E S S E N T I A L E X E R C I S E S YEAR 5 SAMPLE · PDF filemeasurements and creating...

iEssential Exercises – Year 5 Maths

Warwick Marlin © Five Senses Education

E S S E N T I A LE X E R C I S E S

YEAR 5M A T H S

AuthorsJomary Roble B.Sc. Ed.

Warwick Marlin B.Sc. Dip.Ed.

iEssential Exercises – Year 5 Maths


E S S E N T I A LE X E R C I S E S

YEAR 5M A T H S

AuthorsJomary Roble B.Sc. Ed.

Warwick Marlin B.Sc. Dip.Ed.SAM

PLE

vEssential Exercises – Year 5 Maths


Page

CONTENTS

INTRODUCTION

• Acknowledgements iii• Availability of books in this series iv• The New National Australian Curriculum vi• Some features and benefits of this book vii

NUMBER & ALGEBRA

NUMBER AND PLACE VALUE 2

FRACTIONS AND DECIMALS 16

MONEY & FINANCIAL MATHEMATICS 30

PATTERNS AND ALGEBRA 42

MEASUREMENT & GEOMETRY

USING UNITS OF MEASUREMENT 52

SHAPE 66

LOCATION AND TRANSFORMATION 76

GEOMETRIC REASONING 88

STATISTICS & PROBABILITY

CHANCE 100

DATA REPRESENTATION AND INTERPRETATION 110

APPENDIX

USEFUL CHARTS AND OTHER INFORMATION 121

SOLUTIONS TO GRADED EXERCISES 131

NOTE: The New Australian National Curriculum has been split into 3 major strands:

A Number & Algebra B Measurement & Geometry C Statistics & Probability

In the Year 5 content descriptions, these 3 major strands have been further subdivided into the sub-strands shown above.

vEssential Exercises – Year 5 Maths


Page

CONTENTS

INTRODUCTION

• Acknowledgements iii• Availability of books in this series iv• The New National Australian Curriculum vi• Some features and benefits of this book vii

NUMBER & ALGEBRA

NUMBER AND PLACE VALUE 2

FRACTIONS AND DECIMALS 16

MONEY & FINANCIAL MATHEMATICS 30

PATTERNS AND ALGEBRA 42

MEASUREMENT & GEOMETRY

USING UNITS OF MEASUREMENT 52

SHAPE 66

LOCATION AND TRANSFORMATION 76

GEOMETRIC REASONING 88

STATISTICS & PROBABILITY

CHANCE 100

DATA REPRESENTATION AND INTERPRETATION 110

APPENDIX

USEFUL CHARTS AND OTHER INFORMATION 121

SOLUTIONS TO GRADED EXERCISES 131

NOTE: The New Australian National Curriculum has been split into 3 major strands:

A Number & Algebra B Measurement & Geometry C Statistics & Probability

In the Year 5 content descriptions, these 3 major strands have been further subdivided into the sub-strands shown above.

SAMPLE

viEssential Exercises – Year 5 Maths Warwick Marlin © Five Senses Education

The authors acknowledge the dedicated work of the Australian Curriculum, Assessment and Reporting Authority (ACARA) and the many others who have contributed to the development of the Australian curriculum in response to the aims of the 2008 Melbourne Declaration on Educational Goals for Young Australians.

This book provides a summary and interpretation of their guidelines for those interested in developing mathematical understanding in Year 5 students.

The Australian National Curriculum, developed by ACARA, states that, by the end of Year 5, students should be able to do the following:

identify and describe factors and multiples. use estimation and rounding to check if answers look reasonable. solve multiplication and division problems. compare, order and represent decimals. perform addition and subtraction of fractions with the same denominator. continue patterns with fractions and decimals. plan simple budgets. list the outcomes of chance experiments as fractions. pose questions to gather data. construct, describe and interpret different data sets. calculate perimeter and area of rectangles. connect and construct different angles. describe transformations of 2 dimensional shapes. describe the enlargement transformation. identify line and rotational symmetry.

THE MATHEMATICS CURRICULUM OPERATES ON ANOTHER LEVEL, THE SO CALLED PROFICIENCY LEVEL.

The Proficiency strands at this level include:

1. Understanding: includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry.

2. Fluency: includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles.

3. Problem solving: includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans.

4. Reasoning: includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate question for data investigations and interpreting data sets.

THE NEW NATIONAL AUSTRALIAN CURRICULUM

viEssential Exercises – Year 5 Maths Warwick Marlin © Five Senses Education

The authors acknowledge the dedicated work of the Australian Curriculum, Assessment and Reporting Authority (ACARA) and the many others who have contributed to the development of the Australian curriculum in response to the aims of the 2008 Melbourne Declaration on Educational Goals for Young Australians.

This book provides a summary and interpretation of their guidelines for those interested in developing mathematical understanding in Year 5 students.

The Australian National Curriculum, developed by ACARA, states that, by the end of Year 5, students should be able to do the following:

identify and describe factors and multiples. use estimation and rounding to check if answers look reasonable. solve multiplication and division problems. compare, order and represent decimals. perform addition and subtraction of fractions with the same denominator. continue patterns with fractions and decimals. plan simple budgets. list the outcomes of chance experiments as fractions. pose questions to gather data. construct, describe and interpret different data sets. calculate perimeter and area of rectangles. connect and construct different angles. describe transformations of 2 dimensional shapes. describe the enlargement transformation. identify line and rotational symmetry.

THE MATHEMATICS CURRICULUM OPERATES ON ANOTHER LEVEL, THE SO CALLED PROFICIENCY LEVEL.

The Proficiency strands at this level include:

1. Understanding: includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry.

2. Fluency: includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles.

3. Problem solving: includes formulating and solving authentic problems using whole numbers and measurements and creating financial plans.

4. Reasoning: includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate question for data investigations and interpreting data sets.

THE NEW NATIONAL AUSTRALIAN CURRICULUM

SAMPLE

2Year 5 Essential Exercises Warwick Marlin © Five Senses Education

PLACE VALUE

Our number system today is based on the Hindu-Arabic system where the VALUE of a number is determined by its PLACE in a particular column. Example: What does 34 972 really mean?

The place value of 3 is 3 × 10 000 or 30 000.


The place value of 9 is 9 × 100 or 900.



3 MAIN WAYS OF DESCRIBING A NUMBER

1. As an ordinary numeral: 34 972. 2. In words: Thirty Four thousand, nine hundred and seventy two.

3. In expanded notation: (3 × 10 000) + (4 × 1 000) + (9 × 100) + (7 × 10) + (2 × 1).

Note: We can also describe numbers using Base Ten blocks, the abacus, and numeral expanders.

NUMBER AND PLACE VALUE

It can be seen that each column has a different

PLACE VALUE.

The“AustralianCurriculumMathematics”(ACM)referencesforthissub-strandof“NumberandAlgebra”(NA) arebelow:

• Identifyanddescribefactorsandmultiplesofwholenumbersandusethemtosolveproblems (ACMNA098).

• Useestimationandroundingtocheckthereasonablenessofanswerstocalculations(ACMNA099).

• Solveproblemsinvolvingmultiplicationoflargenumbersbyoneortwo-digitnumbersusing efficientmentalorwrittenstrategies,andappropriatedigitaltechnologies(ACMNA100).

• Solveproblemsinvolvingdivisionbyaonedigitnumber,includingthosethatresultina remainder(ACMNA101).

• Useefficientmentalorwrittenstrategiesandappropriatedigitaltechnologiestosolveproblems (ACMNA291).

100

000

10 0

0010

0010

010 1

million

s

hund

red th

ousan

ds

ten th

ousan

ds

thousa

nds

hund

reds

tens

ones

or un

its

1 00

0 00

0

3 4 9 7 2


PLACE VALUE

Our number system today is based on the Hindu-Arabic system where the VALUE of a number is determined by its PLACE in a particular column. Example: What does 34 972 really mean?






3 MAIN WAYS OF DESCRIBING A NUMBER

1. As an ordinary numeral: 34 972. 2. In words: Thirty Four thousand, nine hundred and seventy two.

3. In expanded notation: (3 × 10 000) + (4 × 1 000) + (9 × 100) + (7 × 10) + (2 × 1).

Note: We can also describe numbers using Base Ten blocks, the abacus, and numeral expanders.

NUMBER AND PLACE VALUE

It can be seen that each column has a different

PLACE VALUE.

The“AustralianCurriculumMathematics”(ACM)referencesforthissub-strandof“NumberandAlgebra”(NA) arebelow:

• Identifyanddescribefactorsandmultiplesofwholenumbersandusethemtosolveproblems (ACMNA098).

• Useestimationandroundingtocheckthereasonablenessofanswerstocalculations(ACMNA099).

• Solveproblemsinvolvingmultiplicationoflargenumbersbyoneortwo-digitnumbersusing efficientmentalorwrittenstrategies,andappropriatedigitaltechnologies(ACMNA100).

• Solveproblemsinvolvingdivisionbyaonedigitnumber,includingthosethatresultina remainder(ACMNA101).

• Useefficientmentalorwrittenstrategiesandappropriatedigitaltechnologiestosolveproblems (ACMNA291).

100

000

10 0

0010

0010

010 1

million

s

hund

red th

ousan

ds

ten th

ousan

ds

thousa

nds

hund

reds

tens

ones

or un

its

1 00

0 00

0

3 4 9 7 2

SAMPLE

3Year 5 Essential Exercises


FACTORS

A factor is a number which leaves The factors of 12 are no remainder after division. { 1, 2, 3, 4, 6, 12}.

HIGHEST COMMON FACTOR (HCF)

This is the highest factor which is common to 2 or more numbers.

Example: Find the highest common factor of 12 and 20. Factors of 12 are {1, 2, 3, 4, 6, 12}. Factors of 20 are {1, 2, 4, 5, 10, 20}. \ The HCF of 12 and 20 is 4.

MULTIPLES

Tofindthemultiplesofaparticularcountingnumber,simplymultiplyitbythecounting numbers.

Saywewishedtofindthefirst5multiplesof7.

1 × 7 = 7 OR 2 × 7 = 14 We can 3 × 7 = 21 draw a 4 × 7 = 28 WEB: 5 × 7 = 35

Thefirst5multiplesof7 are {7, 14, 21, 28, 35}.

LOWEST COMMON MULTIPLE (LCM)

This is the lowest multiple which is common to 2 or more numbers.

Example: Find the LCM of 8 and 10. Multiples of 8 are {8, 16, 24, 32, 40, 48,....}. Multiples of 10 are {10, 20, 30, 40, 50,....}. \ The LCM of 8 and 10 is 40.

AVERAGE

Theaverageofasetofscoresisobtainedbyfinding the total, and dividing by the number of scores. The average of 7, 11 and 15 = 7 + 11 + 15 = 33 = 11. 3 3

355

428 3

21

142

7

1

×7

Please refer to page 124 for a more detailed explanation.



FACTORS

A factor is a number which leaves The factors of 12 are no remainder after division. { 1, 2, 3, 4, 6, 12}.

HIGHEST COMMON FACTOR (HCF)

This is the highest factor which is common to 2 or more numbers.

Example: Find the highest common factor of 12 and 20. Factors of 12 are {1, 2, 3, 4, 6, 12}. Factors of 20 are {1, 2, 4, 5, 10, 20}. \ The HCF of 12 and 20 is 4.

MULTIPLES

Tofindthemultiplesofaparticularcountingnumber,simplymultiplyitbythecounting numbers.

Saywewishedtofindthefirst5multiplesof7.

1 × 7 = 7 OR 2 × 7 = 14 We can 3 × 7 = 21 draw a 4 × 7 = 28 WEB: 5 × 7 = 35

Thefirst5multiplesof7 are {7, 14, 21, 28, 35}.

LOWEST COMMON MULTIPLE (LCM)

This is the lowest multiple which is common to 2 or more numbers.

Example: Find the LCM of 8 and 10. Multiples of 8 are {8, 16, 24, 32, 40, 48,....}. Multiples of 10 are {10, 20, 30, 40, 50,....}. \ The LCM of 8 and 10 is 40.

AVERAGE

Theaverageofasetofscoresisobtainedbyfinding the total, and dividing by the number of scores. The average of 7, 11 and 15 = 7 + 11 + 15 = 33 = 11. 3 3

35

5

428 3

21

142

7

1

×7

Please refer to page 124 for a more detailed explanation.

SAMPLE


ROUNDING OFF

In some situations in Maths, particularly when using a calculator, we do not require the exact answer, but an approximate answer only. The question will then ask you to ROUND OFF the given number to the nearest ten, nearest hundred or nearest thousand.

Example: If we round off 73 to the nearest ten, then the answer is 70, because 73 is closer to 70 than it is to 80. If we round off 659 to the nearest hundred, then the answer is 700, because 659 is closer to 700 than it is to 600.

ESTIMATING

When using a calculator, you will be surprised how easy it is to press the wrong button and then get a ridiculous answer which is way out from the correct answer. If we quickly and mentally estimate an approximate answer to begin with, then this will prevent us from making careless blunders. Estimate the answer to 469 + 1 728 469 rounds off to 500. 1 728 rounds off to 1 700. Therefore ESTIMATE = 500 + 1 700 = 2 200

ADDING WHOLE NUMBERS ( + SIGN)

Start with the far right hand column of digits. Add them up and place the ‘carry over’ at the top of the next column in smaller print, as shown in the example below.

3 + 4 + 5 = 12. Write down the number 2 and place the carry over 1 at the top of the next column.

1 + 8 + 9 + 7 = 25. Write down the number 5 and place the carry over 2 at the top of the next column.

Repeat these steps for the next 3 columns as shown.

SUBTRACTING WHOLE NUMBERS ( – SIGN)

The most popular and widely used method is called “TRADING” or “DECOMPOSITION”. Inthefirstunitcolumn,9subtract4=5 In the second tens column, 2 cannot subtract 8. We trade one hundred from the hundreds column and change the 5 into a 4 as shown. We now have 12 in the tenscolumn.12subtract8=4,andfinallyinthe hundreds column, 4 – 3 = 1.

}‘carry over numbers’ 1 1 2 1

7 6 8 35 9 4

+ 8 6 3 7 59 4 6 5 2

Step 2 :

Step 1 :

H T U 4 1

5 2 9 – 3 8 4

1 4 5


ROUNDING OFF

In some situations in Maths, particularly when using a calculator, we do not require the exact answer, but an approximate answer only. The question will then ask you to ROUND OFF the given number to the nearest ten, nearest hundred or nearest thousand.

Example: If we round off 73 to the nearest ten, then the answer is 70, because 73 is closer to 70 than it is to 80. If we round off 659 to the nearest hundred, then the answer is 700, because 659 is closer to 700 than it is to 600.

ESTIMATING

When using a calculator, you will be surprised how easy it is to press the wrong button and then get a ridiculous answer which is way out from the correct answer. If we quickly and mentally estimate an approximate answer to begin with, then this will prevent us from making careless blunders. Estimate the answer to 469 + 1 728 469 rounds off to 500. 1 728 rounds off to 1 700. Therefore ESTIMATE = 500 + 1 700 = 2 200

ADDING WHOLE NUMBERS ( + SIGN)

Start with the far right hand column of digits. Add them up and place the ‘carry over’ at the top of the next column in smaller print, as shown in the example below.

3 + 4 + 5 = 12. Write down the number 2 and place the carry over 1 at the top of the next column.

1 + 8 + 9 + 7 = 25. Write down the number 5 and place the carry over 2 at the top of the next column.

Repeat these steps for the next 3 columns as shown.

SUBTRACTING WHOLE NUMBERS ( – SIGN)

The most popular and widely used method is called “TRADING” or “DECOMPOSITION”. Inthefirstunitcolumn,9subtract4=5 In the second tens column, 2 cannot subtract 8. We trade one hundred from the hundreds column and change the 5 into a 4 as shown. We now have 12 in the tenscolumn.12subtract8=4,andfinallyinthe hundreds column, 4 – 3 = 1.

}‘carry over numbers’ 1 1 2 1

7 6 8 35 9 4

+ 8 6 3 7 59 4 6 5 2

Step 2 :

Step 1 :

H T U 4 1

5 2 9 – 3 8 4

1 4 5

SAMPLE



MULTIPLYING WHOLE NUMBERS ( × SIGN)

When multiplying whole numbers by 10 or 100 or 1 000 simple add on one, two or three zeros onto the end of the whole number. For other multiplications, follow the steps shown in the example below.

(i) 6 × 9 = 54. (ii) Write down 4 and carry over 5. (iii) 6 × 7 = 42 plus 5 = 47. (iv) Write down 7 and carry over 4. (v) 6 × 5 = 30 plus 4 = 34. (vi) Write down 34.

DIVIDING WHOLE NUMBERS ( or ÷ SIGN ) Divisor Dividend = Quotient + Remainder

5 4 6 R 5 7 3 8 2 7 (i) 7 will not divide into 3. (ii) Carry the 3 over to make 38. (iii)7dividesinto38fivetimes,plusremainder3 (iv) Carry the 3 over to make 32. (v) 7 divides into 32 four times, plus remainder 4. (vi) Carry the 4 over to make 47. (vii) 7 divides into 47 six times, plus remainder 5.

PROBLEM SOLVING (See “Appendix” for some strategies)

Problem solving questions are becoming an increasingly important part of the Mathematics syllabus. These sentence type questions are not straight forward, and they usually require the student to interpret the information given, and then to use one or more thinking skills to solve the problem. It will also often involve 2 or more operations (+, –, ×, ÷)tofindthesolutions.Someimportantstrategies for ‘Problem Solving’ are to be found in chapter 1 of the ‘Understanding Year 5 Maths’. Students should also have an understanding of the meaning of some important words given below:

Sum, difference, product, quotient, descending, ascending, average (see page 123)

For further reference, see ‘Understanding Year 5 Maths’ by W. Marlin

H T U 4 5

5 7 9 × 6

3 4 7 4

STEPS:

STEPS:3 3 4

Dividend = 3 827Divisor = 7Quotient = 546Remainder = 5



MULTIPLYING WHOLE NUMBERS ( × SIGN)

When multiplying whole numbers by 10 or 100 or 1 000 simple add on one, two or three zeros onto the end of the whole number. For other multiplications, follow the steps shown in the example below.

(i) 6 × 9 = 54. (ii) Write down 4 and carry over 5. (iii) 6 × 7 = 42 plus 5 = 47. (iv) Write down 7 and carry over 4. (v) 6 × 5 = 30 plus 4 = 34. (vi) Write down 34.

DIVIDING WHOLE NUMBERS ( or ÷ SIGN ) Divisor Dividend = Quotient + Remainder

5 4 6 R 5 7 3 8 2 7 (i) 7 will not divide into 3. (ii) Carry the 3 over to make 38. (iii)7dividesinto38fivetimes,plusremainder3 (iv) Carry the 3 over to make 32. (v) 7 divides into 32 four times, plus remainder 4. (vi) Carry the 4 over to make 47. (vii) 7 divides into 47 six times, plus remainder 5.

PROBLEM SOLVING (See “Appendix” for some strategies)

Problem solving questions are becoming an increasingly important part of the Mathematics syllabus. These sentence type questions are not straight forward, and they usually require the student to interpret the information given, and then to use one or more thinking skills to solve the problem. It will also often involve 2 or more operations (+, –, ×, ÷)tofindthesolutions.Someimportantstrategies for ‘Problem Solving’ are to be found in chapter 1 of the ‘Understanding Year 5 Maths’. Students should also have an understanding of the meaning of some important words given below:

Sum, difference, product, quotient, descending, ascending, average (see page 123)

For further reference, see ‘Understanding Year 5 Maths’ by W. Marlin

H T U 4 5

5 7 9 × 6

3 4 7 4

STEPS:

STEPS:3 3 4

Dividend = 3 827Divisor = 7Quotient = 546Remainder = 5

SAMPLE

6

Level NUMBER ANDPLACE VALUE

Year 5 Essential Exercises Warwick Marlin © Five Senses Education

1 Easier

Q1. Write the number shown on each abacus below: a) b) c)

Q2. Write the following numbers on the place value chart shown:

a) 7 531 b) 6 284 c) 5 076 d) 4 309

Q3. What is the place value of 3 in the following:

a) 432 b) 73 c) 3 168 d) 7 391

Q4. Write the following numbers in descending order (from highest to lowest):

a) 7 312, 7 132, 7 321, 7 231, 7 123

b) 4 609, 4 690, 4 096, 4 906, 4 069

Q5. Write the following numbers in words: a) 1 097 b) 3 592 c) 6 803 d) 2 560

Q6. Write the following numbers as ordinary numerals: a) Four thousand, six hundred and forty eight b)Twothousand,sevenhundredandfive

Q7. Write the following numbers as ordinary numerals: a) (4 × 1 000) + (8 × 100) + (6 × 10) + (3 × 1) b) (7 × 1 000) + (4 × 100) + (9 × 10) + (8 × 1)

Q8. Write the following numbers in expanded notation (this is the reverse of Q7. above):

a) 2 498 b) 5 365 c) 6 803 d) 9 760

Q9. List all the factors of the following:

a) 8 b) 10 c) 20 d) 17

Th H T U Th H T U Th H T U

Thousands Hundreds Tens Units

6

Level NUMBER ANDPLACE VALUE

Year 5 Essential Exercises Warwick Marlin © Five Senses Education

1 Easier

Q1. Write the number shown on each abacus below: a) b) c)

Q2. Write the following numbers on the place value chart shown:

a) 7 531 b) 6 284 c) 5 076 d) 4 309

Q3. What is the place value of 3 in the following:

a) 432 b) 73 c) 3 168 d) 7 391

Q4. Write the following numbers in descending order (from highest to lowest):

a) 7 312, 7 132, 7 321, 7 231, 7 123

b) 4 609, 4 690, 4 096, 4 906, 4 069

Q5. Write the following numbers in words: a) 1 097 b) 3 592 c) 6 803 d) 2 560

Q6. Write the following numbers as ordinary numerals: a) Four thousand, six hundred and forty eight b)Twothousand,sevenhundredandfive

Q7. Write the following numbers as ordinary numerals: a) (4 × 1 000) + (8 × 100) + (6 × 10) + (3 × 1) b) (7 × 1 000) + (4 × 100) + (9 × 10) + (8 × 1)

Q8. Write the following numbers in expanded notation (this is the reverse of Q7. above):

a) 2 498 b) 5 365 c) 6 803 d) 9 760

Q9. List all the factors of the following:

a) 8 b) 10 c) 20 d) 17

Th H T U Th H T U Th H T U

Thousands Hundreds Tens Units

SAMPLE



Q10. ThelistingsyoudidinQ9.shouldhelpyoutofindthehighestcommonfactor (HCF) of the following pairs of numbers:

a) 8 and 10 b) 8 and 20 c) 10 and 20 d) 10 and 15

Q11. a)Listthefirstfourmultiplesof10. b)Listthefirstsixmultiplesof4. c)Listthefirstfivemultiplesof6.

Q12. ThelistingsyoudidinQ9.shouldhelpyoutofindthelowestcommonmultiple (LCM) of the following pairs of numbers:

a) 4 and 10 b) 4 and 6 c) 6 and 10

Q13. a) Is 67 closer to 60 or 70? Now round off 67 to the nearest 10. b) Is 143 closer to 140 or 150? Now round off 143 to the nearest 10. c) Is 95 closer to 90 or 100? Now round off 95 to the nearest 10.

Q14. Inthisquestion,donotfindtheexactanswers.Firstlyinyourhead,roundeach number off, and then give an ESTIMATE of the answer. Ina)andb)roundofftothenearesthundredfirst,andinc)andd)roundoffto thenearesttenfirst.

a) 497 + 308 b) 602 – 389

c) 89 × 11 d) 53 ÷ 9

Q15. Find:

a) b) c) d)

Q16. Find:

a) b) c) d)

Q17. Find:

a) b) c) d)

Q18. Find:

a) 7 84 b) 3 54 c) 5 85 d) 7 30

387 + 295

694 + 127

2 483 + 3 347

5 479 + 2 586

879 365

97 3 ×

996 546

89 6 ×

3 574 1 239

363 8 ×

7 692 4 468

569 7 ×

– –– –

Try not to use a calculator in the

following 4 questions.



Q10. ThelistingsyoudidinQ9.shouldhelpyoutofindthehighestcommonfactor (HCF) of the following pairs of numbers:

a) 8 and 10 b) 8 and 20 c) 10 and 20 d) 10 and 15

Q11. a)Listthefirstfourmultiplesof10. b)Listthefirstsixmultiplesof4. c)Listthefirstfivemultiplesof6.

Q12. ThelistingsyoudidinQ9.shouldhelpyoutofindthelowestcommonmultiple (LCM) of the following pairs of numbers:

a) 4 and 10 b) 4 and 6 c) 6 and 10

Q13. a) Is 67 closer to 60 or 70? Now round off 67 to the nearest 10. b) Is 143 closer to 140 or 150? Now round off 143 to the nearest 10. c) Is 95 closer to 90 or 100? Now round off 95 to the nearest 10.

Q14. Inthisquestion,donotfindtheexactanswers.Firstlyinyourhead,roundeach number off, and then give an ESTIMATE of the answer. Ina)andb)roundofftothenearesthundredfirst,andinc)andd)roundoffto thenearesttenfirst.

a) 497 + 308 b) 602 – 389

c) 89 × 11 d) 53 ÷ 9

Q15. Find:

a) b) c) d)

Q16. Find:

a) b) c) d)

Q17. Find:

a) b) c) d)

Q18. Find:

a) 7 84 b) 3 54 c) 5 85 d) 7 30

387 + 295

694 + 127

2 483 + 3 347

5 479 + 2 586

879 365

97 3 ×

996 546

89 6 ×

3 574 1 239

363 8 ×

7 692 4 468

569 7 ×

– –– –

Try not to use a calculator in the

following 4 questions.

SAMPLE

132Essential Exercises – Year 5 Maths Warwick Marlin © Five Senses Education

Level

These are the answers!

NUMBER AND PLACE VALUE1 Easier

Q1. a) 4 132 b) 9 274 c) 6 309Q2. Write the following numbers on the place value chart shown: a) 7 531 b) 6 284 c) 5 076 d) 4 309

Q3. a) 30 b) 3 c) 3 000 d) 300Q4. a) 7 321, 7 312, 7 231, 7 132, 7 123 b) 4 906, 4 690, 4 609, 4 096, 4 069Q5. a) One thousand and ninety seven b) Three thousand, five hundred and ninety two c) Six thousand, eight hundred and three d) Two thousand, five hundred and sixtyQ6. a) 4 648 b) 2 705Q7. a) 4 863 b) 7 498Q8. a) 2 498 = (2 × 1 000) + (4 × 100) + (9 × 10) + (8 × 1) b) 5 365 = (5 × 1 000) + (3 × 100) + (6 × 10) + (5 × 1) c) 6 803 = (6 × 1 000) + (8 × 100) + (0 × 10) + (3 × 1) d) 9 760 = (9 × 1 000) + (7 × 100) + (6 × 10) + (0 × 1)Q9. a) 8 = { 1, 2, 4, 8 } b) 10 = { 1, 2, 5, 10 } c) 20 = { 1, 2, 4, 5, 10, 20 } d) 17 = { 1, 17 }Q10. a) HCF = 2 b) HCF = 4 c) HCF = 10 d) HCF = 5Q11. a) { 10, 20, 30, 40 } b) { 4, 8, 12, 16, 20, 24 } c) { 6, 12, 18, 24, 30 }Q12. a) LCM = 20 b) LCM = 12 c) LCM = 30Q13. a) 70 b) 140 d) 100Q14. a) 497 + 308 = 500 + 300 ( rounded to nearest 100 ) = 800 ( estimate ) b) 602 – 389 = 600 – 400 ( rounded to nearest 100 ) = 200 ( estimate ) c) 89 × 11 = 90 × 10 ( rounded to nearest 10 ) = 900 ( estimate ) d) 53 ÷ 9 = 50 ÷ 10 ( rounded to nearest 10 ) = 5 ( estimate )

Q15. Find: a) 387 b) 694 c) 2 483 d) 5 479 + 295 + 127 + 3 347 + 2 586 682 821 5 830 8 065

Thousands Hundreds Tens Units7 5 3 16 2 8 45 0 7 64 3 0 9

With 5 always round up.

The brackets involv-ing zero can be left

out if you wish.

1 1 1 1 1 1 1 1 1

132Essential Exercises – Year 5 Maths Warwick Marlin © Five Senses Education

Level

These are the answers!

NUMBER AND PLACE VALUE1 Easier

Q1. a) 4 132 b) 9 274 c) 6 309Q2. Write the following numbers on the place value chart shown: a) 7 531 b) 6 284 c) 5 076 d) 4 309

Q3. a) 30 b) 3 c) 3 000 d) 300Q4. a) 7 321, 7 312, 7 231, 7 132, 7 123 b) 4 906, 4 690, 4 609, 4 096, 4 069Q5. a) One thousand and ninety seven b) Three thousand, five hundred and ninety two c) Six thousand, eight hundred and three d) Two thousand, five hundred and sixtyQ6. a) 4 648 b) 2 705Q7. a) 4 863 b) 7 498Q8. a) 2 498 = (2 × 1 000) + (4 × 100) + (9 × 10) + (8 × 1) b) 5 365 = (5 × 1 000) + (3 × 100) + (6 × 10) + (5 × 1) c) 6 803 = (6 × 1 000) + (8 × 100) + (0 × 10) + (3 × 1) d) 9 760 = (9 × 1 000) + (7 × 100) + (6 × 10) + (0 × 1)Q9. a) 8 = { 1, 2, 4, 8 } b) 10 = { 1, 2, 5, 10 } c) 20 = { 1, 2, 4, 5, 10, 20 } d) 17 = { 1, 17 }Q10. a) HCF = 2 b) HCF = 4 c) HCF = 10 d) HCF = 5Q11. a) { 10, 20, 30, 40 } b) { 4, 8, 12, 16, 20, 24 } c) { 6, 12, 18, 24, 30 }Q12. a) LCM = 20 b) LCM = 12 c) LCM = 30Q13. a) 70 b) 140 d) 100Q14. a) 497 + 308 = 500 + 300 ( rounded to nearest 100 ) = 800 ( estimate ) b) 602 – 389 = 600 – 400 ( rounded to nearest 100 ) = 200 ( estimate ) c) 89 × 11 = 90 × 10 ( rounded to nearest 10 ) = 900 ( estimate ) d) 53 ÷ 9 = 50 ÷ 10 ( rounded to nearest 10 ) = 5 ( estimate )

Q15. Find: a) 387 b) 694 c) 2 483 d) 5 479 + 295 + 127 + 3 347 + 2 586 682 821 5 830 8 065

Thousands Hundreds Tens Units7 5 3 16 2 8 45 0 7 64 3 0 9

With 5 always round up.

The brackets involv-ing zero can be left

out if you wish.

1 1 1 1 1 1 1 1 1

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