Maths Carnival Book 2 by Alston Education

MATHS

The Maths Carnival series is developed for pupils who go to CBSE-affiliated schools to help them achieve the learning outcomes of the latest national curriculum.

Maths Carnival builds a strong foundation in pupils through the use of sound pedagogical principles. Adopting the popular Concrete Pictorial Abstract approach widely used in the Singapore mathematics curriculum, pupils are introduced to new concepts through concrete manipulatives and engaging pictorials before they are led to see their abstract symbolic representations. This allows pupils to have a deeper understanding of key mathematical concepts, thus motivating them to learn.

Sam Kee

The key features of the book are: ✔ Graduated content ensuring logical progression of learning ✔ Clear presentation of key mathematical concepts with solved examples ✔ Plenty of practice exercises ✔ Hands-on maths activities to promote peer interaction and collaborative learning ✔ Ample skill-based questions to develop various skills for applying mathematics in daily life ✔ Formative and Summative assessments mapped to learning outcomes ✔ Real-life application of mathematical concepts

BOOK 2

Content is clearly structured across the levels to ensure a gradual build-up and review of skills as pupils progress up the levels. At the same time, emphasis is given on developing pupils’ creativity, critical thinking and problem-solving skills.

The Maths Carnival Book 2 comprises the following components: ✔ Student Book 2 ✔ Teacher’s Guide Book 2 – Contains lesson plans and wrap-around teacher’s notes, with additional information and tips on conducting and delivering effective Science lessons. ✔ Additional formative and summative assessments are available online for teachers only. ` 325

Empowering Minds • Improving Lives

Sam Kee

Published by Alston Publishing House Pte Ltd 745 Toa Payoh Lorong 5, #03-07, Singapore 319455 enquiry@alstonpublishinghouse.com www.alstonpublishinghouse.com ÂŠ 2017 Alston Publishing House Pte Ltd All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of the copyright owner. Distributed in India by Parle Book Centre Shop No. 6, Anant Co-Operative Society Ltd. D. J. Road,Vile Parle West Mumbai, Maharashtra 400056 India Tel: 022 2618 4082 Email: info@pbcdistributors.com First published 2017 ISBN 978-981-4573-52-8 Publisher: Sim Wee Chee Printed by Replika Press

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MATHS

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Hello there ! Iâ&#x20AC;&#x2122;m Chuckles the Clown. Welcome to Maths Carnival. We are going to have a great time learning mathematics together. Maths Carnival is a place where sums are fun and math practice is like going on a roller coaster ride. So buckle up and get set to enjoy yourselves while you learn all about mathematics.

I am Twinkle.

I am Rinkle.

I am Bubbles. I am Jimbo.

My Name My School My Address

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PREFACE The Maths Carnival series is developed for pupils who go to CBSE-affiliated schools to help them achieve the learning outcomes of the latest national curriculum. Maths Carnival builds a strong foundation of the subject through the use of well-researched and sound pedagogical principles. Adopting the popular Concrete Pictorial Abstract approach widely used in the Singapore mathematics curriculum, pupils are introduced to new concepts through concrete manipulatives and engaging pictorials before they are led to see their abstract symbolic representations.This allows pupils to have a deeper understanding of key mathematical concepts, thus motivating them to learn. The formative and summative assessments allow for continual evaluation of pupils’understanding of concepts.These outcomebased exercises aim to test their understanding and application of mathematical concepts and related skills to solve real life problems.

Welcome to Maths Carnival! Here, learning mathematics has been made a joyful experience with hands-on activities and challenging exercises. Most activities have been designed on the theme of carnival. The different sections are indicated by the relevant signboards: • • • •

Learning Zone Practice Zone Skill Zone Recap Zone

• Testing Zone • Vocabulary Zone • Fun Zone

So, what are you waiting for? Let us enter the Maths Carnival.

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Your fun learning zones Here, you can learn the key concepts of mathematics with solved examples.

Here, you can learn the keywords of mathematics.

Here, you can apply what you have learnt to perform project Refer to Teacher’s Guide TEACHER’S work and creative activities for related Project Work CORNER that will enhance your problem solving skills. TEACHER’S CORNER

Here, you can practice questions on the concepts you have learnt.

Here, you can develop important 21st century skills & life skills. You can also solve higher order thinking questions.

Here, you can test yourself on the learnings acquired from the entire lesson.

Introduces topics in a stimulating way with relevant questions provided to encourage active discussion

What Will You Learn? Appears at the beginning of each chapter to state the focal points of the chapter

Refer to Teacher’s Guide for related Project Work

Teachers will provide fun and interesting projects for pupils to carry out. Refer to Teacher’s Guide TEACHER’S CORNER

Chapter Opener

Teachers will provide different activities in class to promote peer interaction and collaborative learning.

TEACHER’S CORNER

Here, you can recapitulate the key concepts and important points of the lesson.

Refer to Teacher’s Guide for related Activity

for related Activity

Walkthrough Contains key concepts of mathematics

Follow-up questions appear after the teaching of every new concept to provide immediate reinforcement of the lesson learnt

Maths Carnival Book 2

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Contains key mathematical terms

Comprises higher-orderthinking questions for the pupils to apply what they have learnt. They promote 21st century skills as well as civic and moral values

Contains questions based on mental calculation skills

Provides the pupils with questions that encourages them to be good to others and to the things in their environment

Excites pupils with fun and interesting details about the world around them.

Contains a summary of key concepts and mathematical terms to consolidate learning at the end of every chapter

TEACHER’S CORNER

Refer to Teacher’s Guide for related Project Work

TEACHER’S CORNER

Refer to Teacher’s Guide for related Activity

Carefully selected and gradated questions appear at the end of every section as a means of practice to ensure a gradual buildup of skills

Pupils will perform hands-on activities using manipulatives facilitated by teachers

TEACHER’S CORNER

Refer to Teacher’s Guide for related Project Work

Pupils will be given project assignments by teachers to perform in class orTeacher’s at home. Refer to Guide TEACHER’S CORNER

for related Activity

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Table of Contents

Chapter 1

Numbers ................................................ 7

Chapter 2

Addition and Subtraction ................... 28

Chapter 3

Multiplication ....................................... 47

Chapter 4

Division ................................................. 67

Chapter 5

Fractions............................................... 82

Chapter 6

Shapes and Solids ............................... 99

Chapter 7

Patterns .............................................. 116

Chapter 8

Measurement .................................... 127

Chapter 9

Time .................................................... 155

Chapter 10

Money ................................................ 169

Chapter 11

Data Handling ................................... 186

Formative Assessment .............................................. 198 Summative Assessment ........................................... 202

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Numbers

point? ng hi is fin e th to t ge to ed ne e kl in How many more steps does Tw dder skip? How many numbers does the longest la What Will You Learn? By the end of this lesson, you will be able to: ✔ identify and write numerals for numbers up to 1000 ✔ write the place value of digits in a given number ✔ write the expanded form of a number ✔ use place values to compare and order numbers ✔ find the number more than or less than a given number ✔ skip count in ones, twos, threes, fives, tens and hundreds Chapter 1: Numbers

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Numbers up to 1000

Learning Zone

How many cubes are there?

...

Counting in hundreds, tens and ones

100

200

300

400

900 nine hundred 500

600

700

800

Can you count on further in hundreds? How many cubes will there be if you add another

There are 900 cubes. How many cubes will there be if you add 10 cubes? What number will you get if you add 10 cubes ten times to 900 cubes?

Maths Carnival Book 2

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add

900

1000

100

one thousand

100 more than 900 is 1000 (one thousand). A period of 1000 years is called a millennium.

Count the cubes.

First, count on in hundreds. Next, count on in tens. Then count on in ones.

There are 653 (six hundred fifty three) cubes. Practice Zone 1. Write these numbers in numerals. a. five hundred and forty two b. six hundred and sixty five c. eight hundred and fifty seven Chapter 1: Numbers

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2. Write these numbers in words. a. 205 b. 530 c. 999

Learning Zone

Place Values

Rinkle wants to count the number of cubes she has. She uses a place value table to help her count. Hundreds

Tens

Ones

How many tens are there in the number 119?

1 hundred 2 tens 5 ones = 125 In the number 125, a. the digit 1 is in the hundreds place. It stands for 1 hundred and has a value of 100. b. the digit 2 is in the tens place. It stands for 2 tens and has a value of 20. c. the digit 5 is in the ones place. It stands for 5 ones and has a value of 5. The place value of a digit in a number depends on the position of that digit. In 145, the digit 1Â stands for 1Â hundred and it has a value of 100. 10

Maths Carnival Book 2

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Look at the number. How many hundreds, tens and ones are there in the number? Hundreds

Tens

Ones

4 hundreds 6 tens 0 ones = 460 The number 460 can be written as 400 + 60 + 0 according to its place values. To write a number in the standard form, take the first digit in the place values. So, 400 + 60 + 0 = 460.

460

460 400

0 60

If there are 3 hundreds, 0 tens and 7 ones, would you write this number as 37 or 307? TEACHER’S

Refer to Teacher’s Guide for related Project Work

CORNER

TEACHER’S CORNER

Refer to Teacher’s Guide for related Activity

Practice Zone 1. In the number 726, a. The digit 7 stands for

and has a value of

b. The digit 2 stands for

and has a value of

c. The digit 6 stands for

and has a value of

Chapter 1: Numbers

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2. Expand the numbers. a. 350 =

b. 579 =

c. 812 =

d. 901 =

3. Write the standard form. a. 200 + 10 + 3 =

b. 500 + 90 + 9 =

c. 800 + 80 + 8 =

d. 900 + 2 =

Learning Zone

Comparing and Ordering Numbers

Look at the numbers 431 and 528. Which number is greater? Hundreds

Tens

Ones

Hundreds

Tens

Ones

Which number is smaller, 31 or 28?

431

528

You can use a place value table to compare the numbers.

Maths Carnival Book 2

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First, compare the hundreds. 5 hundreds is greater than 4 hundreds. So, 528 is greater than 431. You can also write this as 528 > 431.

â&#x20AC;&#x2DC;>â&#x20AC;&#x2122; means â&#x20AC;&#x2DC;greater thanâ&#x20AC;&#x2122;.

Compare 472 and 475. 472

Hundreds

Tens

Ones

475

Hundreds

Tens

Ones

First, compare the hundreds. Both numbers have 4 hundreds. When the hundreds and the tens are the same, compare the ones.

Next, compare the tens. Both numbers have 7 tens. Then, compare the ones. 2 ones is smaller than 5 ones. So, 472 is smaller than 475. 472 < 475. 475 is greater than 472. 475 > 472.

When comparing three-digit numbers, always compare the digits in the hundreds place first. If they are the same, compare the digits in the tens place. If the digits in the tens place are also the same, compare the digits in the ones place. Compare the numbers 829, 865 and 862. Which is the greatest? Which is the smallest? 829

Hundreds

Tens

Ones

The hundreds are the same, so compare the tens. Chapter 1: Numbers

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865

862

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Compare the tens. 2 tens < 6 tens So, 829 is the smallest. Now, compare the ones in 862 and 865. 5 ones > 2 ones. So, 865 > 862. 865, 862, 829 greatest

smallest

The greatest number is 865. The smallest number is 829. If the numbers are arranged from the greatest to the smallest, it is called descending order.

Twinkle, Rinkle and Jimbo took part in a singing competition. The results of the competition is as shown.

Jimboâ&#x20AC;&#x2122;s score: 257 Twinkleâ&#x20AC;&#x2122;s score: 181 Rinkleâ&#x20AC;&#x2122;s score: 293

Arrange the score each of them received from the smallest to the greatest. Who came in first place? Jimbo 257

Twinkle 181

Hundreds

Tens

Ones

Hundreds Tens 1

Ones 1

First, compare the hundreds. 2 hundreds > 1 hundred So, 181 is the smallest. Now, compare 257 and 293 to see which is smaller.

Maths Carnival Book 2

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Rinkle 293

Hundreds

Tens

Ones

5 tens < 9 tens So, 257 is smaller than 293. 257 < 293

If you order the score each of them received from the smallest to the greatest, you will get 181,

257,

293

smallest

greatest

So, Rinkle came in first place. If the numbers are arranged from the smallest to the greatest, it is called ascending order.

Arrange 456, 95 and 312 from the greatest to the smallest.

456

312

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Hundreds

Tens

Ones

95 is a two-digit number. It is smaller than the other two numbers, 456 and 312.

Compare 456 and 312 to see which is greater. 4 hundreds > 3 hundreds So, 456 > 312.

Arranging the numbers in order from the greatest to the smallest, you will get Refer to Teacher’s Guide TEACHER’S for related Project Work CORNER 456, 312, 95 greatest

smallest

TEACHER’S CORNER

Refer to Teacher’s Guide for related Activity

Chapter 1: Numbers

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Practice Zone 1. Fill in the boxes with > or <. a. 725

246

132

b. 271

284

519

510

2. Arrange these numbers in order. Begin with the smallest. a. 244, 309, 182 ,

485, 748, 480

3. Arrange these numbers in order. Begin with the greatest. a. 673, 598, 679 ,

71, 235, 167

More than and Less than

Learning Zone

What number is 1 more than 186? What number is 1 less than 186? 180

181

182 183 184

1 more 185 186 187

188

189 190

The number that is just after 186 on the number line is 1 more than 186. It So, 187 is 1 more than 186. is the successor. 1 less

180

181

182 183 184

The number that is just before 186 on the number line is 1 less than 186. It is the predecessor. 16

185 186 187

188

189 190

So, 185 is 1 less than 186.

Maths Carnival Book 2

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What number is 10 more than 240? What number is 10 less than 240? 10 more

200 210 220 230 240 250 260 270 280 290 300 10 less

250 is 10 more than 240. 230 is 10 less than 240. What number is 100 more than 758? What number is 100 less than 758? 100 more

458

558

658

758

858

958

100 less

858 is 100 more than 758. 658 is 100 less than 758. Before, After and Between Look at the number line. before 249

250

between

after 251

252

253

254

255

256

You can see on the number line that, 249 comes before 250, 252 comes after 251, 255 comes after 254 and before 256. So, you can say that 255 comes between 254 and 256. Chapter 1: Numbers

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Skip Counting in Ones Describe this number pattern. What number comes next? 5, 6, 7, 8, â&#x20AC;Ś

Look at this number pattern. What is the missing number? 163, 164, 165,

I can use a number line to find out what comes next in the number pattern.

? , 167, 168, 169

In this number pattern, start from 163 and count on in ones to find the next number. 163

164

165

166

167

168

169

So, 166 is the missing number. Skip Counting in Twos Look at this number pattern. What number comes next? 251, 249, 247, 245,

? In this number pattern, start from 251 and count back in twos to find the next number. 243

244

245

246

247

248 249

250

251

So, 243 comes next. Skip Counting in Threes Look at this number pattern. What is the missing number? 306, 309,

? , 315 Will I get the same answer if I count back In this number pattern, start from 306 and count on in threes to find the next number. in threes, starting from 315?

306 307 308 309 310

311

312

313

314

315

312 is 3 more than 309. So, 312 is the missing number. 18

Maths Carnival Book 2

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Skip Counting in Fives What number comes next in this number pattern? 470, 465, 460, 455,

Start from 470 and count back in fives to find the next number. 470

465

460

So, 450 comes next. Skip Counting in Tens What number comes next in this number pattern? 905, 915, 925, 935,

455

450

Look at the number pattern again: 905, 915, 925, 935, 945 What do you notice about the digits in the ones place? What do you notice about the digits in the tens place?

Start from 905 and count on in tens to find the next number. 905

915

925

935

945

So, 945 comes next. Skip Counting in Hundreds Look at this number pattern. What is the missing number? 440, 540, 640, 740,

Look at the number pattern again. What do you notice about the digits in the hundreds and tens place?

Start from 440 and count on in hundreds to find the next number. 440

540

640

740

840

So, 840 is the missing number. Chapter 1: Numbers

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Practice Zone 1. Write the number that is 1 less than 259. 2. Write the number that is 10 more than 621. 3. Write the number that comes between 511 and 513. 4. What number comes next? Describe the number pattern. a. 815, 816, 817, 818,

I count

b. 320, 330, 340, 350,

I count

c. 693, 696, 699, 702,

I count

d. 285, 290, 295, 300,

I count

Learning Zone

Even and Odd Numbers

Let us look at this number pattern. 2, 4, 6, 8, 10 They are also doubles of numbers.

In this pattern, count on in twos to find the next number.

2 = double 1, 4 = double 2, 6 = double 3 These type of numbers are called even numbers. Now look at this number pattern. The numbers in the pattern are even numbers and also doubles of numbers. 12, 14, 16, 18, 20 Compare the number patterns.

Maths Carnival Book 2

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What do you notice about the digits in the ones place? 12, 14, 16, 18, 20 122, 124, 126, 128, 130 The digits in the ones place are the same in both number patterns. When a number has the digits 0, 2, 4, 6 or 8 in the ones place, you can say that the number is even.

Let us look at this number pattern. 1, 3, 5, 7, 9 They are not double of any other number. You cannot find them in the multiplication table of 2. These numbers are called odd numbers.

Count on in twos to find the next odd or Now look at this number pattern. The numbers even number.

in the pattern are also odd numbers. 11, 13, 15, 17, 19 Compare the digits in the ones place in both number patterns. 11, 13, 15, 17, 19 121, 123, 125, 127, 129 The digits in the ones place are the same in both number patterns. When a number has the digits 1, 3, 5, 7 or 9 in the ones place, we say that the number is odd.

Practice Zone 1. Look at these numbers. Are they even or odd? a. 203

b. 312

c. 919

d. 420

e. 717

834 Chapter 1: Numbers

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‘FOUR’ is the only number in the English language that is spelt with the same number of letters as the number itself. FOUR

RECAP

Zone

✔ I can write the place values of the digits in a three-digit number. ✔ I can write the expanded form of a three-digit number. E.g.: 217 = 200 + 10 + 7

✔ I can write the standard form of a three-digit number. E.g.: 300 + 20 + 10 = 321

✔ I can use place values to compare two numbers and find the greater or smaller number. ✔ I can arrange numbers in ascending and descending order according to their values. ✔ I can find the number that is more than or less than a given number. ✔ I know that numbers that can be put into pairs are called even numbers. ✔ I know that numbers that cannot be put into pairs are called odd numbers. ✔ I can skip count in ones, twos, threes, fives and tens to find the missing number in a number pattern. 22

Maths Carnival Book 2

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Vocabulary Zone Read these words aloud and discuss their meanings with your classmates: Greater than

One thousand

Smaller

Greater

Smaller than Ascending order Less than

More than

Descending order

al Thinking Skills 21st Century Skills â&#x20AC;&#x201C; Creative and Critic Higher Order Thinking Skills

Skill Zone Apply What You Know

1. Look at this number line. W

330

Y 340

Z 350

360

Where do these numbers belong in the number line above? Write the correct letter in the boxes below. 354

338

331

347

2. If you count on in threes starting from 1, you will get the following number pattern: 1, 4, 7, 10, ... What is the 20th number in the pattern? Chapter 1: Numbers

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Mental Maths

3. Jimbo is thinking of a three-digit number. Read the clues given. What number is Jimbo thinking of? The digit in the hundreds place is 2 more than the digit in the ones place. The digit in the tens place is 1 more than the digit in the hundreds place. The sum of the three digits is 8. Jimbo is thinking of the number

Values in Action

Skip count in fives and join the dots. 130

125

135

140 150 145 155 160

120 115

195 190

165

185

It gets very hot during the summer. Some birds feel very tired and are unable to fly because of the heat. We can keep water on the windowsills of our schools and homes during the summer so that the birds can drink some water. But remember to clear the water daily to prevent mosquito breeding!

170 175

180

What is the name of the bird? 24

Maths Carnival Book 2

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Testing Zone 1. Write these numbers in numerals. a. two hundred and fifteen b. four hundred and forty c. five hundred and thirty-four d. seven hundred and ninety-one e. eight hundred and thirty-two f.

nine hundred and forty-five

2. Write these numbers in words. a. b. c. d. e.

310 445 704 808 903

3. In 978, a. the digit

is in the hundreds place.

b. the value of the digit 9 is

c. the value of the digit 7 is

d. the digit 8 is in the

place.

4. Fill in the boxes with > or <. a. 313

621

b. 189

145

c. 564

561

d. 257

287

e. 692

860

736

648

g. 426

477

h. 945

949

950

981

Chapter 1: Numbers

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5. Fill in the blanks. a. 100 less than 947 is b. 100 more than 520 is c. 100 less than 476 is 6. Arrange these numbers in order. a. Begin with the smallest. i.

194, 253, 102

ii.

815, 370, 449

iii.

645, 546, 634

b. Begin with the greatest. i.

260, 379, 314

ii.

495, 454, 584

iii.

823, 695, 746

7. Look at these number patterns. Then fill in the missing numbers.

296

996

396

738

744

747

753

Maths Carnival Book 2

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Fun Zone Hannah is on an adventure trail. Help her reach her final checkpoint by counting on in fours.

303 312

289

310

304 308 294

300 284

Hannah 286

288

292

296

196

TEACHER’S CORNER

Refer to Teacher’s Guide for related Project Work

TEACHER’S CORNER

Refer to Teacher’s Guide for related Activity

Chapter 1: Numbers

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MATHS

The Maths Carnival series is developed for pupils who go to CBSE-affiliated schools to help them achieve the learning outcomes of the latest national curriculum.

Maths Carnival builds a strong foundation in pupils through the use of sound pedagogical Pictorial Abstract approach widely used in principles. Adopting the popular Concrete the Singapore mathematics curriculum, pupils are introduced to new concepts through concrete manipulatives and engaging pictorials before they are led to see their abstract symbolic representations. This allows pupils to have a deeper understanding of key mathematical concepts, thus motivating them to learn.

Sam Kee

BOOK 2

Empowering Minds • Improving Lives

Alston_Maths_Cover-2_Final_editedbyJH.indd 1

Sam Kee

2/8/16 5:24 pm