Planet Maths 6th - Sample Pages

Rita ColemanLiam Gaynor

6th

A COMPLETE MATHS PROGRAMME FOR PR IMARY SCHOOLS

A COMPLETE MATHS PROGRAMMEFOR PRIMARY SCHOOLS

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Planet Maths incorporates the best methodology for teaching mathematics and problem solving, with new features such as Real Life Maths sections, integrated digital resources and differentiated material to motivate every child.

Main features include:

Real Life Maths visible throughout the series

Problem Solving units and emphasis on pair and group work

Digital Activities for classroom use

Differentiation catered for all levels of ability

Self Assessment incorporating traffic light system

Curriculum Objectives listed in pupil book

This programme reflects the latest teaching methods in Primary and Post Primary education.

Also available for this programme:

• Satellite activity books to complement each title

• Updateable Teachers Resource Books

• A range of classroom ancillary material

• Teacher’s eBooks and integrated digital resources on www.folensonline.ie

A COMPLETE MATHS PROGRAMME FOR PRIMARY SCHOOLS

Rita Coleman and Liam Gaynor

Author: Rita Coleman and Liam Gaynor

Editor: Sarah Deegan

Design: Liz White Designs

Layout: Niamh Carey, Liz White Designs

Illustrators: Brett Hudson, Sue Woollatt (GCI), Gary Dermody, Brian Fitzgerald and Tim Hutchinson

Photographs: iStockphoto, Stockxchng, Thinkstock

ISBN: 978-1-84741-785-5

© 2011 Rita Coleman and Liam Gaynor

First published in 2011 by: Folens Publishers, Hibernian Industrial Estate, Greenhills Road, Tallaght, Dublin 24.

The paper used in this book is sourced from managed forests.

Folens books are protected by international copyright laws. All rights reserved. The copyright of all materials in this book, except where otherwise stated, remains the property of the author(s). No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means (stencilling, photocopying, etc.) for whatever purpose, even purely educational, without the prior written permission of the publisher. The publisher reserves the right to change, without notice, at any time the specification of this product. The publisher has made every effort to contact copyright holders but if any have been overlooked we will be pleased to make any necessary arrangements. To the best of the publisher’s knowledge, information in this book was correct at the time of going to press. No responsibility can be accepted for any errors.

iiiIntroduction for Parents and Teachers

Planet Maths is a series of Maths textbooks, activity books and corresponding teacher’s manuals for Junior Infants to 6th Class. It is in line with the Revised Primary Curriculum and has been written by primary school teachers. Curriculum Strands, Strand Units and Objectives are detailed throughout.

Planet Maths has been designed to provide students with challenging activities and enjoyable mathematical experiences to help them become confident mathematicians. Pupils using Planet Maths will experience mathematical learning through the following approach:

• Learning the new maths skills associated with a topic with the aid of explanation boxes and/or worked examples that introduce each new concept or operation.

• Practising and reinforcing new skills through drills and repetition, while also providing as much variety and stimulation as possible.• Exploring and applying their skills in ‘real life’ contexts and situations that are relevant, fun and stimulating to young minds.

‘Real life’ themed maths featuresThere are seven two-page ‘real life’ themed maths features spread throughout the 3rd to 6th Class textbooks. They are designed to bring Maths to life, making it more engaging for students by enabling them to use their skills in contexts that are refreshing, relevant and interesting to them. Each ‘real life’ feature uses the skills and knowledge that pupils have acquired in the preceding units.

Warm-Up ActivitiesA warm-up activity appears at the beginning of every new topic along with the instruction, ‘Listen to your teacher’. These game-like activities open each unit of the senior textbooks and are led by the teacher with directions from the accompanying teacher’s manual. Because they are conducted at the start of each unit, these activities provide a mental warm-up for students, preparing them to learn by focusing their attention on the teacher. Warm-up activities are based on the concepts and operations relevant to the topic.

Pair and Group WorkThe series recognises the value of collaborative learning and ample opportunities are provided throughout the textbooks for both pair work and group work. Maths puzzles suited to pairs, straightforward group activities and oral activities such as ‘pretend you are the teacher’ are used in the series.

Differentiation To promote ease of differentiation, a red line appears beside a selection of problems and sums in the 3rd to 6th Class textbooks that could prove more challenging for many pupils. Additionally, the 3rd to 6th Class textbooks contain Challenge Yourself problems designed to provide early finishers with extra stimulus and reward, and to assist with differentiation.

Self-AssessmentSelf-assessment is strong feature of the series. Pupils are encouraged to rate their own performance and understanding of a topic through the use of a traffic light system at the end of every page in each topic. Students can assess their performance at the end – red for difficultly, amber for improvement and green for full understanding.

Check Up Activities Each topic unit concludes with a page of concise check up activities designed to reinforce learning. Check ups include oral, operational, problem-solving and shared activities based on the topic at hand. Oral activities reinforce communicating and expressing as a mathematical skill, and vocabulary-based exercises assess the pupil’s understanding of the mathematical language used in the unit.

Mental MathsSeven dedicated Mental Maths units are placed strategically throughout the 3rd to 6th Class textbooks, with each one including a Multiple Choice component. Each section in Mental Maths contains a score box for pupils to rate their performance. This will encourage them to collaborate in their own progress and to recognise areas where more effort and assistance is needed.

The teacher’s manual accompanying this textbook includes:

• A guide providing comprehensive suggestions on how to make the best use of this series.• Oral and mental maths activity suggestions.• Maths language relevant to each topic.• Suggestions for using concrete materials and manipulatives.• Photocopiable activities for differentiation and extension exercises.• Photocopiable templates for practice and repetition of fundamental concepts.• Answers.• Assessment sheets.• Individual student profile sheets.• Class record sheets.

The activity books in the series contain supplementary and differentiation activities. Interactive activities for this series can also be found at: www.folensonline.ie.

iv Contents

Let’s Look Back ...............................................5

1 Place Value ..........................................11

2 Addition and Subtraction ......................16

3 Data 1 ..................................................21

The Paradise Amusement Park ......................26

Mental Maths 1.............................................28

4 Multiplication 1 .....................................30

5 Lines and Angles ...................................35

6 Division 1 ..............................................40

7 Fractions 1 ............................................45

At the Airport ................................................50

Mental Maths 2.............................................52

8 2D Shapes .............................................54

9 Fractions 2 ............................................59

10 Decimals ...............................................64

11 Numbers ...............................................69

Sam’s Mini-Market Service Station ................74

Mental Maths 3.............................................76

12 Multiplication 2 .....................................78

13 Length ...................................................83

14 Division 2 ..............................................88

15 Percentages 1 ........................................93

The Championship Games ............................98

Mental Maths 4...........................................100

16 Time ...................................................102

17 Percentages 2 ......................................107

18 Area ....................................................112

19 Problem Solving 1 ...............................117

Deep Space ................................................122

Mental Maths 5...........................................124

20 Chance ...............................................126

21 Money ................................................131

22 Directed Numbers ...............................136

23 The Circle ...........................................141

The Virtual World of Quest .........................146

Mental Maths 6...........................................148

24 Using Percentages ...............................150

25 3D Shapes ...........................................155

26 Weight ................................................160

27 Number Rules .....................................165

Measuring Up! ............................................170

Mental Maths 7...........................................172

28 Averages and Charts ............................174

29 Variables .............................................179

30 Capacity and Volume ..........................184

31 Co-ordinates .......................................189

32 Problem Solving 2 ...............................194

Let’s Look Back ...........................................199

Glossary ......................................................204

Tables .........................................................207

Warm-up. Working with numbers.

1. Put these numbers in order from smallest to greatest.

476.5 468.7 86.438 47.65 467.8 468.96

2. Round each of these numbers to the nearest 10. Then round them to the nearest 100.

(a) 784,587 (b) 2,694 (c) 206,715 (d) 3,947

3. Round each of these numbers to the nearest whole number.

(a) 85.2 (b) 96.7 (c) 25.5 (d) 48.1 (e) 78.9 (f) 84.4

4. What is the value of the underlined digits? Write the value in numbers and in words.

(a) 468 (b) 6,936 (c) 73.06 (d) 36.2 (e) 87.84 (f) 485.28

5. Draw an abacus in your copy to show these numbers.

(a) 865.42 (b) 701.94

Strand UnitStrandRevision

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5Let’s Look Back

Fractions

1. Write these improper fractions as mixed numbers.

(a) 134 (b)

258 (c)

165 (d)

237 (e)

356 (f)

418

2. Write these mixed numbers as improper fractions.

(a) 423 (b) 7

45 (c) 5

34 (d) 2

13 (e) 5

14 (f) 3

18

3. Write these equivalent fractions.

(a) 68 = 4 (b)

23 = 9 (c)

14 = 8 (d)

56 =

15 (e)

34 =

12

B

A

My goal is to

revise

5th Class work.

Doggy delights

Grace and Maria went to buy supplies for their dog.

Grace contributed 13 of the cost and Maria contributed the remainder.

They bought 3 bags of dog food, 14 dental sticks, 1 bag of treats and 3 toys.

1. How much money did the dog supplies cost?

2. How much money did each girl contribute?

Challenge

Yourself!

Dog Food €8.65 per bag

Toy€3.94 each

Dental Sticks€0.14

Dog Treats€5.27

Pair work


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Let’s Look Back

Add or subtract.

1. (a) 12 +

34 = ___

2. (a) 58 – 14 = ___

(b) 35 +

410 = ___

(b) 89 –

13 = ___

(c) 23 +

56 = ___

(c) 45 –

12 = ___

3. (a) 34 +

23 = ___ (b)

45 +

610 = ___ (c)

218 +

46 = ___

4. (a) 218 + 3

12 = ___

(c) 423 + 5

14 = ___

(b) 412 + 21

3 = ___

(d) 213 + 11

4 = ___

5. (a) 315 + 2 1

10 = ___ (b) 214 + 1 5

12 = ___

(c) 423 – 21

6 = ___ (d) 912 – 55

6 = ___

Try these calculations.

1. (a) Find 49 of 882 (b) Find

34 of 96

2. Simplify each of these fractions.

(a) 810 (b)

1216 (c)

2128 (d)

2436 (e)

1842 (f)

10100

Try these percentages calculations.

1. Find each of these percentages. (a) 10% of 90 (b) 75% of €34.80 (c) 25% of 160 (d) 15% of 180

(e) 1212% of 10,816 (f) 10% of €163.50 (g) 5% of €1,628.40

2. A pair of jeans was originally priced at €60. There was 20% off in the sale.

(a) What was the sale price of the jeans?

(b) If the price of the jeans had been reduced from €60 to €45, what percentage discount was given to the customer?

3. Find the price of each of these items if they are reduced by these percentages.

(a) Trousers €20 (b) Jacket €50 (c) Skirt €10 (d) Hat €12

5% 10% 1212% 20%

Shapes. Answer the questions.

1. What do the angles in each of these shapes add up to? (a) A triangle (b) A circle

2. How many degrees in right angle?

3. Draw each of these shapes.

(a) A regular hexagon (b) A rhombus (c) A square

A

B

C

D

(c) A rectangle


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7Let’s Look Back

1. What is the next number in each sequence? (a) 2, 4, 6, 8

(d) 3, 4, 6, 9

(b) 3, 9, 27, 81

(e) 14,

18,

116,

132

(c) 7, 12, 17, 22

2. 60% of Mike’s money is €12. How much is his total amount of money?

3. Multiply.

(a) 6 x 518 = ___

(c) 56 x

310 = ___

(b) 12 x

46 = ___

(d) 58 x

712 = ___ (e)

23 x

79 = ___

4. Write these numbers in order, starting with the smallest: 25, 0.3, 45%.

1. Draw a circle with a radius of 4cm in your copy.

2. How many equal sides has each of these triangles? (a) A scalene triangle (b) An isosceles triangle (c) An equilateral triangle3. Measure these angles with a protractor. (a) (b) (c)

4. Name these polygons. (a) 5-sided (b) 4-sided (c) 8-sided (d) 6-sided

5. Measure the length of this line with your ruler.

6. In your copy, draw a net of each of these 3D shapes. (a) A cuboid (b) A tetrahedron (c) A triangular prism

If luxury mints costs €1.50 per 100g how much will 1kg cost?

Muffin making

1. Aoife, Brian, Kate, Evan and Mary made 87 muffins together. Brian made 16 muffins.

Aoife made 1 less muffin than Brian. Kate and Evan each made 3 more muffins than Aoife made. Mary made 2 more muffins than Kate and Evan.

How many muffins did each person make?

2. Brian put blueberries in 14 of his muffins and chocolate chips in the remainder.

Kate put chocolate chips in 13 of her muffins and blueberries in the remainder.

Evan put blueberries in all his muffins.

Mary and Aoife put blueberries in 15 of their muffins and put chocolate chips in the remainder.

(a) How many muffins contain blueberries?

(b) How many muffins contain chocolate chips?

A

B

C

D Pair work


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Let’s Look Back

1. Charlie earns €325 for a five-day working week. How much does he earn in a day?

2. Write each of these times in 24-hour time:

3. Express each of these numbers as a fraction of 15:

4. Which is better value, 8 pens for €1.76 or 10 pens for €2.40 or 5 pens for €1.15?

Time

1. Write these minutes as hours and minutes. (a) 125 mins (b) 86 mins (c) 212 mins (d) 245 mins (e) 130 mins

2.

3.

1. Find the average of each of the following. (a) 15, 16, 9, 8 (c) 1kg 250g, 2kg 500g, 2kg 100g

2. Find the whole number if:

3. (a) 3 x ___ = 27 (b) 8 x ___ = 48 (c) 38 + ___ = 86 (d) ___ x 100 = 386.5

(e) 389.6 ÷ ___ = 38.96 (f) 240 ÷ ___ = 40 (g) ___ % of 30 = 6 (h) 38 of 40 = ___

Calculator work.

6th Class are sorting four types of books in their library. They will put each type of book on its own shelf. The following number of books will fit on a shelf.

Fiction Non-fiction Dictionaries Biographies

72 63 54 18

There are 288 biographies.There are 3 times as many fiction books as biographies.There are half as many dictionaries as fiction books.The number of non-fiction books is 36 less than the number of biographies.1. How many types of each book are there to place on the library shelves?

2. How many shelves are needed for each type of book?

3. What is the average number of shelves needed for each type of book?

A

B

C

D

(a) 3 (b) 10 (c) 5

(a) 16 of the number = 85 (b)

23 of the number =74

(a) 4:20pm (b) 12:55am (c) 6:30pm

(a) hrs mins (b) hrs mins (c) hrs mins (d) hrs mins (e) hrs mins (f) hrs mins2 45

1 23

+ 2 25

1 39

2 30

+ 4 18

2 56

2 35

+ 30

4 16

1 15

+ 2 45

3 46

2 06

+ 3 13

6 34

1 45

+ 25

(a) hrs mins (b) hrs mins (c) hrs mins (d) hrs mins (e) hrs mins (f) hrs mins9 45

– 5 34

7 39

– 4 45

5 56

– 2 58

4 16

– 3 25

6 46

– 3 52

8 34

– 5 45

Pair work

(b) €1.15, €1.20, €2.15


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9Let’s Look Back

Spinner chance

Donal, Rita, James, Maria and Grace are playing a board game. They each have one of the 5 spinners shown above.

• Grace has the best chance of getting yellow.

• Donal and Maria have the same probability of spinning red.

• Grace and Maria have the same probability of getting green.

• Of all the players, Rita has the greatest chance of spinning green.

Which spinner does each person have?

1. Find the area and perimeter of each of these rectangles. (a) Length = 14cm, Width = 9cm (b) Length = 35cm, Width = 24cm2. Complete the table.

Fraction 7100

45

Decimal 0.07 0.47

Percentage 7% 25%

3. 8 x 7 = 50 + y so y = ___

4. Find 40% of €40.

Try these calculations.1. 19.18 + 276.3 + 14.28 = ___

4. 41.63 x 19 = ___

7. 850 ÷ 34 = ___

10. 52.2 ÷ 29 = ___

2. 18.3 + 17.6 + 142.63 = ___

5. 19.3 x 18.4 = ___

8. 1,777.58 ÷ 7 = ___

11. 8.54 ÷ 61 = ___

3. 1,268.34 – 18.63 = ___

6. 1,952 x 18 = ___

9. 8.75m x 65 = ___

12. 7.994kg ÷ 7 = ___

Find the area of this playground.

A

B

C

D

Pair work

30m5m

5m

5m

5m

15m

1. 2. 3. 4. 5.


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Let’s Look Back

Paula, Orla and Brian each took a different route walking home from school. They made a map to show their routes.

1. Fill in the blanks.

Paula’s route:

Take the vertical line on Plunkett St to the right angle. Turn ____________.

Continue to the second parallel line that intersects Sea View Rd.

Turn left. Go down the road that forms an internal ____________ angle with Pearse Drive.

Go the first house and write down its number!

Orla’s route:

Follow the horizontal line, O’Connell St, to the first street that is perpendicular to O’Connell St. Turn right onto ____________.

Continue on to Sea View Road, which forms a ____________ angle with Monk St.

Turn left. Go to the first house and write down its number.

Brian’s route:

Take the horizontal line on O’Connell St past Monk St to the street that makes an obtuse angle with ____________. Turn onto Cedar Walk.

Go to the vertex of three streets. Turn into ____________ Ave, which forms an acute angle with Cedar Walk.

Go to the third house and write down its number.

2. What is the number of the house where each person lives?

3. Trace the path for each person and show the route.

A

SchoolO’Connell St

Plunkett St

Sea View Rd

Maywood Ave

Cedar Walk

Elmwoo

d Av

e

Pearse Drive

Pear

se W

alk

Foxf

ield

Law

n

13

5

8 9 10

40 41

Mon

k St

Warm-up. Listen to your teacher.

Strand UnitStrand602.1 Identify place value in whole numbers.

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Place Value

111

Place Value

Place value in whole numbers

You can write any number using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The value of each digit depends on its place in the number, e.g. you would probably prefer to win €600 prize money than €6!

It is easier to read large numbers when they are in a place value diagram or notation board.

H th T th Th H T U

••• ••••••• ••••• •• ••••••••• ••••

3 7 5 2 9 4

3 hundred thousands 7 ten thousands 5 thousands 2 hundreds 9 tens 4 units

300,000 70,000 5,000 200 90 4= 375,294

Write the numbers shown on each notation board.

H th T th Th H T U••••• ••• ••••••• ••••••••• ••••

1. Ike’s Ice-cream Parlour had these annual sales over the past ten years. Show the sales on a notation board.

(a) 156,670

(f) 597,753

(b) 247,963

(g) 687,630

(c) 362,936

(h) 603,508

(d) 482,821

(i) 301,700

(e) 537,935

(j) 260,700

2. In expanded form we write 536,492 as 500,000 + 30,000 + 6,000 + 400 + 90 + 2. Write these numbers of Dublin to Cork train passengers in expanded form.

(a) 142,364

(f) 672,093

(b) 257,694

(g) 749,598

(c) 352,721

(h) 870,453

(d) 453,504

(i) 908,176

(e) 516,893

(j) 643,154

3. Signatures for a petition were collected and written in expanded form. Write them in the usual, shorter way.

(a) 600,000 + 50,000 + 6,000 + 300 + 30 + 2 (b) 200,000 + 70,000 + 200 + 10 + 1

B

C

A

My goal is t

o identify

place value in

whole numbers.

H th T th Th H T U• ••••• ••• •• ••••••••


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Number

Place Value

Topic 1: Place Value

Writing cheques

For security reasons when a cheque or bank draft is written the amount of money is written in words and in digits.

We often find big numbers in football transfer fees when footballers change clubs!

1. Write these transfer fees in figures.

(a) Six hundred and twenty-five thousand, five hundred and sixteen euro.

(b) Three hundred and forty-nine thousand, seven hundred and twenty-eight euro.

(c) Seven hundred and eighty-nine thousand, six hundred and thirty-one euro.

(d) Nine hundred and twenty-eight thousand and three euro.

(e) Eight hundred and nineteen thousand, five hundred and six euro.

2. Write these football transfer fees in words. (a) €567,943

(f) €809,673

(b) €34,986

(g) €605,483

(c) €23,987

(h) €480,652

(d) €728,953

(i) €507,540

(e) €920,563

(j) €669,328

Make (a) the least number and (b) the greatest number you can with each of these sets of numbers.

1. 3 8 7 2 9 8 2. 3 9 7 5 3 9 3. 8 9 3 5 6 0 4. 3 6 8 4 3 8 5. 4 0 5 8 3 2

Write the venues in order of seats sold, starting with the smallest number (ascending order).

City Lane Benton Dundree Ratham Páirc Siar Baytown Naomh Pól

267,987 348,956 456,875 338,753 332,753 267,942 457,429

742,976 894,673 943,867 805,634 864,576 086,534 790,657

646,853 853,860 963,576 854,874 975,465 905,056 705,477

A

B

C

Shane, Conor, Lorna and Ciara read 3 books from the list for their School Readathon. Nobody read the same combination of books.Mystery 172 pages Series 165 pages Biography 178 pagesScience fiction 194 pages Classic 218 pages Historical 154 pagesVampires 168 pages Adventure 201 pages Sport 186All 4 students read the mystery.Shane was the only student to read the sports book.Ciara read the longest book.Shane and Conor both read the shortest book.Lorna read a book with 13 pages more than a book read by Ciara.Conor read a book with 17 pages less than a book read by Lorna.1. Which 3 books did each person read?

2. Which 2 books were not read?

Challenge

Yourself!

Pair work

National Lottery 11-22-33

112-44566-777-88899-0000

31/8/2010Andrea BloggsTwo hundred and twenty thousand

four hundred and sixty-five euros

Jim Burke

€220,465

Pay

Jim Burke


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Place Value

13Topic 1: Place Value

Introducing millions

The population of Ireland is 4,536,792

M H th T th Th H T U•••• ••••• ••• •••••• ••••••• ••••••••• ••

4 5 3 6 7 9 24 millions 5 hundred

thousands3 ten

thousands6 thousands 7 hundreds 9 tens 2 units

4,000,000 500,000 30,000 6,000 700 90 2

1. What is the value of 7 in each of these numbers? Example: 8,675,934 Answer: 70,000

(a) 5,635,708 (b) 8,659,876 (c) 8,563,587 (d) 8,765,940

(e) 7,864,521 (f) 9,876,594 (g) 5,763,945 (h) 9,856,071

2. Write the value of the underlined digit(s) in each of these numbers.

(a) 5,734,987 (b) 9,843,409 (c) 6,784,574 (d) 4,521,876

(e) 9,745,626 (f) 7,907,634 (g) 4,597,632 (h) 8,674,365

(i) 7,521,408 (j) 7,532,854 (k) 9,075,608 (l) 6,530,859

Fill in the table.

Numbers of voters in election

Add 100 Add 1,100 Subtract 200

Subtract 2,200

1. 2,678,9532. 4,739,8653. 3,856,9084. 1,765,9805. 2,639,000

The million mystery: what is the mystery number?

This number is between 2 million and 3 million. None of the digits are repeated.The last digit is between 6 and 9 and divisible by 4.The digit in the hundreds place is an odd number greater than 4 and divisible by 3.The sum of the digits in the hundreds, tens and units is 18. The digit in the thousands place is greater than 3 and is a factor of 15.The digit in the ten thousands place is an even number. It will give the answer 11 when added to the number in the thousands place.The digit in the hundred thousands place is twice the number in the millions place.The sum of the digits in the millions place and the hundred thousands place is 6.All 7 digits in the mystery number add up to 35.What is the mystery number?

A

Writing cheques

For security reasons when a cheque or bank draft is written the amount of money is written in words and in digits.

We often find big numbers in football transfer fees when footballers change clubs!

1. Write these transfer fees in figures.

(a) Six hundred and twenty-five thousand, five hundred and sixteen euro.

(b) Three hundred and forty-nine thousand, seven hundred and twenty-eight euro.

(c) Seven hundred and eighty-nine thousand, six hundred and thirty-one euro.

(d) Nine hundred and twenty-eight thousand and three euro.

(e) Eight hundred and nineteen thousand, five hundred and six euro.

2. Write these football transfer fees in words.

Make (a) the least number and (b) the greatest number you can with each of these sets of numbers.

1. 3 8 7 2 9 8 2. 3 9 7 5 3 9 3. 8 9 3 5 6 0 4. 3 6 8 4 3 8 5. 4 0 5 8 3 2

Write the venues in order of seats sold, starting with the smallest number (ascending order).

City Lane Benton Dundree Ratham Páirc Siar Baytown Naomh Pól

267,987 348,956 456,875 338,753 332,753 267,942 457,429

742,976 894,673 943,867 805,634 864,576 086,534 790,657

646,853 853,860 963,576 854,874 975,465 905,056 705,477

B

C Pair work


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Number

Place Value

Topic 1: Place Value

Rounding

We round numbers for convenience – to give an approximate answer. We might not want to know the exact number of people who have attended a soccer match, but an approximate number would be very useful to the organisers.

5,000 5,250 5,500 5,750 5,786 5,800

5,786 lies between the hundreds 5,700 and 5,800If we are rounding to the nearest 100, we can see that 5,786 is nearest to 5,800.So we say that 5,786 when rounded to the nearest 100 is 5,800.That same number 5,786 lies between the tens 5,780 and 5,790.If we are rounding to the nearest 10, we can see that 5,786 is nearest to 5,790.So we say that 5,786 is 5,790 when rounded to the nearest 10.

Round each of these numbers to the nearest 10. Example: 275 280 272 2701. 46

6. 3,763,974

2. 739

7. 2,642,729

3. 1,369

8. 3,204,658

4. 65,754

9. 6,538,723

5. 345,892

10. 2,683,412

Round each of these numbers to the nearest 100. Example: 4,163 4,200 4,136 4,1001. 642

6. 7,653,947

2. 927

7. 2,494,602

3. 8,732

8. 3,728,546

4. 85,329

9. 67,453

5. 453,954

10. 428,742

Round each of these numbers to the nearest 1,000. Example: 5,637 6,000 5,237 5,0001. 5,734

6. 6,843

2. 9,734

7. 347,956

3. 897,812

8. 8,659

4. 756,549

9. 4,843

5. 334,534

10. 78,593

Round the total stadium attendances for these Premiership clubs for a full year.

Stadium Attendances To the nearest 10 To the nearest 100 To the nearest 1,000

1. Arsenal 1,148,208

2. Aston Villa 808,469

3. Blackburn Rovers 595,973

A

B

C

D

‘Round to’, ‘Approximate to’ and ‘Write correct to the nearest’ all mean the same thing!

151

Check Up

Explain it!

Explain ‘place value’.

Do it! 1. Round each of these numbers to the nearest 100.

(a) 248,753 (b) 738,645 (c) 56,847 (d) 59,368 (e) 8,075 (f) 362

2. Round each of these numbers to the nearest 10.

(a) 683 (b) 44 (c) 7,485 (d) 946,327 (e) 847,375 (f) 46,735

3. Round each of these numbers to the nearest 1,000.

(a) 6,842 (b) 84,631 (c) 67,473 (d) 94,624 (e) 857,317 (f) 63,738

4. Write each of these numbers using notation boards.

(a) 1,563,749 (b) 7,463,762 (c) 6,426,735

5. What is the value of the 5 in each of these numbers?

(a) 654 (b) 84,528 (c) 654,376 (d) 574,786

Solve it! 1. Make (a) the smallest and (b) the greatest numbers possible from these digits: 7, 4, 6, 9, 0, 2.

2. Write the number nine million, three hundred and forty-five thousand, two hundred and seventy-four as digits.

3. Write the number 4,783,601 in words.

4. Write the number 367,982 in expanded form.

Say it!

1. The value of every digit depends on its place in the number. This is called _ _ _ _ _ _ _ _ _ _.

2. Why is the amount of money written in words and in digits on cheques and bank drafts?

3. Give two examples when it would be useful to round numbers.

4. Describe a notation board to someone who has never seen one.

5. What is the value of the 6 in 562,891?

Share the Challenge!

Find the secret 6-digit code to the safe. Here are your clues.

Units: A number less than 5 and will equal 6 when multiplied by 3.

Tens: A number that will divide evenly into 15 and is between 4 and 9.

Hundreds: A number that when multiplied by 4 and divided by 2 gives 14.

Thousands: A number between 2 and 7 and will divide evenly into 9.

Ten thousands: A number between 1 and 10 and when divided by 3 and multiplied by 8 gives 16.

Hundred thousands: A number between 3 and 10 that will equal 20 when multiplied by 5.

A

C

E

D

B

p v

Warm-up. Listen to your teacher.

1. Plasma TV – €2,589

€455 off

2. Computer – €1,463

Printer – €145

Buy both: discount – €633

3. Barbeque – €249

4. Garden set – €395

Patio heater – €45

Strand UnitStrand605 Add & subtract whole numbers and decimals (to three

decimal places) without and with a calculator.

Obj

ectiv

es16

Number

Operations

2 Addition and Subtraction

Add or subtract. Check your answers with your calculator.

1. 179,855 2. 249,643 3. 874,512 4. 374,284 5. 490,534+ 763,938 + 145,098 + 132,678 + 476,234 + 654,837

6. 674,689 7. 67,493 8. 8,865 9. 9,098 10. 96,4671,384 674 974,532 78,595 784

+ 754 + 631,976 + 9 + 8,563 + 745,052

11. 765,885 12. 87,506 13. 759,454 14. 54,380 15. 468,231– 6,546 – 48,532 – 284,856 – 5,483 – 39,687

A television company has to count the votes cast in the phone-in vote for a talent show.

Candidate Votes

Edel Farrell 67 + 874 + 94,038 + 546

Cyril Maguire 589 + 638 + 8,538 + 27

Fran Mooney 64,839 + 706 + 643 + 7,395

Stephen Harvey 349 + 48,568 + 64 + 6

Katie Smith 5,384 + 58,453 + 8,650 + 8

1. What was the total vote cast for each act?2. Who won the competition?3. Who got the least number of votes?4. Write out the names of the acts in order, starting with

the highest vote catcher.

B

C

A

My goal is

to add

and sub

tract whole

numbers.

Always

keep the place value in

line. Put

the units under the

units, the t

ens under

the tens, etc.



Obj

ectiv

es Number

Operations

17Calculate the following numbers of downloaded music singles.

1. (265,745 + 964,532) – 476,340 = ___

2. (789,674 – 56,453) + 45,371 = ___

3. (56,739 + 856,465) – 674,393 = ___

4. (756,749 – 107,564) + 89,645 = ___

5. (756,454 + 872,483) – 569 = ___

Calculator work. The table shows part of the records of a second-hand car dealer. It shows the price at which she bought and sold each car.

Car Bought for Sold forToyota €6,658 €8,955Mercedes €7,632 €13,785Mazda €7,836 €10,683Volkswagen €5,899 €7,484SUV €12,584 €18,748

1. How much profit did the car dealer make on each car?

2. What was her total outlay in first purchasing the cars?

3. What was her total profit on the sale of all the cars?

4. On which car was the greatest profit made?

5. On which car was the least profit made?

6. What was the difference between the greatest profit and the least profit?

7. What was the combined profit on the two most expensive cars in the showroom?

Find the sum.1. 564,789 + 636,735 = ___

3. 684,745 + 89,654 = ___

5. 7,987 + 56,743 = ___

2. 539,734 + 864,753 = ___

4. 856 + 534,734 = ___

6. 87 + 745,628 = ___

Find the difference between each pair of numbers.1. 86,474 and 345,723

3. 587,809 and 754,360

5. 873,409 and 65,429

2. 65,429 and 54,327

4. 237,836 and 4,745

6. 945,623 and 573,720

Calculator work. True or false?

1. (54,784 + 745) – 5,342 = 50,178 2. (678,534 + 967,453) – 67,845 = 1,578,142

3. 45 + 843 + 85,948 = 86,936 4. 1,000,000 – 673,645 = 346,355

5. 2,357,865 – 458,369 =1,899,496 6. (897,634 + 756,312) – 786 = 1,643,160

A

B

C

D

E

Topic 2: Addition and Subtraction

Always do the

brackets f rst!

Prof t is t

he selling price

minus the buying price.



Obj

ectiv

es18

Number

Operations

Topic 2: Addition and Subtraction

Investigation. Calculator work.

Look at the flight paths below. Answer the questions.

1. What is the shortest distance from LA to London?

2. What is the distance from New York to Paris via London?

3. What is the distance from New York to Prague via Dublin?

4. What is the shortest distance from Oslo to Hong Kong?

5. What is the shortest route from LA to Paris?

6. What is the longest route from Prague to Athens?

7. Mary flies from New York to Paris via Oslo while her friend Miriam flies from New York to Paris via London. What is the difference in km between the two journeys?

8. Joe flies from Sydney to Prague via Hong Kong while Paul flies from Sydney to Prague via Rome. What is the difference in km between their journeys?

Answer the questions.

1. What must be added to 574 to give 23,856?2. Decrease 654,784 by 3,489.3. Increase 34,783 by 24,587.4. How much is 45,789 greater than 23,560?5. Round 4,689 to the nearest 10.6. The difference between two numbers is 4,583.

One of the numbers is 2,639. What is the other number?7. Round 267,473 to the nearest 100.8. What number is 46,976 greater than 29,731?9. Round 358,309 to the nearest 1,000.10. By how much is 4,973 less than 39,628?

A

Oslo

New York Dublin

ParisPrague Hong Kong

Sydney

Athens

Rome

London

LA 3,933km883km

776km

16,300km

1,038km

7,363km

8,733km

459k

m

931km

5,560km

15,315km

5,906km

342km

B

5,130km

998km



Obj

ectiv

es Number

Operations

19Topic 2: Addition and Subtraction

Try these word puzzles.

1. At a football match there were 18,375 in the Hogan Stand, 14,573 in the Nally Stand and 7,803 on Hill 16. How many people altogether were on those three stands?

2. 80,534 attended the All-Ireland football final. The attendance at the All-Ireland hurling final was 7,452 less than that. How many people altogether attended both finals?

3. At that All-Ireland football final, 52,783 of the attendance were men. How many women were at the football final?

4. Dan had €256,500 in shares. Unfortunately, the value of his shares dropped and Dan lost €34,675. What are his shares worth now?

5. A shopkeeper sold 248,456 newspapers last year but sold 18,367 fewer this year. How many newspapers did she sell this year?

6. The bank staff sent 12,679 emails in January and 14,398 in February. In March they sent 2,406 fewer emails than in February. How many emails were sent by the bank in the first three months of the year?

7. In a mobile phone factory, one group of workers produced 145,789 phones in a day while another group produced 34,567 more than that. How many phones did the two groups produce altogether?

8. A property developer bought two apartments in Spain. Each apartment cost €245,650. He made €23,000 profit on one apartment when he sold it on and he made a €36,500 profit on the other apartment. What was the total selling price of the two apartments?

9. Marjorie won the lottery and was thrilled with her win of €1,456,738. She bought a house for €456,378, a car for €34,780 and she went on a holiday which cost €16,387.

(a) How much did Marjorie spend?

(b) How much has Marjorie left?

In order to make the following number sentences correct, I need to leave out one number. Which one? Use your calculator.

1. 35,867 + 8,354 + 742,894 + 247 = 44,468

2. 37,456 + 283,956 + 628 + 79,035 = 400,447

3. 675 + 9,463 + 978,535 + 9,565 = 997,563

4. 89 + 6,847 + 8,953 + 970,574 = 979,616

5. 856 + 842 + 9,685 + 8,357 + 87 = 19,740

6. 694,693 + 279,568 + 748 + 37,580 = 733,021

7. 9,537 + 865 + 9,376 + 83,479 = 93,720

8. 9,679 + 365 + 70,357 + 284,709 = 364,745

Fill in the missing numbers.

1. 24 + ___ = 78 2. 56 + ___ = 83 3. ___ + 39 = 62 4. 94 – ___ = 35

A

B

C

Add all the numbers in the question. Subtract the underlined

answer from that total.

202

Check Up

Explain it! Explain: ‘increase by’, ‘decrease by’ and ‘find the difference between’.

Do it! 1. (a) 45,378 + 2,456 + 473 = ___ (b) (37,649 + 3,893) – 24,351 = ___

2. Increase 387,479 by 483,753. 3. Decrease 895,636 by 58,735.

4. Round 269,639 to: (a) the nearest 10; (b) to the nearest 100; and (c) to the nearest 1,000.

5. Find the difference between 997,542 and 806,532.

Solve it! 1. 406 of the 523 students walk to school. The other students use public transport or are driven.

How many students are driven to school or use public transport?

2. A bestselling author sold 3,693 of her books in December, 5,632 copies in January and 7,375 copies in February. How many copies of the bestseller did she sell altogether?

3. Mary spent €8,356 on office stationery this year. Last year she spent €467 less. How much did she spend on the stationery last year?

4. There were 523 students in secondary school last year. This academic year 93 First Years joined in September but 109 Sixth Years left. How many students are there in the school now?

Say it!

Fill in the missing words.

1. Another word for ‘take away’ is _ _ _ _ _ _ _ _.

2. The _ _ _ _ _ _ _ _ _ _ between 10 and 6 is 4.

3. The _ _ _ of 25 and 30 is 55.

4. When a number is _ _ _ _ _ _ _ _ _ the number becomes less.

5. When a number is increased the number becomes _ _ _ _ _ _ _.

Share it! Barbara, Donal, Aoife and John are having a barbeque for their friends. Each of the four friends brought two packages of meat. These are the packages that were available.

Chicken 1.28kg 0.62kg 1.5kg 1.24 kg 0.88 kg

Lamb 0.95kg 1.32kg 1.65kg 0.64kg 0.62 kg

Donal bought the largest package of lamb and a package of chicken that weighed 1.28kgs. Barbara and Aoife each bought the same size package of lamb, which was 0.33kgs less than the package of lamb bought by Donal. John bought the largest and smallest packages of chicken. Barbara bought a package of lamb which was the same size as a package of chicken that John bought. Aoife bought a package of chicken twice the weight as a package of lamb bought by Barbara.

What was the total weight of meat that each person bought?

A

C

D

E

B

s

sd

d

g

Warm-up. Listen to your teacher. Favourite Hobbies

Strand UnitStrand669 Explore & calculate averages of simple data sets.

Obj

ectiv

es Data

Representing and Interpreting Data

213

Data 1

Averages

Data is information which has been collected.

The average number is the most common in a set of data.

To get an average: add the numbers in the set and divide by the number in the set, e.g. the average of 12, 34 and 23 = ?

12 + 34 + 23 = 69 69 ÷ 3 = 23

Average number = 23

Answer the questions.

1. Find the average of each of these sets of data. (a) 16, 22, 19, 17 and 6

(c) 67kg, 85kg, 43kg and 28kg

(e) 5.8m, 9.4m, 4.73m, 12.5m and 4.07m

(b) €3.56, €8.78, €23.46 and €56.40

(d) 46km, 59km, 43km, 54km and 38km

(f) 3.493 ¬, 4.594 ¬, 6.352 ¬, 3.836 ¬ and 5.8 ¬

2. There are 6 classes in the 3rd Class in St Finbar’s NS. The class sizes are 21, 28, 31, 27, 25 and 24. What is the average number of children in a class?

3. 5 students earn €8.90, €9.40, €9.75, €9.90 and €10.15 an hour. What was the average hourly rate?

4. The Carina travels 22.64km per litre of petrol, the Mini travels 18.48km per litre, the Mazda travels 24.36km per litre and the Nissan travels 21km per litre. What is the average distance travelled per litre of petrol by the four cars?

1. The average of 3 numbers is 8. If 2 of the numbers are 11 and 6, what is the third number?


Challenge

Yourself!

B

A

My goal is

to explore and

calculate a

verages of

data sets.

0

21

3

5

7

9

4

6

8

10

Swimming Football Hurling/CamogieIrish DancingBalletHip-hop

Strand UnitStrand667 Read and interpret trend graphs and pie charts.

Obj

ectiv

es22

Data

Topic 3: Data 1

Trend graphs

A trend graph is often used to show information over a period of time.

The data is plotted as a series of points, then the points are joined with straight lines.

Trend graphs are used for forecasting as they can help to predict future trends.

Look at the trend graph of attendance at the Mars Cinema. Answer the questions.

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

1. (a) Which day has the greatest attendance?

(b) Which days have the least attendance?

2. What is the difference between the greatest and least attendances?

3. How many days was the cinema attendance under 300? Name them.

4. What was the total attendance for the week?

5. Which days showed an increase in attendance from the previous day?

6. Which days showed a decrease in attendance from the previous day?

7. The cinema needed a daily attendance of 300 in order to cover expenses. Which days reached the target?

8. Which day showed neither an increase nor decrease from the previous day?

9. Which day showed the biggest increase from the previous day?

10. Which day showed the biggest decrease from the previous day?

11. Calculate the average daily attendance from Monday to Friday inclusive.

12. Suggest reasons why Mondays and Tuesdays have the lowest attendance.

13. How would you describe the weekly trend of cinema attendance?

14. What implications would this trend have for employing extra or fewer staff during the week?

A

Atte

ndan

ce


700

600

500

400

300

200

100

Strand UnitStrand666 Collect, organise and represent data using pie charts

and trend graphs.

Obj

ectiv

es Data

23Topic 3: Data 1

A computer in a weather station produces the following data on the number of hours of sunshine in the past 7 days in a random manner.

Random data

Days Wed Mon Tues Sun Fri Sat Thurs

Hours of sunshine 4 7 10 2 3 1 6

In order to interpret this random data in a meaningful way it is necessary to organise the data.

1. Organise the data in day order, so that we can prepare trend analysis. Fill in the table.

Days Mon Tues Wed Thurs Fri Sat Sun

Hours of sunshine 4

2. Plot the days of the week and the hours of sunshine on a graph. Time always goes on the x-axis. The data being measured goes on the y-axis.

Title: _____________

Mon Tues Wed Thurs Fri Sat Sun

Join the dots with straight lines. Now you will be able to see a trend and you will be able to analyse the data quickly.

Do these surveys with your class and organise your data on a table.

(a) Our favourite TV shows (b) The number of siblings we have

(c) The amount of time we spend doing homework (d) Our favourite pizza toppings

(e) How we come to school (f) Our favourite films

A

B


The x-axis

is a horizontal

line. The y-axis is a

vertical line.

7 hours

6 hours

5 hours

4 hours

3 hours

2 hours

1 hour

Strand UnitStrand•666Collect,organiseandrepresentdatausingpiecharts

andtrendgraphs.•668Compileandusesimpledatasets.O

bjec

tives

24 Topic 3: Data 1

Travelling to work in Asteroid Town.

Most of the adults living in Asteroid Town are employed in the local spaceship industry. In the year 2095, the average journey time in a spacemobile to work took 70 minutes. The economy boomed and new factories were opened in the year 2096, so the journey took 80 minutes. Major inter-galactic highway repairs took place in the year 2097, so the journey took 95 minutes. In the year 2098 the economy slowed down and a large number of spaceship industries in Asteroid Town were forced to close and the unemployment level rose sharply. The journey time was reduced to 75 minutes.

1. Organise the data.

2. Draw the trend graph.

3. How much longer did the average journey time take in 2096 than in 2095?

4. What factors contributed to the additional travel time in 2096 and 2097?

5. What year had the highest journey time?

6. What year had the lowest journey time?

7. What factors, do you think, contributed to the fall in journey time in 2098?

8. What was the average journey length over the 4-year period?

1. Organise the following data and represent it on a trend graph.

(a) Baby Kevin’s weight was plotted in the baby clinic.

Week 1 5 3 6 2 4

Weight (kg) 5.2 5.3 5.2 5.8 5 5

(b) Marie’s height was measured at different ages.

Age 12 14 10 13 11 15

Height (cm) 136 142 127 138 130 150

(c) Cars sold in Gary’s Garage.

Month Jan Feb Sept Oct Nov Dec

Cars sold 160 100 40 30 20 20

(d) Sales of bicycles in Bea’s Bike Shop.

Month July Mar Oct Jan Sept June Aug Feb Dec Apr May Nov

Sales 40 10 20 70 35 50 30 15 75 25 35 70

2. Compose eight questions based on your trend graphs. Your partner can answer your questions.

A

B

Data


Pair work

Pair work

253

Check Up

Explain it!

Explain: ‘trend graph’ and ‘data’.

Do it! 1. Find the average of 6.5, 5.5, 4.4 and 2.0.

2. Find the average of 55m, 49m, 45m, 54m and 47m.


4. Theaveragetemperatureoverathreedayperiodis20˚C.Thefirst2dayswere16˚C.Whatwas the temperature on the third day?

5. This table shows the hours of sunshine per day for the past week. Find the average.

Monday Tuesday Wednesday Thursday Friday Saturday Sunday

10 8 5 2 11 13 7

Solve it!

Mon Tues Wed Thurs Fri Sat Sun

3 hours

2 hours

1 hour

212 hours

112 hours

1. Which day does the class spend the most time watching TV?

2. Which days do the class spend the least time watching TV?

3. What is the average time for TV watching from Monday to Friday inclusive?

4. What is the difference between the most and least times spent watching TV?

5. Suggest a reason for the most and least times spent watching TV.

Say it!

Fill in the missing words.

1. A _ _ _ _ _ _ _ _ _ _ shows information over a period of time.

2. The _ -axis is a horizontal line.

3. When we collect the data we must _ _ _ _ _ _ _ _ the data.

4. The vertical line is called the _ - _ _ _ _.

5. We organise the data by making a _ _ _ _ _.

Share it! Do a survey with your class. Organise your data and draw a table to show it. Plot a trend graph for your data. Survey: Amount of time spent on the computer each week.

A

C

D

E

B

t g

o

t

Time spent watching TV

26 The Paradise Amusement Park

1. During the holiday season in the Paradise Amusement Park approximately 1 million competitors entered the hammer hitting competition to win a teddy. These are the scores.

Number of competitors Height score

718 7m3,215 6m29,821 5m

382,714 4m479,122 3m81,767 2m17,584 1m

(a) For each of the totals above, write the value of the digit 1. (b) Write out the number of competitors

(i) in expanded form and (ii) in words. (c) Order the list of competitors starting

with the smallest number. (d) Round the number of competitors (i) to the nearest 10 and (ii) to the nearest 100. (e) Round the number of competitors to the nearest 1,000.

27The Paradise Amusement Park

2. Look at the hammer hit scores.

(a) Find the total number of competitors who scored 3 metres or more. Use your calculator.

(b) How many competitors scored 3 metres and under?

(c) How many competitors scored 4 metres, 5 metres or 6 metres?

(d) What is the difference between the number of competitors who achieved the highest and lowest scores?

(e) What is the difference between the competitors who scored 1, 2 or 3 metres and those who scored 5, 6 or 7 metres?

3. Complete the data based on the scores.

Number of competitors

47,692 181,294 484,642 249,335 24,789 8,726 684

Competitors rounded to the nearest 1,000Scores achieved in metres

1 2 3 4 5 6 7

(a) Round the number of competitors to the nearest 1,000.

(b) What is the most common score?

(c) What is the least common score?

(d) Approximately what percentage of competitors scored 4 metres? Hint: There are approximately 1 million competitors.

4. Fast Photo Shop recorded monthly sales of its Dream Disposable Camera.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec50 60 70 90 80 130 140 120 100 80 40 60

(a) Draw a trend graph of the monthly sales. Hint: Put the months on the x-axis. Put the sales on the y-axis. Use intervals of 10 e.g. 50, 60, 70.

(b) What is the total number of Dream Disposable Cameras sold in the year?

(c) What was the average number of the cameras sold each month? Use your calculator.

(d) Which month recorded the highest sales? Suggest reasons for this.

(e) Which month recorded the lowest sales? Suggest reasons for this.

(f) Discuss reasons for the trend which you observe on the graph.

___ 10

B

28 MENTAL MATHS 1

A

1. Write this number in expanded form: 3,895,307.

2. In the graph the ___-axis is a horizontal line.

3. Round 2,585,385 to the nearest 100.

4. Find the difference between 864,603 and 37,903.

5. Write out the multiples of 5 up to 50.

6. Write 14 as a percentage.

7. How many sides has a hexagon?

8. A triangle with 3 sides the same length is called an __________ triangle.

9. Name this shape.

10. Draw a circle. Label the radius r.

11. Draw a line perpendicular to this line. _______________________________

12. Name this type of angle.

13. 2,378m = ___km

14. Name this shape.

15. 1kg = ___g

1. Write the number shown on the notation board below.

H th T th Th H T U

•••••• •• •••••••• ••••• ••••

2. Round 4,698,317 to the nearest 10.

3. What is the greatest number you can make with these numbers? 1 2 4 7 0 4 2

4. Find the sum of 735,803 + 28,604.

5. Write 410 as a decimal.

6. One of the factors of 12 is 4. What are the other factors of 12?

7. Write 13 as a percentage.

8. How many sides has a pentagon?

9. Name this shape.

10. Draw a circle. Put in the diameter. Label the diameter d.

11. Draw a line parallel to this line. ___________

12. Name this type of angle.

13. 100m = ___km

14. Draw a net of a cylinder.

15. Name this shape. ___ 15

___ 15

90˚

Planet Maths 6th - Sample Pages

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