Primary Mathematics - Back to Basics: Book G - Ages 11+ by Teacher Superstore

RIC-6062 4.7/179

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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 F)

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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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 and reinforce 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 sentences and patterns................................ 42–43 Special numbers............................................................ 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 Reducing and enlarging . ............................................ 56–57 Directions and coordinates . ...................................... 58–59 Map features and scales . .......................................... 60–61

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Length ............................................................................ 62–63 Perimeter . ..................................................................... 64–65 Circumference . ............................................................ 66–67 Area . .............................................................................. 68–69 Volume and capacity . ................................................. 70–71 Mass .............................................................................. 72–73 Angles ............................................................................ 74–75 Time ................................................................................ 76–77 Calendars, timetables and time lines........................ 78–79

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Chance and data Chance and predictions . ............................................ 80–81 Data ............................................................................... 82–83 Diagrams and tables .................................................. 84–85 Graphs .......................................................................... 86–87 Statistics . ..................................................................... 88–89

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 show 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.

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 name of the related strand is given.

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

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

WM4.4, WM3.4, WM5.4

Number

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

Measurement

M9b.4, M10a.4, M10B.4, M11.4

Chance and data

C&D12.4, C&D13A.4

Space

S15a.4, S15b.4, S15c.4

Algebra

PA17a.4, PA17b.4, PA18.4, PA19.4

New South Wales Working mathematically Number

r o e t s Bo r e p ok u S WMS3.1, WMS3.2, WMS3.4, WM3.5 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, DS3.1

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, MANUP401, 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

4.1, 4.2

Number

4.6, 4.7, 4.8

Measurement

4,4, 4.5, 4.9

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Working mathematically

Chance and data Space

Algebra

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4.1, 4.2, 4.3

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4.9, 4.12, 4.13, 4.14 4.10

Queensland Working mathematically

—

Number

N 4.1, N 4.2, N 4.3

Measurement

M 4.1, M 4.2

Chance and data

CD 4.1, CD 4.2

Space

S 4.1, S 4.2

Algebra

PA 4.1, PA 4.2

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South Australia

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Primary mathematics: Back to basics

WRITING numbers NUMBER

Teacher information Indicator Reads and writes whole numbers to seven digits.

Concepts required

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

Answers

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Knowledge of numbers to seven digits Ordering numbers More than, Less than

forty-four nine hundred and nine eight thousand, seven hundred and sixty-five two thousand, eight hundred and forty twenty thousand two million, nine hundred and eighty-seven thousand, three hundred and four

7, 77, 177, 707, 777, 7000 246, 264, 442, 462, 624, 642 28, 82, 888, 2282, 2828, 8888 55 005, 55 050, 55 505, 55 515, 55 550, 55 555 1, 111, 1001, 1101, 1110, 1111

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

33 333, 33 033, 3333, 3033, 333, 33 9987, 9978, 9098, 1978, 987, 978 101 010, 100 000, 10 000, 1010, 1000, 100 6 000 000, 66 060, 6660, 6606, 6060, 6006 2 222 000, 2 202 202, 2 200 200, 2 020 020, 2 000 002

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2. (a) 87 (b) 101 (c) 1010 (d) 16 017 (e) 250 000 (f) 5 000 000

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5. (a) 0, 200 (d) 6800, 7000

(b) 1000, 1200 (e) 10 025, 10 225

6. Answers will vary.

Primary mathematics: Back to basics

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WRITING numbers NUMBER 1. Write these numbers in words.

(a) 44

(b) 909

(d) 2840

(e) 20 000

(f) 2 987 304

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(a) eighty-seven

(d) sixteen thousand and seventeen

(e) two hundred and fifty thousand

(f) five million

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(b) one hundred and one

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3. Order these groups of numbers from smallest to largest.

(a) 77, 707, 7, 7000, 777, 177

(b) 462, 442, 642, 246, 624, 264

(d) 55 050, 55 550, 55 005, 55 505, 55 555, 55 515

(e) 111, 1, 1001, 1111, 1101, 1110

4. Order these groups of numbers from largest to smallest.

(a) 3033, 3333, 333, 33 033, 33, 33 333

(b) 987, 978, 9987, 9978, 1978, 9098

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STUDENT NAME

2. Write each as a numeral.

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(e) 2 000 002, 2 200 200, 2 020 020, 2 222 000, 2 202 202

5. Write the number that is 100 less and 100 more.

(a)

100

(d)

6900

(f)

(b)

1100

(e)

(c)

5000

10 125

2 045 045

6. (a) Write your birth date using eight numerals (e.g. 22051995).

(b) Arrange the numerals to make the largest possible number.

(d) Write the number that is 100 less and 100 more.

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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.

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Materials needed Calculator

Answers

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

hundreds ten thousands thousands tens hundred thousands ten thousands ones millions

4 x 100 2 x 10 000 6 x 1000 8 x 10 7 x 100 000 9 x 10 000 3 x 1 5 x 1 000 000

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

800, 90 10 000, 8000, 400, 60, 2 14 758 30 000, 5000, 800, 70, 6 600 000, 50 000, 600, 50, 5 200 000, 50 000, 5000, 50, 5 6 462 897

400 20 000 6000 80 700 000 90 000 3 5 000 000

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Place value to millions Expanded notation Representing numbers as an addition sum

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3. (a) 700 (d) 80 000 (g) 10

(b) 20 000 (e) 400 000 (h) 50 000

4. Teacher check setting out. (a) 39 729 (b) 888 484

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Place value NUMBER

1. Complete the table.

Example:

Place value

Expanded form

Meaning

8765

thousands

8 x 1000

8000

(a)

12 482

(b)

25 007

(c)

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(d)

351 885

(e)

720 529

(g)

495 006

3 000 083

(h)

5 555 555

2. Write the missing numbers.

(a) 4892 = 4000 +

(b) 18 462 =

(c)

(d) 35 876 =

(e) 655 655 =

(f) 2 255 255 = 2 000 000 +

+2 +

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(d) 89 050 =

(g) 9 461 111 =

(g)

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+ 5000 + +

+ +

+ 200 +

= 6 000 000 + 400 000 + 60 000 + 2000 + 800 + 90 + 7

3. Write the meaning of the underlined number; e.g. 888 = 80 (a) 9721 =

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(f)

STUDENT NAME

Number

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(b) 28 407 =

(e) 1 426 500 =

(f) 8 041 261 =

(h) 6 456 789 =

(i) 4 444 444 =

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

(a) 33 + 3030 + 33 000 (b) 842 + 861 420 + 8054 (c) 60 + 2 000 000 + 6200 + 6 + 333 + 3333 + 18 088 + 80 + 2620 + 262 626

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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. Demonstrates rounding to one and two decimal places.

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

Answers

1. (a) 280 (d) 24 820 (g) 306 010

(b) 3420 (e) 38 050 (h) 502 100

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

2600 34 000 70 100 4 655 700

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

3100 18 600 411 100 6 990 000

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

8000 17 000 106 000 2 401 000

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

7000 81 000 234 000 2 209 000

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

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4. (a) 84 (d) 333 (g) 2046

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(b) 77 (e) 641 (h) 17 001

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5. (a) 7.6 (d) 19.1 g) 54.6

(b) 9.6 (e) 21.1 (h) 101.1

6. (a) 2.62 (d) 0.73 (g) 16.59

(b) 4.56 (e) 4.57 (h) 21.10

7. (a) 5000 + 2000 = 7000 (c) 55 000 + 105 000 = 160 000

Primary mathematics: Back to basics

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(b) 6000 – 3000 = 3000 (d) 48 000 – 24 000 = 24 000

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ROUNDING NUMBER 1. Round these numbers to the nearest 10.

(a)

281

(b)

3416

(c)

1242

(d)

24 815

(e)

38 046

(f)

121 121

(g) 306 007

(h) 502 096

(i) 4 261 584

(a)

2645

(d)

34 045

(g)

70 095

(j) 4 655 655

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(b)

3098

(c)

21 285

(e)

18 589

(f)

10 999

(h)

411 111

(i) 1 432 045

(k) 6 989 989

3. Round these numbers to the nearest 1000.

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(a)

8250

(b)

7045

(c)

5555

(d)

16 908

(e)

80 999

(f)

55 125

(g) 106 495

(h) 234 098

(i) 1 485 795

(j) 2 401 286

(k) 2 208 908

(a)

(d)

(g)

4. Round these numbers to the nearest whole number. 84.2

(b)

76.5

(c)

145.9

333.3

(e)

640.5

(f)

1200.9

2045.5

(h) 17 000.6

5. Round these numbers to one decimal place.

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STUDENT NAME

2. Round these numbers to the nearest 100.

(a)

7.61

(b)

9.57

(c)

11.35

(d)

19.05

(e)

21.08

(f)

80.98

(g)

54.59

(h)

101.11

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6. Round these numbers to two decimal places.

(a)

2.621

(d)

0.729

(g)

16.585

(b)

4.559

(c)

8.041

(e)

4.565

(f)

8.008

(h)

21.098

7. Estimate these answers by rounding to the nearest 1000.

(a) 4650 + 2095 =

(b) 6091 – 2995 =

–

(d) 48 125 – 23 995 =

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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.

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Place value Trading Problem solving

Answers

1. (a) 592 (d) 1032

(b) 743 (e) 1084

2. (a) 5351 (d) 10 812

(b) 6855 (e) 12 218

3. (a) 26 214 (d) 711 914

(b) 58 015 (e) 1 512 511

4. (a) 640 (d) 63 306

(b) 7216 (e) 620 219

5. (a) 795 (d) 107 330

(b) 7695 (e) 1 524 077

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(e)

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368 (b) + 355 723

686 (c) 3242 (d) 7045 + 389 + 1468 + 2899 1075 4710 9944

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6. (a)

321 (f) 12 556 (g) 2061 (h) 5976 248 + 7 568 2601 2841 + 276 20 124 + 2004 + 3503 845 6666 12 320

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(i) 6 090 090 + 3 900 919 9 991 009

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ADDITION NUMBER 1.

347

(b)

508

(c)

479

(d)

645

(e)

+ 245

+ 235

+ 284

+ 387

(a)

2143

(b)

4066

(c)

3458

(d)

8417

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+ 3208

+ 2789

+ 2784

+ 2395

12 045

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(a)

(b)

34 658

(c)

421 500

(d)

385 929

+ 23 357

+ 378 999

+ 325 985

248

(b)

3460

(c)

5624

7654 + 4564

845 845 + 666 666

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+ 14 169

(a)

+ 298

(e)

786

(e)

(d)

21 462

(e)

201 455

237

2548

5895

20 555

286 209

+ 155

+ 1208

+ 2417

+ 21 289

+ 132 555

(a)

(b)

1417

(c)

7209

(d)

19 405

(e)

742 581

224

1582

6318

11 652

330 609

312

2091

5427

22 074

199 500

+ 125

+ 2605

+ 4536

+ 54 199

+ 251 387

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(a)

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6. Find the missing numbers to complete each sum.

(a)

3 6

(b)

+ 3 5 5 2 3

(f)

7 5

+ 3 8

(g)

2 4

0 2

4 2

(d)

4 6

7 0 4

+ 2

4 7 1 0

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(h)

9 7 6

+ 3

0 3

3 2 0

(e)

(i)

6 +

8 7 6

8 4 5 9 0

9 0 9 9

3 2 2

9 9

8 4

0 0

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(c)

0 1 9

0 0

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.

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Place value Trading Problem solving

Materials needed Calculator

Answers

1. 713 km

5. 22 222 people 6. 30 112 votes

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7. 19 526 votes 8. 192 620 people 9. 11 916 downloads

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10. 1 524 681 people 11. (a) 760 630 (c) 1 218 586

(b) 4 135 811 (d) 11 830

12. Teacher check word problem—3498 + 1979 = 5477

13. Teacher check word problem—52 405 + 48 960 = 101 365

Primary mathematics: Back to basics

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ADDITION PROBLEMS 2. How many students altogether if 345 are girls and 387 are boys?

3. A website recorded 2769 hits one day and 2875 the next. How many altogether?

4. Three batsmen recorded scores of 188, 149 and 215. What is the combined total?

5. 9472 people attended a concert on Friday and 12 750 attended on Saturday. What was the total attendance?

6. In a TV phone poll, 23 487 viewers voted ‘Yes’ and 6625 voted ‘No’. How many registered to vote?

7. Three reality show contestants attracted votes of 4516, 2548 and 12 462. How many votes were registered altogether?

8. The Grand Final attracted 102 985 people in 2007. The figure for 2006 was 89 635. How many attended both games?

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1. Emily travelled 427 km before taking a break. If she drove another 286 km, how far did she travel altogether?

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9. Over four days, one popular track was downloaded the following number of times—2327, 2691, 3182 and 3716. How many times was the track downloaded?

10. Greensboro has a population of 442 471, Redsboro has 350 749 people and there are 731 461 people in Bluesboro. What is the total population of the three towns?

11. Use a calculator.

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(a) 91 + 462 + 1379 + 41 082 + 717 616 =

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STUDENT NAME

NUMBER

(b) 4 126 521 + 38 + 591 + 8652 + 9 =

(d) 2 + 8791 + 3 + 1978 + 55 + 1001 =

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Write your own word problems using the numbers given. Set out and solve each problem. 12. 3498 + 1979

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13. 52 405 + 48 960

Primary mathematics: Back to basics

MENTAL ADDITION NUMBER

Teacher information Indicator Shows proficiency with mental addition facts.

Concepts required

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Answers

100

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Mentally add one and two digits with answer up to 100 Problem solving

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MENTAL ADDITION NUMBER B

9+6=

18 + 4 =

50 + 15 =

60 + 40 =

12 + 12 =

10 + 12 =

11 + 11 =

21 + 22 =

37 + 4 =

8 + 43 =

7 + 13 =

30 + 60 =

7 + 20 =

88 + 8 =

22 + 22 =

15 + 8 =

9 + 12 =

63 + 7 =

6+5=

3 + 78 =

33 + 0 =

16 + 14 =

9 + 42 =

12 + 13 =

15 + 65 =

2 + 47 =

37 + 0 =

56 + 4 =

7 + 35 =

83 + 9 =

13 + 13 =

8 + 27 =

4+8=

4 + 27 =

88 + 12 =

44 + 44 =

71 + 11 =

18 + 3 =

26 + 9 =

13 + 9 =

15 + 24 =

49 + 7 =

5 + 17 =

99 + 1 =

31 + 13 =

90 + 9 =

11 + 9 =

14 + 22 =

20 + 9 =

12 + 6 =

25 + 25 =

8 + 16 =

31 + 29 =

21 + 8 =

93 + 7 =

42 + 18 =

22 + 23 =

72 + 8 =

4 + 12 =

15 + 60 =

5 + 30 =

6+6=

10 + 27 =

9 + 21 =

7 + 28 =

40 +20 =

18 + 8 =

22 + 9 =

12 + 78 =

13 + 0 =

5 + 22 =

7+6=

51 + 15 =

2 + 89 =

8 + 25 =

33 + 33 =

66 + 11 =

14 + 14 =

24 + 13 =

15 + 10 =

7 + 14 =

36 + 3 =

29 + 9 =

88 + 11 =

22 + 11 =

55 + 45 =

9+1=

86 + 7 =

25 + 4 =

4 + 36 =

10 +10 =

84 + 12 =

2 + 24 =

98 + 2 =

82 +9 =

25 + 35 =

18 + 81 =

15 + 6 =

56 + 7 =

3+3=

2 + 38 =

16 + 6 =

71 + 17 =

8+8=

21 + 31 =

35 + 41 =

44 + 4 =

11 + 14 = 7+7= 51 + 5 =

8+6=

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3 + 27 =

STUDENT NAME

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40 + 50 = 16 + 16 = 5+5=

20 + 80 = 17 + 21 =

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5 + 31 = 9+9=

50 +1 =

56 + 6 =

77 + 7 =

14 + 15 = 10 +85 =

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99 + 0 =

Each 3 x 2 box, row and column has to contain all the numbers 1 to 6. 6

4 3

3 2

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1 4

3 6

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 six digits.

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

Answers

ew i ev Pr

Teac he r

Place value Trading Problem solving

1. (a) 512

(b) 601

(d) 5432

(e) 2132

2. (a) 413

(b) 515

(d) 3526

(e) 12 012

3. (a) 275

(b) 155

(d) 2346

(e) 22 183

4. (a) 879

(b) 1349

(d) 15 589

(e) 221 866

6. (a) 474 505

500 (d) 2749 (e) 7414 – 137 – 1739 – 4285 363 1010 3129

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(f) 35 352 (g) 9000 (h) 101 101 – 13 069 – 6957 – 30 725 22 283 2043 70 376

Primary mathematics: Back to basics

(e) 59 375

(b) 516 908

7. (a) 256 (b) 651 (c) – 172 – 143 84 508

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(d) 2054

m . u

5. (a) 169

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SUBTRACTION NUMBER 1.

747

(b)

846

(c)

6458

(d)

9999

(e)

– 235

– 245

– 2135

– 4567

(a)

652

(b)

873

(c)

4764

(d)

8983

– 239

– 358

– 2428

– 5457

(a)

434

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

613

(c)

6412

(d)

7423

– 3285

– 5077

Teac he r

– 458

3461

(b)

6214

(c)

24 134

(d)

54 127

– 2582

– 4865

– 22 699

– 38 538

(a)

400

(b)

1300

(c)

6000

– 14 569

35 241 – 12 058

(e)

26 581

ew i ev Pr

– 159

(a)

– 12 743

(e)

14 875

(e)

(d)

10 000

427 361

– 205 495

(e)

– 695

– 2467

– 7 946

100 000

– 40 625

6. (a) Subtract 25 495 from half a million.

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m . u

STUDENT NAME

(a)

(b) Subtract 483 092 from one million.

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7. Find the missing numbers.

(a)

(b)

5 6

– 1 7

–

8 4

(f)

3 5

–

4 3

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–

3 7

(d)

– 1 7

3 6 3

(g)

3 0 6 9 2

(c)

6 5

– 6 9

2 0

4 1 4

– 4

0 1 0

(h)

(e)

3 1 2 9

0 1 –

0 1

7 2

7 0

Primary mathematics: Back to basics

SUBTRACTION PROBLEMS NUMBER

Teacher information Indicators Calculates and solves subtraction word 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. 217 females

ew i ev Pr

Teac he r

Place value Trading Problem solving

4. 1573 songs 5. 2287

6. 13 296

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m . u

7. 5949 votes 8. 14 699 9. 18 718

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10. 11 428 tickets 11. 121 524

o c . che e r o t r s super

12. 4 124 571

13. Teacher check word problem. 6345 – 4069 = 2276 14. Teacher check word problem. 5000 – 3849 = 1151

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SUBTRACTION PROBLEMS 2. At a school with 1865 students, 397 were in high school. How many were primary school students?

3. Ben needed to write a 1500 word essay. A word count check showed he had 987 words. How many more words did he need to write?

4. Out of a possible 2000, Kate has 427 songs on her iPod™. How many more songs can she download?

5. 8764 people attended a concert. If 6477 booked tickets, how many bought tickets on th e night?

6. 7943 people live in one town and 21 239 live in another. What is the difference in population?

7. One contestant received 24 055 votes and the other received 18 106. What was the difference?

8. 53 136 attended one match and 38 437 attended another. What was the difference?

Teac he r

1. 425 people met for a reunion. If there were 208 males, how many were females?

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

ew i ev Pr

9. Greensville has a population of 40 500. The closest town has 21 782 people. What is the difference in population?

Use a calculator.

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11. Subtract 128 476 from a quarter of a million.

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12. Subtract 875 429 from five million.

m . u

STUDENT NAME

NUMBER

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Write your own word problems using the numbers given. Set out and solve each problem. 13. 6345 – 4069

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14. 5000 – 3849

Primary mathematics: Back to basics

MENTAL SUBTRACTION NUMBER

Teacher information Indicator Shows proficiency with mental subtraction facts.

Concepts required

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

ew i ev Pr

Teac he r

Mentally subtracting one and two digits with answers less than 100 Using a code to solve problems

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o c . che e r o t r s super

1. 462 2. – 231 231

Primary mathematics: Back to basics

m . u

974 3. – 362 612

8734 – 6521 2213

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MENTAL SUBTRACTION NUMBER A

50 – 10 =

90 – 9 =

45 – 6 =

81 – 9 =

10 – 3 =

15 – 7 =

54 – 45 =

96 – 8 =

20 – 8 =

42 – 7 =

45 – 25 =

12 – 11 =

25 – 21 =

31 – 5 =

90 – 10 =

10 – 7 =

100 – 4 =

72 – 6 =

100 – 36 =

27 – 16 =

82 – 4 =

r o e t s Bo r e p ok u S 27 – 8 =

47 – 15 =

59 – 27 =

38 – 8 =

48 – 8 =

100 – 13 =

75 – 6 =

41 – 31 =

60 – 6 =

34 – 8 =

66 – 37 =

15 – 9 =

31 – 11 =

60 – 30 =

90 – 20 =

62 – 42 =

72 – 9 =

75 – 9 =

100 – 52 =

52 – 2 =

22 – 12 =

100 – 10 =

21 – 3 =

14 – 6 =

49 – 7 =

19 – 4 =

50 – 22 =

75 – 15 =

66 – 36 =

84 – 12 =

42 – 24 =

42 – 6 =

31 – 13 =

28 – 15 =

7–0=

20 – 9 = 100 – 40 =

50 – 17 =

100 – 50 =

70 – 35 =

ew i ev Pr

Teac he r

37 – 14 =

66 – 11 =

20 – 7 =

37 – 0 =

33 – 23 =

68 – 17 =

12 – 9 =

73 – 7 =

67 – 7 =

25 – 10 =

40 – 20 =

77 – 7 =

80 – 40 =

98 – 89 =

92 – 12 =

36 – 15 =

32 – 4 =

60 – 25 =

20 – 13 =

44 – 11 =

100 – 49 =

25 – 25 =

56 – 8 =

17 – 6 =

65 – 15 =

60 – 12 =

80 – 10 =

58 – 37 =

57 – 16 =

44 – 24 =

90 – 1 =

100 – 8 =

17 – 8 =

14 – 3 =

63 – 9 =

20 – 6 =

8–7=

25 – 18 =

76 – 9 =

28 – 18 =

50 – 1 =

54 – 6 =

100 – 99 =

85 – 35 =

100 – 21 =

75 – 20 =

72 – 12 =

90 – 45 =

15 – 8 =

81 – 9 =

99 – 11 =

16 – 8 =

90 – 4 =

82 – 8 = 14 – 5 =

29 – 19 =

45 – 35 = 25 – 19 =

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33 – 23 = 57 – 8 =

54 – 9 =

m . u

STUDENT NAME

21 – 7 =

19 – 11 =

67 – 46 =

o c . che e r o t r s super

Use the code to solve each. 1

–

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Primary mathematics: Back to basics

MULTIPLICATION NUMBER

Teacher information Indicators Understands the role of place value when multiplying numbers. Calculates multiplication problems by one and two digits.

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

Answers

ew i ev Pr

Teac he r

Place value Trading Problem solving

1. (a) 99

(b) 156

(d) 155

(e) 88

(f) 306

2. (a) 92

(b) 220

(d) 280

(e) 511

(f) 420

3. (a) 402

(b) 729

(d) 1524

(e) 2030

(f) 2680

4. (a) 7239

(b) 7296

(d) 12 216

(e) 33 744

5. (a) 1155

(b) 726

(d) 2240

(e) 3450

6. (a) 2352

(b) 2948

(d) 8625

(e) 23 276

7. (a) 340 (b) 608 or 603 (c) 399 x 2 x 4 x 4 x6 680 2432 2412 2394

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(d) 45 (e) 406 x 22 x 34 90 1 624 900 12 180 990 13 804

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Primary mathematics: Back to basics

m . u

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MULTIPLICATION NUMBER 1.

(b)

(c)

(d)

(e)

(f)

x 3

x 4

x 5

x 2

(a)

(b)

(c)

(d)

(e)

x 4

x 5

x 4

x 5

x 7

(a)

134

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

243

(c)

352

(d)

508

(e)

x 3

x 4

x 3

Teac he r

x 3

(a)

2413

(b)

1824

(c)

2605

(d)

x 3

x 4

x 5

(a)

406

(f)

670

x 5

3054

(e)

5624

x 4

(b)

(c)

(d)

(e)

x 22

x 13

x 35

w ww (a)

112

(b)

134

(c)

232

(d)

345

x 21

Find the missing numbers.

(a)

(b)

x 2 8

(c)

0 x 4 2

(d)

4 x

2 3 9

(e)

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x 46

x 3 4

1 2 3

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506

x 25

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x 31

x 46

(e)

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x 22

x 21

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(f)

STUDENT NAME

(a)

1 8 8

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. 212 mm 2. 510 books 3. 2920 days 4. 2583 pages

ew i ev Pr

Teac he r

Place value Trading Problem solving

(b) 27 888 m

6. 17 500 words 7. 1176 pages

8. 1344 words

10. 23 360 km

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11. 29 896 m2 12. Teacher check word problem. 2415 x 5 = 12 075

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13. Teacher check word problem. 75 x 35 = 2625

Primary mathematics: Back to basics

m . u

9. 7590 loaves

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MULTIPLICATION PROBLEMS 1. Each side of a square measures 53 mm. What is the perimeter?

NUMBER 2. Six boxes each held 85 books. How many books were there altogether?

4. Each of nine books had exactly 287 pages. How many pages in total?

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

6. Ten students each wrote a 1750 word story to enter a competition. How many words did the judge have to read?

7. If there were 98 pages in each magazine, how many pages in total for 12 magazines?

Teac he r

5. (a) A running track is 498 m long. If an athlete ran the track eight times in one session, how many metres did he run?

ew i ev Pr

(b) How many metres would the athlete cover in seven training sessions?

10. Steve travelled 584 km each week. Find the total km travelled in 40 weeks.

11. What is the area of an outdoor space 808 m long and 37 m wide?

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8. If there was an average of 14 words printed on one line, how many words would there be on a page with 96 lines?

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m . u

STUDENT NAME

3. How many days in eight years? (No leap years)

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Write your own word problems using the numbers given. Set out and solve each problem. 12. 2415 x 5

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13. 75 x 35

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Primary mathematics: Back to basics

MENTAL MULTIPLICATION NUMBER

Teacher information Indicator Shows proficiency with mental multiplication facts.

Concepts required

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

Answers A

100

ew i ev Pr

Teac he r

Mentally multiplying up to and including 12 x table Calculator use Crossword format

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120

132

110

144

121

m . u

o c . che e r o t r s super 21

108

110

108

132

120

Teacher check crossword

Primary mathematics: Back to basics

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MENTAL MULTIPLICATION A

12 x 1 =

6x4=

11 x 3 =

8 x 12 =

8x1=

9x3=

8x5=

10 x 10 =

11 x 7 =

12 x 4 =

6x6=

10 x 4 =

9x6=

6x2=

6 x 10 =

8x7=

3x4=

5x1=

12 x 10 =

7x5=

10 x 9 =

12 x 7 =

7x8=

5 x 11 =

9x1=

5x8=

4x7=

8x2=

6 x 12 =

9x4=

8x9=

3 x 12 =

11 x 6 =

3x8=

2 x 12 =

9 x 10 =

5x2=

7x2=

12 x 2 =

4 x 11 =

8 x 11 =

4x3=

11 x 12 =

7x4=

10 x 6 =

5x4=

11 x 9 =

3x2=

10 x 11 =

12 x 6 =

2x8=

10 x 1 =

11 x 2 =

10 x 3 =

8x8=

9x2=

4x8=

2 x 12 =

4 x 12 =

3x6=

6x8=

8x4=

6x7=

7 x 12 =

3x9=

4x1= 3x3= 11 x 5 =

7x6=

12 x 12 = 4x2=

7 x 10 = 3x1=

11 x 11 =

8x3=

12 x 5 =

2 x 10 =

4x4=

10 x 5 =

7x7=

12 x 9 =

7x9=

5 x 10 =

11 x 10 =

5x5=

6x3=

5x3=

10 x 2 =

6x5=

9 x 12 =

5x9=

9x5=

6x1=

7x1=

4 x 10 =

10 x 8 =

6 x 11 =

12 x 8 =

4x9=

12 x 3 =

7x3=

3x5=

5x7=

3 x 11 =

6x9=

8 x 10 =

10 x 12 =

11 x 8 =

4x5=

9x7=

5 x 12 =

9 x 11 =

3x7= 4x6=

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12 x 11 = 10 x 7 =

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2x9= 9x8=

m . u

9x9=

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Teac he r

3 x 10 = STUDENT NAME

NUMBER C

5x6=

7 x 11 = 8x6=

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11 x 1 =

Create your own multiplication crossword. Use a calculator to help. Across

Down

11.

12.

10.

13.

11.

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11.

13.

Primary mathematics: Back to basics

DIVISION NUMBER

Teacher information Indicators Calculates division problems up to four 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) 142

(b) 231

(d) 32

(e) 51

2. (a) 2003

(b) 1060

(d) 802

(e) 302

3. (a) 183

(b) 293

(d) 1173

(e) 652

4. (a) 32r 4

(b) 298 r1

(d) 33 r1

(e) 197 r1

5. (a) 482 r2

(b) 327 r1

(d) 2334 r1

(e) 892 r2

ew i ev Pr

Teac he r

Concepts required

7. 96 students

m . u

8. 2300 books

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9. 250 brochures 10. 930 m

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11. 155 cm 12. $875

13. $156.25

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14. Teacher check word problem. 265 ÷ 5 = 53

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DIVISION NUMBER 1. (a) 2 284

(b) 3 693

(d) 4 128

(e) 5 255

2. (a) 4 8012

(b) 6 6360

(d) 3 2406

(e) 7 2114

3. (a) 4 732

Teac he r 5. (a) 7 3376

(d) 4 4692

(e) 7 4564

(b) 2 597

(d) 8 265

(e) 4 789

(b) 6 1963

(d) 4 9337

ew i ev Pr (e) 3 2678

6. 205 books were placed equally on five shelves. How many books were on each shelf?

7. 384 students were divided into four factions. How many were in each faction?

8. A publisher sent 9200 books to four stores. How many books did each store receive?

9. 2000 brochures need to be delivered. If there are eight people, how many will each deliver?

10. During training, an athlete covered 5580 m over six days. What distance did he average each day?

11. Nine people had a combined height of 1395 cm. What was the average height?

12. $3500 was shared among four charities. How much did each receive?

13. James had a total of $1250 to spend over an eight-day trip. What average amount could he spend each day?

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. te

m . u

STUDENT NAME

4. (a) 6 196

r o e t s Bo r e p ok u S (b) 3 879

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14. Write your own word problem for 265 ÷ 5. Set out and solve the problem.

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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 Materials needed Calculator

Answers A

ew i ev Pr

Teac he r

Mentally dividing up to and including by 12 Crossword format

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. te

m . u

o c . che e r o t r s super

Teacher check crossword. Primary mathematics: Back to basics

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MENTAL DIVISION A

120 ÷ 12 =

36 ÷ 9 =

110 ÷ 11 =

12 ÷ 6 =

45 ÷ 9 =

42 ÷ 7 =

60 ÷ 10 =

56 ÷ 7 =

40 ÷ 10 =

120 ÷ 10 =

108 ÷ 9 =

55 ÷ 11 =

32 ÷ 8 =

132 ÷ 12 =

42 ÷ 6 =

60 ÷ 5 =

30 ÷ 3 =

18 ÷ 6 =

24 ÷ 4 =

21 ÷ 7 =

77 ÷ 11 =

54 ÷ 6 =

72 ÷ 12 =

30 ÷ 5 =

88 ÷ 11 =

48 ÷ 8 =

21 ÷ 3 =

90 ÷ 9 =

10 ÷ 5 =

24 ÷ 2 =

90 ÷ 10 =

44 ÷ 4 =

14 ÷ 2 =

8÷4=

20 ÷ 2 =

14 ÷ 7 =

64 ÷ 8 =

144 ÷ 12 =

45 ÷ 5 =

36 ÷ 12 =

27 ÷ 3 =

36 ÷ 3 =

28 ÷ 7 =

18 ÷ 3 =

72 ÷ 6 =

63 ÷ 7 =

84 ÷ 7 =

6÷2=

80 ÷ 8 =

24 ÷ 12 =

8÷2=

22 ÷ 11 =

63 ÷ 9 =

33 ÷ 3 =

24 ÷ 8 =

9÷9=

6÷3=

81 ÷ 9 =

40 ÷ 4 =

30 ÷ 6 =

10 ÷ 2 =

48 ÷ 6 =

121 ÷ 11 =

99 ÷ 9 =

99 ÷ 11 =

36 ÷ 6 = 88 ÷ 8 = 110 ÷ 10 =

25 ÷ 5 =

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

ew i ev Pr

Teac he r

32 ÷ 4 =

55 ÷ 5 =

96 ÷ 12 = 12 ÷ 4 =

49 ÷ 7 = 16 ÷ 8 =

20 ÷ 10 =

12 ÷ 12 =

4÷2=

10 ÷ 10 =

48 ÷ 4 =

66 ÷ 6 =

77 ÷ 7 =

15 ÷ 5 =

54 ÷ 9 =

108 ÷ 12 =

18 ÷ 2 =

35 ÷ 5 =

22 ÷ 2 =

11 ÷ 11 =

18 ÷ 9 =

48 ÷ 12 =

40 ÷ 5 =

100 ÷ 10 =

28 ÷ 4 =

12 ÷ 3 =

72 ÷ 9 =

84 ÷ 12 =

24 ÷ 3 =

50 ÷ 10 =

44 ÷ 11 =

9÷3=

20 ÷ 4 =

72 ÷ 8 =

12 ÷ 2 =

16 ÷ 4 =

33 ÷ 11 =

50 ÷ 5 =

66 ÷ 11 =

70 ÷ 7 =

35 ÷ 7 =

27 ÷ 9 =

40 ÷ 8 =

60 ÷ 12 =

20 ÷ 5 =

60 ÷ 6 =

16 ÷ 2 = 56 ÷ 8 =

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15 ÷ 3 =

70 ÷ 10 =

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36 ÷ 4 =

80 ÷ 10 =

m . u

STUDENT NAME

NUMBER C

30 ÷ 10 = 24 ÷ 6 =

132 ÷ 11 =

o c . che e r o t r s super

96 ÷ 8 =

Create your own division crossword. Use a calculator to help.

Across

Down

11.

12.

10.

13.

11.

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13.

Primary mathematics: Back to basics

FRACTIONS NUMBER

Teacher information Indicators Represents fractions. Writes equivalent fractions. Adds and subtracts whole numbers and fractions. Simplifies and orders fractions.

r o e t s Bo r e p ok u S Fractional parts Equivalent fractions Common denominators Using < and > signs Simplifying fractions Rounding Problem solving

ew i ev Pr

Teac he r

Concepts required

Answers

(e) 2/2

(f) 4/10

3. (a) <

(e) >

(f) <

(b) >

4. (a) 4/8 = 1/2

(b) 3/6 = 1/2

(e) 74/6 = 72/3

(f) 76/8 = 73/4

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

(b) 5/10 = 1/2

(e) 12/4 = 11/2

(f) 26/8 = 23/4

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6. (a) 2 7. 5

8. $75

(b) 5

(d) =

(d) 35/5 = 4

(d) 32/6 = 31/3

(d) 6

(e) 4

(f)

m . u

2. Answers may vary. Possible answers— (a) 2/4 (b) 4/6 (c) 3/4 (d) 1/3

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9. 3 1/4 metres 10. 4 litres

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FRACTIONS NUMBER

1. Represent each of the following. /4

1 1/2

2. Write an equivalent fraction for each. (a) (e)

/2 =

(b)

(f)

(e) 3/4

Teac he r

/3 =

(c)

/8 =

(d)

/12 =

/5 =

/10

(c)

(d) 5/10

4. Add each, then simplify the answer.

(a)

/8 + 3/8 =

(b)

/6 + 2/6 =

(d) 1 3/5 + 2 2/5 =

(e) 4 1/6 + 3 3/6 =

(f) 5 4/8 + 2 2/8 =

5. Subtract each, then simplify the answer.

(a)

/8 – 3/8 =

(b) 9/10 – 4/10 =

(c)

/6 – 3/6 =

(d) 5 3/6 – 2 1/6 =

(e) 4 3/4 – 3 1/4 =

(f) 6 7/8 – 4 1/8 =

6. Round each to the nearest whole number.

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(a) 1 3/4

(b) 5 3/8

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(d) 5 6/7

(e) 4 2/6

7. In a class of 20, 3/4 were girls. How many were boys?

m . u

ew i ev Pr

(f)

(a) 1/4

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3. Use <, > or =.

STUDENT NAME

(b)

(f) 8 4/5

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8. Molly saved 1/4 of her $100 birthday money. How much did she spend?

9. Ruby had 5 1/2 metres of fabric. If she used 2 1/4 metres, how much did she have left?

10. Kayde used 2 3/4 litres of white paint and 1 1/4 litres of blue paint. How many litres did he use altogether?

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Primary mathematics: Back to basics

DECIMALS NUMBER

Teacher information Indicators Rounds decimals to the nearest whole number and one decimal place. Writes equivalent decimals for fractions. Adds and subtracts decimals to three decimal places.

r o e t s Bo r e p ok u S Place value Rounding Whole numbers and parts of whole numbers Equivalent decimals and fractions Addition and subtraction with trading

Answers

1. (a) 9 (f) 6

(b) 11 (g) 8

(d) 48 (i) 16

(e) 51 (j) 21

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Concepts required

(d) 18.2 (i) 24.9

(e) 20.1 (j) 213.0

3. (a) 0.5 (f) 2.1

(b) 0.45 (g) 3.5

(d) 0.25 (i) 5.75

(e) 0.20 (j) 8.25

4. (a) 8.3 (f) 79.19

(b) 29.5 (g) 108.80

(d) 81.6 (i) 16.281

(e) 458.7 (j) 121.723

(b) 10.6 (g) 25.05

(d) 5.3 (i) 1.849

(e) 60.6 (j) 19.439

5. (a) 6.8 (f) 12.86

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Primary mathematics: Back to basics

m . u

(b) 8.8 (g) 42.1

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2. (a) 2.5 (f) 34.5

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DECIMALS NUMBER 1. Round these decimals to the nearest whole number.

(a) 8.7 =

(b) 11.1 =

(d) 47.7 =

(e) 50.5 =

(f) 6.44 =

(g) 8.01 =

(h) 12.75 =

(i) 15.50 =

(j) 21.21 =

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(a) 2.51 =

(f) 34.45 =

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(b) 8.79 =

(d) 18.15 =

(e) 20.05 =

(g) 42.11 =

(h) 45.95 =

(i) 24.89 =

(j) 212.95 =

3. Write an equivalent decimal for these fractions.

(a)

/10 =

(f) 2 1/10 =

(b)

/100 =

(c)

(g) 3 1/2 =

/4 =

(d)

(h) 7 7/10 =

/4 =

(i) 5 75/100 =

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/100 =

(j) 8 25/100 =

4. Add the following decimal numbers.

(a)

5.8

(c)

24.8

(d)

51.7

(e)

+ 16.9

+ 25.8

+ 29.9

32.51

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(f)

12.6

+ 2.5

(b)

(g)

+ 46.68

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79.84

(h)

+ 28.96

0.781

(i)

+ 0.597

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STUDENT NAME

2. Round these to one decimal place.

9.684

+ 6.597

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(j)

260.8 + 197.9

72.758 + 48.965

5. Subtract the following decimal numbers.

(a)

9.3

(b)

27.4

(c)

50.6

(d)

64.2

(e)

– 2.5

– 16.8

– 28.8

– 58.9

(f)

27.42

(g)

60.60

(h)

7.045

(i)

9.701

(j)

– 14.56

– 35.55

– 4.156

– 7.852

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125.4 – 64.8

42.505 – 23.066

Primary mathematics: Back to basics

PERCENTAGES NUMBER

Teacher information Indicators Compares, orders and writes percentages relating to decimals and fractions. Calculates percentage of dollar amounts.

r o e t s Bo r e p ok u S Solves percentage problems.

Equivalent percentages, fractions and decimals Ordering Reading and solving word problems

Answers

(a) 100% (c) 1% (e) 5% (g) 50% (i) 80% (k) 20%

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

1.0 0.01 0.05 0.50 0.80 0.20

/100 1 /100 5 /100 1 /2 80 /100 20 /100

(b) 30% (d) 75% (f) 25% (h) 10% (j) 125% (l) 150%

100

0.30 0.75 0.25 0.10 1.25 1.50

/100 /100 1 /4 10 /100 125 /100 or 11/4 150 /100 or 11/2 30 75

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Concepts required

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3. (a) $30 (f) $60

(b) $6 (g) $60

(d) $8 (i) $20

(e) $110

4. $125

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5. 60

6. (a) $16

o c . che e r o t r s super (b) $64

7. (a) $4.50

(b) $18.00

(d) $90.00

8. (a) $9.00

(b) $18.00

(d) $90.00

Primary mathematics: Back to basics

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2%, 7%, 25%, 37%, 45%, 89%, 90%, 100% 0.25, 30%, 0.5, 55%, 80%, 98%, 0.99, 1.0 7 /100, 17/100, 20/100, 37%, 60%, 70/100, 75%, 77% 2 /100, 12/100, 20%, 22%, 0.25, 0.28, 50%, 0.52

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PERCENTAGES NUMBER 1. Complete the table to show each equivalent percentage, decimal and fraction. Percentage

Decimal

100%

1.0

(a)

Fraction

(d) (e)

/100

0.50 10%

(i)

r o e t s Bo r e p ok u S 0.75

(j)

0.05

(k)

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(h)

Fraction

/100

1.25

20%

(l)

2. Order these from smallest to largest

(a) 90%, 25%, 7%, 100%, 89%, 45%, 37%, 2%

(b) 0.5, 80%, 0.25, 1.0, 55%, 30%, 0.99, 98%

(d) 0.25, 20%, 2/100, 12/100, 0.52, 50%, 22%, 0.28

11/2

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3. Complete the following. 50% of $60 =

(b)

25% of $24 =

(c)

(d)

20% of $40 =

(e) 50% of $220 =

(f) 60% of $100 =

(h)

(i)

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(a)

(g) 30% of $180 =

20% of $60 =

4. Riley needs to save $250. If she already has 50%, how much has she saved?

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75% of $20 =

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STUDENT NAME

(f)

Decimal

(g)

(b) (c)

Percentage

40% of $50 =

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5. Mr Russell had 100 students in his group. If 40% were girls, what number of boys were in the group?

6. An item was marked 20% off the regular price of $80. (a) How much was the discount? (b) What was the new price?

7. The following prices were reduced by 10%. Find the new price for each. (a) $5.00

(b) $20.00

(d) $100.00

8. The following prices were reduced by 25%. Find the new price for each. (a) $12.00 R.I.C. Publications®

(b) $24.00

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(d) $120.00 Primary mathematics: Back to basics

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

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

Answers

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Concepts required

1. (a) $1046.25 (d) $94 031.79

(b) $5294.54

(b) $511.85

2 (a) $20.65 (d) $1157.06

4. $1 520 750 5. $710.51

6. $145 225

8. $10 620

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9. $29 920 10. $211.40

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11. (a) $150 (d) $488.55

(b) $399.50

12. (a) $460 (d) $990.75

(b) $374.50

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7. $594

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13. Answers will vary.

Primary mathematics: Back to basics

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MONEY 1.

$748.75

(b)

$38 406.95

(d)

+ $297.50

+ $2695.55

+ $22 595.59

(a)

$48.20

(b)

$749.50

(c)

$804.65

+ $38 955.99

(d)

– $27.55

– $237.65

– $716.99

$5000.05 – $3842.99

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3. Over a four-month period, Shenay received the following mobile phone accounts — $42.75, $59, $48.25 and $39.55. What was the total?

4. An investor has properties worth $429 000, $358 750, $410 500 and $322 500. What is the total value?

5. Jess has a $2000 credit card limit. Her last statement shows purchases totalling $1289.49. How much credit does she have left?

6. The Harris family decided to purchase a new home for $565 000. If they sold their current home for $419 775, how much did they borrow?

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$55 075.80

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9. Three charities were to benefit equally from $89 760. How much did each charity receive?

10. Cassie saved $1268.40 over six months. How much did she save each month?

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7. Lucas paid a flat rate of $49.50 a month for his mobile phone. How much did he pay in a year?

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STUDENT NAME

(a)

NUMBER $2598.99 (c)

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11. Find the change from $500. (a) $350

(b) $100.50

(d)

$11.45

(d)

$9.25

12. Find the change from $1000. (a) $540

(b) $625.50

13. What would you like to buy if you had: (a) $20?

(b) $100?

(d) $10 000?

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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

Answers

1. (a) $529.25 (b) $470.75 2. (a) $13 125 (b) $3975

3. (a) 3472 km (b) 6366 km (c) 35 061 km (d) 14 939 km

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Addition, subtraction, multiplication and division of whole numbers and decimal numbers Place value Problem solving Reading tables

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Primary mathematics: Back to basics

(b) 45 108

(d) 22 813

(e) 1890

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4. (a) 44 721

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MIXED PROBLEMS NUMBER

1. (a) Find the total of these accounts: $42.78, $27.30, $105.45, $285 and $68.72.

(b) How much remains from $1000 after paying the accounts?

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2. 525 adults paid $25 a ticket to attend a show. 265 children paid $15 a ticket.

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(a) What was the total of adult sales?

(b) What was the total of children sales?

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3. Before setting off on a trip, the car odometer read 28 695 km. After a week of travelling, the odometer read 32 167.

(a) How many km were travelled the first week?

(b) If 2894 km were covered the second week, how many km were travelled in total?

(d) How many more km have to be travelled to reach 50 000 on the odometer?

4. Use the table which shows results of a local election to answer the questions.

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Candidate

Fraser

Martino Atkins

Sheldon Wilson

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No. of votes

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STUDENT NAME

(a) Find the total number of votes.

4799 21 908 6766

o c . che e r o t r s super 2909 8339

(b) If there were 387 invalid votes, how many people voted altogether?

(d) How many voted against the winner? (Ignore the invalid votes.)

(e) What is the difference in the number of votes between the two candidates who polled the lowest?

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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 Answers

132

110

100

144

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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 Magic square format Codes

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Concepts required

Primary mathematics: Back to basics

(b) 407 293 + 828 689 1 235 982

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2. (a) 83 077 – 54 388 28 689

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MIXED MENTAL A

10 + 7 =

32 ÷ 4 =

2 x 12 =

3x3=

9x3=

60 – 20 =

41 – 6 =

82 – 5 =

120 ÷ 12 =

51 + 5 =

6x6=

8+6=

63 ÷ 7 =

6x5=

48 ÷ 4 =

36 – 9 =

12 x 1 =

50 – 12 =

20 – 9 =

3x7=

88 ÷ 8 =

24 ÷ 12 =

32 + 11 =

5 + 40 =

73 + 8 =

80 – 4 =

8x7=

43 – 34 =

25 ÷ 5 =

25 + 10 =

6 + 32 =

84 ÷ 12 =

7x6=

90 +9 =

88 – 8 =

5 + 36 =

15 – 7 =

65 – 20 =

43 + 0 =

81 – 8 =

80 ÷ 10 =

56 ÷ 8 =

55 – 6 =

10 x 9 =

79 + 12 =

12 x 6 =

32 – 4 =

10 x 3 =

52 – 32 =

15 – 6 =

20 ÷ 4 =

60 ÷ 5 =

96 ÷ 8 =

50 + 20 =

42 – 2 =

85 – 15 =

16 ÷ 2 =

81 ÷ 9 =

108 ÷ 9 =

4x6=

8 + 29 =

13 – 9 =

4x9=

20 ÷ 10 =

88 – 11 =

21 + 9 =

38 – 14 =

40 ÷ 8 =

11 x 10 =

10 – 7 =

5x7=

16 + 9 =

27 + 4 =

40 ÷ 5 =

78 + 11 =

35 – 25 =

11 x 5 =

60 ÷ 6 =

8x4=

97 + 3 =

13 + 6 =

32 + 33 =

5x4=

56 – 8 =

9x8=

33 ÷11 =

110 ÷10 =

44 ÷ 4 =

3 + 27 =

35 ÷ 5 =

8 + 26 =

55 – 35 =

15÷ 5 =

55 ÷ 11 =

48 ÷ 6 =

12 x 12 =

9–8=

48 ÷ 12 =

100 – 40 = 11 + 14 = 3 x 10 =

42 ÷ 7 =

12 x 11 = 33 ÷ 3 = 7+7=

39 – 19 =

77 ÷ 11 =

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8x6=

54 + 4 = 9x9=

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5 x 10 =

9x1=

100 – 9 = 36 ÷ 6 =

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7+7=

99 + 0 =

15 + 16 =

132 ÷ 11 =

12 x 4 =

45 – 25 =

1. Place the numbers 10 – 18 in a square so each row, column and diagonal adds up to 42.

65 – 15 =

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14 + 0 =

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Teac he r

16 – 8 =

STUDENT NAME

NUMBER C

9+9= 4x5=

2. Use the code to solve the problems.

(a)

RWZSS

(b) VZSXQW

17 14

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– UVWRR

+ RXRTRQ

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Primary mathematics: Back to basics

NUMBER SENTENCES AND PATTERNS NUMBER

Teacher information Indicators Continues and completes number patterns by following set rules. Recognises and writes missing components in number sentences.

r o e t s Bo r e p ok u S Rules and patterns Use of <, > and = signs Using brackets first in any number sentence Fractions, decimals, percentages

Answers

1. (a) 18 (d) 230

(b) 46 (e) 1098

2. (a) 7 (d) 71

(b) 18 (e) 365

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Teac he r

Concepts required

16, 32, 64, 128, 256 – Double each number 16, 25, 36, 49, 64 – Add on by odd numbers 9, 8, 11, 10, 13 – Add 3, subtract 1 16, 64, 32, 128, 64 – Halve, multiply by 4

4. (a) > (d) < (g) <

(b) = (e) > (h) >

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5. (a) (7 x 3) + 4 = 25 (c) (3 x 3) + (10 –3) > 15 (e) (11 – 7) x (36 ÷ 12) = 12

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(b) 8 + (3 x 5) < 25 (d) (30 x 5) – 50 = 100 (f) (24 ÷ 8) x (8 – 6) = 6

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6. (a) false (d) true (g) false

(b) false (e) true (h) true

7. Answers will vary.

Primary mathematics: Back to basics

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NUMBER SENTENCES AND PATTERNS NUMBER 1. Double each number.

(a)

(b)

23 =

(e) 549 =

(f) 3425 =

(d) 115 =

(d) 142 =

2. Halve each number.

(a) 14 =

(b)

36 =

(e) 730 =

(f) 5550 =

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(a) 1, 2, 4, 8,

(b) 0, 1, 4, 9,

(d) 8, 4, 16, 8, 32,

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, ,

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4. Use <, > or = to make these number sentences true.

(a) 8 + 2

6.75 + 1.25

(d) 20% of 100

(g) (20 – 16) x 11

(b) 75%

0.75

4 x 10

(f) 3 x (6 + 2)

(e) 50 x 50

(h) 2.5

250

25%

(i) 72

6 + (9 x 7)

5. Add brackets to make these number sentences true. (a) 7 x 3 + 4 = 25

(b) 8 + 3 x 5 < 25

(d) 30 x 5 – 50 = 100

(e) 11 – 7 x 36 ÷ 12 = 12

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6. Write true or false.

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(a) 19 – 6 = 12

(d) /2 + /4 = 0.75

(g) (6 x 4) + 18 < 40

(i) 0.42 + 0.58 < 100

(f) 24 ÷ 8 x 8 – 6 = 6

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STUDENT NAME

3. Complete these number sequences. Write the rule.

(b) 91 x 0 = 91

(e) 7 x 8 > 55

(f) 25% of 100 > 25

(h) (9 x 9) + 9 = 9 + (9 x 9)

7. Write a number sentence to equal each number. Use each of the four operations in each number sentence.

(a) 40 =

(b) 100 =

(d) 201 =

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Primary mathematics: Back to basics

SPECIAL NUMBERS NUMBER

Teacher information Indicators Identifies prime, composite, negative, roman and square numbers. Writes factors to represent numbers in power form.

r o e t s Bo r e p ok u S Prime numbers Composite numbers Negative numbers Roman numerals Square numbers Numbers in power form

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Concepts required

Answers

1. (a) Prime numbers are — 2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 51, 53, 57, 59, 61, 67, 73, 79, 83, 87, 89, 91, 97. (b) Composite numbers are all other numbers except 1. (c) 50 (d) 50 (e) Answers may vary (4, 8, 12, 16, 20, 24, 28, 32) (f) Answers may vary (7, 14, 21, 28, 35, 42, 49, 56)

4. (a) XXVI (b) XXXII (c) LIV (f) CL (g) LD (h) DI (k) CMXCIX (l) MXXIV (m) MMM

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(d) 15 (i) 100 (n) 950

(e) 20 (j) 115 (o) 2100

(d) CXXI (i) M (n) MMXL

(e) LXVI (j) CCCXLIX (o) MMML

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3. (a) 3 (f) 50 (k) 99

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5. 52 = 25, 62 = 36, 72 = 49, 82 = 64, 92 = 81 6. (a) 53 = 5 x 5 x 5 = 125

(b) 24 = 2 x 2 x 2 x 2 =16

7. (a) 36 (f) 66

(b) 503

(d) 124

(e) 1002

(b) 103

(d) 105

(e) 106

8. (a) 102

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SPECIAL NUMBERS NUMBER 1. (a) Shade the prime numbers blue.

(b) Shade the composite numbers green.

(d) How many odd numbers?

(e) Write 8 numbers divisible by 4.

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

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51 52 53 54 55 56 57 58 59 60

(f) Write 8 numbers divisible by 7.

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

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2. Give an example when negative numbers might be used.

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

3. Write the number for these Roman numerals.

(a)

III

(b)

(c)

XII

(d)

(f)

(g) LXX

(h)

(i)

(k) XCIX

(l) MC

(m) MCM

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(e)

(j)

CXV

(n) CML

(o) MMC

(e)

4. Write the Roman numerals for these numbers. (a)

(b)

(c)

(d) 121

(f)

150

(g) 450

(h)

501

(i) 1000

(k) 999

(l) 1024

(m) 3000

(n) 2040

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5 = 2

6. (a) 53 =

(j)

(o) 3050

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5. If 22 = 4, 32 = 9 and 42 = 16, find the next five square numbers. ,

(b)

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STUDENT NAME

349

24 =

(b) 50 x 50 x 50 is

7. Write these numbers in power form.

(a) 3 x 3 x 3 x 3 x 3 x 3 is

(d) 12 x 12 x 12 x 12 =

(e) 100 x 100 is

8. Write these numbers as powers of 10.

(a) 100

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(b) 1000

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(d) 100 000

(e) 1 000 000

Primary mathematics: Back to basics

LINES AND ANGLES SPACE

Teacher information Indicator Identifies and draws different lines and angles.

Concepts required

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

1. Teacher check 2. Teacher check 3. (a) 90° (d) less 4.

(a) (d) (g) (h)

(b) 180° (e) reflex

4 right angles (b) 3 acute angles 6 obtuse angles (e) 8 obtuse angles 2 obtuse and 2 acute angles 2 obtuse and 2 acute angles

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Line types—vertical, horizontal, parallel, perpendicular, diagonal Angles—right, acute, obtuse, straight, reflex

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Primary mathematics: Back to basics

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LINES AND ANGLES

(a) vertical

(d) perpendicular

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(b) horizontal

r o e t s Bo r e p ok u S (e) diagonal

2. Draw each of the following types of angles.

(a) acute

(b) obtuse

(d) straight

(e) reflex

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3. Complete the following

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(a) A right angle equals

(b) A straight angle equals

than 90°.

(d) An acute angle is

angle is greater than 180°.

(f) An obtuse angle is

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STUDENT NAME

SPACE 1. Draw something that shows the following types of lines.

than 90°. than 180°.

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4. Mark and name the angles on each shape.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

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Primary mathematics: Back to basics

2-D SHAPES SPACE

Teacher information Indicator Identifies and represents 2-D shapes and their properties.

r o e t s Bo r e p ok u S Recognition of 2-D shapes Identifying properties of 2-D shapes Describing and drawing different types of triangles Using a compass to draw circles Identifying properties of circles

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Teac he r

Concepts required

Materials needed Compass Ruler

Answers

(b) rhombus (e) square

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2. Equilateral triangle—3 equal sides and 3 equal angles Isosceles triangle—2 equal sides and 2 equal angles Scalene triangle—0 equal sides and 0 equal angles

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radius centre

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diameter

circumference

4. (a) Teacher check circle (b) 6 cm

Primary mathematics: Back to basics

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2-D SHAPES SPACE 1. Uses words like ‘sides’, ‘angles’, ‘lines’, ‘equal’ and ‘parallel’ to write ‘What am I’ descriptions for each shape.

(a) What am I?

(b) What am I?

(d) What am I?

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

(e) What am I?

2. Draw each type of triangle and complete the description. Equilateral

equal sides and equal angles

(f) What am I?

Isosceles equal sides and equal angles

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Scalene

equal sides and equal angles

4. (a) Use a compass to draw a circle with a 3 cm radius.

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3. Label the circle.

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STUDENT NAME

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(b) What is the diameter?

Primary mathematics: Back to basics

3-D SHAPES SPACE

Teacher information Indicators Identifies 3-D shapes and their properties. Identifies cross-sections of 3-D shapes.

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

Answers

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

cube – 6, 12, 8 triangular prism – 5, 9, 6 cylinder – 3, 2, 0 square pyramid – 5, 8, 5 rectangular prism – 6, 12, 8 cone – 2, 1, 1 triangular pyramid – 4, 6, 4 pentagonal prism – 7, 15, 10

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

triangular prism cube rectangular pyramid cone

Answers may vary. (a) cylinder (b) cube (c) pyramid (d) prism

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Teac he r

Recognition of 3-D shapes Properties of 3-D shapes— faces, edges, vertices, nets, and cross-sections

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3-D SHAPES SPACE

1. Complete the table. Shape

Name

Faces

Edges

Vertices

(a)

cube (b)

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triangular prism

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cylinder

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(d)

square pyramid

(e)

(f)

cone (g)

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STUDENT NAME

(c)

triangular pyramid

(h)

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pentagonal prism

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2. Name the 3-D shapes that are represented by each net.

(a)

(b)

(c)

(d)

3. Name a 3-D shape that has the following cross-section.

(a)

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(c)

Primary mathematics: Back to basics

PERSPECTIVE AND TRANSFORMATIONS SPACE

Teacher information Indicators Draws objects from different perspectives. Rotates, reflects and translates images.

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

Answers

1. Teacher check

2 Teacher check

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Teac he r

Perspective—top, side and front views Changing shapes by rotating, reflecting and translating

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Primary mathematics: Back to basics

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PERSPECTIVE AND TRANSFORMATIONS SPACE 1. Sketch two different 3-D shaped objects. Draw the top, side and front view of each.

Teac he r

Top view

Side view

Front view

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

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2. Find an object from home and put it on the table in front of you. Draw the object from three different perspectives.

(a) As you are looking at it now.

(b) As if you were on the floor, looking up at it.

3. Rotate this pattern by making four quarter turns to the right.

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4. Reflect this picture.

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STUDENT NAME

3-D shape

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5. Translate this picture.

Primary mathematics: Back to basics

SYMMETRY SPACE

Teacher information Indicators Identifies and draws lines of symmetry. Identifies shapes with point and rotational 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)

(b)

(c)

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Recognising different lines of symmetry

(d)

(e)

(f)

(g)

(h)

(i)

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2. a, c, e, g 3. a, b, c, e

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4. Teacher check

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SYMMETRY SPACE 1. Draw lines of symmetry on each shape.

(a)

(b)

(c)

STUDENT NAME

Teac he r

(a)

(b)

(c)

(e)

(d)

(e)

(c)

(d)

(g)

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(a)

(d)

(f)

Shade the shapes that have rotational symmetry.

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

Shade the shapes that have point symmetry.

3. Shapes that are turned 90°, 180°, 270° and 360° on the centre point and still appear exactly the same have rotational symmetry.

(h)

(i)

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(f)

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2. Shapes that are turned 180° on the centre point and still appear exactly the same have point symmetry.

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(g)

(e)

4. Make these pictures symmetrical.

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Primary mathematics: Back to basics

REDUCING AND ENLARGING SPACE

Teacher information Indicator Reduces and enlarges images using a grid.

Concepts required

r o e t s Bo r e p ok u S Scale—reducing and enlarging

Answers

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Teac he r

1. Teacher check 2. Teacher check

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Primary mathematics: Back to basics

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REDUCING AND ENLARGING SPACE

Teac he r

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

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2. Enlarge and copy these pictures on the grid squares provided.

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STUDENT NAME

1. Reduce and copy these pictures on the grid squares provided.

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Primary mathematics: Back to basics

DIRECTIONS AND COORDINATES SPACE

Teacher information Indicators Uses compass points to locate places. Uses latitude and longitude coordinates.

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

(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k)

Compass directions Locating information on a map Latitude and longitude Coordinates

Materials needed Atlas or world map

Answers Chile north-west north-east Colombia Brazil Caracas east west south-east south-west north-west

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Teac he r

Concepts required

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2. Answers will vary.

Primary mathematics: Back to basics

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DIRECTIONS AND COORDINATES SPACE 1. Use the map of South America to answer the questions.

(a) What country is located along the south-west coast of the continent?

(b) What direction is Peru from Bolivia?

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(e) Which country is located in the east of the continent?

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(f) Which is the northernmost city shown on the map?

(g) The Atlantic Ocean is to the

South America.

(h) The Pacific Ocean is to the

South America. (i) What direction is Montevideo from Bogotá?

(j) What direction is Brasilia from Salvador?

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STUDENT NAME

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

(d) What is the most north-western country?

(k) The Amazon River runs through the

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City

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Latitude

Longitude

part of Brazil.

Direction

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2. Plan a trip around the world where you visit 12 cities. Use an atlas for this question.

(a) Write each city on the table in order of travel.

(b) Write the latitude and longitude coordinates for each city.

Primary mathematics: Back to basics

MAP FEATURES AND SCALES SPACE

Teacher information Indicators Identifies map symbols. 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 Identifying symbols from a street directory Scale Compass directions Locating information on a map

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Teac he r

Concepts required

Materials needed Street directory Ruler

(a) (c) (e) (g) (i) (k) (m) (o)

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car park picnic area traffic lights public toilets patrolled beach railway station bicycle path church

2. (a) 300 km (e) 225 km

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(b) (d) (f) (h) (j) (l) (n) (p)

hospital freeway fuel telephone post office roundabout lake police station

(b) 600 km (f) 525 km

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(d) 1500 km (h) 2250 km

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3. (a) north-east (b) west (c) 300 km (d) 700 km (e) south-east (f) 450 km (g) 1350 km (h) 150 km, 270 km, 210 km, 330 km, 280 km = total of 1240 km

Primary mathematics: Back to basics

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MAP FEATURES AND SCALES SPACE

(b)

(i)

(j)

Teac he r

(a)

(c)

(d)

(e)

(f)

(g)

r o e t s Bo r e p ok u S (k)

(l)

(m)

(n)

(o)

2. The scale on a map reads 1 cm = 150 km. Convert these cm to km.

(a) 2 cm =

(e) 1.5 cm =

(b) 4 cm =

(f) 3.5 cm =

(g) 20 cm =

3. Use the map of New Zealand to answer the questions.

(h)

(p)

•Pol

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(h) 15 cm =

(a) What direction is Mt Cook from Invercargill?

(b) What direction is Nelson from Wellington?

(d) Approximately how many km long is the South Island?

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(e) What direction is Rotorua from Auckland?

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(f) How many km is it from Stewart Island to Christchurch?

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STUDENT NAME

1. Identify the following map symbols found in a street directory.

(g) Approximately how many km would you travel if you

went from Invercargill to Dunedin (

on to Christchurch (

Nelson (

Mt Cook (

Invercargill (

Total km =

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km),

km), then km), km) and back to km)?

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Primary mathematics: Back to basics

LENGTH MEASUREMENT

Teacher information Indicators Identifies formal measurement units. Measures length in mm and cm. 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 Adding and subtracting measurements

ew i ev Pr

Teac he r

Concepts required

Materials needed Ruler

(b) 9.5 cm (c) 135 mm

(d) 7.8 cm

(e) 117 mm

2. (a) 20 mm (b) 3.5 cm (c) 400 cm (d) 550 cm (f) 4.241 km (g) 30 cm (h) 60 300 cm

(e) 44.2 cm

3. Answers will vary. (c) 156 cm

(d) 320 m

(e) 31 mm

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5. Answers will vary. 6. (a) 4.5 cm or 45 mm (c) 395 mm or 39.5 cm (e) 18 m or 1800 cm

(b) 6.6 m or 660 cm (d) 9.5 km or 9500 m (f) 10 m or 10 000 mm

7. (a) 1 m or 100 cm (c) 5.1 cm or 51 mm (e) 11.9 m or 1190 cm

(b) 8.4 m or 840 cm (d) 7.5 km or 7500 m (f) 50 km or 50 000 cm

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Primary mathematics: Back to basics

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4. (a) 182 mm (b) 10 m

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LENGTH MEASUREMENT 1. Use a ruler to measure each line.

cm cm mm cm

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

(a)

2 cm =

(b)

35 mm =

(c)

4m=

(d)

5.5 m =

(e) 442 mm =

(f) 4241 m =

(g) 300 mm =

(h)

Teac he r

603 m =

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3. Use a ruler to measure the width (in mm) of each item from home.

(a)

fork =

(b)

book =

(d) pillow =

(e)

plate =

(f) door =

4. Circle the best measure for each. (a) length of a new pencil

—

182mm

182 cm

182 m

(b) length of a living room

—

10 mm

10 cm

10 m

—

156 mm

156 cm

156 m

(d) height of a building

—

320 mm

320 cm

320 m

—

31 mm

31 cm

31 m

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(e) length of a paper clip

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STUDENT NAME

2. Complete these conversions.

5. Name something that measures about:

(a) 10 mm

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(b) 50 mm

6. Add the following lengths.

(a) 4 cm and 5 mm =

(e) 10.5 m and 750 cm =

cm or

mm or

m or

(b) 6 m and 60 cm =

(d) 4 km and 5500 m =

(f) 9.7 m and 300 mm =

m or km or m or

cm m mm

7. Find the difference between the following lengths.

(a) 3 m and 200 cm =

(e) 12 m and 100 cm =

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m or

cm or m or

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(b) 8.8 m and 400 cm = mm (d) 10.5 km and 3000 m =

(f) 55 km and 5000 cm =

m or

km or

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) 100 mm

(b) 101 mm

2. Teacher check

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Teac he r

Proficient use of a ruler to measure accurately in mm and cm Addition/multiplication skills

(d) 176 mm

4. 600 mm 5. 48 cm

6. 956 mm 7. 110.4 cm

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8. 46.4 m 9. Answers will vary.

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Primary mathematics: Back to basics

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PERIMETER MEASUREMENT 1. Use a ruler to measure the perimeter of each shape.

(a) P =

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

(b) P =

(d) P =

2. Draw a shape with a perimeter of:

(b) 86 mm

Teac he r

(a) 12 cm

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3. Find the perimeter of a square with sides measuring 2.5 cm.

4. Find the perimeter of a square with sides measuring 150 mm.

P =

5. Find the perimeter of a rectangle if the length is 15 cm and the width is 9 cm.

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P =

6. Find the perimeter of a square with sides measuring 239 mm. P =

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STUDENT NAME

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7. Find the perimeter of a book 36.4 cm long and 18.8 cm wide.

8. What is the distance around a pool 18.5 m long and 4.7 m wide?

P =

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9. Draw three items from home and use a ruler to measure the sides of each in mm. Record the measurements on each diagram and calculate the perimeters.

(a) P =

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Primary mathematics: Back to basics

Circumference MEASUREMENT

Teacher information Indicator Calculates the circumference of circles.

Concepts required

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

Answers

1. (a) 12.56 cm

(b) 94.2 mm

2. 21.98 cm

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Teac he r

Circumference is 3.14 x diameter Multiplying with decimals Problem solving

5. 75.36 mm 6. 219.8 mm

7. 55.892 cm

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Primary mathematics: Back to basics

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8. Answers will vary.

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R.I.C. Publications®

Circumference MEASUREMENT To find the circumference of a circle, multiply 3.14 by the diameter. If you only have the radius, double it before multiplying by 3.14. C = 3.14 x d C = 3.14 x (r x 2) 1. Find the circumference of each circle.

(a)

3.14 d = 4 cm

x 4

15 r = 15 mm

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

x 2

Teac he r

3.14 x

2. Find the circumference of a circle if the diameter is 7 cm.

3. Find the circumference of a circle if the diameter is 12 cm.

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4. Find the circumference of a circular garden bed if the diameter is 9.5 m.

5. A wedding ring has a diameter of 24 mm. Find the circumference.

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6. Find the circumference of a circle with a 35 mm radius.

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STUDENT NAME

(b)

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7. Find the circumference of a circle if the radius is 8.9 cm.

8. Measure the diameter of two different items. Calculate the circumference of each.

(a) Item 1:

(b) Item 2:

d =

C =

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Primary mathematics: Back to basics

AREA MEASUREMENT

Teacher information Indicator Calculates area.

Concepts required

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

Answers

1. (a) 30 m2

(b) 88 cm2

2. (a) Bedrooms 2 and 3 (b) 13.65 m2 (c) 22 m2 2 (f) 21 m (g) 17.39 m2

(d) 66 cm2

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Teac he r

Area = length x width Multiplication Analysing a floor plan

(e) 10.8 m2

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Primary mathematics: Back to basics

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3. Answers will vary.

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AREA MEASUREMENT 1. Find the area of the following.

(a) Length = 6 m

Width = 5 m

Area =

(b) Length = 11 cm

Width = 8 cm

Area =

cm2

Width = 5 m

Area =

(d) Length = 16.5 cm

Width = 4 cm

Area =

cm2

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

Teac he r

(a) Which two bedrooms will have the same area?

(b) Calculate the area of the largest bedroom.

What is the total area of bedroom 4 and the study combined?

(d) Bedroom 4 =

(e) Study =

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(f) Total =

(g) Calculate the area of the lounge room.

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STUDENT NAME

2. Use the house plan below to complete the following.

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(h) If carpet costs $25 per square metre, how much will it cost to carpet the lounge?

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3. Calculate the area of your bedroom. L = W = A =

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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 in millilitres and litres. Calculates volume.

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

Knowledge of formal measurement units—millilitres and litres Equivalent units of measurement Ordering capacities Volume = length x width x height Problem solving

Answers

1. (a) 1000 ml

(b) 3 L

2. (a) 0.75 L or 750 mL (c) 2.5 L or 2500 mL

(d) 2.3 L

(b) 1.2 L or 1200 mL (d) 6.75 L or 6750 mL

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Teac he r

Concepts required

(b) 50

5. (a) 40 cm3

(b) 160 m3

6. 825 m3

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Primary mathematics: Back to basics

m . u

7. 13.125 L

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VOLUME AND CAPACITY MEASUREMENT 1. (a) 1 L =

(b) 3000 mL =

(d) 2300 mL =

2. Find the difference between the following. (a) 1 L and 250 mL =

L or

(b) 1.4 L and 200 mL =

L or

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

L or

mL mL

(d) 10 L and 3250 mL =

Teac he r

Item

Capacity

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4. (a) How many 5 mL teaspoons to fill a 250 mL cup? (b) How many 20 mL tablespoons to fill a 1 L jug? (c) How many 250 mL cups to fill a 4.5 L bucket?

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5. Volume = length x width x height (e.g.v = 10 x 5 x 20 = 1000 cm3)

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(a) Find the volume if l = 4 cm, w = 2 cm, h = 5 cm.

cm3

6. Find the volume of a pool 25m long, 11 m wide and 3 m deep. v =

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(b) Find the volume if l = 8 m, w = 2 m, h = 10 m.

7. How many litres of water would it take to fill a tank that is 3.5 m high, 1.5 m wide and 2.5 m long?.

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STUDENT NAME

3. Find six items from home that are measured in litres or millilitres. Write the items in order of their total capacity.

Primary mathematics: Back to basics

MASS MEASUREMENT

Teacher information Indicators Identifies formal units of measuring mass. Orders items in grams and kilograms. Calculates equivalent measures. Solves mass-related problems.

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

Teac he r

Answers

1. (a) 1 kg

(b) 0.25 kg

2. (a) 1 kg or 1000 g (c) 400 g or 0.4 kg

(b) 2250 g or 2.25 kg (d) 1.75 kg or 1750 g

(d) 750 g

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Knowledge of formal measurement units—grams and kilograms Equivalent units of measurement Ordering Problem solving

4. (a) 10g, 50 g, 100 g, 250 g, 1000g, 1500 g (b) 0.6 kg, 6 kg, 6.5 kg, 16 kg, 60 kg, 66 kg (c) 40 g, 400 g, 0.45 kg, 4 kg, 4.4 kg, 40 kg

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5. (a) 330.7 kg (b) 28.2 kg 6. 5280 g or 5.28 kg 7. 5.75 kg

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8. 5.975 kg

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9. Answers will vary.

Primary mathematics: Back to basics

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MASS MEASUREMENT 1. (a) 1000 g =

(b) 250 g =

(d) 0.75 kg =

2. Find the difference between each of the following.

(a) 2 kg and 1000 g =

kg or

(b) 750 g and 3 kg =

g or

(d) 3.25 kg and 1500 g =

kg kg or

3. Find six items from home that are measured in grams or kilograms. Write the items in order of their total mass.

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

Heaviest

Teac he r 4

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3 2

Lightest

4. Order these from lightest to heaviest.

(a) 1000 g, 100 g, 1500 g, 10 g, 250 g, 50 g

(b) 6 kg, 16 kg, 0.6 kg, 66 kg, 6.5 kg, 60 kg

(b) Find the difference between the heaviest and lightest person.

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5. (a) Find the total mass if five people weighed 84.2 kg, 56 kg, 59.5 kg, 63.2 kg and 67.8 kg.

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6. A box holds 12x 440 g cans of soup. What is the total mass?

Total mass =

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Difference =

Total mass =

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8. Find the total weight of these grocery items—2.4 kg chicken, 500 g ham, 750 g cheese, 1.5 kg sausages and 825 g bacon.

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STUDENT NAME

Mass (g/kg)

7. A crate held 15 kg of potatoes. What was the weight after 9.250 kg were sold?

kg 9. Find the total mass of the household items listed in Question 3.

Total mass =

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Primary mathematics: Back to basics

ANGLES MEASUREMENT

Teacher information Indicators Uses a protractor to measure angles. Identifies types of angles.

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

Materials needed Protractor Ruler

Answers

1. (a) acute 35°

(b) right 90°

Angle B = 80° Angle B = 45°

Angle C = 50° Angle C = 45°

ew i ev Pr

Teac he r

Proficient use of a protractor to measure angles Understanding that three angles of a triangle equal 180° Types of angles

Angle A = 50° Angle A = 90° 180° 360°

(b) 90° (d) 45° (f) 105°

4. (a) right (d) obtuse

(b) acute (e) straight

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3. (a) 30° (c) 15° (e) 135°

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5. Teacher check

Primary mathematics: Back to basics

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ANGLES MEASUREMENT 1. Name each type of angle. Use a protractor to measure each angle. °

° °

(a)

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

(b)

(c)

2. Measure the angles of these triangles. (a)

Teac he r

Angle A =

Angle B =

Angle C =

(d) What do the four angles of a square equal?

(b)

Angle A =

3. Use a protractor to measure each angle.

(b) Angle AGD

(d) Angle FGE

(e) Angle AGE

(f) Angle BGE

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4. Name each type of angle.

(a) Angle DGF

(b) Angle BGC

(d) Angle FGB

(f) Angle EGB

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(e) Angle AGF

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(a) Angle AGB

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STUDENT NAME

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5. Use a protractor to draw the following angles.

(a) 40°

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(b) 85°

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(d) 170°

Primary mathematics: Back to basics

TIME MEASUREMENT

Teacher information Indicators Calculates elapsed time. Solves time-related problems.

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

Answers

ew i ev Pr

Teac he r

Equivalent time frames 24-hour times Problem solving

1. (a) 60 (e) 365

(b) 60 (f) 10

(d) 52

2. (a) 18:30 (e) 12:10

(b) 23:55 (f) 22:40

(d) 13:25 (h) 14:51

3. (a) 2 h 30 m

(b) 5 h

(d) 11 h 30 m

4. (a) 1.30 am

(b) 9.15 am

(d) 2.50 pm

5. (a) 6 pm

(b) midnight

(d) 12.50 pm

7. (a) 4 h 45 m

(b) 6 h 5 m

8. (a) 50 m

(b) 4.20 pm

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Primary mathematics: Back to basics

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TIME MEASUREMENT 1. (a) 1 minute =

seconds

(d) 1 year =

weeks

(b) 1 hour =

minutes

(e) 1 year =

days

(f) 1 decade =

hours years

2. Convert the following to 24-hour times.

(a) 6.30 pm

(e) 12.10 pm

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(b) 11.55 pm

(d) 1.25 pm

(f) 10.40 pm

(g) 7.11 pm

(h) 2.51 pm

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(a) 6.00 pm

(b) 8.30 pm

4. Write the time it will be five hours before these times.

(a) 6.30 am

(b) 2.15 pm

5. Write the time it will be 90 minutes after these times.

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(d) 7.50 pm

(a) 4.30 pm

(b) 10.30 pm

(d) 11.20 am

6. Sienna left for a trip at 3.15 pm and arrived at 7.35 pm. How long did the trip take?

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STUDENT NAME

3. If it is 3.30 pm, how long until:

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7. Drew spent 90 minutes at football training on Tuesday and Thursday, 45 minutes at the swimming pool on Wednesday and an hour at the gym on Friday.

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(a) How much time did he spend on exercise in a week?

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(b) If he also walked for 40 minutes every Monday and Saturday, how much time was spent on exercise altogether? (c) Find the total time spent on exercise in one month.

8. Holly left home at 1.30 pm and arrived at the airport at 2.20 pm. (a) How long did the trip take?

(b) Although her flight was scheduled to depart at 3.35 pm, it was delayed for 45 minutes. What time did the flight actually depart?

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Primary mathematics: Back to basics

CALENDARS, TIMETABLES AND TIME LINES MEASUREMENT

Teacher information Indicators Organises and records events in a timetable and on a time line. Interprets information from a calendar.

r o e t s Bo r e p ok u S Creating a timetable of activities Using a calendar Elapsed time Sourcing information to create a time line

Materials needed Current calendar Access to Internet/books to source history events

Answers

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Concepts required

2. Answers depend on current year

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Primary mathematics: Back to basics

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3. Answers will vary

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CALENDARS, TIMETABLES AND TIME LINES MEASUREMENT 1. Create a timetable to schedule your ‘Perfect weekend’.

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Sunday

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2. Use a current calendar to answer the questions.

(a) What will be the date three weeks from today?.....................................................................

(b) How many days are there in the first half of the year?.................................................................

(d) Mark took holidays on 7 September and returned on 1 October. For how many days was he away from work?......................................

(e) How many days until the end of the year?..........

(f) How many days make up the summer months?.................................................................. (g) How many weeks are there between your birthday and Christmas Day?...............................

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STUDENT NAME

Saturday

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3. Create a time line to show ten significant events that have shaped your country’s history.

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Primary mathematics: Back to basics

CHANCE AND PREDICTIONS CHANCE AND DATA

Teacher information Indicator Describes chance and makes predictions.

Concepts required

r o e t s Bo r e p ok u S Predicting possible outcomes and chance events

Answers

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1. Answers will vary. 2. Answers will vary. 3. Answers will vary.

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CHANCE AND PREDICTIONS CHANCE AND DATA

(a) watching television tomorrow

(b) being caught in a snowstorm next week

(d) wearing something pink tomorrow

(e) swimming in the ocean some time this month

(f) learning to drive a car next year

(g) sending a text message tomorrow

(h) meeting your favourite celebrity

(i) using a computer tonight

(j) winning an Olympic medal

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2. Make predictions about the following.

(a) The weather in Sydney in February.

(b) The weather in New York in January.

(d) What type of car you will drive when you have your licence.

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(e) What sport you will be involved in next year.

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3. Describe a goal or dream you have for yourself for each time frame. Predict your chances of achieving each goal/dream. (a) By the end of this year I

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I predict my chances are

(b) In five years’ time I

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STUDENT NAME

1. Describe your chance of the following:

I predict my chances are

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Primary mathematics: Back to basics

DATA CHANCE AND DATA

Teacher information Indicators Formulates appropriate survey questions. Represents given data in appropriate formats.

r o e t s Bo r e p ok u S Understanding purpose and construction of survey Considering important issues Understanding suitable formats for representing data— tables, diagrams, graphs

Answers

1. Answers will vary. 2. Answers will vary.

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Concepts required

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DATA CHANCE AND DATA 1. Consider two issues that are important to your school, local community and country. Devise an appropriate survey question for each issue. Think carefully about the wording of each survey question.

Ask: ‘Do I want a yes/no answer?’ ‘Will my question give me the data I need?’

School issues:

•

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Community issues:

•

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•

Country issues:

•

2. Choose two different formats to represent the following data.

Ella, Olivia, Riley, Andrew, Lewis, Blake and Lily all had birthdays during the summer months. During autumn, Brett, Glen, Lucas, Kate and Natalie had birthdays. Mark, David, Sam, Chris, Rose, Zoe, Grace, Lana and Jessica had a birthday during the winter months. During spring, Zac, Jayden, Molly, Rebecca, Jane and Emily had a birthday.

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STUDENT NAME

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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 Answers

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

25 Jake, Eve 10 Alex, Tess, Josh, Lauren 20% Cass, Matt, Amanda 2 Brody, Chris, Kim, Jemma, Ruby 2 40%

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

8 Saints Swans, Hawks, Eagles Swans, Lions, Cats, Magpies Cats, Crows

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Venn diagram Tree diagram Two-way table Percentage

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10 Shaun Emily, Matilda 70% 50%

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DIAGRAMS AND TABLES CHANCE AND DATA 1. Use the Venn diagram to answer the questions.

(a) How many people were surveyed?

(b) Who played three instruments?

(d) Who played two instruments?

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(e) What percentage played guitar only?

(f) Who played no instruments?

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(g) How many played both violin and piano?

(h) Who played violin only?

(i) How many played guitar and piano only?

(j) What percentage played guitar or violin only?

2. The tree diagram shows the results of a football finals series.

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(a) How many teams made the finals series?

(b) Who was the eventual winner?

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(a) How many people were surveyed?

(b) Who doesn’t read newspapers or magazines?

(d) What percentage of people read magazines?

(e) What percentage don’t read newspapers but do read magazines?

(f) Add your name to the table.

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(e) Who did the Eagles beat to make the final?

3. Use the table to answer the questions.

(d) Which teams were eliminated in the first round?

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STUDENT NAME

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Reads newspapers

Doesn’t read newspapers

Reads magazines

Doesn’t read magazines

Emily

Oliver

Emily

Aiden

Matilda

Hannah

Oliver

Shaun

Aiden

Kiara

Matilda

Kristy

Shaun

Kiara

Darcy

Hannah

Blake

Darcy Blake

Primary mathematics: Back to basics

GRAPHS CHANCE AND DATA

Teacher information Indicator Analyses data presented in tables and graphs.

r o e t s Bo r e p ok u S Strip graph How to construct a pie graph Percentage Use of a protractor Sourcing data Selecting an appropriate format to represent data

Materials needed Protractor Ruler

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Concepts required

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Primary mathematics: Back to basics

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3. Teacher check

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GRAPHS Making calls—17

(a) Use the results to create a strip graph.

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Text messaging—19

Camera—8

Video—3

Email—3

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(b) Write three questions about your graph.

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2. Create a pie graph using the following data. Use a protractor. Remember that a circle has 360°. Type of books sold

Fiction

120

Cooking

Health

Gardening

Childrens

Total

360

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CHANCE AND DATA 1. 50 people were asked what was the most used function of their mobile phone.

3. Collect the information required and use it to create a graph of your choice.

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Household items Item

Dinner plates Cereal bowls Coffee cups/mugs

Number

Teaspoons Forks Glasses Televisions Telephones Total R.I.C. Publications®

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Primary mathematics: Back to basics

STATISTICS CHANCE AND DATA

Teacher information Indicator Uses data to calculate the mean, mode, median and range.

Concepts required

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

Answers

1. (a) 95.166

(b) 100%

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Interpreting data Addition Division Tallying results

(d) 85% – 100%

(b) 28 mm

(d) 21 – 30 mm

3. (a) 32.875

(b) 34°

(d) 29° – 37°

4. (a) 157.428

(b) 160 cm

(d) 154 – 160 cm

No. Children

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Tally

Total

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STATISTICS CHANCE AND DATA A set of numbers given is: 5, 3, 6, 1, 5. The mean is the average of this set: 5 + 3 + 6 + 1 + 5 = 20 ÷ 5 = 4 The mode is the number that occurs the most often: 5 The median is the number in the middle when the numbers are in order: 1, 3, 5, 5, 6 = 5 (If there is no middle score, an average of the two middle scores is taken.) The range is the lowest and highest number: 1–6

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Use the different sets of numbers to find the mean, mode, median and range. Use a calculator to find the mean.

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(a) mean =

3. 29°, 34°, 35°, 29°, 31°, 34°, 34°, 37°

(a) mean =

(b) mode =

(d) range =

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4. 155 cm, 154 cm, 160 cm, 156 cm, 160 cm, 157 cm, 160 cm

(a) mean =

(b) mode =

(d) range =

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2. 21 mm, 28 mm, 26 mm, 28 mm, 22 mm, 25 mm, 30 mm

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1. 96%, 100%, 85%, 100%, 100%, 90%

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5. A survey was carried out on a group of 50 people to see how many children were in each family. The statistics are below. Complete the table. 2 4 5 1 5 2 2 3 4 1 (a) No. Children Tally Total 2 1 2 4 2 3 3 3 2 4 1

Find the:

(b) mode =

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Primary mathematics: Back to basics