13

w ww

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7. Find the missing numbers to complete each sum. (a)

x 8 (d)

52 (f) x 10

4 2

(e)

4 x

x 8

(c)

262 x4

63 x 14

334 x 23

o c . che e r o t r s super (b)

48 x9

m . u

45 x2

62 x4

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4. (a)

51 (e) x 3

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35 (b) x 3

STUDENT NAME

42 (d) x 3

2. (a)

5. (a)

33 (c) x 2

x 1

(f)

0 6

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Primary mathematics: Back to basics

MULTIPLICATION PROBLEMS NUMBER

TEACHER INFORMATION Indicators Calculates and solves multiplication word problems. Uses place value knowledge to solve multiplication problems.

r o e t s Bo r e p ok u S Concepts required

Answers

1. 66 books 2. 252 oranges 3. 64 cm 4. 378 days 5. 200 hours 6. 1062 people

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Place value Trading Problem solving

9. 780 weeks

10. 192 members 11. 1200 pies

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13. (a) Teacher check word problem 150 x 8 = 1200 (b) Teacher check word problem 44 x 14 = 616

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12. 1584 pages

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MULTIPLICATION PROBLEMS 2. Four crates each held 63 oranges. How many oranges were there altogether?

3. Each side of a square measures 16 cm. What is the perimeter?

4. How many days are there in 54 weeks?

5. If Lucy works eight hours each day, how many hours would she work in 25 days?

6. If one row seats 118 people, how many people are there in nine rows?

7. Exactly 428 newspapers were sold on each of five days. How many were sold altogether?

8. If there are 365 days in one year, how many days are there in five years?

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1. Thirty-three students each have two books. How many books are there altogether?

r o e t s Bo r e p ok u S

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10. Twelve soccer © R. I . C.Pub l i ca t i o n16s teams each have members. How many members are there •f orr evi ew pur p o s e s onl y• altogether?

9. How many weeks are there in fifteen years?

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11. Twenty-five stores each ordered 48 pies. How many pies were ordered in total?

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m . u

STUDENT NAME

NUMBER

12. Twelve books each had 132 pages. How many pages were there altogether?

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13. Write your own word problems using the numbers given. Set out and solve each problem. (a) 150 x 8

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(b) 44 x 14

Primary mathematics: Back to basics

MENTAL MULTIPLICATION NUMBER

TEACHER INFORMATION Indicator Shows proficiency with mental multiplication facts.

Concept required

r o e t s Bo r e p ok u S Mentally multiplying up to and including 11 x table

Answers

(a)

18 36 54 72 90

14 28 42 56 70

10 20 30 40 50 6

12 18 24 30

ew i ev Pr

Teac he r

4 36 8 36 © R . I . C . P ubl c t i o144ns 24i 60a 120 132 20 81 80 48 60 22 55 110 121 132 12 72 21 20 99 •f o r r e v i e w p u r p osesonl y• 20 48 33 40 50 20 50 100 110 120 18

(b)

121

110

100

w ww

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18 45 90 99 108 16 40 80 88 96

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R.I.C. Publications®

MENTAL MULTIPLICATION NUMBER

11 x 1 =

6x3=

9 x 10 =

7x1=

9x1=

8x4=

9x4=

3x2=

9x0=

11 x 8 =

5 x 11 =

12 x 2 =

5x9=

8x5=

3x7=

7x9=

5x3=

11 x 3 =

10 x 3 =

7 x 10 =

6x4=

6x8=

4x6=

8 x 11 =

2x5=

2x9=

7x7=

5x2=

10 x 9 =

10 x 6 =

3x8=

11 x 6 =

2 x 11 =

2x2=

3 x 12 =

8x1=

4x9=

9x9=

10 x 8 =

12 x 4 =

5 x 12 =

12 x 1 =

6 x 12 =

7x3=

2 x 10 =

4x5=

8x6=

3 x 11 =

5x8=

6 x 11 =

11 x 2 =

6x2=

9x3=

7x2=

12 x 0 =

5x5=

3x5=

8 x 10 =

8x2=

2x6=

11 x 11 =

8x7= 9x2= 3x6=

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10 x 2 =

r o e t s Bo r e p ok u S

ew i ev Pr 9 x 11 =

5 x 10 = 7x6=

8x9=

10 x 0 =

10 x 5 =

4x8=

2x7=

10 x 11 =

12 x 3 =

8x0=

5x4=

6x1=

2x4=

9x7=

11 x 5 =

11 x 7 =

6x5=

8x8=

4 x 11 =

12 x 5 =

4 x 12 =

7x8=

11 x 10 =

7x5=

4x4=

5x1=

3x9=

6x9=

10 x 10 =

8x3=

4x7=

10 x 1 =

4 x 10 =

4x1=

6x6=

3x4=

5x7=

7 x 12 =

4x2=

9x8=

4x3=

11 x 9 =

8 x 12 =

7 x 11 =

7x4=

6 x 10 =

11 x 4 =

w ww

11 x 0 =

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9x5=

2x3=

10 x 7 =

(b)

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5x6=

10 x 4 =

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2x8=

9x6=

3x3=

6x7=

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Complete the multiplication tables. (a) 9

3 x 10 =

m . u

STUDENT NAME

Primary mathematics: Back to basics

DIVISION NUMBER

TEACHER INFORMATION Indicators Calculates division problems of up to three numbers with one divisor. Calculates division problems with remainders. Uses place value knowledge to solve division problems.

r o e t s Bo r e p ok u S Place value Trading Remainders Problem solving

Answers

1. (a) 6 (d) 8

(b) 9

2. (a) 24 (d) 302

(b) 32 (e) 32

3. (a) 23 (d) 261

(b) 17 (e) 130

4. (a) 29 r1 (d) 195 r2

(b) 24 r1 (e) 468 r1

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Teac he r

Concepts required

m . u

6. 122 plums

w ww

7. 42 cm 8. 48 books

. te

9. 226 cartons 10. 155 cm 11. $47

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12. 275 L and 2 L remaining

13. (a) Teacher check word problem 564 ÷ 4 = 141 (b) Teacher check word problem 969 ÷ 8 = 121 r1

Primary mathematics: Back to basics

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R.I.C. Publications®

DIVISION NUMBER

1. (a) 54 ÷ 9 =

(d) 56 ÷ 7 =

2. (a) 2 4 8

(b) 3 9 6

(d) 3 9 0 6

(e) 4 1 2 8

3. (a) 4 9 2

(b) 5 8 5

(d) 3 7 8 3

(e) 5 6 5 0

4. (a) 3 8 8

r o e t s Bo r e p ok u S (b) 4 9 7

(d) 3 5 8 7

6. A total of 488 plums needed to be equally packed into four crates. How many were in each crate?

7. The perimeter of a square is 168 cm. How long is each side?

8. There are 240 books equally arranged on five shelves. How many books are on each shelf?

Teac he r

5. Ninety-six players were divided into three groups. How many were in each group?

(e) 2 9 3 7

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were delivered to four stores. How many cartons went to each store?

11. Six people equally shared a restaurant bill that totalled $282. How much did they each pay?

. te

930 cm. What was their average height?

m . u

STUDENT NAME

(b) 72 ÷ 8 =

12. Three trucks equally shared 827 litres of fuel. How many litres did each truck receive?

o c . che e r o t r s super

13. Write your own word problems using the numbers given. Set out and solve each problem.

(a) 564 ÷ 4

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(b) 969 ÷ 8

Primary mathematics: Back to basics

MENTAL DIVISION NUMBER

TEACHER INFORMATION Indicator Shows proficiency with mental division facts.

Concepts required

r o e t s Bo r e p ok u S Mentally dividing up to and including by 12 Division wheels

(a)

6 1

6 12

36 ÷

9 4

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Teac he r

Answers

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w ww

Primary mathematics: Back to basics

(b)

1 10

2 8

40 ÷

5 8

m . u

o c . che e r o t r s super

(c)

54 ÷

3 18

1 54

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R.I.C. Publications®

MENTAL DIVISION NUMBER

24 ÷ 2 =

20 ÷ 4 =

72 ÷ 6 =

30 ÷ 3 =

15 ÷ 5 =

60 ÷ 6 =

96 ÷ 8 =

12 ÷ 2 =

7÷7=

9÷3=

48 ÷ 4 =

21 ÷ 7 =

120 ÷ 10 =

32 ÷ 8 =

18 ÷ 6 =

16 ÷ 8 =

12 ÷ 3 =

99 ÷ 9 =

16 ÷ 4 =

49 ÷ 7 =

6÷6= 33 ÷ 3 = 56 ÷ 8 =

r o e t s Bo r e p ok u S 72 ÷ 9 =

40 ÷ 4 =

80 ÷ 10 =

10 ÷ 2 =

66 ÷ 11 =

36 ÷ 3 =

54 ÷ 6 =

54 ÷ 9 =

84 ÷ 7 =

132 ÷ 11 =

30 ÷ 10 =

60 ÷ 5 =

9÷9=

10 ÷ 5 =

44 ÷ 11 =

45 ÷ 5 =

55 ÷ 5 =

36 ÷ 4 =

64 ÷ 8 =

12 ÷ 4 =

70 ÷ 10 =

14 ÷ 7 =

48 ÷ 12 =

2÷2=

40 ÷ 8 =

6÷2=

12 ÷ 6 =

45 ÷ 9 =

66 ÷ 6 =

55 ÷ 11 =

18 ÷ 2 =

88 ÷ 8 =

3÷3=

72 ÷ 8 =

56 ÷ 7 =

44 ÷ 4 =

33 ÷ 11 =

40 ÷ 5 =

28 ÷ 7 =

110 ÷ 11 =

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22 ÷ 2 =

Teac he r

77 ÷ 7 =

24 ÷ 3 =

121 ÷ 11 = 108 ÷ 9 =

42 ÷ 6 = 5÷5=

18 ÷ 9 =

12 ÷ 12 =

20 ÷ 10 =

90 ÷ 9 =

48 ÷ 6 =

24 ÷ 6 =

24 ÷ 4 =

4÷2=

50 ÷ 5 =

8÷2=

60 ÷ 12 =

6÷3=

32 ÷ 4 =

110 ÷ 10 =

50 ÷ 10 =

27 ÷ 3 =

63 ÷ 9 =

60 ÷ 10 =

11 ÷ 11 =

70 ÷ 7 =

48 ÷ 8 =

88 ÷ 11 =

24 ÷ 12 =

14 ÷ 2 =

25 ÷ 5 =

63 ÷ 7 =

30 ÷ 5 =

27 ÷ 9 =

w ww

15 ÷ 3 =

99 ÷ 11 =

81 ÷ 9 =

100 ÷ 10 =

18 ÷ 3 =

30 ÷ 6 =

28 ÷ 4 =

36 ÷ 9 =

22 ÷ 11 =

40 ÷ 10 = 8÷8=

20 ÷ 5 =

. te

R.I.C. Publications®

35 ÷ 5 =

o c . che e r o t r s super 20 ÷ 2 =

90 ÷ 10 =

35 ÷ 7 =

10 ÷ 10 =

42 ÷ 7 =

24 ÷ 8 =

21 ÷ 3 =

8÷4=

36 ÷ 6 =

16 ÷ 2 =

(b)

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4÷4=

(c)

6 36 ÷ 12

77 ÷ 11 =

80 ÷ 8 =

Complete the division wheels. (a) 1

36 ÷ 12 =

m . u

STUDENT NAME

1 4

40 ÷ 5

18 8

54 ÷ 3

Primary mathematics: Back to basics

FRACTIONS NUMBER

TEACHER INFORMATION Indicators Identifies and shows knowledge of simple fractions. Writes equivalent fractions. Compares and orders fractions. Adds and subtracts fractions with common denominators.

r o e t s Bo r e p ok u S Fractional parts Equivalent fractions Common denominators Ordering Rounding to the nearest whole number

Answers

1. (a) 5/12 (d) 1/4

(b) 3/8 (e) 3/6, 1/2

2. Answers may vary. (a) 1/2 (d) 8/10

(b) 1/3 (e) 6/8

3. (a) 1/6, 2/6, 3/6, 5/6, 6/6 (c) 1/5, 3/5, 4/5, 1, 22/5

(b) 2/9, 3/9, 5/9, 6/9, 8/9 (d) 1/4, 4/12, 3/6, 6/8, 1

4. (a) 2 (d) 9 (g) 3

(b) 3 (e) 4 (h) 6

5. (a) 4/8 = 1/2 (d) 5/10 = 1/2

(b) 2/4 =1/2 (e) 6/6 = 1

6. (a) 2/4 = 1/2 (d) 5/10 = 1/2

(b) 4/6 = 2/3 (e) 4/8 = 1/2

7. (a) 2 (d) 4

(b) 4 (e) 7

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Concepts required

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Primary mathematics: Back to basics

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FRACTIONS NUMBER

1. What fraction of each shape is shaded? (b)

(c)

(d)

r o e t s Bo r e p ok u S

Teac he r

(e)

(f)

2. Write an equivalent fraction for each. (a) 2/4 =

(b)

/6 =

(d) 4/5 =

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3. Order the fractions from smallest to largest.

(e) 3/4 =

(b) 3/9, 8/9, 2/9, 5/9, 6/9

(a) 1/4 of 8 =

(b) 1/2 of 6 = (f) 1/3 of 12 =

w ww

(e) 2/5 of 10 =

(d) 3/4 of 12 =

(g) 1/4 of 12 =

(h) 2/3 of 9 =

m . u

STUDENT NAME

(a)

5. Add each of the following and write the lowest equivalent fraction for each answer.

. te

(a) 3/8 + 1/8 =

(d) 2/10 + 3/10 =

o c . che e r o t r s super =

(b) 1/4 + 1/4 =

(e) 4/6 + 2/6 =

(f) 5/12 + 4/12 =

= =

6. Subtract each of the following and write the lowest equivalent fraction. (a) 3/4 – 1/4 =

(d) 7/10 – 2/10 =

(b) 6/6 – 2/6 =

(e) 7/8 – 3/8 =

(f) 6/8 – 4/8 =

7. Round each amount to the nearest whole number. (a) 21/4 = R.I.C. Publications®

(b) 33/4 =

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(d) 34/5 =

(e) 63/4 = Primary mathematics: Back to basics

DECIMALS NUMBER

TEACHER INFORMATION Indicators Uses correct knowledge of place value to read and write decimal numbers. Compares and orders decimals to one decimal place.

r o e t s Bo r e p ok u S Adds and subtracts decimals to two decimal places.

Place value Whole numbers and parts of whole numbers Ordering Rounding to whole numbers and one decimal place Equivalent decimals and fractions Addition and subtraction, with trading

Answers

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Concepts required

hundreds

tens 8

2 1

0 2

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(a) (b) (c) (d) (e) (f) (g) (h)

2. (a) 4 (d) 8

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3. (a) 2.2 (d) 8.9 4.

(a) (b) (c) (d)

ones 2 0 3 7 0 0 6 3

(b) 4 (e) 12

• • • • • • • • •

tenths 4 8 0 1 4 9 6 9

hundredths 5 1 8 5 9 5 4 9

o c . che e r o t r s super (b) 4.5 (e) 7.0

2.4, 3.7, 4.1, 5.5, 8.1, 8.5, 8.9 7.0, 7.06, 7.1, 7.5, 7.55, 7.6, 7.9 0.08, 0.8, 0.85, 1.08, 1.8, 18.1 12.05, 12.5, 21.0, 21.05, 21.5, 21.95

5. (a) 0.5 (d) 5.4

(b) 0.9 (e) 6.35

6. (a) 16.5 (d) 31.09

(b) 1.5 (e) 779.71

Primary mathematics: Back to basics

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R.I.C. Publications®

DECIMALS NUMBER

1. Write each number on the place value chart. hundreds

ones

•

(a) 82.45

•

(b) 0.81

•

(d) 127.15

tenths

hundredths

r o e t s Bo r e p ok u S • •

(e) 10.49

•

(f) 0.95

Teac he r

(g) 106.64

• •

(h) 23.99

2. Round these decimals to the nearest whole number. (a) 4.2

(e) 11.5

(b) 3.6

(f) 91.09

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(d) 8.02

(e) 6.95

(f) 10.19

4. Order the decimals from smallest to largest.

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m . u

STUDENT NAME

tens

(a) 4.1, 3.7, 8.9, 8.1, 5.5, 2.4, 8.5

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(b) 7.6, 7.06, 7.0, 7.1, 7.5, 7.9, 7.55

o c . che e r o t r s super

(d) 21.5, 12.5, 21.05, 12.05, 21.95, 21.0

5. Write the equivalent decimal for these fractions. (a) 1/2

(b) 9/10

(d) 54/10

(e) 635/100

6. Complete the following equations. (a) 7.9 (b) 8.3 (c) 42.55 (d) 58.07 (e) 129.72 (f) 804.31 + 8.6 – 6.8 + 36.46 – 26.98 + 649.99 – 574.62

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Primary mathematics: Back to basics

PERCENTAGES NUMBER

TEACHER INFORMATION Indicators Represents percentages. Compares, orders and writes percentages relating to decimals and fractions.

r o e t s Bo r e p ok u S Percentage is part of a hundred Equivalent percentages, fractions and decimals Ordering Reading and solving simple problems

Materials needed Coloured pencils

Answers

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Teac he r

Concepts required

(b) 25% = 25/100 = 0.25 (d) 30% = 30/100 = 0.30 (f) 5% = 5/100 = 0.05

3. (a) 100%, 91%, 85%, 70%, 50%, 35%, 20% (b) 100%, 90/100, 75%, 0.50, 40/100, 0.25, 0.10 (c) 100%, 0.45, 44/100, 42%, 40%, 14/100, 4%

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4. 75 5. 55

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6. (a) $20

Primary mathematics: Back to basics

(b) $60

m . u

2. (a) 50% = 50/100 = 0.50 (c) 10% = 10/100 = 0.10 (e) 9% = 9/100 = 0.09

o c . che e r o t r s super

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R.I.C. Publications®

PERCENTAGES NUMBER

1. Use the 100-block squares to represent the following percentages.

Teac he r

r o e t s Bo r e p ok u S

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2. Write the equivalent percentage, fraction and decimal.

©= 0.R. I . C .Pub l i cat i o=n s (b) 25% = 0. 100 100 •f orr evi ew pur posesonl y• 10

(a) 50% =

(c)

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(e)

100

= 0.

(d)

= 0.09

(f) 5% =

= 0.

100

3. Order the amounts from largest to smallest.

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100

= 0.30

m . u

STUDENT NAME

(a) Shade the block 50% green, 25% blue (b) Shade the block 50% blue, 10% yellow, and 25% red. 30% green and 10% red.

o c . che e r o t r s super

(a) 20%, 91%, 85%, 50%, 100%, 35%, 70% (b) 100%, 0.50, 0.25, 40/100, 75%, 90/100, 0.10 (c) 4%, 40%, 0.45, 14/100, 44/100, 100%, 42%

4. Ms Green bought 100 stickers. If she used 25% of them in the first week, how many did she have left? 5. There were 100 cartons of juice. If 20% were mango and 25% were apple, how many were orange? 6. (a) 20% of $100 = R.I.C. Publications®

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(b) 60% of $100 = 35

MONEY NUMBER

TEACHER INFORMATION Indicators Calculates addition and subtraction problems in a monetary context. Chooses appropriate operations to solve problems in a monetary context.

r o e t s Bo r e p ok u S Concepts required

Teac he r

Answers

1. (a) $9.50 (d) $17.55

(b) $4.25

2. (a) $50.50 (d) $87.05

(b) $17.05

3. (a) $408.35 (d) $1723.97

(b) $574.70

4. (a) $321.05 (d) $105.55

(b) $115.95

5. (a) $1185.70

(b) $314.30

6. (a) $76.50

(b) $459.00

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Calculating change from given amounts Addition, subtraction, multiplication and division with trading Place value Problem solving

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7. $85.50

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8. $3177.30

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9. (a) $170.00

Primary mathematics: Back to basics

m . u

(b) $204

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R.I.C. Publications®

MONEY NUMBER

1. Work out the change from $20.00 for each of the amounts spent. (a) $10.50

(b) $15.75

(d) $2.45

2. Work out the change from $100.00 for each of the amounts spent. (b) $82.95

(d) $12.95

r o e t s Bo r e p ok u S

$984.99 + $738.98

4. (a) $425.50 (b) $505.90 (c) $525.50 (d) – $104.45 – $389.95 – $289.99

$1000.50 – $894.95

Teac he r

3. (a) $262.85 (b) 366.45 (c) $408.55 (d) + $145.50 + $208.25 + $295.55

5. (a) The following amounts were raised for a charity: $250, $425.75 and $509.95. What was the total amount?

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(b) If the goal was to raise $1500 for the charity, how much more money was needed?

6. (a) Six children earned money by washing cars. Each child washed nine cars and received $8.50 for each car. How much did each child earn?

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7. An amount of $427.50 was charged to a credit card for five concert tickets. How much was each ticket?

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m . u

STUDENT NAME

(a) $49.50

8. Repayments on a loan were $529.55 per month. How much was paid off after six months?

o c . che e r o t r s super

9. Theme park entry for a day is $42.50 for adults and $25.50 for children.

(a) Find the total for four (b) Find the total for eight (c) Find the grand total for adults. children. the 12 people.

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Primary mathematics: Back to basics

MIXED PROBLEMS NUMBER

TEACHER INFORMATION Indicator Selects and uses the appropriate operation required to solve a word problem.

r o e t s Bo r e p ok u S Concepts required

Teac he r

Answers

1. 296.8 km 2. 65.8 kg

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Addition, subtraction, multiplication and division of whole numbers and decimal numbers Place value Problem solving Averages Percentages Fractions

6. $47.60

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8. 205.3 kg 9. (a) $18 625

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(b) $3725

10. (a) 52.5 metres

(b) $262.50

11. (a) 583.8 cm

(b) 145.95 cm

Primary mathematics: Back to basics

m . u

7. 20 children

o c . che e r o t r s super

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MIXED PROBLEMS 2. Before starting an exercise program, Jasmine weighed 74.2 kg. If she lost 8.4 kg, what was her new weight?

3. Twenty-five litres of fuel were needed to fill a petrol tank. How many more litres are needed if there is already 16.5 L in the tank?

4. Four players recorded batting scores of 87, 209, 158 and 189. What was the combined total?

5. Caitlin donated 15% of the $100 prize she won. How much did she keep?

6. How much would it cost to fill a 40 L tank if petrol was $1.19 a litre?

7. Three-quarters of a group of 80 were adults. How many children were there?

8. Four people recorded the following weights: 52 kg, 48.7 kg, 49.9 kg and 54.7 kg. What was their combined weight?

9. (a) Asha decided to buy a $25 000 car. If she paid a deposit of $6375, how much did she owe?

(b) If she took five years to pay the balance owing, how much did Asha pay each year?

10. (a) One item requires 3.75 m of fabric to make. How much fabric is needed for 14 items?

(b) If the fabric is $5 per metre, what is the total cost?

Teac he r

1. Mark travels 42.4 km daily. How far does he travel in one week?

r o e t s Bo r e p ok u S

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11. (a) Four people recorded the following heights: 150.5 cm, 145 cm, 147.9 cm and 140.4 cm. What was their combined height? R.I.C. Publications®

m . u

STUDENT NAME

NUMBER

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(b) What was the average height of the four people?

Primary mathematics: Back to basics

MIXED MENTAL NUMBER

TEACHER INFORMATION Indicator Shows proficiency with mental addition, subtraction, multiplication and division facts.

r o e t s Bo r e p ok u S

Mentally adding one- and two-digit numbers Mentally subtracting one- and two-digit numbers Mentally multiplying to 12 x Mentally dividing by up to 12 x Magic square format

Answers

100

(a)

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Teac he r

Concepts required

5 13 6 © R. I . C.Publ i c a t i o ns •f orr evi ew pur p6os s nl y• 13e 8 o

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Primary mathematics: Back to basics

(b)

(c)

m . u

o c . che e r o t r s super

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R.I.C. Publications®

MIXED MENTAL NUMBER

35 – 5 =

80 + 10 =

12 – 10 =

7x6=

17 + 10 =

19 + 5 =

4x4=

11 x 8 =

56 – 4 =

12 – 9 =

56 ÷ 8 =

10 + 40 =

30 ÷ 6 =

6x6=

17 + 20 =

5 x 10 =

12 + 13 =

33 ÷ 3 =

100 – 40 = 9x1=

r o e t s Bo r e p ok u S 44 – 22 =

30 – 9 =

90 ÷ 9 =

19 – 5 =

15 + 15 =

3 + 37 =

100 – 2 =

5x1=

110 ÷ 10 =

2x8=

50 – 49 =

3 x 10 =

12 x 5 =

11 + 10 =

10 x 7 =

99 + 1 =

41 + 9 =

19 – 7 =

19 – 10 =

10 x 0 =

6+6=

10 + 20 =

13 + 6 =

44 – 4 =

3x7=

100 – 60 =

9x5=

8÷8=

23 + 5 =

21 – 8 =

60 ÷ 6 =

3x3=

40 ÷ 10 =

12 ÷ 4 =

35 – 15 =

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4 + 12 = 9 x 11 = 16 ÷ 8 =

Teac he r

21 – 20 = 50 ÷ 5 =

2 x 11 = 4x7=

5x6=

5+8=

15 + 1 =

11 + 20 =

85 – 5 =

8+6=

25 – 18=

70 + 10 =

10 x 9 =

10 – 4 =

7 x 10 =

22 + 4 =

5 x 12 =

15 + 12 =

20 ÷ 5 =

41 – 0 =

40 + 1 =

50 + 1 =

99 ÷ 11 =

97 – 2 =

9x6=

2x5=

2÷2=

2x3=

4 + 46 =

45 ÷ 9 =

11 ÷ 11 =

53 – 23 =

6x7=

8+7=

13 – 6 =

14 + 7 =

75 – 15 =

48 – 24 =

10 x 4 =

3 + 15 =

55 + 10 =

62 – 0 =

15 ÷ 3 =

24 ÷ 2 =

14 ÷ 2 =

6÷6=

77 ÷ 7 =

2 + 23 =

11 x 7 =

8x3=

8x9=

11 x 5 =

10 – 10 =

22 – 2 =

30 + 30 =

26 – 13 =

72 + 0 =

4x9=

20 + 80 =

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15 + 5 =

40 ÷ 5 =

75 – 5 =

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28 ÷ 7 =

m . u

STUDENT NAME

88 ÷ 8 =

4 x 12 =

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10 – 9 =

Complete the magic squares, making sure that each column, row and diagonal adds up to the same amount. (a) (b) (c) 10 3 11 6 8 6 7 5 R.I.C. Publications®

6 www.ricpublications.com.au

5 41

10 Primary mathematics: Back to basics

NUMBER SEQUENCES AND PATTERNS NUMBER

TEACHER INFORMATION Indicators Continues and completes number patterns by following set rules. Identifies prime and composite numbers.

r o e t s Bo r e p ok u S Concepts required

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Teac he r

Rules and patterns Prime numbers Composite numbers

Materials needed Calculator

Answers

1. (a) 2, 4, 8, 16, 32, 64, 128, 256, 512 Rule: double each number

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(e) 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0 Rule: Add 0.5 (f) 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45% Rule: Add 5%

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(d) 810, 790, 770, 750, 730, 710, 690, 670 Rule: Subtract 20

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(g) 5, 10, 9, 18, 17, 34, 33, 66, 65, 130 Rule: Double, then subtract one.

(h) 100, 98, 95, 91, 86, 80, 73, 65, 56, 46 Rule: Subtract 2 then 3, 4, 5, 6, 7, 8, 9, 10 2. Answers will vary

3. Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 85, 89, 97.

4. Composite numbers are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91,92, 93, 94, 95, 96, 98, 99, 100.

Primary mathematics: Back to basics

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R.I.C. Publications®

NUMBER SEQUENCES AND PATTERNS NUMBER

1. Complete these number sequences. Write the rule to match each sequence. (a) 2, 4,

, 16,

, 27, 36,

Rule:

Teac he r

Rule:

(d) 810,

, 15,

, 750,

, 72,

, 2.0,

, 36,

, 690,

Rule:

, 3.5,

Rule:

(f) 10%,

r o e t s Bo r e p ok u S

(e) 0.5,

, 25%,

, 45%

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(g) 5, 10, 9, 18,

(h) 100, 98, 95, 91,

56, Rule:

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2. Use a calculator to create four patterns of your own. Write the rule for each.

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(a)

Rule:

(b)

Rule:

numbers between 1 and 100.

m . u

STUDENT NAME

, 128,

Rule:

(b) 9,

3. List the prime numbers between 1 and 100.

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(c)

Rule:

(d)

Rule:

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Primary mathematics: Back to basics

NUMBER SENTENCES NUMBER

TEACHER INFORMATION Indicators Constructs and solves number sentences. Recognises and writes missing components in number sentences.

r o e t s Bo r e p ok u S Number sentence structure Use of >, <, =, +, –, x, ÷ signs Completing brackets first in any number sentence Fractions, decimals, percentages

Answers

1. (a) 35 (d) 11 (g) $10

(b) 8 (e) 24 (h) 12

2. (a) ÷ (d) + (g) x

(b) – (e) x (h) ÷

3. (a) (d) (g) (j)

(b) (e) (h) (k)

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Teac he r

Concepts required

13 6 7 40

4 18 90 50

15 48 0 4

(b) 8 (e) 2

5. (a) < (d) < (g) <

(b) > (e) < (h) <

(b) false (e) false

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4. (a) 4 (d) 4

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6. (a) true (d) true

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o c . che e r o t r s super

7. Answers will vary—examples for a; (6 x 3) + 50 = 68 or

(50 – 3) + 5 = 52

Primary mathematics: Back to basics

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R.I.C. Publications®

NUMBER SENTENCES NUMBER

1. Fill in the missing number to complete the number sentence. (a) 26 + 9 =

(e) 92 –

(b) 72 ÷

= 9

= 68 (f) 9.5 +

(c)

+ 23 = 60

= 17.5 (g)

(d) 12 x

= 132

– $5.10 = $4.90 (h) 120 ÷ 10 =

2. Fill in the missing signs. (a) 55

r o e t s Bo r e p ok u S

5 = 11

(e) $20

(b) 10.8

$5 = $100

6.4 = 4.4

(f) 42

58 = 100

9 = 81

(g) 5.1

2 = 10.2

(d) 61

61 = 122

(h) 72

6 = 12

Teac he r

(a) 7 + (3 x 2) =

(b) 40 ÷ (2 x 5) =

(d) 36 ÷ (5 + 1) =

(e) 15 + (12 – 9) =

(g) (13 + 8) ÷ 3 =

(h) (8 x 8) + 26 =

(j) (4 x 2) + (8 x 4) =

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(f) (7 x 4) + 20 =

(k) (10 x 7) – (4 x 5) =

(i) (64 ÷ 8) – 8 =

(l) (48 ÷ 4) ÷ (12 ÷ 4) =

4. Fill in the missing number to complete the number sentence. (a) (28 ÷ (d) (

) + (3 + 4) = 14

(b) (60 ÷ 10) x (24 ÷

x 9) + (2 x 7) = 50

(e) (20 –

) = 18 (c) (5 x 10) ÷ (

) – (3 x 6) = 0

(f) (

5. Complete the following by using > or <.

w ww

(a) 40 + 55 (e) 7 x 9

100 (b) 3/4

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22.24

8.4 (g) 7071

7171

(f) 2.4 + 2.4

x 5) = 5

÷ 7) x (10 – 4) = 66

m . u

STUDENT NAME

3. Complete these number sentences.

(d) 0.25

(h) 81 ÷ 9

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50% 19 – 9

6. Write if each number sentence is true or false. (a) 5 x 8 = 38 + 2

(b) 75% > 3/4

(d) 2 hours < 200 minutes

(f) 7.1 + 7.9 = 45 – 30

7. Use the sets of numbers to write number sentences. Answer each number sentence. (a) 6, 3, 50

(b) 6, 3, 2, 4

(d) 2, 3, 5, 18

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Primary mathematics: Back to basics

LINES AND ANGLES SPACE

TEACHER INFORMATION Indicators Identifies and describes a variety of line types. Identifies and draws a variety of angles.

r o e t s Bo r e p ok u S Concepts required

Materials needed

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Teac he r

Line types: horizontal, vertical, parallel, perpendicular, diagonal Angles: right, acute, obtuse

Ruler Protractor

Answers

1. (a) Horizontal lines run in the same direction as the horizon.

(c) Parallel lines run side by side, always with the same angle so they never meet. (d) Perpendicular lines occur when a horizontal line and a vertical line meet at right angles.

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2. Answers will vary 3. Teacher check (a) right angle = 90º (c) obtuse angle = more than 90º

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acute angle = less than 90º

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4. Answers will vary

Primary mathematics: Back to basics

(b)

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(e) Diagonal lines are slanted.

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R.I.C. Publications®

LINES AND ANGLES SPACE

1. Write a description and draw an example of each type of line.

(a) horizontal

(b) vertical

r o e t s Bo r e p ok u S

Teac he r

(e) diagonal

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2. Draw an example of something at home that has the following types of lines. (a) parallel lines

(b) diagonal lines

3. Use a ruler to draw the following angles. (a) right angle

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(b) acute angle

m . u

STUDENT NAME

(d) perpendicular

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4. Draw an example of something at home that has the following types of angles. (a) a right angle

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(b) an acute angle

Primary mathematics: Back to basics

2-D SHAPES SPACE

TEACHER INFORMATION Indicators Identifies and represents 2-D shapes. Identifies properties of 2-D shapes.

r o e t s Bo r e p ok u S Concepts required

Teac he r

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Recognition of 2-D shapes Identifying properties of polygons, quadrilaterals, triangles and circles Recognition of different types of triangle – right-angled, equilateral, isosceles and scalene Use of a compass and set radius to draw circles Knowledge of circle properties – centre, circumference, radius, diameter

Materials needed Compass Ruler

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(b) Teacher check 3. (a) right-angled has one angle of 90º

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(b) equilateral has three equal sides and angles

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1. Polygons are shapes which have three or more straight sides. Teacher check

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4. Teacher check circles. (Answer is not to scale.) diameter

radius centre

circumference

Primary mathematics: Back to basics

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R.I.C. Publications®

2-D SHAPES SPACE

1. Draw and label four different polygons. Write the number of sides and angles for each.

sides:

Teac he r

sides:

angles:

2. (a) What is a quadrilateral? (b) Draw three examples.

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3. Write a description and draw an example of each type of triangle.

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(d) scalene

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4. Use a compass to draw a circle with a 3-cm radius. Label the following.

(a) centre (b) circumference (c) radius (d) diameter

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m . u

STUDENT NAME

angles:

r o e t s Bo r e p ok u S sides:

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Primary mathematics: Back to basics

3-D SHAPES SPACE

TEACHER INFORMATION Indicators Identifies and names 3-D shapes. Identifies properties of pyramids and prisms.

r o e t s Bo r e p ok u S Concepts required

Answers

Name triangular pyramid square pyramid rectangular pyramid pentagonal pyramid hexagonal pyramid octagonal pyramid

Base shape

Face shape

No. of faces

No. of edges

No. of vertices

triangle

square

triangle

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Teac he r

Recognition of 3-D shapes Properties of 3-D shapes Understanding of nets

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Name triangular prism square prism rectangular prism pentagonal prism hexagonal prism octagonal prism

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3. (a)

Primary mathematics: Back to basics

rectangle

triangle

pentagon

triangle

hexagon

triangle

octagon

triangle

Front/Back shape

Face shape

No. of faces

No. of edges

No. of vertices

triangle

rectangle

m . u

o c . che e r o t r s super square

rectangle

rectangle rectangle

pentagon rectangle

hexagon

rectangle

octagon

rectangle

(b)

(c)

(d)

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R.I.C. Publications®

3-D SHAPES SPACE

1. Describe the following pyramids by completing the table.

Teac he r

Name

Base shape

Face shape

Number of Number of Number of faces edges vertices

r o e t s Bo r e p ok u S

2. Describe the following prisms by completing the table. Shape

Name

Front/Back shape

Face shape

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Number of faces

Number of edges

Number of vertices

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3. Draw the following shapes and their nets. (a) cube (b) triangular pyramid

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STUDENT NAME

Shape

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(d) cylinder

Primary mathematics: Back to basics

PERSPECTIVE AND TRANSFORMATIONS SPACE

TEACHER INFORMATION Indicators Draws tessellating shapes. Draws shapes that reflect, translate and rotate. Draws perspective. Reduces and enlarges images using a grid.

r o e t s Bo r e p ok u S

Identification of tessellations Polygons Changing shapes by reflecting, translating and rotating Bird’s-eye perspective Scale – reducing and enlarging

Answers

1. Answers will vary A polygon is a shape with three or more sides. Tessellating shapes fit together without any gaps or overlapping.

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Teac he r

Concepts required

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(b)

(c)

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4. Teacher check reduced image.

5. Teacher check enlarged image.

Primary mathematics: Back to basics

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R.I.C. Publications®

PERSPECTIVE AND TRANSFORMATIONS SPACE

1. Make a tessellating pattern using a polygon. 2. Sketch a bird’s-eye view of your bedroom.

r o e t s Bo r e p ok u S

3. Move the position of the following shapes.

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Reflected

Translated

Rotated 90º anticlockwise

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4. Draw a reduced copy of the picture.

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5. Draw an enlarged copy of the picture.

m . u

STUDENT NAME

Shape

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Primary mathematics: Back to basics

SYMMETRY SPACE

TEACHER INFORMATION Indicators Identifies and draws lines of symmetry. Completes pictures to show symmetry.

r o e t s Bo r e p ok u S Concepts required

Materials needed Ruler

Answers

1. (a) 3

(b) 2

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Teac he r

Understands that a line of symmetry divides a shape or object into two halves where one half is an exact mirror image of the other. Understands that there may be one line of symmetry, multiple or no lines of symmetry.

(f) 5

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(d) 1

2. Answers will vary

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3. Teacher check

Primary mathematics: Back to basics

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R.I.C. Publications®

SYMMETRY SPACE

1. Draw and record the number of lines of symmetry for each shape. (a)

(b)

(c)

(d)

(e)

r o e t s Bo r e p ok u S

(f)

2. Draw two items from home that show:

Teac he r

(b) multiple lines of symmetry.

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3. Complete the pictures to make them symmetrical. Draw your own picture for (d). (a)

(b)

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(c)

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STUDENT NAME

(a) no lines of symmetry.

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Primary mathematics: Back to basics

DIRECTIONS SPACE

TEACHER INFORMATION Indicators Describes direction using conventional locational language. Describes location using compass point directions.

r o e t s Bo r e p ok u S Concepts required

Materials needed Atlas

Answers

N NW

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Teac he r

Compass directions Locating information on a map

(b) west

3. (a) (c) (e) (g)

(b) (d) (f) (h)

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2. (a) east

Seattle Houston Los Angeles east

Boston, New York north-east St Louis Boston

4. Answers will vary

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Primary mathematics: Back to basics

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DIRECTIONS SPACE

2. (a) From which direction does the sun rise?

1. Add the direction abbreviations to the compass.

(b) In which direction does the sun set? Seattle

r o e t s Bo r e p ok u S Salt Lake City

Teac he r

3. Answer the questions about this map of the United States of America.

Las Vegas

Los Angeles

Chicago

New York

St Louis

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(a) What city is directly located in the far north-west.

Houston New Orleans

(b) What two cities are located on the east coast?

(e) What city is south-west of Las Vegas?

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(f) What city is south-west of New York? (g) In which direction is Salt Lake City from San Francisco?

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STUDENT NAME

San Francisco

Boston

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(h) What is the most eastern city marked on the map?

4. Use the map of Australia, an atlas and compass directions to answer the questions. (a) Label the city or town where you live. (b) I live

of Canberra.

coast.

(d) The Great Barrier Reef is to the where I live. (e) Uluru is located to the

of where I live.

(f) The Indian Ocean is located to the R.I.C. Publications®

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of where I live. 57

Primary mathematics: Back to basics

MAP FEATURES AND SCALES SPACE

TEACHER INFORMATION Indicators Designs a key to represent map features. Uses a scale to interpret distance. Uses compass point directions to describe location.

r o e t s Bo r e p ok u S A key uses symbols to represent specific features. Scale Compass directions Locating information on a map

Materials needed Ruler

Answers

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Teac he r

Concepts required

3. (a) (d) (g) (h)

east/north-east (b) north (c) 600 km 400 km (e) south-west (f) 300 km Shikoku, Kyushu, Hokkaido, Honshu 400 km, 1200 km, 500 km, 500 km; total = 2600 km

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Primary mathematics: Back to basics

(b) 25 km (e) 7.5 km (h) 102.5 km

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2. (a) 10 km (d) 35 km (g) 75 km

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MAP FEATURES AND SCALES SPACE

park

1. Design a key to suit the features of the suburb/town where you live. Use eight different symbols to identify the features you choose; for example,

r o e t s Bo r e p ok u S

(a) 2 cm =

(d) 7 cm =

(g) 15 cm =

Teac he r

(b) 5 cm =

(e) 1.5 cm =

(h) 20.5 cm =

3. Answer the questions about this map of Japan.

(a) In which direction is Tokyo from Kyoto?

(b) In which direction is Otaru from Tokyo?

(d) How many km is it from Nagasaki to Hiroshima?

(g) List the four islands in order of size from smallest to largest.

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(h) How many km would you travel if you travel from

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Otaru

Kushiro

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Kushiro to Otaru (

then Kyoto (

Total km =

km), onto Tokyo (

km),

km) and then Hiroshima (

km?

Hiroshima Nagasaki KYUSHU Kagoshima

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HOKKAIDO

m . u

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STUDENT NAME

2. The scale on a map reads 1 cm = 5 km. Convert these cm to km.

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Osaka

SHIKOKU

HONSHU Kyoto

Tokyo N W

S Scale 1 cm = 200 km (Scale may not represent actual distances.)

Primary mathematics: Back to basics

LENGTH MEASUREMENT

TEACHER INFORMATION Indicators Identifies formal measurement units. Measures length in centimetres. Finds equivalent measures. Adds and subtracts lengths.

r o e t s Bo r e p ok u S Formal measurement units – mm, cm, km Proficient use of a ruler Equivalent units of length Estimating Adding and subtracting measurements

Materials needed Ruler Tape measure

ew i ev Pr

Teac he r

Concepts required

(b) 100 cm

(b) 300 (e) 75 (h) 4100

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3. (a) 40 (d) 1200 (g) 4200

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4. Answers will vary

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2. Answers will vary

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5. (a) 510 cm or 5.1 m (c) 5.5 km or 5500 m

(b) 5.05 m or 505 cm (d) 25 mm or 2.5 cm

6. (a) 1.5 m or 150 cm (c) 730 cm or 7300 mm

(b) 10 m or 1000 cm (d) 6 km or 6000 m

7. Answers will vary

Primary mathematics: Back to basics

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LENGTH MEASUREMENT

1. (a) 1 cm =

(b) 1 m =

(d) 1 m =

2. Complete the table by listing four things you could best measure using each unit. Centimetres (cm)

Metres (m)

Kilometres (km)

r o e t s Bo r e p ok u S

Teac he r

3. Complete the conversions. (a) 4 cm =

(b) 3 m =

(d) 120 cm =

(e) 7.5 cm =

(g) 4.2 km =

(h) 410 m =

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(f) 4.5 m =

4. Use a ruler (or tape measure) to measure the length of each item at home. (a) television (b) phone (c) toaster

length =

length = (d) fridge

length =

5. Add the following lengths.

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(a) 10 cm and 5 m = (c) 3 km and 2500 m =

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cm or

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STUDENT NAME

Millimetres (mm)

m (b) 5 m and 5 cm =

km or

m or

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(d) 20 mm and 0.5 cm =

mm or

6. Calculate the range of difference between the following lengths. (a) 2 m and 50 cm =

(b) 10.8 m and 80 cm =

m or

cm or

km or

7. (a) Estimate the distance from your front door to the road. (b) Estimate the distance from your house to school. R.I.C. Publications®

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m km Primary mathematics: Back to basics

PERIMETER MEASUREMENT

TEACHER INFORMATION Indicators Uses a ruler to measure perimeter and draw to scale. Calculates perimeter from given measurements.

r o e t s Bo r e p ok u S Concepts required

Materials needed Ruler

Answers

1. (a) 160 mm

(b) 95 mm

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Teac he r

Knowledge that perimeter is the distance around a shape Proficient use of a ruler to measure accurately in mm and cm Addition skills

3. (a) (i) 20 cm, (ii) 10 cm

(b) 60 cm

4. 15.6 cm 5. 556 mm 6. 46 cm

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7. 32 m 8. Answers will vary

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Primary mathematics: Back to basics

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PERIMETER MEASUREMENT

1. Use your ruler to measure the perimeter, in millimetres, of each shape.

(a) P =

r o e t s Bo r e p ok u S mm

(b) P =

2. Draw a shape with a perimeter of:

Teac he r

(b) 90 mm.

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(i)

3. (a) Use the measurements given to determine 6 cm the lengths of sides (i) and (ii). (The shape is not to scale.)

(ii)

8 cm

4 cm

12 cm © R. I . C.Pub l i c a t i o n s 5. Find the perimeter 4. Find the perimeter of a square if one of a • square if one f o r r e v i e w p u r p osesonl y• side measures 139 side measures (b) What is the perimeter of the shape?

working out

mm.

3.9 cm. P =

P =

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6. Find the perimeter of a rectangle if the length is 14 cm and the width is 9 cm. P =

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STUDENT NAME

(a) 150 mm.

7. What is the perimeter of an area that is 10.6 m long and 5.4 m wide?

working out

o c . che e r o t r s super P =

8. Draw three items from home and use a ruler to measure the sides of each in centimetres. Record the measurements on each diagram and calculate the perimeters. (a) P =

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(b) P =

Primary mathematics: Back to basics

AREA MEASUREMENT

TEACHER INFORMATION Indicators Measures the area of shapes using informal and formal units. Calculates area.

r o e t s Bo r e p ok u S Concepts required

1. (a) (d) (g) (j)

Materials needed Calculator

Answers 20 24 45 16

ew i ev Pr

Teac he r

Area = length x width Multiplication Use of a calculator

(b) 44 (e) 40 (h) 29

(b) 28 m2 (e) 13.75 m2

(b) 8800 cm2

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5. (a) 95.46 m2 (d) 40 656 mm2 6. Answers will vary

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Primary mathematics: Back to basics

m . u

4. 25.2 m2

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AREA MEASUREMENT

1. Count the squares to find the area of each shape. Write the area inside each shape. (b)

(a)

(d)

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(g)

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(f)

(j)

(i)

(h)

2. Calculate the area of the following shapes. (Area = L x W) (a) Length = 4 cm

Width = 2 cm

Area =

cm2

(b) Length = 7 m

Width = 4 m

Area =

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(e) Length = 5.5 m

Width = 2.5 m Area =

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3. Find the area of a square with sides of 14 cm. A =

4. Find the area of a rectangle if the length is 8.4 m and the width is 3 m.

cm2

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STUDENT NAME

(e)

(c)

o c . che e r o t r s super A =

5. Use a calculator to work out each shape’s area. (a) L = 12.9 m W = 7.4 m A = (c) L = 152 mm (d) L = 242 mm

m2 (b) L = 275 cm W = 32 cm A =

W = 98 mm

mm2

W = 168 mm

mm2

cm2

6. Measure the length and width of three items from home. Find the area of each. (a) Item =

(b) Item =

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Primary mathematics: Back to basics

VOLUME AND CAPACITY MEASUREMENT

TEACHER INFORMATION Indicators Identifies formal units of volume and capacity. Orders the capacity of items measured in millilitres and litres. Calculates volume.

r o e t s Bo r e p ok u S Concepts required

Teac he r

Answers

1. (a) 1000 (d) 2500 (g) 6100

(b) 2000 (e) 4.5 (h) 2.49

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Knowledge of formal measurement units – millilitres and litres Equivalent units of measurement Ordering Subtraction Volume = length x width x height

3. (a) 0.5 L or 500 mL (c) 2.5 L or 2500 mL

(b) 1.6 L or 1600 mL (d) 7.5 L or 7500 mL

4. 9 doses

(b) 18 cm3 (e) 14 cm3

7. (a) 4 m3

(b) 18 m3

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6. (a) 32 cm3 (d) 11 cm3

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Primary mathematics: Back to basics

m . u

5. 16 cups

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VOLUME AND CAPACITY MEASUREMENT

1. (a) 1 L =

(b) 2 L =

(d) 2.5 L =

(e) 4500 mL =

(f) 4.4L =

(g) 6.1 L =

(h) 2490 mL =

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2. Find six items used in your home that are measured in millilitres. Write the items in order of their total capacity. Start with the smallest capacity. Item

Teac he r

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Largest

3. Calculate the range of difference between the following measurement of capacity. L or mL © R. I . C .Pub l i cat i ons (b) 2 L and 400 mL = L or mL •f orr evi ew pur posesonl y• (a) 1 L and 500 mL =

L or

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4. How many 5 mL doses are in a 45 mL bottle of medicine?

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STUDENT NAME

Smallest

Capacity

5. How many 250 mL cups of water are needed to fill a 4 L container?

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6. Write the volume of these 3-D cube models.

(a) V =

cm3 (b) V =

cm3 (c) V =

cm3 (d) V =

cm3 (e) V =

cm3

7. Find the volume of the following. (Volume = L x W x H) (a) Length = 2 m Width = 1 m Height = 2 m Volume =

(b) Length = 3 m Width = 2 m Height = 3 m Volume =

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Primary mathematics: Back to basics

MASS MEASUREMENT

TEACHER INFORMATION Indicators Identifies formal units of measuring mass. Orders the mass of items in grams and kilograms. Calculates equivalent measures.

r o e t s Bo r e p ok u S Concepts required

Teac he r

Answers

1. (a) kg (d) g

(b) g (e) kg

3. (a) 1000 (d) 0.25

(b) 0.5 (e) 4500

4. (a) 0.5 kg or 500 g (c) 2.5 kg or 2500 g

(b) 1.4 kg or 1400 g (d) 7.5 kg or 7500 g

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Knowledge of formal measurement units – grams and kilograms Lighter/Heavier than Equivalent units of measurement Ordering Calculating weight measurements Problem solving

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5. (a) (b) (c) (d) (e)

150 g, 200 g, 250 g, 500 g, 750 g, 920 g 4 kg, 9 kg, 14 kg, 21 kg, 50 kg, 75 kg 15.9 kg, 25.5 kg, 50.5 kg, 55.5 kg, 105.5 kg, 155.5 kg 500 g, 750 g, 1000 g, 1.2 kg, 1300 g, 1.5 kg 200 g, 0.25 kg, 0.5 kg, 2000 g, 2.1 kg, 2500 g

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6. (a) 145.4 kg (d) 7.5 kg

Primary mathematics: Back to basics

(b) Riley

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MASS MEASUREMENT

1. Write whether you would best measure each of the following in grams (g) or kilograms (kg). (a) yourself

(b) four pencils

(d) an apple

(e) six house bricks

2. Complete the following statements about weight.

r o e t s Bo r e p ok u S

(a) A newborn baby is lighter than (b) My bed is heavier than (c)

is heavier than

Teac he r

is lighter than

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3. Convert the following measurements. (a) 1 kg =

(d) 250 g =

(b) 500 g =

(e) 4.5 kg =

(f) 1.25 kg =

4. Find the range of difference between each of the following measurements of mass.

kg or

(b) 2 kg and 600 g =

(d) 10 kg and 2500 g =

kg or

5. Order the measurements from lightest to heaviest.

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STUDENT NAME

(d)

(a) 200 g, 920 g, 150 g, 500 g, 250 g, 750 g

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(b) 4 kg, 21 kg, 14 kg, 75 kg, 9 kg, 50 kg (c) 50.5 kg, 55.5 kg, 15.9 kg, 155.5 kg, 105.5 kg, 25.5 kg

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(d) 1.5 kg, 1000 g, 750 g, 1.2 kg, 1300 g, 500 g

(e) 0.25 kg, 0.5 kg, 200 g, 2000 g, 2.1 kg, 2500 g

6. Quang weighs 49.5 kg, Riley weighs 44.2 kg and Ben weighs 51.7 kg. (a) What is the total mass of the boys?

(b) Who is the lightest? (c) Who is the heaviest?

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(d) What is the difference between the lightest and heaviest?

kg Primary mathematics: Back to basics

TEMPERATURE MEASUREMENT

TEACHER INFORMATION Indicators Reads, records and orders temperatures in degrees Celsius. Analyses information from a table of data.

r o e t s Bo r e p ok u S Degrees Celsius Cº Reading and recording thermometers Ordering Extracting information from specific data Sourcing required information

ew i ev Pr

Teac he r

Concepts required

Materials needed

Newspaper/Television/Internet climatic temperature source

Answers

2. Darwin, Brisbane, Sydney, Perth, Melbourne, Hobart 3. (a) New Delhi (d) 30 ºC (g) 18 ºC

(b) Berlin (c) Bangkok (e) 28 ºC (f) 23 ºC (h) Dubai and New Delhi

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Primary mathematics: Back to basics

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4. Teacher check

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TEMPERATURE MEASUREMENT

1. Record the temperature of each city on the wall thermometers. (a) Perth (b) Brisbane (c) Hobart (d) Sydney (e) Melbourne (f) Darwin 22 ºC 28 ºC 16 ºC 27 ºC 21 ºC 33 ºC C

r o e t s Bo r e p ok u S

Teac he r

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3. Use the table, showing the maximum and minimum temperatures (ºC) of cities around the world, to answer the questions.

(a) Which city had the highest maximum temperature?

(b) Which city was the coldest overnight?

Max.

Min.

Athens

19 ºC

14 ºC

(d) What is the difference in temperature between the highest and lowest maximums?

(e) What is the difference in temperature between the highest and lowest minimums?

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City

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26 ºC 1 ºC

Dubai

38 ºC

28 ºC

Dublin

15 ºC

8 ºC

Honolulu

25 ºC

20 ºC

London

21 ºC

8 ºC

Moscow

9 ºC

2 ºC

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STUDENT NAME

2. Order the cities above from warmest to coolest.

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(f) What is the difference in maximum temperature between Dubai and Dublin?

New Delhi

39 ºC

29 ºC

New York

20 ºC

13 ºC

(g) What is the difference in minimum temperatures between Bangkok and London?

Tokyo

18 ºC

14 ºC

(h) Which two cities recorded the most varying temperatures?

and

4. Use a source to record the following temperatures for your city. Yesterday Max.

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Today Min.

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Max.

Tomorrow Min.

Max.

Min.

Primary mathematics: Back to basics

ANGLES MEASUREMENT

TEACHER INFORMATION Indicators Identifies markings on a protractor. Identifies and measures angles. Uses a protractor to measure and draw specific angles.

r o e t s Bo r e p ok u S Concepts required

Materials needed Coloured pencils Protractor

Answers

1. Teacher check

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Teac he r

Familiarity with protractors and how to use them correctly Types of angles — right, acute, obtuse, straight, reflex

(a) (b) (c) (d)

A right angle equals 90º. An acute angle is less than 90º. An obtuse angle is more than 90º and less than 180º. A reflex angle is larger than 180º.

3. (a) acute, 40º (d) straight, 180º

(b) right, 90º (e) reflex, 270º

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Primary mathematics: Back to basics

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4. Teacher check

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R.I.C. Publications®

ANGLES MEASUREMENT

1. (a) Complete the measurements on the protractor. (b) Use different colours to mark: (i) a right angle (ii) an acute angle (iii) an obtuse angle.

90 100

120

180 170 1 60

r o e t s Bo r e p ok u S

160

2. Write a description for each type of angle.

Teac he r (b) acute

3. Identify each type of angle, then measure each with a protractor.

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(d)

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(e)

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(a)

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STUDENT NAME

(a) right

(f)

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4. Use a protractor to draw the following angles. (a) 20º

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(b) 160º

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Primary mathematics: Back to basics

TIME MEASUREMENT

TEACHER INFORMATION Indicators Records analog, digital and 24-hour times. Calculates elapsed time. Solves time-related problems.

r o e t s Bo r e p ok u S Reading and recording of analog and digital times 24-hour time Calculating elapsed time Problem solving

ew i ev Pr

Teac he r

Concepts required

Answers

1. (a) 17 past 12, 12.17 (d) 12 to 7, 6.48

(b) 21 past 5, 5.21 (e) 7 past 7, 7.07

2. (a) 1400 (d) 1525 (g) 2148

(b) 2030 (e) 2355 (h) 1705

3. (a) 7.48 am (d) 3.13 am

(b) 3.25 pm

4. (a) 50 min (d) 5 h 25 min

(b) 50 min

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6. 7.05 am 7. 10 hr 15 min 8. 6 hr 20 min

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9. 1 hr 20 min 10. 4.30 pm

Primary mathematics: Back to basics

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R.I.C. Publications®

TIME MEASUREMENT

1. Write the analog and digital time shown on each clock face. (a) 11

(b) 11

10 8

Teac he r

10 8

(f)

(a) 2.00 pm

(b) 8.30 pm

(e) 11.55 pm

(f) 12.32 pm

(g) 9.48 pm

to . 11

2 3

9 8

to past . . 2. Change the following to 24-hour times.

3 8

r o e t s Bo r e p ok u S 11

4 7

to .

ew i ev Pr (d) 3.25 pm (h) 5.05 pm

4. How much time has passed between the following times?

(b) 8.35 pm and 9.25 pm

(d) 10.20 am and 3.45 pm

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(a) 1.09 am and 1.59 am

5. Blake started work at 8.30 am and finished at 4.15 pm. How long did he spend at work?

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STUDENT NAME

4 7

past . (e)

2 3

past . (d) 11

(c)

4 7

10 3

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6. Natalie left home at 6.15 in the morning. If it took her 50 minutes to reach her destination, what time did she arrive? 7. Caitlin went to sleep at 8.55 pm and woke at 7.10 am. How long did she sleep for?

8. The first leg of our trip took three hours and 25 minutes. The second leg took two hours and 55 minutes. How long was the trip in total?

9. Drew arrived at the airport at 11.45 am to catch a flight scheduled to depart at 1.05 pm. How long did he wait? 10. A game is played in 20 minute quarters. There are two 10 minute breaks and one 20 minute break. If a game starts at 2.30 pm, what time will it finish? R.I.C. Publications®

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Primary mathematics: Back to basics

CALENDARS AND TIMETABLES MEASUREMENT

TEACHER INFORMATION Indicators Interprets information from calendars and timetables. Organises and records events in a timetable.

r o e t s Bo r e p ok u S Using a calendar Number of days, weeks, months in a year Elapsed time Creating a timetable of activities Reading a television timetable

Materials needed Current calendar Current television guide

ew i ev Pr

Teac he r

Concepts required

1. Teacher check (a) to (f) (g) Months with 31 days – January, March, May, July, August, October, December 2. Answers will vary

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Primary mathematics: Back to basics

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3. Answers will vary

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CALENDARS AND TIMETABLES MEASUREMENT

1. Use a calendar to answer the questions. (a) On what day of the week is your birthday this year? (b) What is the date three weeks before your birthday? (c) What is the date four weeks after your birthday? (d) What will be the date seven weeks and two days from today?

r o e t s Bo r e p ok u S

(e) What was the date 15 days ago?

(f) How many days are there in the current month?

Teac he r

2. Write a timetable to show what you did yesterday. Time (am)

Activity

Time (pm)

ew i ev Pr Activity

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STUDENT NAME

(g) List all the months that have 31 days.

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3. Use today’s TV guide and choose ONE channel’s timetable to answer the questions. (a) What program begins at 6 pm?

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(b) How much time is scheduled for:

(i) sport programs?

(ii) news programs?

o c . che e r o t r s super (iv) movies?

(v) game shows? (c) If you had a total of 90 minutes of viewing time, what programs would you choose to watch? (e) If you turned the TV on right now, what program would be playing? (d) If you turned the TV on as soon as you woke up this morning, what program would have been showing? R.I.C. Publications®

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Primary mathematics: Back to basics

CHANCE CHANCE AND DATA

TEACHER INFORMATION Indicator Identifies and predicts outcomes.

Concepts required

r o e t s Bo r e p ok u S Materials needed Coin

Answers

1. Answers will vary 2. Answers will vary

ew i ev Pr

Teac he r

Terms – likely, unlikely, possible, impossible, certain Percentage relating to chance Interpreting results from a chance experiment

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Primary mathematics: Back to basics

m . u

3. Answers will vary

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CHANCE CHANCE AND DATA

1. Complete the following statements based on what you think is likely to occur tomorrow. (a) It’s likely (b) It’s impossible (c) It’s very likely (d) It’s possible

r o e t s Bo r e p ok u S

(e) It’s unlikely (f) It’s certain

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On the weekend, there is a:

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(a) 100% chance I will (b) 50% chance I will (c) 25% chance (d) 75% chance

3. Flip a coin ten times and record the results. 1

(a) What chance did you have of flipping a head on your first toss?

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(b) What percentage of turns did you flip heads?

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% %

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STUDENT NAME

2. Complete the following statements.

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(d) What is the chance of recording the same results if you flipped a coin 10 times?

(e) Repeat the experiment. 1

(f) What percentage of turns did you flip heads? (g) What percentage of turns did you flip tails?

% %

(h) Which side came up the most in both experiments? R.I.C. Publications®

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DATA CHANCE AND DATA

TEACHER INFORMATION Indicators Writes survey questions and makes predictions. Uses data to construct and interpret a line graph. Chooses appropriate formats for representing data.

r o e t s Bo r e p ok u S Understanding purpose and construction of surveys Line graphs Interpreting data Different forms of representing data

Answers

1. Answers will vary 2.

(a) (b) (c) (d) (e)

Teacher check line graph. suggested: Maximum temperatures for Perth during one week Sunday Thursday Monday and Friday

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Concepts required

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4. Answers will vary

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DATA CHANCE AND DATA

1. (a) Think of a question to ask your friends to find out what item from a list of choices they use the most. (b) List the six items to include in your survey for others to choose from.

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2. (a) Use the following data to create a line graph.

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These maximum temperatures were recorded for Perth over the period of one week: Monday 23 ºC Tuesday 25 ºC Wednesday 19 ºC Thursday 18 ºC Friday 23 ºC Saturday 27 ºC Sunday 30 ºC

(b) What title would you give this graph? (c) On what day was the highest maximum temperature recorded?

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STUDENT NAME

(d) Which item do you think would be the least popular?

(d) On what day was the lowest maximum temperature recorded?

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(e) What days recorded the same maximum temperature?

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3. List six different forms of representing data.

4. Decide on the most appropriate format of representing the following data. (a) types of food sold at the school canteen (b) possible outcomes of throwing a die 20 times (c) favourite sports played by classmates (d) time spent on daily activities (e) yearly rainfall recorded R.I.C. Publications®

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Primary mathematics: Back to basics

DIAGRAMS AND TABLES CHANCE AND DATA

TEACHER INFORMATION Indicator Analyses data presented in diagrams and tables.

Concepts required

r o e t s Bo r e p ok u S

(a) (b) (c) (d) (e)

Answers eight Sartorni Gibson, Messino, Knight Anderson, Gibson, Novakoss, Wallace Knight

2. (a) 20 (b) six (d) Ella, Ben, Chris, Amal (e) 50%

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Tree diagram Venn diagram Two-way table Percentage

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3. (a) 10 (b) six (c) Jaxon and Dean (d) 50 % (e) Lucy, Anthony, Peter (f) Answer will vary

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DIAGRAMS AND TABLES CHANCE AND DATA

1. This tree diagram shows the results of a tennis tournament. Use it to answer the questions. ANDERSON

MESSINO

SARTORNI

KNIGHT

(c) Which players did he/she need to beat to win the tournament? SARTORNI (d) Which players were eliminated in the first round?

KNIGHT

(e) Who was the winner’s opponent in the final?

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NOVAKOSS XU

(b) Who was the eventual winner?

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GIBSON

WALLACE

2. Use the Venn diagram to answer the questions. (a) How many people were surveyed? Preferred holiday location Australia

USA

l (b) How many preferred © R. I . C .Pub i c at i on s the USA? Tess Ella Zac Tengu (c) How many preferred Australia? Lana • f o r r e v i e w p u r posesonl y• Chris Amanda Logan Olivia

Alex

Ben

Rebecca

Dylan

Amal

Lin Isaac

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Rose

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(d) Who liked both destinations? (e) What percentage of people preferred Australia?

Lee

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STUDENT NAME

(a) How many players started in the tournament?

Asha

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3. Use the two-way table to answer the questions. (a) How many people were surveyed? Love coffee Hate coffee Love tea Hate tea Jaxon

Lucy

Fadwa

Jaxon

Fadwa

Anthony

Grace

Anthony

Dean

Peter

Taylor

Lucy

Ismail

Grace

Ismail

Peter

Taylor

Kiara

Dean

Kiara

(d) What percentage of people love tea? (e) Who hates coffee and tea? (f) Add your name to the table.

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(b) How many hate coffee? (c) Who loves coffee but hates tea?

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Primary mathematics: Back to basics

GRAPHS CHANCE AND DATA

TEACHER INFORMATION Indicators Analyses data presented in tables and graphs. Uses data to construct a bar graph.

r o e t s Bo r e p ok u S Reading tables Constructing bar graphs Pie graphs Strip graphs Scale Percentage

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Concepts required

Materials needed Ruler

(b) Answers will vary

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3. (a) (c) (e) (g)

eight black and pink white and green blue

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Primary mathematics: Back to basics

(b) two (d) blue (f) red, blue and green

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2. (a) peanuts (b) peanuts and pecans or peanuts and macadamias (c) 1/4 (d) 50%

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GRAPHS CHANCE AND DATA

1. Nick rolled a die 50 times and recorded the following results. Title

(a) Use the information to create a bar graph. Number

Total

5 6

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(b) Write three questions about the graph.

•

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2. Use the pie graph to answer the questions. (a) What was the most popular type of nut?

Cashews

(b) What two types of nut made up half of the total?

Peanuts

Almonds

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(d) What percentage chose peanuts or macadamias?

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STUDENT NAME

Tally

3. Twenty people were asked what their colour car is. Use the results from the strip graph to answer questions. (1 cm = 1 car)

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Red

Blue

(a) How many have a white car?

Green

Black

Pink

(b) How many have a green car?

(c) What are the least popular colours? (d) What is the second most popular colour? (e) Which two colours make up 50% of the results? (f) Which three colours make up 50%? (g) Which colour makes up 25%? R.I.C. Publications®

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Primary mathematics: Back to basics

AVERAGES CHANCE AND DATA

TEACHER INFORMATION Indicator Calculates the average from a set of data.

Concepts required

r o e t s Bo r e p ok u S Interpreting data in different forms Adding and dividing to calculate averages

1. 4 + 2 + 9 + 8 + 8 + 3 + 1 = 35 mm ÷ 7, Average is 5 mm

2. 150 + 165 + 142 + 153 +160 = 770 cm ÷ 5, Average is 154 cm 3. 60 + 50 + 65 + 45 + 55 + 55 = 330 kg ÷ 6, Average is 55 kg 4. 27 + 31 + 7 + 25 + 50 + 15 + 0 + 4 + 19 + 1 + 8 = 187 runs ÷ 11, Average is 17 runs 5. 28.5 + 51.2 + 42.1 + 26.5 + 38 + 62.4 + 12.4 = 261.1 km ÷ 7,

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Answers

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Average is 37.3 km

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AVERAGES CHANCE AND DATA

Calculate the average for each set of data. 1. Daily rainfall for one week 10

Add

Divide

8 6 4

Average daily rainfall

2 M

Name

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Scarlett Matilda

kg 55 50 45

Add

mm Divide

Height (cm) 150 165

Baye

142

Emily

153

Jessica

160

W T Days

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STUDENT NAME

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Average height =

Add

Body weight of six boys

Divide

Hussan Sam

Nick

Ian

Glen

Lee Add

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4. The school cricket team’s batting card was:

Alex – 27

Luke – 31

Imran – 25

Brett – 50

Josh – 15

Ben – 0

Jay – 4

Chari – 19

Riley – 1

Kane – 8

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Brady – 7

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Divide

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Average runs scored =

Day

km travelled

Monday

28.5

Tuesday

51.2

Wednesday

42.1

Thursday

26.5

Friday

38.0

Saturday

62.4

Sunday

12.4

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Add

mm Divide

Average km travelled = 87

Primary mathematics: Back to basics