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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Acknowledgements i. I-stock Photos. ii. Clip art images have been obtained from Microsoft Design Gallery Live and are used under the terms of the End User License Agreement for Microsoft Word 2000. Please refer to www.microsoft.com/permission.

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Series: Striving to Improve Title: Integers © 2013 Ready-Ed Publications Printed in Australia Edited by Mirella Trimboli Contributing authors are: Jane Bourke, Mirella Trimboli

Copyright Notice

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2.

Copies are made only by reprographic means (photocopying), not by electronic/digital means, and not stored or transmitted;

3.

Copies are not sold or lent;

4.

Every copy made clearly shows the footnote, ‘Ready-Ed Publications’.

educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under Act. For details of the CAL licence for educational institutions contact: Copyright Agency Limited Level 19, 157 Liverpool Street Sydney NSW 2000 Telephone: (02) 9394 7600 Facsimile: (02) 9394 7601 E-mail: info@copyright.com.au

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The Act allows a maximum of one chapter or 10% of the pages of this book, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that

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Except as otherwise permitted by this blackline master licence or under the Act (for example, any fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address below.

o c . che e r o t r s super Published by: Ready-Ed Publications PO Box 276 Greenwood WA 6024 www.readyed.net info@readyed.com.au

ISBN: 978 186 397 850 7 2

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Any copying of this book by an educational institution or its staff outside of this blackline master licence may fall within the educational statutory licence under the Act.

Reproduction and Communication by others


Contents Teachers’ Notes Curriculum Links

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Calculating with Integers: Teachers’ Notes Rule Of Order 1 Rule Of Order 2 Addition 1 Addition 2 Addition: Regrouping 1 Addition: Regrouping 2 Addition: Regrouping 3 Addition: Regrouping 4 Subtraction 1 Subtraction 2 Subtraction: Regrouping 1 Subtraction: Regrouping 2 Subtraction: Regrouping 3 Subtraction: Regrouping 4 Addition And Subtraction 1 Addition And Subtraction 2 Real Life Addition Real Life Subtraction Real Life Addition And Subtraction Multiplication: Regrouping 1 Multiplication: Regrouping 2 Multiplication: Regrouping 3 Multiplication: Regrouping 4 Multiply These! Division 1 Division 2 Division With Remainders 1 Division With Remainders 2 Division With Regrouping 1 Division With Regrouping 2 Real Life Multiplication Real Life Division

6 7 8 9 10 11 12 13 14 15 16 17 18 19

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Understanding Integers: Teachers’ Notes Place Value 1 Place Value 2 Place Value 3 Greater Than/ Less Than Rounding 1 Rounding 2 Estimation 1 Estimation 2 Counting By Multiples Factors Imagining Negative Numbers Where Am I?

4 5

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 51 52

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53 3


Teachers’ Notes This resource is focused on the Number and Algebra Strand of the Australian Curriculum for lower ability students and those who need further opportunity to consolidate these core areas in Mathematics.

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Each section provides students with the opportunity to consolidate written and mental methods of calculation, with an emphasis on process and understanding.

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The section entitled Understanding Integers enables students to reencounter ideas of place value, rounding, estimation, factors, multiples and the concept of a directed number. These activities are a useful way to scaffold a new unit of Mathematics and will help build confidence for lower ability students to attempt more challenging problems at their year level.

The section entitled Calculating With Integers walks students through the four core calculations. The activities are designed to guide student learning with minimal input from the teacher and there is a strong emphasis on process and understanding. Students explore addition and subtraction with two and three digit sums and can apply what they have learned to some real life application problems. Similarly, students explore the various levels of multiplication and division before applying them to a variety of applications.

© ReadyEdPubl i cat i ons The• activities canr be used for individual students needing further f o r e v i e w p u r p o s e s onl y• consolidation in a mainstream classroom or as instructional worksheets for

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a whole class of lower ability students. The activities are tied to Curriculum Links in the Australian Curriculum ranging from grade levels of Year 4 through to Year 7 and are appropriate for students requiring extra support in Years 7, 8 and 9.

It is hoped that Integers will be used to help teachers provide appropriate resources and support to those students in greatest need. The book as a whole can be used as a programme of work for those students on a Modified Course or Independent Learning Programme. Activities are sufficiently guided so that students can work independently and at their own pace without constant supervision and guidance from the teacher.

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Curriculum Links Understanding Integers Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

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Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

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Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

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

Investigate everyday situations that use positive and negative whole numbers and zero. Locate and represent these numbers on a number line (ACMNA124)

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Calculating With Integers

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

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Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Solve problems involving multiplication of large numbers by one- or twodigit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

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Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

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Teachers’ Notes

Understanding Integers

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The activities in this section allow students to revise many of the core Number properties and ideas. Before introducing lower ability students to new work on Integers, these activities will encourage students to consolidate concepts from previous years.

Place Value

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The concepts covered include:

Students have the opportunity to explore what they know about place value for integers and to understand the composition and relative magnitude of numbers. These activities are particularly useful before moving on to calculations and work with numbers involving decimals.

Rounding

As a concept with which many students experience difficulty, it is important to allow for a thorough consolidation of rounding integers to specified place values. This is important work to include prior to work on rounding decimals, working with scientific notation and significant figures.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Estimation

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Factors and Multiples

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To assist students with building their appreciation and understanding of working with numbers, estimation is a core skill. These activities will encourage students to reflect on whether their calculations are providing reasonable solutions.

As a precursor to working on patterns and number theory, students need to have a strong grasp of the factors and multiples that compose a number. These activities allow students to revise these concepts.

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As the majority of work on Directed Numbers is taught in Lower Secondary, these activities allow students to understand, through real life applications, the contexts for negative integers.

6


*   Place Value 1 zz If the number is whole, then the last digit on the right is in the ones column. Digit value tells you how much a digit is worth in a number. Look at the digits in the number 1 234 589 below:

Example

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

1

2

3

4

5

8

9

200 000

30 000

4 000

500

80

9

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Value 1 000 000

*  Task a

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Digit

Write the values for the numbers in the table below.

Start by placing the last whole digit in the ones column, then work from right to left until there are no more digits. Thousands

Hundreds

Tens

Ones

©R eadyE dPubl i at i ons 3 000 600 40c 7 orr evi ew pur posesonl y• 8 427•f 3 647

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3 975

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5 927

. t o Write the value of the 4 in each number.   Task b e c * . che e r o Value Value Number Number t r s super e.g. 347

40

1004

4 273

3430

9 274

4638

3 476

10342

7


*   Place Value 2 zz If the number is whole, then the last digit on the right is in the ones column. Digit value tells you how much a digit is worth in a number. Look at the digits in the number 1 234 589 below:

Example Digit

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

1

2

3

4

5

8

9

200 000

30 000

4 000

500

80

9

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Value 1 000 000

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Write the values for these digits. Work from right to left.

Number

Thousands

Hundreds

Tens

3 647

3 000

600

40

2 364 9 845

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*  Task a

Ones 7

599

5 738

3 126

3 921

5 991

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© ReadyEdPubl i cat i ons the value of the bold digit. *  Task b•Write f orr e vi ew pur po sesonl y • Value Value Number Number

o c . toh write the number. e   Task c Use thesec r * e o t r sOnes su per Thousands Hundreds Tens Number 9 032

8

4 679

5000

300

40

2

2000

400

70

6

8000

200

60

6

9000

500

50

3

5342


*   Place Value 3

  Task A Write this number so that the digits are in the correct columns. * Seven million, four hundred and fifty-six thousand, three hundred and twenty-two. Millions 1 000 000

Ten Thousands 10 000

Thousands

Hundreds

Tens

Ones

1 000

100

10

1

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Show these numbers on the table below. 1 000 000 100 000

5 498 765

10 000

1 000

100

10

1

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*  Task b

Hundred Thousands 100 000

2 098 634 4 200 049 187 685

© ReadyEdPubl i cat i ons 35 497 •f orr evi ew pur posesonl y• *  Task c Write the following numbers in expanded form. 280 097

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3 487 978

E.g. (3 x 1 000 000) + (4 x 100 000) + (8 x 10 000) + (7 x 1000) + (9 x 100) + (7 x 10) + (8 x 1).

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_______________________________________________________________________ 2 876 543

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o c . 7 653 012 che e r o t r _______________________________________________________________________ s super _______________________________________________________________________

*  Task d Number

Write the place value and the face value for the underlined numbers below. Place Value

3 425 643 ten thousands 3 298 765

Face Value

Number

20 000

5 364 243

Place Value

Face Value

2 509 345 9


*   Greater Than / Less Than zz > means “greater than” < means “less than”. The “pointed part” always points to the smaller number, and the “wide open part” opens to the larger number. Look at the examples below. Example

Compare 460 and 4007.

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Which number has MORE place values (before the decimal point)? Thousands Hundreds 4

Tens

Ones

6

0

Thousands Hundreds 4

0

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Example

Compare 4570 and 4507.

Ones

0

7

460 < 4007

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460 does not have anything in the Thousands, so 4007 is larger.

Tens

If both numbers have the same number of place values, start comparing from the left until you find the number that has the FIRST largest place value. Thousands Hundreds 4

5

Tens

Ones

7

0

Thousands Hundreds 4

5

Tens

Ones

0

7

*  Task a

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© Re adyEdPSame ubl i c at i o ns Same Larger Same Smaller f o r r e i ew ur p eson l y • 7 is larger• than 0, so 4570 isv larger. This isp written aso …s 4570 > 4507 Same

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Place the > or < in between these sets of numbers to show which is greater. 1. 276

982

9. 44

______

1200

3. 401

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4. 1872

______

5. 780

______

6. 1457

______

999

14. 986 002 ______

986 020

7. 2790

______

2900

15. 788 987 ______

98 987

8. 3000

______

2899

16. 565 231 ______

542 956

2. 986

*  Task b

10

______

______ ______

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10. 9778

______

410

11. 45 961

______

45 916

1287

12. 49 876

______

49 878

708

13. 415 987 ______

415 899

Use a separate piece of paper to write your own.

9807


*   Rounding 1 zz Rounding means finding the closest 10, 100 or 1000. When the number ends in 5, like 5, 15, 25 you can round up or down (usually up).

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22

12. Task a Circle the numbers r o e t *  How B r many squares is ite away from 10?__________ o

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How many squares is it away from 20?__________

1

2

3

4

5

6

7

8

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12 is closer to 10, so you round 12 to 10.

9 10 11 12 13 14 15 16 17 18 19 20 21 22

*  Task b Round these numbers to the nearest 10. Circle the correct answer. 8 = 10 or 20 = 10 or 20 19 = 10 or 20 16 = 10 or 20 © Re13ad yEdP ubl i cat i ons •f orr evi ew pur posesonl y• 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

15 = ______ or ______

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10

*  Task D

18 = ______

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Round these numbers to the nearest 10.

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*  Task c

25 = ______ or ______

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20

30

40

50

60

30 = ______

70

80

90

100

Use these numbers to find the rounded answers.

23 = ______

67 = ______

45 = ______ or ______

99 = ______

52 = ______

38 = ______

75 = ______ or ______

14 = ______

11


*   Rounding 2 zz Rounding means finding the closest 10 or 100 or 1000. When the number ends in 5, like 5, 15, 25 you can round up or down (usually up). Circle the number 12 in the number grid below. Is it closer to 10 or 20? 12 is closer to 10, so you round 12 to 10.

Example 1

2

3

4

*  Task a

5

*  Task b

9 10 11 12 13 14 15 16 17 18 19 20 21 22

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13 = _______ 18 = _______ 20 = _______ 15 = _______ or _______

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8

4

5

6

7

8

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2

7

Round these numbers to the nearest 10.

6 = _______

1

6

9 10 11 12 13 14 15 16 17 18 19 20 21 22

Use the number grid below to find the rounded numbers.

22 = _______

64 = _______

35 = _______ or _______

98 = _______

©R eadyEdPubl i cat i ons 20 30 40 50 60 70 80 90 100 •f orr evi ew pur posesonl y•   Task c   Task d * * Fill in the missing numbers to show Fill in the chart like you did left, then 10

Round Down

0

100

Half way

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150 250 350 450

Round Down

Half way

100

0

50

100

200

100

150

200

300

200

250

300

399

400

401

500

500

600

626

700

772

Round Up

Round Number Answer Up

80

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600 800 850 1000 12

round the number to the nearest 100.

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where you would round up or down to the nearest 100.

100

120

OR


*   Estimation 1 *  Task a

Look, guess then count the number of boxes.

Guess: ____________

Was it close? ____________

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Count: ____________

Guess: ____________

Count: ____________

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Look, guess then count the number of diamonds:

Was it close? ____________

  Task c Round numbers and do the sum. * 31 31 is close to 30 Estimate: 30 + 60 = 90 + 58 58 is close to 60 Count up by 10’s in your head. © R e a d y E d P u bl i cat i ons Answer 89 •f o r e i e pur p oseson y•= 22 r 22 isv close tow ________ Estimate: + l

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47 is close to ________

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+ 47 Answer 69

Estimate by rounding. Work out the real sum on a spare piece of paper.

37 + 22

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Estimate:___________

Answer:___________

Was it close? ___________

51 + 79

Estimate:___________

Answer:___________

Was it close? ___________

36 + 58

Estimate:___________

Answer:___________

Was it close? ___________

31 + 68

Estimate:___________

Answer:___________

Was it close? ___________

48 + 49

Estimate:___________

Answer:___________

Was it close? ___________

19 + 99

Estimate:___________

Answer:___________

Was it close? ___________

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*   Estimation 2

zz To estimate an answer we can think about what each number is close to. The number 43 is close to 40. 162 is close to 160.

*  Task a a)

Fill in each of the empty boxes to help you estimate what the answer should be. The first one is done for you.

r o e t s Bo r e p ok u S 70 .

So the answer is about

 − 

e)

289 − 32 is about

d)

.  − 

So the answer is about

 + 

. .

So the answer is about

.

So the answer is about

32 + 11 is about

151 + 39 is about

 + 

.

So the answer is about f)

. .

531 − 49 is about

.

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79 − 19 is about

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c)

b)

61 + 8 is about 60  +  10 .

 + 

.

.

So the answer is about

70

60

65

b. 89 – 32 =

50

60

55

c. 368 + 11 =

370

380

390

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a. 52 + 9 =

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© ReadyEdPubl i cat i ons   Task b•f orr evi ew pur posesonl y• * Circle the best and closest answer, without doing any calculations.

. 270 260 250 te o c f. 998 – 12 = 980 990 1000 . ch= e 1550 1560 1570 e r g. 1232 + 328 o r st super d. 831 – 29 =

790

800

810

e. 247 + 19 =

  Task c: small group challenge *Form a small group of 4 to 5 students.

• Measure your heights in centimetres and then estimate the total of your heights. • Write down the time it takes for each of you to travel to school in minutes and then estimate your total travel time. • Write down the amount of television each of you watches each week in minutes and then estimate your total television viewing time. 14

Height (centimetres) Travel time to school (minutes) Television viewing per week (minutes)


*   Counting By … *  Task a

Complete the number patterns to count by …

Twos:

2, 4, 6, 8,_____________________________________________ 20

Threes:

3, 6, 9,_______________________________________________ 30

Sixes:

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Sevens:

7, 14, 21, _ ___________________________________________ 70

Eights:

8, 16, 24,_____________________________________________ 80

Nines:

9, 18, 27,_____________________________________________ 60

Fours:

5, 10, 15,_____________________________________________ 50 6, 12, 18,_____________________________________________ 60

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Fives:

4, 8, 12, _ ____________________________________________ 40

10, e 20,a 30,_ __________________________________________ ©R d yEdPubl i cat i ons 100 • f or e vi ew pur posesonl y• 110 Elevens: 11,r 22, 33___________________________________________ Tens:

Thirteens:

13, 26, 39___________________________________________ 130

Fourteens:

14, 28, 42___________________________________________ 140

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12, 24, 36 ___________________________________________ 120

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Twelves:

. 150 te15, 30, 45___________________________________________ o c . ch Sixteens: 16, 32, 48___________________________________________ 160 e r er o t s s r u e p Seventeens: 17, 34, 51___________________________________________ 170 Fifteens:

Eighteens:

18, 36, 54___________________________________________ 180

Nineteens:

19, 38, 57___________________________________________ 190

Twenties:

20, 40, 60___________________________________________ 200

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*   Multiples

  Task a * List the first 10 multiples for each of these numbers. The first one has been done for you. a. 3:

3

6

12

15

18

21

24

4

b. 2: c. 7:

9

7

27

30

18

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20

e. 25:

70

75

60

f. 15:

24

g. 12:

175

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d. 10:

105 72

120

What is a Lowest Common Multiple? A Lowest Common Multiple (LCM) is the lowest multiple that two numbers have in common. To find the LCM for 3 and 4 we list some of their multiples and then look for the lowest one they have in common.

© ReadyEdPubl i cat i ons o3,r6,r e12, vi ew pur p s16o…nl y• 3 and 4 •f 3: 9, 15, 18 … 4:o 4,s 8,e 12, Find the lowest common multiple for each of the following:

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*  Task b

a. 3 and 5 b. 6 and 7

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c. 10 and 15 d. 6 and 8

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*  Task c: Partner Challenge

Create a one page mini quiz for your partner on multiples and LCMs. Before giving it to your partner to try, make sure you have already written out a detailed marking key with all the answers on a separate piece of paper.

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As we can see, the lowest number they have in common is 12.

Quiz !


*  Task a

  Factors * List all of the factors for each of the following numbers. The first one has been done for you. 1

a. 8:

2

4

2

b. 10: c. 24:

10

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e. 36:

3

6

4

10

3

f. 48:

25

9

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d. 100:

8

What is a Highest Common Factor? A Highest Common Factor (HCF) is the largest factor that two numbers have in common. To find the HCF for 12 and 18 (Task B - a), we firstly list each of their factors and then look for the largest factor they have in common. As we can see, the largest number they have in common is 6. This is the HCF.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•   Task b Find the highest common factor for each of these numbers. *

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b. 15 and 60

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c. 27 and 36 d. 36 and 90 e. 20 and 24

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

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a. 12 and 18

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Personal Challenge *  ToTaskfindc:a faster way to find the HCF, research Euclid’s Algorithm. An algorithm is a set of rules to follow to complete a calculation. It’s a lot like following a recipe. Once you have understood how the algorithm works, use it find the HCF for these numbers: a) 252 and 105 b) 2322 and 654 17


*   Imagining Negative Numbers   Task a The hilly town of Siena in Tuscany has a special sort of multi-level shopping centre.

*

Look at the store directory sign right and study it carefully before answering the following questions.

a. What number could you use to represent the level that the Butcher and Bakery are on?

Siena Shopping r o e t s BoVillage Directory r e p ok u S Store Level

_________________________________________________

b. What do the negative level numbers represent?

_________________________________________________

c. If you park in Car Park A and travel on the lift to the Medical Centre, how many floors will you pass?

_________________________________________________

d. You leave the Post Office and travel 4 levels down on the lift. Do you arrive at the Laundromat?

Appliances

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5

Medical Centre

4

Post Office/Newsagent

3

Greengrocer

2

Supermarket © ReadyEdPubl i c at i ons 1 e. If you leave the Laundromat and travel up the lift 5 floors, Butcher/Bakery • f o evi ew pur pose sonl y•G where do you endr up?r _________________________________________________

_________________________________________________

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f. Maria parks in Car Park A, travels up 4 floors, then up 3 more floors, down one floor, up 3 floors and then down 9 floors. Write down all the places that she visited.

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_________________________________________________

_________________________________________________

-1

Laundromat

-2

Customer Service

-3

Car Park A

-4

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g. Gianni starts on level G, travels to level -2, then to level 3, followed by level 1, then back to level G. Describe Gianni’s movements on the lift.

_________________________________________________

_________________________________________________

_________________________________________________

18

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*   Where Am I? *  Task a

Use the number line to help you answer each of the following questions.

a. 5 is eight places above

f. -8 is five places above

b. 2 is seven places below

g. 15 is twenty places above

d. 0 is ten places above

i. -12 is four places below

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h. 3 is sixteen places below

e. -7 is thirteen places below

*  Task b

j. -1 is eleven places above

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c. -3 is five places below

You may like to use the number line to answer each of these questions.

a. 12 more than 3 is b. 10 less than 5 is

e. 2 more than -5 is

which is 3 less than

f. 7 less than 2 is

which is 4 more than

g. 9 more than 1 is

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which is 8 less than

h. 50 less than 10 is

which is 6 more than

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i. 86 more than 17 is

j. 37 more than -14 is k. 12 less than -62 is l. 150 less than -210 is

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© ReadyEdPubl i cat i ons d. 12 more than -18 is •f orr evi ew pur posesonl y• c. 6 less than -4 is

o c . che e r o t r s super

which is 10 less than

which is 15 less than

which is 21 more than

which is 325 more than

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15 -16 -17 -18 -19 -20

ask c: class Challenge *  TEach member of the class is to write down one clue, similar to those above, which represents an integer value. Each member of the class will then state their clue to the class and the others in the class will write down the number they were thinking of. Once all class members have given their clue, go through the answers with your teacher.

19


Teachers’ Notes

Calculations With Integers Lower ability students struggle with their confidence in Mathematics as much as they struggle with learning new concepts. Before beginning units of work for Number in Lower Secondary, these activities encourage students to consolidate the written methods and algorithms that they have encountered previously while building confidence in their abilities.

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

Teac he r

ew i ev Pr

This section focuses on calculations involving addition, subtraction, multiplication and division and also includes activities for real life applications.

Each subsection is well scaffolded and allows students to concentrate on one core area of calculation before moving on to the next.

These activities should encourage independent learning, rather than requiring significant teacher input, and will thus enable students to build confidence in their resourcefulness and abilities.

w ww

. te

20

m . u

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s super


*   Rule Of Order 1 zz Sometimes sums have more than one thing to do in them. The rule of order states that you must do × and ÷ before + and – . Look at these two examples: Example

6+3×4

10 – 16 ÷ 4

Example

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

You do the ÷ first, i.e. 16 ÷ 4 = 4

So 6 + 3 × 4 = 6 + 12

So 10 – 16 ÷ 4 = 10 – 4

6 + 12 = 18

10 – 4 = 6

*  Task a

a. 4 × 2 + 7

Re-write these sums and then solve them. = 8 + 7 =

i. 4 ÷ 2 + 6

ew i ev Pr

Teac he r

You do the × first, i.e. 3 × 4 = 12

= 2 + 6 =

©R ea dy EdPj. ub l i cat i on s= = + = 6 ÷ 3 + 5 = + •f orr evi ew pur posesonl y•

b. 2 × 3 + 2

w ww d. 8 × 2 + 5

=

+

=

k. 10 ÷ 5 – 2 =

=

+

=

l. 12 – 9 ÷ 3 = 12 –

=

3 =

. te= 3 + 12 = m. 20 – 24 ÷ 6 = – o c . che e r o t r 4 + 3 × 5 = + =s n. r 15 + 18 ÷ 3 = + s upe

e. 3 + 2 × 6

f.

m . u

c. 5 × 6 + 3

=

=

g. 8 + 4 × 9

=

+

=

o. 21 – 12 ÷ 4 =

+

=

h. 9 – 2 × 4

=

=

p. 36 ÷ 9 + 3 =

+

=

21


*   Rule Of Order 2 zz The rule of order states that you must do × and ÷ before + and – . Example 1

6+3×4

Example 2

So 6 + 3 × 4 = 6 + 12 = 18

*  Task a

So 10 – 16 ÷ 4 = 10 – 4 = 6

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

Re-write these sums and then solve them. = 15 + 7 =

e. 11 + 9 × 5 =

+

=

ew i ev Pr

Teac he r

a. 5 × 3 + 7

10 – 16 ÷ 4

b. 9 × 3 + 6

=

+

=

f. 30 – 4 × 4 =

+

=

c. 7 × 8 + 9

=

+

=

g. 45 ÷ 5 – 7 =

+

=

d. 6 + 7 × 7

= 6 + 49 =

h. 60 – 42 ÷ 6 =

=

© ReadyEdPubl i cat i ons zz If the sum has more than one × or ÷ part to it, you just do them in the order they appear.• Look at these two examples: f o rr e v i ew pur posesonl y• Example 2 65 – 30 ÷ 5 × 3

65 – 30 ÷ 5 × 3 = 65 – 6 × 3 = 65 – 18 = 47 Divide first Then multiply Then subtract

Solve these sums by following the rule of order. *  Task b . te

a. 3 × 4 + 2 × 7

b. 30 ÷ 3 + 4 × 5

22

m . u

w ww

Example 1 4 × 5 ÷ 10 + 3 4 × 5 ÷ 10 + 3 = 20 ÷ 10 + 3 = 2 + 3 = 5 Multiply first Then divide Then add

o = c . che e r o t r s = sup e = = r = 12 + 14

= 12 + 2 × 7

c. 7 + 16 ÷ 4 × 3 =

=

=

d. 40 ÷ 8 × 2 – 3

=

=

=

e. 24 ÷ 6 + 48 ÷ 8 =

=

=


*   Addition 1 Look at the following sum, 564 + 432.

Example

+

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

5

6

4

5

6

4

5

6

4

4

3

4

3

2

9

9

6

r o e t s Bo r e p ok u S 2

+

4

6

Teac he r

2

9

6

Step 2: Add the Tens 6+3=9

zz Remember to work from right to left.

*  Task a H

Try these.

T

O

H

T

O

Step 3: Add the Hundreds 5+4=9

H

T

O

© adyE2d5Pu l i cat i o8ns 6 R 4e 5b 5 2 • o evi ew u p seso y 4 f 2 r 1r + 4p 3r 3o + n 1l 3• 1

w ww

*  Task b.Try these sums.

te 42

+ 22

221 + 573

m . u

5

+

+

ew i ev Pr

Step 1: Add the Ones 4+2=6

3

o 852 c . + 147 che e r o r st super 46 + 51

264 + 721

343 + 625

465 + 322

337 + 622

23


*   Addition 2

Look at the following sum, 564 + 432.

Example

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

5

6

4

5

6

4

5

6

4

4

3

4

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

3

2

9

9

6

2

+

4

6

Teac he r

2

9

6

Step 2: Add the Tens 6+3=9

zz Remember to work from right to left.

*  Task a 35 + 24

Try these sums. 21 + 70

537 + 422

346 + 143

582 + 411

+

Step 3: Add the Hundreds 5+4=9

ew i ev Pr

Step 1: Add the Ones 4+2=6

3

243 + 515

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

842 + 131

w ww

832 + 121

*  Task b

. te

235 + 624

m . u

+

Hundreds

o c . che e r o t r s super 373 + 522

864 + 121

253 + 735

Try these on some spare lined paper.

626 + 373

847 + 142

448 + 321

793 + 102

4263 + 5132

6351 + 3220

1262 + 7127

4462 + 3231

24


*   Addition: Regrouping 1 Look at the following sum: 564 + 428.

Example

1

+

5

6

4

2

1 4

5

6

4

4

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

2

8

9

9

2

8

5 +

4

2

6

4

2

2

9

2

Step 2: Add the Tens 1+6+2=9

+

Step 3: Add the Hundreds 5+4=9

ew i ev Pr

Step 1: Add the Ones 4 + 8 = 12 The 2 is placed in the Ones column and the 1 is regrouped to the Tens.

Teac he r

1

zz Remember to work from right to left.

a Try these. *  Task © ReadyEdPubl i cat i ons • o evi ew2pu p7oseson y 5 f 6 r 4r 5r 8l 5 •6 4

2

9

+

4

3

7

+

1

3

5

w ww

m . u

+

. Now try without the grid. te * o c . 856 ch e 48 46 254 r o + 137 t + 22 + e 36 + s 729 r super   Task b

367 + 129

416 + 229

7348 + 1439

4526 + 1347

25


*   Addition: Regrouping 2 Look at the following sum: 564 + 428.

Example

1

+

5

6

4

2

1 4

5

5

4

6

4

4

2

8

9

9

2

r o e t s Bo r e p ok u S 8

+

4

2

2

2

9

2

Step 2: Add the Tens 1+6+2=9

zz Remember to work from right to left.

+

Step 3: Add the Hundreds 5+4=9

ew i ev Pr

Step 1: Add the Ones 4 + 8 = 12 The 2 is placed in the Ones column and the 1 is regrouped to the Tens.

Teac he r

6

1

w ww 546 + 136

. te

437 + 225

*  Task b

336 + 247

546 + 315

m . u

Try these. *  Task a © ReadyEdPubl i cat i ons 35 11 37 243 orr e vi w pur p eson+ l y + 27•f + 79e + o 24 s 219•

228 + 524

o c . che e r o t r s super 328 + 523

258 + 128

237 + 239

Try these on some spare lined paper.

224 + 349

647 + 128

435 + 226

293 + 108

4257 + 3136

6147 + 2225

1545 + 3126

3429 + 3138

26


*   Addition: Regrouping 3 Look at the following sum: 565 + 359.

Example

1

+

5

6

3

5

5

1

1

5

6

1

5

6

5

3

5

9

9

2

4

r o e t s Bo r e p ok u S 9

+

3

4

5

9

2

4

+

Step 2: Add the Tens Step 3: Add the Hundreds 1+5+3=9 1 + 6 + 5 = 12 The 2 is placed in the Tens column and the 1 is regrouped to the Hundreds.

ew i ev Pr

Step 1: Add the Ones 5 + 9 = 14 The 4 is placed in the Ones column and the 1 is regrouped to the Tens.

Teac he r

5

1

*  Task a Try these. © ReadyEdPubl i cat i ons 4 6 5 7 7 • f o r4r evi ew2pu r p7oseson l y •6 4

5

9

+

4

4

7

+

1

3

5

w ww

m . u

+

. Now try without the grid. te o c . che e r o t r s super

*

  Task b

668 + 252

346 + 576

254 + 649

+

588 + 134

463 + 277

674 266

+

656 177

+

462 359

27


*   Addition: Regrouping 4 Look at the following sum: 464 + 459. Remember to work from right to left. Each time the answer is 10 or more, you must regroup the 1 in the next column.

Example

1

4

6

4

5

9

2

*  Task a

4

Step 1:

Add the Ones 4 + 9 = 13 Put down the 3, regroup the 1.

9

Step 2:

Add the Tens 1 + 6 + 5 = 12 Put down the 2, regroup the 1.

3

Step 3:

Add the Hundreds 1+ 4 + 4 = 9 Put down the 9.

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

Try these.

135 + 477

481 + 129

677 + 224

ew i ev Pr

Teac he r

+

1

243 + 269

© ReadyEdPubl i cat i ons •f orr e vi ew pur poseson l y• 576 386 446 198

w ww 237 + 285

. te

*  Task b

+ 347

+ 395

378 + 424

257 + 168

+ 524

m . u

+ 136

287 + 237

o c . che e r o t r s super

Try these on some spare lined paper.

185 + 349

697 + 129

236 + 286

297 + 358

4257 + 3186

6148 + 2275

1547 + 3186

3429 + 3179

9873 + 149

1684 + 2157

7483 + 2189

9862 + 3169

28


*   Subtraction 1 Look at the following sum: 964 – 632.

Example

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

9

6

4

9

6

4

9

6

4

6

3

6

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

3

2

3

3

2

2

6

2

Teac he r

2

3

2

Step 2: Take away the Tens 6 –3=3

Step 3: Take away the Hundreds 9 –6=3

ew i ev Pr

Step 1: Take away the Ones 4 –2=2

3

zz Remember to work from right to left.

Hundreds

Tens

Ones

4

5

1

Hundreds

Tens

Ones

4

3

3

w ww

Try these sums. *  Task b. te 42 – 22

998 – 773

Hundreds

Tens

Ones

6

3

1

m . u

*  Task a Try these. © ReadyEdPubl i cat i ons 5 6 2 9 5 3 8 5 2 •f orr evi ew pur posesonl y•

o c . ch 52 864 859 e r o – e 41 – 721 – 747 r st super 847 – 625

465 – 352

937 – 622

29


*   Subtraction 2 Look at the following sum: 964 – 632.

Example

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

9

6

4

9

6

4

9

6

4

6

3

6

3

2

3

3

2

r o e t s Bo r e p ok u S 2

6

2

Teac he r

2

3

2

Step 2: Take away the Tens 6 –3=3

zz Remember to work from right to left.

*  Task a

Try these sums.

Step 3: Take away the Hundreds 9 –6=3

ew i ev Pr

Step 1: Take away the Ones 4 –2=2

3

d 81 b 37l s 846 © Rea y E d P u i c a t i o n – 70 – 26 – 515 •f orr evi ew pur posesonl y•

w ww

942 – 831

832 – 721

*  Task b

. te

388 – 143

692 – 471

835 – 624

m . u

35 – 24

o c . che e r o t r s super 373 – 162

864 – 621

859 – 735

Try these on some spare lined paper.

998 – 373

847 – 642

448 – 326

793 – 392

8263 – 7142

6391 – 5260

8268 – 7157

4462 – 3251

30


*   Subtraction: Regrouping 1

Look at the following sum, 964 – 636.

Example

9

6

4

6

3

6

9

5

6

1

6

4 6

3

r o e t s Bo r e p ok u S 8

9 6

5

1

6

Step 2: The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8

9

4

3

6

2

8

5

1

6

6

3

3

2

ew i ev Pr

Teac he r

Step 1: Take away the Ones. 4 – 6 can’t be done so regroup from the Tens.

4 6

8

© ReadyEdPu bl ca t i o n s Step 4:i Take away the Hundreds 9 –6=3 •f orr evi ew pur posesonl y•

Step 3: Take away the Tens 5 –3=2

*  Task a

Try these.

w ww 5

4

6

2

5 4 . t e

9

5

3

m . u

zz Remember to work from right to left.

8

5

o c . che e r o t r s super –

4

3

*  Task b

Now try without the grid.

46 – 28

64 – 47

6

865 – 729

6

3

2 5

851 – 747

31


*   Subtraction: Regrouping 2 Look at the following sum, 964 – 636. Remember to work from right to left.

Example

5

9 6

3

3

2

*  Task a

4 6

Take away the Tens 5 –3=2

8

Take away the Hundreds 9 –6=3

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

Try these.

35 – 27

91 – 79

33 – 24

546 – 136

336 – 247

546 – 315

ew i ev Pr

Teac he r

1

6

Take away the Ones. 4 – 6 can’t be done so regroup from the Tens. The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8

243 – 119

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

*  Task b

. te

m . u

w ww 437 – 225

528 – 224

o c . che e r o t r s super 528 – 323

458 – 128

937 – 239

Try these on some spare lined paper.

844 – 329

647 – 128

435 – 226

293 – 108

4257 – 3136

6547 – 2225

9545 – 3126

3425 – 3138

32


*   Subtraction: Regrouping 3 Look at the following sum, 964 – 676. Remember to work from right to left.

Example

9

6

4

6

7

6

9

5

6

6

1

4 6

7

r o e t s Bo r e p ok u S 8

8

9 6

15

1

6

Step 2: The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8 8

4

7

6

8

8

9

5

6

6

7

2

8

1

ew i ev Pr

Teac he r

Step 1: Take away the Ones. 4 – 6 can’t be done so regroup from the Tens.

4

6

8

© ReadyEdPu bl i cat i ons Step 4: Take away the Hundreds 8o – 6s = 2e •f orr evi ew pur p sonl y•

w ww

*  Task a 6

4

Try these.

m . u

Step 3: Take away the Tens 5 – 7 can’t be done so regroup from the Hundreds. The 5 becomes 15 and the 9 becomes 8.

. t – – 8e 4 4 7 6 6 o6 c . che e r o t r s super

*  Task b 736 – 658

6

2

9

5

3

8

4

2 5

Now try without the grid. 964 – 777

865 – 589

651 – 267

33


*   Subtraction: Regrouping 4 Look at the following sum, 964 – 636. Remember to work from right to left.

Example

8

15

1

6

6

7

2

8

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

Take away the Tens 5 – 7 can’t be done so regroup from the Hundreds. The 5 becomes 15 and the 9 becomes 8. 15 – 7 = 8

8

Take away the Hundreds 8 –6=2

Try these sums.

835 – 257

411 – 179

524 – 337

– 146

– 237

– 345

427 – 235

838 – 593

628 – 159

ew i ev Pr

*  Task a

4 6

Teac he r

9

Take away the Ones 4 – 6 can’t be done so regroup from the Tens. The 4 becomes 14 and the 6 becomes 5. 14 – 6 = 8

623 – 239

© ReadyEdPubl i cat i ons •f orr e vi ew pur p oseson l y • 533 446 536 828

*  Task b

4237 – 3156

34

m . u

w ww 864 – 399

. te

– 524

857 – 279

o c . che e r o t r s super 627 – 148

425 – 236

8127 – 2245

9535 – 3186

563 – 198

Challenge: 9449 – 3188


*   Addition And Subtraction 1 Calculate each of the following using the written strategies you have learnt. Be sure to clearly show your working out. 84 – 47

d

b

75 + 42

c

23 + 10 + 45

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

32 + 51 + 12

e

58 + 27

f

ew i ev Pr

Teac he r

a

53 -24

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

68 – 11 – 25

w ww

. te

j

74 – 36

h

87 – 12 – 35

i

84 + 32

m . u

g

o c . che e r o t r s su95p 62 – 47 –e 49 r k

l

35


*   Addition And Subtraction 2 Calculate each of the following using the written strategies you have learnt. Be sure to clearly show your working out. 453 – 236

c

542 + 813

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

775 – 491

e

262 + 374

f

ew i ev Pr

d

b

672 – 538

Teac he r

a

995 – 128

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

724 + 269

w ww

. te

j

36

462 – 225

h

529 – 381

i

341 + 923

m . u

g

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

246 + 671

l

949 – 362


*   Real Life Addition

Answer each of these word problems and be sure to show how you got your answer. If James has $25 and Melissa has $32 more than James, how much does Melissa have?

e

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

In the summer months the Bradley household uses 742 units of electricity and in the winter months they use 595 units of electricity. How much have they used altogether?

d

Brett and Susie are going on a holiday. They drive 175 km from Perth to Bunbury and then another 279 km. How far is the total journey?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• f

In a local primary school there are 24 students in Year 1, 31 students in Year 2 and 29 students in Year 3. How many students are there in total in these three year groups?

Michael is 12 years older than Nicole. Nicole is 32 years older than Jamie. Jamie is 8 years old. How old is Michael?

w ww

. te

g

The Kirtz family drank 5423 ml of milk last week and this week they’ve drunk 2374 ml of milk. How much milk have they drunk in two weeks?

m . u

c

b

ew i ev Pr

Teac he r

a

o c . che e r o Samantha is writing a story. On t Max looks at his bank statement and r s super Monday she wrote 435 words, on sees that he spent $230 on clothes, h

$157 on groceries and $75 on petrol. How much did he spend altogether?

Tuesday she wrote 240 words and on Wednesday she wrote 562 words. How many words has she written so far?

37


*   Real Life Subtraction Answer each of these word problems and be sure to show how you got your answer. Jonathon is 12 years younger than Amy, who is 44 years old. How old is Jonathon?

e

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

Jack has $50 to spend at Seaworld. He has already spent $23. How much money does he have left to spend?

The Lims have a jar of money in their kitchen with $75 in it. Lucy took $11, Mrs Lim took $22 and Mr Lim took $32. How much money is left in the jar?

w ww

38

d

Martin is reading a book that has 356 pages. So far he has read 125 pages. How many pages does he have left to read?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

. te

g

A group of friends are playing Pass-theParcel at Cynthia’s birthday. Cynthia’s mum wrapped the parcel 20 times and 7 layers of paper have been removed. How many layers are left?

f

Tania is watching a YouTube video which is 195 seconds long. She pauses the video and sees she has 80 seconds left to watch. How much has she watched already?

m . u

c

b

ew i ev Pr

Teac he r

a

o c . che e r o t r s super

On a particular T.V. game show, Team A has 125 points, Team B has 187 points and Team C has 163 points. How many points does Team A need to beat Team B?

h

The Dibley family have 25 000 MB of internet data to use each month. So far they have used 13 500 MB. How much do they have left to use this month?


*   Real Life Addition And Subtraction Answer each of these word problems and be sure to show how you got your answer. Michelle is writing a short story for her teacher. It has to be 1 200 words long. So far Michelle has written 865 words. How many more words does she need before she’s completed her story?

e

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

Rebecca’s dad is 186 cm tall. Rebecca is 55 cm shorter than her dad. How tall is Rebecca?

d

Sam and Emily are on the same team playing a computer game. Sam has scored 245 points and Emily has scored 223 points. Oliver and Jane are on the other team and Oliver has scored 195 points and Jane has scored 264 points. Which team is winning?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

w ww

There are 18 433 cities and towns in the USA. Pierre has visited 125 cities and 62 towns. How many places hasn’t he been to in the USA?

. te

g

A set of triplets have just been born. Timothy weighs 2 200 grams, Teneille weighs 3 100 grams and Tash weighs 2 750 grams. How much do the triplets weigh altogether?

f

There are 40 320 ways to arrange 8 people in a line for a photo. The fussy photographer has so far tried 280 different ways to arrange these 8 people. How many more ways can the photographer arrange these 8 people?

m . u

c

b

ew i ev Pr

Teac he r

a

o c . che e r o t r s super

The McKay family are doing a 1 000 piece jigsaw puzzle. Kelly has completed 123 pieces of the jigsaw. Michael has completed 340 pieces of the jigsaw. Mr McKay has completed 238 pieces of the jigsaw. How many pieces do they have left to complete?

h

Paul has 16 000 MB of space on his phone. He has used 8 200 MB for his photos, 4 300 MB for his songs and 245 MB for his phone list. How much space does he have left?

39


*   Multiplication: Regrouping 1

To multiply 25 × 3

Example Tens

Ones

Tens

Ones

Tens

Ones

2

5

2

5

2

5

3

×

5

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

Step 1: Multiply the Ones by the bottom number. 5 × 3 = 15

*  Task a

5

6

0

+

1

5

6

0

7

5

Step 3: Now you add

Step 2: Multiply the Tens by the bottom number. 2 × 3 = 6 Because you are in the Tens column, you put down a zero in the Ones column FIRST.

the answer rows.

15 + 60 = 75

Try these sums. Some parts have been done for you. Tens

2

×

w ww

+

*  Task b

Ones

Tens

3

4

×

+

Ones

m . u

Ones

+

. te o Try these sums. c . che e r o t r s4 9 super 2 7

Hundreds

Tens

× 2

+

40

1

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Tens

×

3

×

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1

3

×

Ones

Hundreds

4

×

8 +

Tens

Ones

3


*   Multiplication: Regrouping 2

To multiply 25 × 3

Example

Tens

Ones

2

5

Step 1: 5 × 3 = 15

3

Step 2:

× 1

+

6

*  Task a

+

r o e t s Bo r e p ok u S 2×3=6

0

Step 3: 15 + 60 = 75

5

+ 6 0 7 5

Try these. Some parts have been done for you. Ones

Tens

Ones

2

6

1

5

Hundreds

Tens

Ones

2

9

× 2 4 ©R eady EdP ubl i ca×t i ons 4 1 2 0 • f or r evi ew2 pu r poses+onl y•

0

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+

+

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18 × 4

17 × 5

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26 × 4

+

1 5

Put down the zero.

5

Tens

  Task b * 36 ×

3

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×

×

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Teac he r

7

2 5

+

19 × 4

+

18 × 2

+

16 × 9

+

28 × 2

+

41


*   Multiplication: Regrouping 3

To multiply 65 × 3

Example Hundreds

Tens

Ones

6

5

Step 1: 5 × 3 = 15

(5 in the Ones column and 1 in the Tens.)

r o e t s Bo r e p ok u S 3

× 1

+

8

1

9

*  Task a H

Put down the zero.

5

6 × 3 = 18

5

1 9 5

Step 3: 15 + 180 = 195

Try these.

T

O

H

T

O

5

6

H

H

T

8 ×

+

42

O

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7 4

+

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0

+

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+

T

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×

1 5

+ 1 8 0

(8 in the Tens column and 1 in the Hundreds.)

0

3

×

Step 2:

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Teac he r

1

6 5

o c . che 3 6 2 e r o t r s s r u e p × × 5 H

+

T

O

H

+

T

O

9 6


*   Multiplication: Regrouping 4 To multiply 65 × 3

Example Hundreds

Tens

Ones

6

5

(5 in the Ones column and 1 in the Tens.)

Teac he r *  Task a H

T

0

9

5

6 × 3 = 18

Step 3: 15 + 180 = 195

Try these. H

T

1 9 5

O

H

T

O

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+

+

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*  Task b ×

+ 1 8 0

(8 in the Tens column and 1 in the Hundreds.)

O

1 5

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1

Put down the zero.

47 6

+

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+

8

3

×

Step 2:

5

1 1

6 5

r o e t s Bo r e p ok u S 3

×

×

Step 1: 5 × 3 = 15

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Try these.

×

74 5

×

75 7

×

86 3

43


*   Multiply These!

Calculate each of the following using the written strategies you have learnt. Be sure to clearly show your working out. 94 × 5

c

432 × 6

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

514 × 7

e

83 × 4

f

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d

b

87 × 2

Teac he r

a

97 × 5

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

352 × 8

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j

44

48 × 4

h

613 × 3

i

72 × 6

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g

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721

l

654


*   Division 1 Example

)

This sign means divided.

2 ) 24

This means how many times will 2 go into 24.

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

*  Task a

3 ) 63

12 Divide the Ones column next: 4 ÷ 2 = 2 2 24 The answer is 12.

Fill in the blanks.

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Teac he r

1 Divide the Tens column first: 2 ÷ 2 = 1 2 ) 24

This means how many times will 3 go into 63.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 2 Divide the Tens column first: 6 ÷ 3 = _________ 3 ) 63

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The answer is _________.

teFill in the blanks. *   Task B. 2 ) 48

2 ) 48 2 ) 4 8

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2 1 Divide the Ones column next: 3 ÷ 3 = _________ 3 ) 6 3

o c . Thisc means how many times will ________e go into ________. her r o t s super

Divide the Tens column first: ________ ÷ ________ = ________ Divide the Ones column next: ________ ÷ ________ = ________ The answer is ________. 45


*   Division 2 Example

)

This sign means divided.

2 ) 24

This means how many times will 2 go into 24?

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

*  Task a

3 ) 96 4 ) 84 3 ) 93

12 Divide theOnes column next: 4 ÷ 2 = 2 2 24 The answer is 12.

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Teac he r

1 Divide the Tens column first: 2 ÷ 2 = 1 2 ) 24

Try these.

The answer goes here.

9 ÷ _____ 3 = _____ 3 and _____ 6 ÷ _____ 3 = _____ 2 Answer = _____ 32 Sums are _____

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____

Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____

3 ) 99

Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____

*  Task b 63 ÷ 3

46

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Sums are _____ ÷ _____ = _____ and _____ ÷ _____ = _____ Answer = _____

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2 ) 26

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Write these like the ones above. (Hint: the smaller number goes first.) 60 ÷ 2


*   Division With Remainders 1

1 2 ) 25

Divide the Tens column first: 2 ÷ 2 = 1 (write 1 on top of the 2)

12 r1 2 ) 25

Divide the Ones column next: 5 ÷ 2

Count by twos: 2, 4, 6

What is the highest number less than 5? = 4 (goes in 2 times) (Write 2 on top of the 5.)

How many left over before you get to 5? = 1

1 is your remainder.

This means how many times will 2 go into 25.

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

Answer = 12 remainder 1 or 12 r 1

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Teac he r

25 ÷ 2 =

2 ) 25

© ReadyEdPubl i cat i ons a Fill in the blanks. *  Task •f o r evi ew pur posesonl y• r

57 ÷ 5 = 5 ) 57

5 ) 57 5 ) 57

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Divide the Tens column first: ________ ÷ ________ = ________ Divide the Ones column next: ________ ÷ ________ = ________

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This means how many times will 5 go into ________.

Count by twos: 5, 10

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What is the highest number less than 7?

How many left over before you get to 7? ________ is your remainder.

Answer = ________ r____

*  Task b

4 ) 86

= ________ (goes in ____ times) = ________

Try these.

2 ) 29

3 ) 68

6 ) 69 47


*   Division With Remainders 2 1 2 ) 25

Divide the Tens column first: 2 ÷ 2 = 1 (write 1 on top of the 2)

12 r1 2 ) 25

Divide the Ones column next: 5 ÷ 2

Count by twos: 2, 4, 6

This means how many times will 2 go into 25.

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

What is the highest number less than 5? = 4 (goes in 2 times) (Write 2 on top of the 5.) How many left over before you get to 5? = 1 1 is your remainder.

Answer = 12 remainder 1 or 12 r 1

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Teac he r

25 ÷ 2 =

2 ) 25

© ReadyEdPubl i cat i ons Try these. a f o rr evi ew pur posesonl y• *  Task•

w ww

4 ) 46

2 ) 46

*  Task b

3 ) 91

2 ) 69

3 ) 98

6 ) 67

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2 ) 60

6 ) 69

3 ) 69

Word problem:

There are 34 students in the class. If I want to make 3 rows, how many students are in each row? How many are left over?

3 ) 34

48

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2 ) 49

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4 ) 83


*   Division With Regrouping 1 In division, you regroup if you cannot divide into the first digit evenly. 2 ) 34

Divide the Tens column first: 3 ÷ 2 = 1 r 1 (Does not divide evenly)

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

Regroup by writing the remainder next to the Ones. 1 2 ) 314

Divide the Ones column next 14 ÷ 2 = 7 (Divides evenly) Answer = 17

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Teac he r

17

2 ) 314

*  Task a

Fill in the blanks.

3 ) 57

Divide the Tens column first: 5 ÷ _______ = _______ r _______

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Regroup by writing the remainder next to the Ones.

3 ) 5 7

Answer = ________

b Fill in the blanks. *  Task . te

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Divide the Ones column next: _______ ÷ _______ = _______

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3 ) 5 7

o c . 4 ) 96 Dividec the Tens column first: ______ ÷ ______ e = ______ r ______ her r o t s s r u e p Regroup by writing the remainder next to the Ones. 4 ) 9 6

Divide the Ones column next: _______ ÷ _______ = _______

4 ) 9 6

Answer = ________

49


*   Division With Regrouping 2 In division, you regroup if you cannot divide into the first digit evenly. 2 ) 34

Divide the Tens column first: 3 ÷ 2 = 1 r 1 (Does not divide evenly)

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

Regroup by writing the remainder next to the Ones.

Divide the Ones column next 14 ÷ 2 = 7 (Divides evenly)

17

2 ) 314

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Teac he r

1 2 ) 314

Answer = 17

Try these. *  Task a © Re dyEdPu l i cat i ons a b 5 ) 8 0 4 ) 6 4 3 ) 7 7 3 ) 9 8 •f orr evi ew pur posesonl y•

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7 ) 7 6 4 ) 8 6

*  Task b 69 ÷ 4

50

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9 ) 9 1

3 ) 5 5

8 ) 9 8

3 ) 5 6

6 ) 7 5

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7 ) 8 4

3 ) 8 8

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7 ) 9 5

Work these out below. 86 ÷ 4

94 ÷ 7

3 ) 5 0


Real Life Multiplication * Answer each of these word problems and be sure to show how you got your answer. 1

2

3

Sally is making party bags for her friends to take home after her party. She puts 3 snake lollies in each bag and she has 27 friends coming to her party. How many snakes does she need altogether?

r o e t s Bo r e p ok u S 4

A new dress-up doll comes with 7 pairs of shoes and 32 dresses. How many different outfits can be made?

5

A bus can sit 4 people in each row. If there are 17 rows, how many people can have a seat on this bus?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 6

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In a History multiple choice test you have 35 questions, each with 4 possible answers. How many possible answers are there in total?

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Nick can type really fast. Each minute he can type 62 words. If he has been typing for 9 minutes, how many words has he typed?

7

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Teac he r

Seven friends decide to give $6 each to buy a present for their friend’s birthday. How much money do they have altogether?

o c . che e r o t r s super 8

Matthew is making a rice dish for some friends. It says he needs 2 cups of rice for 4 people. If he has 11 friends coming over, plus himself, how many cups of rice will he need?

Samantha has only $10 and $20 notes in her purse. If she knows she has $440 in her purse and 8 $20 notes, how many $10 notes does she have?

51


Real Life Division * Answer each of these word problems and be sure to show how you got your answer. 1

2

3

Miss Thompson has 30 students in her Year 3 class. She wants to arrange the desks in groups of 5. How many groups does she need?

r o e t s Bo r e p ok u S 4

A family needs to take 21 litres of drinking water on a camping trip. How many 3 litre bottles will they have to take to make sure they have enough?

5

Robert has 64 DVDs that he wants to put in his DVD shelves. If he can fit 16 DVDs on one shelf, how many shelves does he need?

© ReadyEdPubl i cat i ons •f orr evi ew pu r posesonl y• 6

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o c . che e r o t r s super 8

Nicole needs to write a 1 500 word report for her science project. If she uses 6 pages to write her report, how many words will be on each page?

52

Billy has lived in his new house for 126 days. How many weeks is this?

m . u

w ww

Each week Craig’s parents give him $7 for doing his chores. How many weeks will he need to do chores to save up enough money to buy a $56 computer game?

7

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Teac he r

Michaela needs to make 48 cupcakes. She only has one cupcake tray with 12 spaces for cupcakes. How many times does she need to use this tray?

126 people are waiting in line to ride the Ferris Wheel. If only 14 people can be on the ride each time, and all these people want two rides on the Ferris Wheel, then how many how many rides will it take to make all these people happy?


*   Answers

Place Value 1 Page 7 Task A: 8000, 400, 20, 7 3000, 900, 70, 5 5000, 900, 20, 7 Task b: 4000, 4, 400 4, 400, 4000, 40

Task c:

Place Value 2 Page 8 Task A: 2000, 300, 60, 4 9000, 800, 40, 5 Task b: 40, 8, 900, 702, 9000, 6, 5000, 70 Task c: 2476, 8266, 9553

Teac he r 9 9 0 8 8 3

100 200 300 400 500 600 700 800 900 1000

8 8 0 7 0 5

7 6 0 6 0 4

6 3 4 8 9 9

5 4 9 5 7 7

Task d: 0 100 200 300 400 500 600 700

50 150 250 350 450 550 650 750

100 200 300 400 500 600 700 800

80 120 250 399 401 500 626 772

100 100 200 or 300 400 400 500 600 800

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4 0 2 1 2

50 150 250 350 450 550 650 750 850 950

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

Place Value 3 Page 9 Task A: 7 456 322 Task B: 5 2 4

0 100 200 300 400 500 600 700 800 900

Estimation 1 Page 13 Task A: 34, Task b: 16 Task c: 22 is close to 20, 47 is close to 50, estimate = 70 Task d: Estimate Answer 60 59 130 130 100 94 100 99 100 97 120 118

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(7 × 1 000 000) + (6 × 100 000) + (5 × 10 000) + (3 × 1000) + (1 × 10) + (2 × 1) Task d: Millions = 3 000 000, Thousands = 4000, Hundred thousands = 500 000 Greater Than/Less Than Page 10 1.<, 2.>, 3.<, 4.>, 5.>, 6.>, 7.<, 8.>, 9.<, 10.<, 11.>, 12.<, 13.>, 14.<, 15.>, 16.>

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Task C: (2 × 1 000 000) + (8 × 100 000) + (7 × 10 000) + (6 × 1000) + (5 × 100) + (4 × 10) + (3 × 1)

o c . che e r o t r s super

Rounding 1 Page 11 Task A: 2(1 also acceptable), 8 (7 also acceptable) Task b: 8 = 10, 13 = 10, 19 = 20, 16 = 20 Task c: 15 = 10 or 20, 18 = 20, 25 = 20 or 30, 27 = 30, 12 = 10, 30 = 30 Task d: 23 = 20, 67 = 70, 45 = 40 or 50, 99 = 100, 52 = 50, 38 = 40, 75 = 70 or 80, 14 =10

Estimation 2 Page 14 Task a: b. 32 + 11 = 30 + 10 = 40 c. 79 – 19 = 80 – 20 = 60 d. 151 + 39 = 150 + 40 = 190 e. 289 – 32 = 290 – 30 = 260 f. 531 – 49 = 530 – 50 = 480 Task b: a.60, b.60, c.380, d.800, e.270, f.990, g.1560

Rounding 2 Page 12 Task A: 6 = 10, 13 = 10, 18 = 20, 20 = 20, 15 = 10 or 20 Task b: 22 = 20, 64 = 60, 35 = 30 or 40, 98 = 100

Counting By … Page 15 10, 12, 14, 16, 18 12, 15, 18, 21, 24, 27 16, 20, 24, 28, 32, 36 20, 25, 30, 35, 40, 45 53


Rule Of Order 1 Page 21 Task a: 15, 6 + 2 = 8, 30 + 3 = 33, 16 + 5 = 21 15, 4 + 15 = 19, 8 + 36 = 44, 9 – 8 = 1 8, 2 + 5 = 7, 2 – 2 = 0 9, 20 – 4 = 16, 15 + 6 = 21, 21 – 3 = 18, 4 + 3 = 7 Rule Of Order 2 Page 22 Task A: 22, 27 + 6 = 33, 56 + 9 = 65 55, 11 + 45 = 56, 30 – 16 = 14, 9 – 7 = 2, 60 – 7 = 53 Task b: 26, 10+ 20= 30, 7 + 4×3 = 7 + 12 = 19, 5×2-3 = 10 – 3 = 7, 4 + 6 = 10

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

Multiples Page 16 Task A: b. 2, 6, 8, 10, 12, 14, 16, 20 c. 14, 21, 28, 42, 49, 56, 63, 70 d. 10, 30, 40, 50, 60, 80, 90, 100 e. 25, 50, 100, 125, 150, 200, 225, 250 f. 15, 30, 45, 75, 90, 120, 135, 150 g. 12, 36, 48, 60, 84, 96, 108 Task b: a. 15 b. 42 c. 30 d. 24

Addition: 1 Page 23 Task A: 985, 688, 983 Task b: 64, 97, 985, 999, 794, 968, 787, 959 Addition: 2 Page 24 Task A: 59, 91, 959, 758 973, 489, 993, 859 953, 895, 985, 988 999, 989, 769, 895 9395, 9571, 8389, 7693

ew i ev Pr

Teac he r

24, 30, 36, 42, 48, 54 28, 35, 42, 49, 56, 63 32, 40, 48, 56, 64, 72 36, 45, 54, 63, 72, 81 40, 50, 60, 70, 80, 90 44, 55, 66, 77, 88, 99 48, 60, 72, 84, 96, 108 52, 65, 78, 91, 104, 117 56, 70, 84, 98, 112, 126 60, 75, 90, 105, 120, 135 64, 80, 96, 112, 128, 144 68, 85, 102, 119, 136, 153 72, 90, 108, 126, 144, 162 76, 95, 114, 133, 152, 171 80, 100, 120, 140, 160, 180

Regrouping 1i Page 25s © ReadyEdAddition: Pub l i cat on Task A: 993, 694, 991 Factors Page 17 Task b: 70, 82, 983, 993 •f orr evi ew p496, ur p8787, os esonl y• Task a: 665, 5873

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Imagining Negative Numbers Page 18 a. 0 b. below ground level c. 7 d. No e. Post Office f. -4 + 4 + 3 – 1 + 3 – 9 Butcher/Bakery, Post Office/Newsagent, Greengrocer, Appliances, Car Park A g. Down 2, up 5, down 2, down 1

o c . che e r o t r s super

Where Am I? Page 19 Task a: a.-3 b.9 c.2 d.-10 e.6 f.-13 g.-5 h.19 i. -8 j.-12 Task b: a.15 b.-5 c.-10 d.-6 e.-3, 0 f.-5, -9 g.10, 18 h.-40, -46 i.103, 113 j.23, 38 k.-74, -95 l.-360, -685 54

Addition: Regrouping 2 Page 26 Task A: 62, 90, 61, 462 682, 583, 861, 752 662, 851, 386, 476 Task b: 573, 775, 661, 401 7393, 8372, 4671, 6567

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b. 1, 2, 5, 10 c. 1, 2, 3, 4, 6, 8, 12, 24 d. 1, 2, 4, 5, 10, 20, 25, 50, 100 e. 1, 2, 3, 4, 6, 9, 12, 18, 36 f. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Task b: b. 15 c. 9 d. 18 e. 4

Addition: Regrouping 3 Page 27 Task A: 923, 704, 911 Task b: 920, 922, 903, 833 940, 722, 740, 821

Addition: Regrouping 4 Page 28 Task A: 612, 610, 901, 512 712, 733, 841, 722 522, 802, 425, 524 Task b: 534, 826, 522, 655 7443, 8423, 4733, 6608 10 022, 3841, 9672, 13 031


Subtraction 1 Page 29 Task A: 111, 520, 221 Task b: 20, 11, 143, 112 225, 222, 113, 315

Real Life Subtraction Page 38 44 - 12 = 32 yo 20 – 7 = 13 layers 50 – 23 = $27 356 – 125 = 231 pages 75 – 11- 22- 32 = $10 95 – 80 = 115 seconds 187 – 125 = 62, so 63 points 25 000 – 13 500 = 11 500 MB

Subtraction 2 Page 30 Task A: 11, 11, 11, 331 111, 245, 221, 211 111, 211, 243, 124 625, 205, 122, 401 1121, 1131, 1111, 1211

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

Subtraction: Regrouping 2 Page 32 Task A: 8, 12, 9, 124 410, 89, 231, 304 212, 205, 330, 698 Task b: 515, 519, 209, 185 1121, 4322, 6419, 287 Subtraction: Regrouping 3 Page 33 Task A: 178, 477, 177 Task b: 78, 187, 276, 384

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Teac he r

Subtraction: Regrouping 1 Page 31 Task A: 108, 517, 217 Task b: 18, 17, 136, 104

Real Life Addition And Subtraction Page 39 1200 – 865 = 335 words 2200 + 3100 + 2750 = 8050 g 186 – 55 = 131 cm 245 + 223 = 468 195+ 264 = 459 Sam and Emily 18433 – 125- 62 = 18246 places 40320 – 280 = 40 040 ways 1000 – 123 – 340 – 238 = 299 pieces 16 000 – 8200 – 4300 – 245 = 3255MB Multiplication: Regrouping 1 Page 40 Task A: 72, 81, 96 Task b: 108, 147

Multiplication: Regrouping 2 Page 41 Task A: 52, 60, 116 Task b: 72, 72, 85, 36 104, 76, 144, 56

© ReadyEdPubl i cat i ons Subtraction: Regrouping 4 Page 34 orr evi ew pur posesonl y• Task A: •f

Addition And Subtraction 1 Page 35 a.37, b.117, c.78, d. 95, e.85, f.29, g.32, h.40, i.116 j.38, k.46, l.15

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Multiplication: Regrouping 3 Page 42 252, 476, 222 348, 180, 174

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578, 232, 187, 384 387, 209, 191, 304 192, 245, 469, 578 465, 479, 189, 365 Task b: 1081, 5882, 6349, 6261

Multiplication: Regrouping 4 Page 43 Task A: 90, 399, 144 Task b: 282, 370, 525, 258

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Addition And Subtraction 2 Page 36 a.134, b.217, c.1355, d.284, e.636, f.867, g.993, h.148, i.1264, j.237, k.917, l.587 Real Life Addition Page 37 25 + 32 = $57 5423 + 2374 = 7797 ml 742 + 595 = 1337 units 175 + 279 = 454 km 8 + 32 + 12 = 52 yo 24 + 31 + 29 = 84 students 230 + 157 + 75 = $462 435 + 240 + 562 = 1237

Multiply These! Page 44 a. 174 b. 470 c. 2592 d. 3598 e. 332 f. 485 g. 2816 h. 1839 i. 432 j. 192 k. 1442 l. 1962 Division 1 Page 45 21, 24

Division 2 Page 46 Task A: 8÷4 = 2, 4÷4=1 Answer = 21 9÷3 = 3, 3÷3=1, Answer = 31 2÷2=1, 6÷2=3, Answer = 13 9÷3=3, 9÷3=3, Answer = 33

55


Division With Remainders 1 Page 47 Task A: 5÷5=1, 7÷5 (goes in 1 time), 2 left over, 2 is your remainder. Answer = 11 r2 Task b: 21 r 2; 14 r 1; 22 r 2; 11 r 3 Division With Remainders 2 Page 48 Task A: 20 r 3; 24 r 1; 30 r 1; 11 r 1; 11 r 2; 34 r 1; 32 r 2; 11 r 3; 23; 33; 30; 23 Task b: 11 r 1

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Division With Regrouping 2 Page 50 Task A: 16; 14; 25 r 2; 32 r 2; 12; 10 r 1; 18 r 1; 12 r 3; 10 r 6; 12 r 2; 18 r 2; 29 r 1; 21 r 2; 16 r 2; 13 r 4; 16 r 2 Task b: 17 r 1; 21 r 2; 13 r 3

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

Division With Regrouping 1 Page 49 Task A: Divide the tens column first: 5÷3 = 1 r 2 Divide the ones column next: 27 ÷ 3 =9 Answer = 19 Task b: Divide the tens column first: 9 ÷4 = 2 r 1 Divide the ones column next: 16 ÷4 = 4 Answer = 24

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1. 7×6=$42. 2. 27×3=81 lollies 3. 7×32=224 outfits 4. 17×4=68 people 5. 62×9=558 words 6. 35×4=140 answers 7. 3×2=6 cups of rice 8. 28 $10 notes

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Real Life Division Page 52 1. 48÷12=4 times 2. 30÷5= 6 groups 3. 21÷3 = 7 bottles 4. 64÷16 = 4 shelves 5. 56÷7 = 8 weeks 6. 126 ÷7 = 18 weeks 7. 1500 ÷ 6 = 250 words 8. 18 rides

56

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© ReadyEdPubl i cat i ons •f or r e i ew pur posesonl y• Real Life Multiplication Page 51v

o c . che e r o t r s super


Striving to Improve: Mathematics - Integers