RUKUN NEGARA Bahawasanya Negara Kita Malaysia mendukung cita-cita hendak: Mencapai perpaduan yang lebih erat dalam kalangan seluruh masyarakatnya; Memelihara satu cara hidup demokrasi; Mencipta satu masyarakat yang adil di mana kemakmuran negara akan dapat dinikmati bersama secara adil dan saksama; Menjamin satu cara yang liberal terhadap tradisi-tradisi kebudayaannya yang kaya dan pelbagai corak; Membina satu masyarakat progresif yang akan menggunakan sains dan teknologi moden. MAKA KAMI, rakyat Malaysia, berikrar akan menumpukan seluruh tenaga dan usaha kami untuk mencapai cita-cita tersebut berdasarkan prinsip-prinsip yang berikut: KEPERCAYAAN KEPADA TUHAN KESETIAAN KEPADA RAJA DAN NEGARA KELUHURAN PERLEMBAGAAN KEDAULATAN UNDANG-UNDANG KESOPANAN DAN KESUSILAAN (Sumber: Jabatan Penerangan, Kementerian Komunikasi dan Multimedia Malaysia)
i Dewan Bahasa dan Pustaka Kuala Lumpur 2021 STANDARD-BASED CURRICULUM FOR PRIMARY SCHOOL (REVISED 2017) DUAL LANGUAGE PROGRAMME WRITERS Chan Yook Lean Gobi a/l Krishnan Rozaili bin Mohd Ali TRANSLATORS Ahmad Azrul Arefe bin Ahmad Rosdi Jeyasingam a/l Govindaraj Ng Lee Ching Norehan binti Mohamed Shaharoun EDITORS Ainol Rafezah binti Alias Asmahanim binti Ab Rahman Mohd ‘Udzair bin Depanaik Nurul Shaheza binti Zamri DESIGNERS Roszaini binti Md Yussof Rohaizah binti Hamzah ILLUSTRATOR Mohd. Faizal bin Razali
ii Serial No.: 0023 KK 513-221-0102011-49-3328-20101 ISBN 978-983-49-3328-9 First printing 2021 © Ministry of Education Malaysia 2021 All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system without permission in writing from the Director General of Education Malaysia, Ministry of Education Malaysia. Negotiation is subject to the calculation of royalty or honorarium. Published for the Ministry of Education Malaysia by: Dewan Bahasa dan Pustaka, Jalan Dewan Bahasa, 50460 Kuala Lumpur. Telephone: 03-21479000 (8 hunting lines) Facsimile: 03-21479643 Website: http://www.dbp.gov.my Design and Typeset: PNMB Education and Publication Sdn. Bhd. Text Typeface: Azim Text Size: 13 point Printed by: Percetakan Selaseh Sdn. Bhd., No. 30 & 32, Jalan Selaseh Indah, Taman Selaseh Fasa 1, 68100 Batu Caves, Selangor Darul Ehsan. ACKNOWLEDGEMENTS The publication of this textbook involved various parties. Sincerest appreciation and gratitude particularly to the following: • The Panel of Evaluators, Educational Resources and Technology Division, Ministry of Education Malaysia. • The Educational Resources and Technology Division, and Curriculum Development Division, Ministry of Education Malaysia. • The Panel of Evaluators, Dewan Bahasa dan Pustaka. • Officers of the English Language Teaching Centre (ELTC), Ministry of Education Malaysia. • SK Pengkalan Rinting, Johor. • Teacher Education Institute, Kampus Perempuan Melayu, Melaka. • Dr. Shahrir Affandi bin Daud@Mohamed. • Dato’ Mohamad Kamil bin Dato’ Haji Shafie. • All parties involved in the process of publishing this book.
iii CONTENTS 1 WHOLE NUMBERS AND OPERATIONS 1 3 MONEY 103 PREFACE v 2 FRACTIONS, DECIMALS, AND PERCENTAGES 61 Read and Say Numbers 1 Think Smart 3 Number Patterns 4 Think Smart 8 Recognise Fraction of a Million and Decimal of a Million 9 Convert Numbers 1 1 Decimal of a Million and Fraction of a Million to Whole Numbers 1 1 Think Smart 12 Whole Numbers to Decimal of a Million and Fraction of a Million 13 Basic Operations 15 Addition 15 Subtraction 19 Multiplication 22 Division 25 Think Smart 26 Mixed Operations 28 Addition and Subtraction 28 Multiplication and Division 30 Addition and Multiplication 31 Subtraction and Multiplication 32 Addition and Division 33 Subtraction and Division 34 Basic Operations and Mixed Operations Involving Unknown 35 Think Smart 35 Think Smart 36 Think Smart 38 Prime Numbers and Composite Numbers 42 Try It Out 44 Solve the Problems 45 Let’s Practise 58 Let's Explore 60 Division of Fractions 61 Dividing Proper Fractions with Whole Numbers 61 Dividing Mixed Numbers with Whole Numbers 63 Dividing Proper Fractions with Proper Fractions 64 Dividing Mixed Numbers with Proper Fractions 65 Think Smart 66 Basic Operations 68 Multiplication of Decimals 68 Think Smart 69 Division of Decimals 70 Convert Decimals to Percentages 73 Addition and Subtraction of Percentages 75 The Value of Quantity and The Value of Percentages 77 Think Smart 77 Mixed Operations 80 Addition and Subtraction 80 Multiplication and Division 82 Addition and Multiplication 84 Think Smart 85 Subtraction and Multiplication 86 Addition and Division 88 Think Smart 89 Subtraction and Division 90 Think Smart 9 1 Try It Out 92 Solve the Problems 93 Let’s Practise 99 Let's Explore 102 Recognise Cost Price, Selling Price, Profit, and Loss 103 Recognise Discount, Rebate, and Voucher 107 Discount 107 Rebate 108 Think Smart 109 Voucher 110
iv Recognise Time Zone 141 Think Smart 146 Solve the Problems 148 Try It Out 152 Let’s Practise 153 Let's Explore 154 Solve the Problems 155 Length and Mass 155 Length and Volume of Liquid 158 Mass and Volume of Liquid 160 Let’s Practise 163 Let's Explore 164 Let's Form Angles 165 50° Angle 165 90° Angle 166 108° Angle 166 Try It Out 167 Draw and Measure Interior Angles of Regular Polygons 168 Equilateral Triangle 169 Square 171 Distance Between Two Coordinates 187 Think Smart 188 Ratio Between Two Quantities 191 Think Smart 195 Try It Out 195 Determine the Proportionate Quantity 197 Think Smart 198 Solve the Problems 201 Think Smart 203 Let’s Practise 205 Let's Explore 206 Complete Pie Chart and Interpret Data 207 Think Smart 210 Try It Out 211 Likelihood 213 Certain or Impossible 216 Equally Likely 217 More Likely or Less Likely 217 Think Smart 218 Try It Out 218 Solve the Problems 220 Let’s Practise 223 Let's Explore 224 SELF-TEST 225 GLOSSARY 231 ANSWERS 233 CONTENTS 4 TIME 141 5 MEASUREMENT 155 6 SPACE 165 8 DATA HANDLING AND LIKELIHOOD 207 7 COORDINATES, RATIO, AND PROPORTION 187 Regular Pentagon 172 Regular Hexagon 174 Regular Heptagon 175 Regular Octagon 176 Think Smart 177 Recognise Circles 178 Centre of a Circle, Diameter, and Radius 178 Let’s Draw Circles 180 Think Smart 182 Solve the Problems 183 Let’s Practise 185 Let's Explore 186 Recognise Invoice, Bill, Receipt, and Service Tax 112 Invoice 112 Bill 113 Receipt and Service Tax 114 Interest and Dividend 116 Interest 116 Dividend 117 Try It Out 119 Recognise Asset, Liability, Insurance, and Takaful 120 Asset and Liability 120 Insurance and Takaful 121 Solve the Problems 123 Let’s Practise 133 Let's Explore 136 SELF-TEST 137
v The publication of the Standard-Based Curriculum for Primary School (Revised 2017) has reached the sixth year. This textbook is based on the National Education Philosophy and focuses on the challenges in the 21st century and the Malaysia Education Blueprint (MEB) 2013-2025, the New Economic Model and the latest learning theories, as well as the latest assessment methods. The Mathematics Year 6 Textbook focuses on building holistic human capital, balanced in terms of physical, emotional, intellectual, and socio-cultural aspects of the Malaysian society, as well as the integration of the Cross Curricular Elements (CCE), Information and Communication Technology, and Entrepreneurship as we head towards world-class education. The content of this textbook is systematically designed with eight topics to meet the requirements of the Dokumen Standard Kurikulum dan Pentaksiran (DSKP) published by the Curriculum Development Division, Ministry of Education Malaysia. This textbook emphasises the concepts and skills in the Learning Standard to prioritise pupils’ engagement in learning. This book includes several sections of practice in the Let’s Do It, Let’s Practise, and Self-Test to help pupils assess their levels of competency in each skill that they have learned. These exercises will help teachers carry out assessment of the pupils to achieve the desired performance standard. Teacher’s Notes enables teachers to implement learning activities effectively. Suggestions of websites are provided for pupils to explore the knowledge learned and to carry out additional exercises through information technology. The aim of this textbook is to be the source of knowledge for the pupils through various strategies and activities that have been integrated to the learning process. Apart from that, this textbook serves the purpose of assisting the teachers to implement a systematic teaching and learning process, as well as to create a wide range of teaching strategies in order to achieve the learning objectives. Additional information is also included in the Tips and Do you know? sections. Learning materials are also provided in the Quick Response (QR) code and Augmented Reality (AR) to enhance the effectiveness of the learning process. In order to cultivate pupils’ cognitive skills, reasoning questions are posed by the mascot and the feedback to the questions can be discussed with teachers or peers. In addition, the Higher Order Thinking Skills (HOTS) questions are prepared in the Think Smart and Let’s Practise sections to challenge pupils’ critical thinking. Project-based learning or games are also provided in the Try It Out and Let's Explore to assist pupils’ understanding and enhance their skills. This textbook has been designed in a user-friendly manner with the elements to attract pupils’ interest in mathematics. The elements of national integration and patriotism are also incorporated through the use of names and characters. The users of this textbook may find the explanation of the icons used in the next page. Chan Yook Lean Gobi a/l Krishnan Rozaili bin Mohd Ali PREFACE
GLOSSARY vi Recreational activities in the form of edutainment. Exercises to assess pupils’ mastery of newly learned skills. Questions to challenge the intellectual ability, Higher Order Thinking Skills (HOTS), and encourage critical and creative thinking. Exercises to evaluate and reinforce the skills acquired in each topic. Exercises for revision to reinforce pupils’ understanding. List of mathematical terms and their meanings that encompasses all topics. List of answers for Think Smart, Let’s Practise, and Self-Test. Type “AR Matematik Thn. 6 SK/DLP” in Google Play (Google) or App Store (Apple) and download it. QR code contains learning materials that need to be scanned using QR scanner. 1.1.1 6 SPACE Emphasis on the learning activities and suggestions on additional activities. TOPIC Topic based on learning area. SUBTOPIC The learning standard that needs to be mastered. MASCOT Poses questions that stimulate pupils’ mind to encourage reasoning. CONTENT STANDARD AND LEARNING STANDARD NUMBER TRY IT OUT LET’S DO IT LET’S DO IT THINK SMART THINK LET’S PRACTISE ANSWERS Activities to enhance the skills learned. TIPS Useful information on skills learned. Skill indicators to be mastered based on the DSKP for Mathematics Year 6. FUNCTIONS OF THE ICONS SELF-TEST Additional information for pupils’ knowledge. LET'S EXPLORE SCAN ME
1 1.1.1 1 The infographic below shows the number of users of various devices who are able to access the Internet in a country. Smartphone 10 000 000 Laptop 4 405 792 Smart television 1 237 483 Smartwatch 246 015 one million two hundred thirty-seven thousand four hundred and eighty-three a What is the number of users of smart television who are able to access the Internet? Emphasise saying numbers correctly based on place values. Carry out activities on saying numbers at random based on information from the infographic above. millions hundred thousands ten thousands one thousands hundreds tens ones 1 2 3 7 4 8 3 Say the number of users of smartphone and desktop computer who are able to access the Internet. WHOLE NUMBERS AND OPERATIONS 1 READ AND SAY NUMBERS Desktop computer 2 800 806
2 1.1.1 Use flash cards for activities in saying and writing numbers in numerals or words. 7 290 005 8 000 080 Four million forty-five thousand seven hundred and ninety-two. Did Rani say the number correctly? Discuss. seven million two hundred ninety thousand and five TUESDAY 11 JANUARY 2022 TUESDAY 11 JANUARY 2022 eight million and eighty Write three million five hundred four thousand and thirteen'' in numerals. b 2 3 Jaslin Aizam 3 504 130 3 504 013 I write the number in words. I write in numerals. Number of laptop users who are able to access the Internet 4 405 792 Number Place value of digit 1 1 000 000 millions 1 000 000 000 billions 1 000 000 000 000 trillions Who wrote the numerals correctly? ''
3 1 Say the numbers. a 2 189 234 b 9 273 180 c 6 031 095 d 3 006 070 2 Write the numbers in words. a 4 238 452 b 8 093 120 c 5 700 106 d 10 000 000 3 Write the numbers in numerals. a nine hundred fifteen thousand one hundred and twenty-five b two million five hundred three thousand three hundred and sixty-one c eight million seven hundred fifty thousand and forty-three d six million three thousand nine hundred and seven e three million and six f five million fifteen thousand and seventy-eight g four million three hundred and two h seven million nine hundred and nineteen 4 Form three seven-digit numbers from the digit cards above. Say and write the numbers in words. 5 Say a number involving the value of millions. Write the number in numerals and words. 1.1.1 Use the digit cards above to form four seven-digit numbers beginning with digit 3. Two even number digits must always be adjacent. Say and write the numbers in numerals. 1 6 5 4 7 3 9 0 3 4 1 5 7 0 LET’S DO IT THINK SMART THINK SMART SMART
4 1.1.2 Begin the lesson with numbers such as 3 000 000 and simple number patterns such as adding 100 and 1 000 to stimulate pupils' understanding at various levels of mastery. The scientific calculator is only used as teaching aid to represent and determine number pattern. What is the ninth number in this pattern? 1 Arrange the number cards in a number pattern in ascending order by eight hundreds. + 800 2 390 795 2 391 595 2 392 395 2 394 795 2 393 995 2 393 195 + 800 + 800 + 800 I use a calculator to calculate the next number. NUMBER PATTERNS THURSDAY 13 JANUARY 2022 third number fourth number fifth number second number
5 1.1.2 Ask pupils to find the next number in the number pattern above. 3 095 475 3 096 475 3 097 475 What is the above number pattern? 2 2 890 740 3 890 740 4 890 740 5 890 740 6 890 740 Count backwards from 6 890 740 in millions. This number pattern is in descending order by millions. The hundreds digit for the three numbers are different. – 1 000 000 – 1 000 000 – 1 000 000 – 1 000 000 3 4 Identify the number pattern from A to E. State the pattern. The value of the number becomes smaller. The number pattern is in descending order. 7 6 5 7 8 5 0 − 7 6 5 7 4 5 0 4 0 0 7 6 5 7 4 5 0 − 7 6 5 7 0 5 0 4 0 0 Calculate the difference. 7 657 850, 7 657 450, 7 657 050, 7 656 650, 7 656 250 This number pattern is in descending order by four hundreds .
6 12 4 15 4 2 10 1 3 5 5 5 3 0 – 1 3 0 7 2 9 5 4 8 2 3 5 3 10 13 1 4 0 3 7 6 5 – 1 3 5 5 5 3 0 4 8 2 3 5 1 1 1 1 1 4 0 3 7 6 5 + 4 8 2 3 5 1 4 5 2 0 0 0 Step 1 Step 2 1.1.2 5 Look at the number pattern below. What is the value of x? 6 The number cards below are arranged in descending order. What is the value of p? The value of p is 5 065 273 . The value of x is 1 452 000 . Add 1 403 765 and 48 235 to get the value of x. Find the difference between two numbers. 1 307 295 1 355 530 1 403 765 x 1 500 235 Conduct a quiz in pairs for pupils to identify ascending and descending number patterns. What is another method to find the value of x? State the sixth number in the number pattern. 5 086 423 5 079 373 5 072 323 p 5 058 223 Find the difference between two adjoining numbers. Subtract 7 050 from 5 072 323 to find the value of p. 7 16 3 12 5 0 8 6 4 2 3 − 5 0 7 9 3 7 3 7 0 5 0 6 12 2 12 5 0 7 2 3 2 3 − 7 0 5 0 5 0 6 5 2 7 3 5 0 7 9 3 7 3 − 5 0 7 2 3 2 3 7 0 5 0 9
1.1.2 7 Guide pupils to find the product for Figure 7. 7 Look at the number pattern below. What is the value of p? 8 What is the number pattern below? State the value of t. 100, 600, 3 600, 21 600, 129 600, p, q Multiply the previous number by 6. Now, calculate the value of q. The value of p is 777 600 . Pattern Figure 1 1 × 1 = 1 Figure 2 2 × 2 = 4 Figure 3 3 × 3 = 9 Figure 4 4 × 4 = 16 Figure 5 5 × 5 = 25 If this pattern continues, what is the product for Figure 7? 100, 600, 3 600, 21 600, 129 600, p, q × 6 × 6 × 6 × 6 × 6 9 Study the pattern of the figures below. 1 5 3 1 2 9 6 0 0 × 6 7 7 7 6 0 0 128 64 32 16 t The number pattern is in descending order divided by twos. The value of t is 8 . 2 64 1 28 – 1 28 0 2 32 6 4 – 6 4 0 ÷ 2 ÷ 2 ÷ 2 ÷ 2 128, 64, 32, 16, t t = 16 ÷ 2 = 8
8 1.1.2 The picture shows a number pattern. a State the number pattern. b What is the sixth number? c Based on the number pattern, at which position is 4 964 116? 2 Five number cards are arranged in a pattern. State the value of x. 3 a What is the number pattern above? b State the value of p and q. 4 The figure above shows an arrangement of matchsticks in a pattern. What is the number of matchsticks in Figure 5? 200 1 600 12 800 p q 7 208 185 7 105 285 7 002 385 x 6 796 585 Figure 1 Figure 2 Figure 3 Study the following number pattern. Carry out a Think-Pair-Share activity to arrange a set of numbers in ascending or descending pattern and state the pattern. Calculators can be used in the Think Smart activity. 1 = 1 × 1 121 = 11 × 11 12 321 = 111 × 111 1 234 321 = × What are the values in the empty boxes? 1 LET’S DO IT THINK SMART THINK SMART SMART
9 1.1.3 1.1.4 three and nine-tenths of a million 3 9 10million Adapted and retrieved October 8, 2021 from https://bit.ly/3AB5CX0 LANGKAWI: The total number of tourists to this island is only 1 1 2 million until October this year. Chief Executive Officer of the Langkawi Development Authority (LADA), Dr. Hezri Adnan said the total is lesser than the total number of tourists last year, which is 3 9 10 million. 2 3 4 million is two and three-fourths of a million. What is another way of saying this fraction? 2 One point two million. Carry out activities on saying decimal of a million and fraction of a million at random using numeral cards or word cards. Emphasise how to say decimal of a million and fraction of a million correctly. 1 Item Number of items Face mask 0.75 million Hand sanitiser 1.2 million one and a half million 1 1 2 million one and one over two million RECOGNISE FRACTION OF A MILLION AND DECIMAL OF A MILLION Production in Week 1 WEDNESDAY 19 JANUARY 2022 Nancy, say the number of face masks. Kumar, say the number of hand sanitisers. Zero point seven five million.
10 1.1.3 1.1.4 4 Three pupils write five and three quarters of a million in numerals. 1 Say the numbers. a 3 10 million b 9.5 million c 0.87 million d 6 3 4 million e 1.023 million 2 Write the numbers in words. a 1 5 million b 7.6 million c 1.034 million d 8 1 2 million e 5.902 million 3 Write the numbers in numerals. a two-fifths of a million b zero point seven million c six and three-eighths of a million d four point zero two six million Write the following numbers in numerals. THURSDAY 20 JANUARY 2022 7.401 million seven point four zero one million 3 Conduct 21st Century Learning activity (Rally Robin) to enhance pupils' acquisition of skills in saying and writing numbers in numerals and words. three-fifths of a million 3 5 million LET’S DO IT Who wrote the number correctly? Anisah Kathleen Ravi Discuss. 5 3 4 million 5 1 4 million 5 3 8 million
1.1.5 11 Adapted and retrieved October 8, 2021, from https://bit.ly/3xxHx1y 1 Convert 5.78 million to a whole number. 5.78 million = Method 1 Method 2 Use method 1 as shown above to solve question 2. Peninsular Malaysia has a forest area of 5.78 million hectares and 4.91 million hectares of Permanent Reserved Forest. Sarawak has 4 3 10 million hectares of permanent forest estates while 0.674 million hectares are permanent protected areas. As for Sabah, the Sabah Forestry department has allocated 3 3 5 million hectares of state land as forest reserves. Carry out quizzes where pupils match decimal of a million with whole numbers. Place value millions hundred thousands ten thousands thousands hundreds tens ones Digit value 5 7 8 0 0 0 0 2 0.674 million = Convert 8.91 million to a whole number. 5.78 million = 5 780 000 DECIMAL OF A MILLION AND FRACTION OF A MILLION TO WHOLE NUMBERS CONVERT NUMBERS 5.78 million = 5.78 × 1 million = 5.780000 × 1 000 000 = 5 780 000 0.674 million = 0.674 × 1 million = 0.674000 × 1 000 000 = 674 000 0.674 million = 674 000 5.78 million = 5 millions + 0.7 millions + 0.08 millions = 5 millions + 7 hundred thousands + 8 ten thousands
12 1.1.5 Method 1 3 Convert 4 3 10 million to a whole number. 4 3 10 million = 4 300 000 4 3 10 million = 4 3 10 = 4.3 4 3 10 million = 4 3 10 × 1 million = 4.300000 × 1 000 000 = 4 300 000 3 3 5 million = 3 3 5 million = 3 600 000 3 3 5 million = 3 million + 3 5 million = 3 000 000 + 600 000 = 3 600 000 Convert 1 2 5 million to a whole number. Based on the number line above, state the values of p and q in whole numbers. 2 1 8 million 2 5 8 2 million 1 2 million p q 3 million 3 5 million = 600 000 2 5 million = 400 000 Use fraction charts, fraction strips, or number lines to explain the relationship between whole numbers and fraction of a million. Scan QR code to obtain the fraction of a million chart. 4 Convert 4 3 10 to an improper fraction, 43 10 . 1 million = 1 000 000 1 5 million 1 5 million 1 5 million 1 5 million 1 5 million 200 000 200 000 200 000 200 000 200 000 4 3 10 million = 4 3 10 × 1 million = 43 10 × 1 000 000 = 4 300 000 Method 2 THINK SMART THINK SMART SMART SCAN ME FRACTION OF A MILLION CHART
1.1.5 13 1 State 700 000 in decimal of a million. 700 000 = million 700 000 = 0.7 million 2 Convert 5 230 000 to a decimal of a million. 5 230 000 = million 700 000 = ( 700 000 1 000 000 ) million = 7 10 million = 0.7 million 800 000 = ( 800 000 1 000 000 ) million = 8 ÷ 2 10 ÷ 2 million = 4 5 million 800 000 = 4 5 Convert 3 725 000 to a million decimal of a million. Vary questions on the relationship of decimal of a million and fraction of a million to whole numbers and vice versa. Emphasise that fraction of a million must be written in the simplest form. 3 State 800 000 in fraction of a million. 800 000 = million Place value millions hundred thousands ten thousands thousands hundreds tens ones Digit value 0 7 0 0 0 0 0 700 000 = 0.7 million WHOLE NUMBERS TO DECIMAL OF A MILLION AND FRACTION OF A MILLION The digit value in the millions place value is 0. Place the decimal point between the millions place value and hundred thousands place value. Ignore the digit 0 after 7. Write the word million. The answer is 0.7 million. 5 230 000 = (5 230 000. ÷ 1 000 000) million = 5.23 million 5 230 000 = 5.23 million Method 1 Method 2
14 1.1.5 4 Convert 1 900 000 to a fraction of a million. 5 Are the values in the three cards equal? Discuss. 1 900 000 = million 1 Convert decimal of a million to whole numbers. a 0.4 million = b 0.12 million = c 1.08 million = d 1.5 million = e 0.032 million = f 9.013 million = 2 Convert fraction of a million to whole numbers. a 9 10 million = b 1 2 million = c 1 4 million = d 9 3 4 million = e 8 4 5 million = f 6 7 8 million = g 2 1 5 million = h 3 5 8 million = i 7 3 8 million = 3 Complete the following table. Whole number 500 000 2 750 000 Decimal of a million 2.3 million Fraction of a million 6 1 8 million 1 4 5 million 4 3 625 000 is equal to 3 5 8 million. Prove it. Carry out activities on saying whole numbers, fraction of a million, and decimal of a million of equal values. Give examples of fraction of a million with denominators of 2, 4, 5, 8 and 10 only. 1 900 000 = ( 1 900 000 1 000 000 ) million = 19 10 million = 1 9 10 million 1 900 000 = 1 9 10 million LET’S DO IT 6 375 000 million 63 8 million 6.375 million
1.2.1 15 1 The table shows the population of three districts in Seberang Perai in 2020. District in Seberang Perai North Middle South Population 405 100 467 800 235 100 What is the total population of all three districts in Seberang Perai? 405 100 + 467 800 + 235 100 = 405 100 + 467 800 + 235 100 = 1 108 000 The total population of all three districts in Seberang Perai is 1 108 000. Retrieved October 8, 2021, from https://bit.ly/2VHO1O7 1 405 100 + 467 800 872 900 1 1 1 872 900 + 235 100 1 108 000 4 305 612 + 780 107 = 5 085 719 Vary calculation methods such as by arranging the numbers with the larger number on top, and by estimating to check the answers. 4 305 6 12 + 780 107 5 085 7 19 1 2 4 305 612 + 780 107 = 3 9 408 + 3 071 592 + 68 043 = State the population in decimal of a million. Solve it. Which method is easier? Arrange the digits in the correct place value. 9 4 0 8 3 0 7 1 5 9 2 + 6 8 0 4 3 1 1 1 1 3 0 7 1 5 9 2 + 9 4 0 8 3 0 8 1 0 0 0 3 0 8 1 0 0 0 + 6 8 0 4 3 ADDITION BASIC OPERATIONS Method 1 Method 2
16 1.2.1 2 3 10 million = 2 million + 3 10 million = 2.0 million + 0.3 million = 2.3 million 2 3 10 million + 4 100 000 = 2.3 million + 4.1 million = 6.4 million Can you give the answer in fraction? 4 5 240 780 + 0.65 million = 5 240 780 + 0.65 million = 5 890 780 Step 1 0.65 million = 0.650000 × 1 000 000 = 650 000 Step 2 5 240 780 + 650 000 5 890 780 2 3 10 million = 2.3 million = 2.300000 × 1 000 000 = 2 300 000 5 2 3 10 million + 4 100 000 = 2 3 10 million + 4 100 000 = 2 300 000 + 4 100 000 = 6 400 000 2 3 10 million + 4 100 000 = 6 400 000 or 6.4 million Give the answer in a whole number and in decimal of a million. Emphasise the need to convert decimal and fraction of a million to whole numbers before solving addition based on the questions’ requirement. 4 100 000 = ( 4 100 000 1 000 000) million = 41 10 million = 4.1 million Calculation 1 Calculation 2
1.2.1 17 6 a Calculate the total number of pupils who participated in online learning in states R and S. Give the answer in a whole number. b Add the number of pupils who participated in online learning in states P and Q . The total number of pupils who participated in online learning in states P and Q is 8 1 2 million. The total number of pupils who participated in online learning in states R and S is 1 930 000. 0.89 million + 1.04 million = 0.89 million + 1.04 million = 1 930 000 2 1 10 million + 6 2 × 2 5 × 2 million = 2 1 10 million + 6 4 10 million = 8 5 ÷ 5 10 ÷ 5 million = 8 1 2 million 2 1 10 million + 6 2 5 million = million 2 1 10 million + 6 2 5 million = 8 1 2 million Vary questions based on the data given in example 6 above. Now, use another method to solve this. Online learning in four states Step 1 1 0.89 million + 1.04 million 1.93 million P 2 1 10 million pupils Q 6 2 5 million pupils R 0.89 million pupils S 1.04 million pupils Step 2 1.93 million = 1.930000 × 1 000 000 = 1 930 000
18 1.2.1 7 4.052 million + 3 3 8 million = million 4.052 million + 3 3 8 million = 7.427 million 8 2.12 million + 680 000 + 1 4 5 million = State the sum in decimal of a million. 1 1 2. 12 million 0.68 million + 1.80 million 4.60 million 2.12 million + 680 000 + 1 4 5 million = 4.6 million Who holds the card that has the same value as 4.6 million? Encourage pupils to check their answers using a calculator. State the answer in a whole number. 4 3 5 million 460 000 Afiyah Siew Lin 3 3 8 million = 27 8 million = 3.375 million 3 . 3 7 5 8 2 7 . 0 0 0 − 2 4 3 0 − 2 4 6 0 − 5 6 4 0 − 4 0 0 1 4 5 million = 1 million + 4 × 2 5 × 2 million = 1 million + 8 10 million = 1.0 million + 0.8 million = 1.8 million 1 4.0 5 2 million + 3.3 7 5 million 7 .4 2 7 million 680 000 = ( 680 000 1 000 000 ) million = (68. ÷ 100) million = 0.68 million
19 Step 1 Step 2 1.2.1 1 The pictures show four types of digital thermometer produced by a factory. a Calculate the difference in the number of digital thermometer A and digital thermometer B. The difference in the number of digital thermometer A and digital thermometer B is 1 125 000. 4 305 127 – 3 180 127 = 4 305 127 – 0.96 million = 4 305 127 – 3 180 127 = 1 125 000 b How many more is the number of digital thermometer A compared to the number of digital thermometer C? The number of digital thermometer A is 3 345 127 more than the number of digital thermometer C. 4 305 127 – 0.96 million = 3 345 127 Emphasise the arrangement of digits according to the correct place values in order to carry out subtraction in vertical form. millions hundred thousands ten thousands thousands hundreds tens ones 2 10 4 3 0 5 1 2 7 – 3 1 8 0 1 2 7 1 1 2 5 0 0 0 State the answer in fraction of a million. 12 3 2 10 4 3 0 5 1 2 7 – 9 6 0 0 0 0 3 3 4 5 1 2 7 SUBTRACTION A B C D 0.96 million = 0.960000 × 1 000 000 = 960 000
20 1.2.1 Method 1 Method 2 c How much lesser is the number of digital thermometer D compared to the number of digital thermometer B? 3 180 127 – 7 10 million = Which card shows the correct calculations? Discuss. 2 RM8.75 million – RM3.906 million = million 3 Subtract 6 1 4 million from 9 3 5 million. State the balance in a whole number. RM8.75 million – RM3.906 million = RM4.844 million 9 3 5 million – 6 1 4 million = 9 3 5 million – 6 1 4 million = 9 3 5 × 4 × 4 million – 6 1 4 × 5 × 5 million = 9 12 20 million – 6 5 20 million = 3 7 20 million = 3 million + = 3 000 000 + = Emphasise that fraction of a million which has different denominator must be made equal first before subtracting. Complete the calculations. Compare method 1 to method 2. Which is easier? State the answer in a whole number. 9 3 5 million = 9.6 million = 9 600 000 6 1 4 million = 7 17 4 10 RM 8. 7 5 0 million – RM 3.9 0 6 million RM 4.8 4 4 million 9 6 0 0 0 0 0 – 3 180 127 – 7 10 million = 3 180 127 – 70 000 = 3 110 127 3 180 127 – 7 10 million = 3 180 127 – 700 000 = 2 480 127 Card P Card Q
21 715 000 = ( 715 000 1 000 000) million = 0.715 million Step 1 Encourage pupils to solve number sentences in vertical form. Remind pupils to identify what the question requires before converting and solving operations. 1.2.1 4 6 1 4 million – 2.035 million = 6 1 4 million – 715 000 – 2.035 million = a Find the difference of value in cards L and K. State the answer in a whole number. Three number cards K,L, and M are as follows. The difference of value in cards L and K is 4 215 000. b Subtract the value of cards M and K from the value of card L. State the answer in decimal of a million. 6 1 4 million – 2.035 million = 4 215 000 Step 1 6 1 4 million = 6 million + 1 4 million = 6 000 000 + 250 000 = 6 250 000 Step 2 2.035 million = 2.035000 × 1 000 000 = 2 035 000 6 1 4 million – 715 000 – 2.035 million = 3.5 million K 2.035 million L 6 1 4 million M 715 000 Step 3 4 10 6 2 5 0 0 0 0 – 2 0 3 5 0 0 0 4 2 1 5 0 0 0 6 1 4 million = 25 4 million 6 . 2 5 million 4 2 5 . 0 0 million − 2 4 1 0 − 8 2 0 − 2 0 0 Step 2 Step 3 5 12 4 10 6.2 5 0 million – 0. 7 1 5 million 5.5 3 5 million 5.5 3 5 million – 2.0 3 5 million 3.5 0 0 million
22 1.2.1 1 A factory produces 1 150 000 bars of soap weekly. How many bars of soap are produced in 8 weeks? The number of soap produced in 8 weeks is 9 200 000 bars. 8 × 1 150 000 = State the answer in decimal of a million and fraction of a million. 2 32 × 25 000 = State the answer in decimal of a million. Emphasise that the answers must be given in whole numbers, fraction of a million, or decimal of a million based on what the questions require. 1 150 000 × 8 9 200 000 1 4 8 × 1 150 000 = 9 200 000 Step 1 MULTIPLICATION 32 × 25 000 = 0.8 million Method 1 Method 2 Step 1 Step 2 800 000 = ( 800 000 1 000 000 )million = 8 10 million = 0.8 million 25 000 × 32 50 000 +7 50 000 800 000 1 1 32 × 25 000 = 800 000 8 0 0 0 0 0 Step 2 (800 000. ÷ 1 000 000) million = 0.8 million 2 5 0 0 0 × 3 2 0 0 1 1 0 0 0 0 0 0 6 4 5 0 0 0 0 0 0 0 1
1.2.1 23 State the answer in a whole number. Train pupils to convert fraction of a million and decimal of a million to whole numbers and vice versa. 3 9 × 0.75 million = 9 × 0.75 million = 9 1 × 3 4 million = 27 4 million = 6 3 4 million State the answer in decimal of a million or fraction of a million. 9 × 0.75 million = 6.75 million or 6 3 4 million 0.75 = 75 ÷ 5 100 ÷ 5 = 15 ÷ 5 20 ÷ 5 = 3 4 6 4 2 7 − 2 4 3 My answer is in decimal of a million. I answered in fraction of a million. 6 4 0.7 5 million × 9 6.7 5 million Calculation 1 Calculation 2 WEDNESDAY WEDNESDAY 16 FEBRUARY 2022 16 FEBRUARY 2022
24 1.2.1 5 Calculate the product of 5 and 1.25 million. State the answer in fraction of a million. 5 × 1.25 million = 4 4 × 1 9 10 million = 4 × 1 9 10 million = 7 600 000 or 7 3 5 million 12 × 3 4 million = A 0.009 million B 0.09 million C 0.9 million D 9 million Which method is easier? 5 × 1.25 million = 5 × 1 1 4 million = 5 × 5 4 million = 5 1 × 5 4 million = 25 4 million = 6 1 4 million Ask pupils to write answers for questions 4 and 5 in decimal of a million. 6.25 million = 6 25 ÷ 25 100 ÷ 25 million = 6 1 4 million 1 2 1 .2 5 million × 5 6.2 5 million 5 × 1.25 million = 6 1 4 million Method 1 Method 2 4 × 1 9 10 million = 4 × 1.9 million = 4 × 1.900000 × 1 000 000 = 4 × 1 900 000 = 7 600 000 Calculation 1 4 × 1 9 10 million = 4 × 19 10 million = 38 5 million = 7 3 5 million 2 5 Calculation 2
25 DIVISION 1.2.1 How many plastic packages of gloves are produced? Give the answer in a whole number and in decimal of a million. The number of plastic packages of gloves produced is 120 000 or 0.12 million. 1 200 000 ÷ 10 = 1 200 000 ÷ 10 = 120 000 or 0.12 million 2 8.25 million ÷ 3 = million State the answer in a whole number and in fraction of a million. Encourage pupils to use vertical form when dividing two numbers. 1 2 . 7 5 million 3 8 . 2 5 million − 6 2 2 − 2 1 1 5 − 1 5 0 8.25 million ÷ 3 = 2.75 million 1 200 000 pairs of gloves are to be packed equally into several plastic packages. Each plastic package has 10 pairs of gloves. 1 200 000 10 = 120 000 Calculation 1 1 200 000 10 = 120 000 = (120 000. ÷ 1 000 000) million = 0.12 million Calculation 2
26 Step 1 Step 2 1.2.1 3 Divide 6 4 5 million by 8. Give the answer in a whole number. 6 4 5 million ÷ 8 = 6 6 800 000 ÷ 8 = 4 × 2 5 × 2 million = 6 8 10 million = 6.8 million = 6.800000 × 1 000 000 = 6 800 000 4 Find the quotient when 9 3 8 million is divided by 15. 9 3 8 million ÷ 15 = million Complete the calculations above. Which value is equal to your answer in example 4? Complete the number sentence based on the given numbers. ÷ = 0.89 million 6.23 8 7 million 6 1 4 million Vary questions on division involving whole numbers, fraction of a million, and decimal of a million to reinforce pupils' understanding and acquisition of skills. Encourage pupils to solve division in vertical form. 62 500 625 000 5 8 million 7 8 million Step 1 Step 2 9 3 8 million = 75 8 million = 9.375 million 9.3 7 5 8 7 5.000 −7 2 3 0 −2 4 60 − 56 40 −40 0 . million 15 9.3 7 5 million −0 9 3 −9 0 3 7 − 7 5 − 0 THINK SMART THINK SMART SMART
1.2.1 27 1 Find the sum. a 38 075 + 991 002 + 75 600 = b 4 305 120 + 114 880 = c State the answer in fraction of a million. i 1 720 900 + 1 079 100 = ii 4 225 965 + 899 035 = d i 6 480 521 + 0.4 million = ii 1.53 million + 68 304 = iii 320 159 + 3 4 million = iv 2 1 2 million + 470 000 = e i 4.28 million + 3 1 5 million = ii 7 1 10 million + 370 000 + 0.83 million = iii 0.93 million + 65 000 + 6 7 10 million = 2 Find the difference. a i 6 732 189 – 5 401 207 = ii 7 982 000 – 2 483 000 = b i 892 147 – 0.84 million = ii 54 5 million – 328 950 = iii 3.98 million – 1 7 8 million = iv 5 330 472 – 0.9 million – 2 1 8 million = v 64 5 million – 3 020 490 – 1. 45 million = 3 a Find the product. i 6 × 230 000 = ii 3 × 385 000 = iii 25 × 276 000 = b Calculate. Give the answer in whole numbers. i 7 × 0.24 million = ii 9 × 3 5 million = iii 8 × 1 1 8 million = iv 32 × 0.002 million = 4 a Divide. i 3 051 000 ÷ 5 = ii 1 071 000 ÷ 9 = iii 1 500 000 ÷ 12 = b Calculate. State quotients in whole numbers. i 0.86 million ÷ 4 = ii 3 5 million ÷ 6 = iii 1 3 10 million ÷ 26 = Encourage pupils to check answers using a calculator. LET’S DO IT
28 Step 1 Step 2 Step 1 1.2.1 1 The following table shows the number of orders and sale of face shields. Calculate the number of unsold face shields. 0.4 million – 372 000 + 5 1 4 million = million 0.4 million – 372 000 + 5 1 4 million = 5.278 million The number of unsold face shields is 5.278 million. 2 6 1 2 million + 2 501 479 – 3.008 million = Give the answer in a whole number. 6 1 2 million = 6.5 × 1 000 000 = 6 500 000 3.008 million = 3.008 × 1 000 000 = 3 008 000 6 1 2 million + 2 501 479 – 3.008 million = 5 993 479 Emphasise working from left to right for mixed operations of addition and subtraction. SUBTRACTION (372 000. ÷ 1 000 000) million = 0.372 million Orders in 2019 0.4 million Sales in 2019 372 000 Orders in 2020 5 1 4 million 5 1 4 million = 21 4 million = 5.25 million 0.0 2 8 million + 5.2 5 0 million 5.2 7 8 million 9 3 10 10 0.4 0 0 million – 0.3 7 2 million 0.0 2 8 million MIXED OPERATIONS 1 6 5 0 0 0 0 0 + 2 5 0 1 4 7 9 9 0 0 1 4 7 9 9 9 8 10 10 11 9 0 0 1 4 7 9 – 3 0 0 8 0 0 0 5 9 9 3 4 7 9 Step 2 FACE SHIELD FACE SHIELD FACE SHIELD Convert 372 000 and 5 1 4 million to decimal of a million first. 5 . 2 5 million 4 2 1 . 0 0 million − 2 0 1 0 − 8 2 0 − 2 0 0 ADDITION AND SUBTRACTION
29 Step 1 1 . 4 million 5 7 . 0 million − 5 2 0 − 2 0 0 1.2.1 Complete steps 2 until 4 to get the answer. 3 5 120 900 – (2.65 million + 1 2 5 million) = State the answer in a whole number. 4 6.4 million + (3.9 million – 1 1 2 million) = Give the answer in fraction of a million. 5 120 900 – (2.65 million + 1 2 5 million) = 1 070 900 Step 3 0 12 5 1 2 0 9 0 0 − 4 0 5 0 0 0 0 1 0 7 0 9 0 0 Provide additional exercises on mixed operations as reinforcement activities. Emphasise that operations in brackets must be solved first. 1 2 5 million = 7 5 million = 1.4 million Solve the operations in brackets first. Step 2 1 2.6 5 million + 1 .4 0 million 4.0 5 million 4.050000 × 1 000 000 = 4 050 000 TIPS Step 1 1 1 2 million = 1.5 million Step 2 3.9 million − 1 .5 million million Step 3 6.4 million + million million Step 4 million = million = ÷ ÷ million = million
30 1.2.1 1 How many face masks are received by each hospital? 1 8 million × 7 ÷ 5 = 1 8 million × 7 ÷ 5 = 175 000 The number of face masks received by each hospital is 175 000. Vary questions on multiplication and division to reinforce pupils' understanding. Guide pupils to calculate using strategies suited to their abilities. MULTIPLICATION AND DIVISION 2 0.02million ÷8×24 = million 3 4 1 5 million ÷ (20 × 3) = million 4.2 million ÷ (20 × 3) = 4.2 million ÷ 60 = 0.07 million 0.02 million ÷ 8 × 24 = 0.06 million 0.02million ÷8×24 = 0.02 million 8 ×24 = 0.02 million × 3 = 0.06 million 1 3 Solve the operations from left to right. 1 8 million × 7 = 7 8 million = 0.875 million Step 1 Step 2 0. 1 7 5 million 5 0.8 7 5million − 0 0 8 − 5 3 7 − 3 5 2 5 − 2 5 0 Step 3 4 1 5 million = 21 5 million = 4.2 million 4.2million 5 2 1.0million −20 1 0 − 1 0 0 4 1 5 million ÷ (20 × 3) = 0.07 million 0.8 7 5million 8 7 .0 0 0million − 0 7 0 − 6 4 6 0 − 5 6 4 0 − 4 0 0 A container has 1 8 million pieces of face masks. There are 7 similar containers. Distribute the face masks equally to 5 hospitals. TIPS 0.175 million = 0.175000 × 1 000 000 = 175 000
31 Step 1 1.2.1 1 Calculate the current number of bottles of vitamin pills. The current number of bottles of vitamin pills is 460 180 bottles. 0.46 million + 12 × 15 = Step 2 Step 3 460 000 + 180 = 460 180 0.46 million + 12 × 15 = 460 180 3 14 × (0.001 million + 1 2 million) = 2 3 10 million + 0.48 million × 6 = million 14 × (0.001 million + 1 2 million) = 14 × ( + 500 000) = 14 × = Which card shows the correct calculations? Encourage pupils to create questions on mixed operations of addition and multiplication. Then, solve and check answers using a calculator. 3 10 million + 0.48 million × 6 = 0.3 million + 0.48 million × 6 = 0.78 million × 6 = 4.68 million Card A 3 10 million + 0.48 million × 6 = 0.3 million + 0.48 million × 6 = 0.3 million + 2.88 million = 3.18 million Complete this. We still have 12 boxes of vitamin pills in our stock. Each box contains 15 bottles of vitamin pills. I just received 0.46 million bottles of vitamin pills. Order of operation × first, then +. 1 1 2 × 1 5 6 0 + 1 2 0 1 8 0 ADDITION AND MULTIPLICATION TIPS Card B 0.46 million = 0.460000 × 1 000 000 = 460 000
32 Step 2 0. 7 5million 4 3.0 0million − 0 3 0 − 2 8 2 0 − 2 0 0 Step 1 Convert the answer to a whole number. 1 000 boxes of blankets have been distributed to victims of COVID-19. Each box has 40 pieces of blankets. Calculate the remaining number of blankets after distribution. The remaining number of blankets is 710 000. 3 4 million – 1 000 × 40 = 3 4 million – 1 000 × 40 = 710 000 2 1.4 million × 6 – 5 1 10 million = million 3 (4 2 5 million – 4.1 million) × 25 = million (4 2 5 million – 4.1 million) × 25 = 7.5 million 4 2 5 million = 22 5 million = 4.4 million 1.4 million × 6 – 5 1 10 million = 3.3 million 1 Emphasise that the operations in the brackets must be solved first. In example 3, guide pupils to convert 4 2 5 million to 4.4 million. 2 1.4 million × 6 8.4 million 8.4 million − 5.1 million 3.3 million 4.4 million − 4.1 million 0.3 million 1 000 × 40 40 000 Step 3 7 50 000 − 40 000 7 1 0 000 1.2.1 SUBTRACTION AND MULTIPLICATION Order of operation × first, then –. 1 0 . 3 million × 2 5 1 5 + 0 6 0 0 7 . 5 million 4.4million 5 2 2.0million − 2 0 2 0 − 2 0 0 Our charity organisation received 3 4 million pieces of blankets. TIPS 0.75 million = 0.750000 × 1 000 000 = 750 000
33 Step 1 Encourage pupils to solve basic operations using vertical form. Vary questions so that pupils are proficient in converting fraction of a million and decimal of a million to solve number sentences. Step 3 1 1.6 million + 0.7 million 2.3 million 1.2.1 How many tiles will Alpha Company receive after the distribution? Alpha Company received 2.3 million tiles. 1 3 5 million + 4.9 million ÷ 7 = million 1 3 5 million + 4.9 million ÷ 7 = million 2 0.072 million ÷ 24 + 1 9 10 million = million 3 (2.08 million +4 1 4 million)÷40 = 0.072 million ÷ 24 + 1 9 10 million = 1.903 million (2.08 million + 4 1 4 million) ÷ 40 = (2.08 million + ) ÷ 40 = million ÷ 40 = ÷ 40 = 1 0 . 7 million 7 4 . 9 million − 0 4 9 − 4 9 0 Our factory will distribute 4.9 million more tiles to Alpha Company and 6 other companies equally. Alpha Company received 1 3 5 million pieces of tiles. Order of operation ÷ first, then +. ADDITION AND DIVISION Step 2 1 . 6 million 5 8 . 0 million − 5 3 0 − 3 0 0 1 3 5 million = 8 5 million 0.0 0 3million 24 0.0 7 2million − 0 0 0 − 0 0 7 − 0 7 2 − 7 2 0 1 9 10 million = 19 10 million = 1.9 million 0.0 0 3 million + 1.9 0 0 million 1.9 0 3 million TIPS 2.3
34 1.2.1 6 3 5 million ÷ 5 – 1.07 million = million 6 3 5 million ÷ 5 – 1.07 million = 0.25 million 2 9.9 million – 6 1 2 million ÷ 13 = 3 (8.04 million – 3 2 5 million) ÷ 16 = (8.04 million – 3 2 5 million) ÷ 16 = 290 000 or 0.29 million 9.9 million – 6 1 2 million ÷ 13 = 9.9 million – 6.5 million ÷ 13 = 9.9 million – = 1 How many flags are distributed to the rural areas? The number of flags distributed to the rural areas is 0.25 million. State A State C City 1.07 million Rural areas State B State D State E 6 3 5 million flags are distributed equally Between calculation 1 and calculation 2, which is easier? Which value is the same as the answer, 1 4 million or 1 2 million? Emphasise that division must be solved first for questions which do not involve brackets. SUBTRACTION AND DIVISION Distribution of flags in conjunction with National Day celebration. 1 .3 2 million 5 6.6 0 million − 5 1 6 − 1 5 1 0 − 1 0 0 6.6 million 5 3 3.0 million − 3 0 3 0 − 3 0 0 2 12 1 .3 2million − 1 .0 7million 0.2 5million 6 3 5 million = 33 5 million (8.04 million – 32 5 million) ÷16 = (8 040 000 – 3 400 000)÷16 = 4 640 000 ÷ 16 = 290 000 Calculation 1 (8.04 million – 32 5 million) ÷ 16 = (8.04 million – 3.4 million) ÷ 16 = 4.64 million ÷ 16 = 0.29 million Calculation 2
1.2.1 35 BASIC OPERATIONS AND MIXED OPERATIONS INVOLVING UNKNOWN Type of clothes Total clothes manufactured Long-sleeved 0.6 million Short-sleeved x Total 1.3 million 1 2 y – 1 8 million = 3 4 million What is the value of y? How many short-sleeved clothes are manufactured by Factory T? 0.6 million + x = 1.3 million 0.6 million + x = 1.3 million x = 1.3 million – 0.6 million x = 0.7 million Simple example. 2 + x = 5 x = 5 – 2 Simple example. y – 3 = 4 y = 4 + 3 0.6 million + 0.7 million = 1.3 million The number of short-sleeved clothes manufactured by Factory T is 0.7 million. y – 1 8 million = 3 4 million y = 3 4 million + 1 8 million y = 3 × 2 4 × 2 million + 1 8 million y = 6 8 million + 1 8 million y = 7 8 million Clothes Manufactured by Factory T 7 8 million – 1 8 million = 3 4 million 0 13 1 .3 million − 0.6 million 0. 7 million SCAN ME APPLICATION OF THE CONCEPT OF EQUALITY Given x – 0.92 million = 1.67 million and 1 200 000 – y = 0.35 million. THINK Find the value of x – y in decimal of a million. SMART THINK SMART SMART The value of y is 7 8 million.
36 1.2.1 4 g ÷ 7 = 0.04 million Find the value of g. 3 3 × = 1 500 000 Find the value of h. Simple example. g ÷ 2 = 3 g = 3 × 2 Simple example. 4 × h = 8 h = 8 ÷ 4 3 × h = 1 500 000 h = 1 500 000 3 h = 500 000 3 × 500 000 = 1 500 000 The value of h is 500 000. 5 1 g ÷ 7 = 0.04 million g = 0.04 million × 7 = 0.28 million r ÷ 6 = 1 2 million r = 1 2 million × r = The value of r is . 0.28 million ÷ 7 = 0.04 million The value of g is 0.28 million. 4 × k = 6 800 000. Find the value of k. 8 ÷ 4 can be written as 8 4 . Complete these. Given 8 × g = 9.6 million and g ÷ 4 = m. Find the value of m. THINK SMART THINK SMART SMART h
1.2.1 37 6 p ÷ 2 × 3 = 750 000 There are k number of spectators for the first match. Calculate the value of k. Calculate the value of p in fraction of a million. The value of k is 100 200. Simple example. k – 5 + 3 = 4 k = 4 + 5 – 3 Simple example. p ÷ 4 × 5 = 10 p = 10 ÷ 5 × 4 First football match Second football match 0.1 million spectators left and 0.04 million entered. The total number of spectators is 40 200 people. k – 0.1 million + 0.04 million = 40 200 k = 40 200 + 0.1 million – 0.04 million k = 40 200 + 100 000 – 40 000 k = 140 200 – 40 000 k = 100 200 100 200 – 0.1 million + 0.04 million = 40 200 1 2 million ÷ 2 × 3 = 750 000 The value of p is 1 2 million. 5 Use small number values to explain how to solve mixed operations involving unknown. p ÷ 2 × 3 = 750 000 p = 750 000 ÷ 3 × 2 p = 250 000 × 2 p= 500 000 p = 500 000 1 000 000 million p= 5 ÷ 5 10 ÷ 5 million p = 1 2 million k – 0.1 million + 0.04 million = 40 200
38 1.2.1 7 y + 3 × 0.2 million = 900 000 0.3 million + 3 × 0.2 million = 900 000 y + 3 × 0.2 million = 900 000 y + 0.6 million = 0.9 million y = 0.9 million – 0.6 million y = 0.3 million What is the value of y? The value of y is 0.3 million. The value of m is 7 10 million. 8 m – 1 10 million × 2 = 0.5 million What is the value of m? First, multiply. Then, relate addition with subtraction to solve. 7 10 million – 1 10 million × 2 = 0.5 million m – 1 10 million × 2 = 0.5 million m – 2 10 million = 5 10 million m = 5 10 million + 2 10 million m = 7 10 million Carry out suitable simulation to reinforce pupils' understanding in finding unknown. Given p × q = 7 3 8 million and w + p × q = 9.09 million. Find the value of w. Solve this. s × 6 ÷ 7 = 0.24 million s = 0.24 million ÷ × s = million THINK SMART THINK SMART SMART Simple example. m − 2 × 4 = 5 m − 8 = 5 m = 5 + 8 Simple example. y + 2 × 3 = 7 y + 6 = 7 y = 7 − 6
39 Step 2 Step 3 Encourage pupils to use different ways to solve mixed operations involving unknown. 1.2.1 9 k − 2.86 million ÷ 22 = 0.37 million 10 4.3 million + h ÷ 3 = 5.99 million 4.3 million + 5.07 million ÷ 3 = 5.99 million 1 2 million − 2.86 million ÷ 22 = 0.37 million The value of k is 1 2 million. What is the value of k in fraction of a million? k − 0.13 million = 0.37 million k = 0.37 million + 0.13 million = 0.50 million 0.5 million = 50 100 million = 5 ÷ 5 10 ÷ 5 million = 1 2 million What is the value of h? The value of h is 5.07 million. Step 1 0. 1 3 million 22 2.8 6 million − 0 2 8 − 2 2 6 6 − 6 6 0 0.3 7 million + 0. 1 3 million 0.5 0 million 4.3 million + h ÷ 3 = 5.99 million h ÷ 3 = 5.99 million − 4.3 million h ÷ 3 = 1.69 million h ÷ 3 = 1.69 million h = 1.69 million × 3 h = 5.07 million 5. 9 9 million – 4. 3 0 million 1. 6 9 million Step 1 Step 2 2 2 1.69 million × 3 5.0 7 million 1
40 1.2.1 Guide pupils to understand how to solve unknown involving brackets. 11 ( p + 0.006 million) × 4 = 36 000 ( 3 000 + 0.006 million) × 4 = 36 000 Calculate the value of p. The value of p is 3 000. 12 (2 9 10 million – m ) ÷ 1 000 = 500 Find the value of m. (2 9 10 million – 2 400 000 ) ÷ 1 000 = 500 The value of m is 2 400 000. Step 1 0.006 million = 0.006000 × 1 000 000 = 6 000 Step 2 (p + 0.006 million) × 4 = 36 000 p + 0.006 million = 36 000 ÷ 4 p + 6 000 = 9 000 p = 9 000 − 6 000 p = 3 000 Relate multiplication with division. Relate addition with subtraction. Step 1 2 9 10 million = 2.9 million = 2.900000 × 1 000 000 = 2 900 000 Step 2 (2 9 10 million – m) ÷ 1 000 = 500 2 9 10 million – m = 500 × 1 000 2 9 10 million – m = 500 000 2 9 10 million – 500 000 = m 2 900 000 – 500 000 = m 2 400 000 = m Relate division with multiplication.
41 1 Solve and write answers in whole numbers. a 0.9 million – 800 000 + 1.7 million = b 2.5 million + 500 000 – 1.3 million = c 9 000 000 – 34 5 million + 1.3 million = d 3 700 000 + 5 1 2 million – 7.375 million = e 0.3 million + 1 900 × 6 = f 1.2 million + 1.08 million × 3 = g 3 4 million + 2.07 million ÷ 3 = h 3 5 million ÷ 2 + 4 1 10 million = i 1.09 million – 324 000 × 2 = j 9.825 million – 5 × 1.94 million = k 8 1 4 million – 1.6 million ÷ 5 = l 0.2 million – 0.875 million ÷ 8 = m 1 5 million × 3 ÷ 5 = n 19 × 0.028 million ÷ 4 = o 14 × (0.4 million + 3 10 million) = p (3 2 5 million – 2.84 million) × 10 = q (480 000 – 2 5 million) ÷ 20 = r (6.904 million + 2 9 10 million) ÷ 15 = 2 Solve and write answers in decimal of a million. a 4.7 million – 100 000 + 2 1 10 million = b 0.8 million + 900 000 × 6 = c 2 1 5 million + 4.02 million ÷ 6 = d 8.071 million – 2 × 0.92 million = e 5 1 4 million – 3.003 million ÷ 3 = f 3 4 million × 4 ÷ 5 = g 7 × (0.75 million + 3 5 million) = h (4 3 8 million – 1.9 million) ÷ 9 = 3 Solve and write answers in fraction of a million. a 8.1 million + 0.9 million – 3 1 5 million = b 0.03 million × 12 + 0.14 million = c 6 4 5 million + 5.6 million ÷ 7 = d 5.14 million – 5 × 0.488 million = e 3.51 million – 1.21 million ÷ 11 = f 3 4 million ÷ 8 × 24 = g (3 7 8 million – 3.85 million) × 100 = h (0.8 million + 2 2 5 million) ÷ 32 = 4 Find the values of p. a p + 0.35 million = 1.4 million b p – 6 1 4 million = 1 1 2 million c 9 × p = 0.027 million d p ÷ 2 = 5 000 000 e p – 3 5 million + 0.08 million = 115 096 f p ÷ 7 × 4 = 0.065 million g p + 4 × 0.3 million = 1 5 8 million h p – 4 5 million × 6 = 2.09 million i p + 1.04 million ÷ 16 = 1 000 000 j (1 7 10 million – p) ÷ 10 = 0.081 million 41 1.2.1 LET’S DO IT
42 PRIME NUMBERS AND COMPOSITE NUMBERS 1.3.1 I use yellow for prime numbers. A prime number is only divisible by itself and number 1. Those are composite numbers except number 1. 2 Number 9 is a composite number because it is divisible by number 1, itself, and other numbers without any remainder. Recall pupils' previous knowledge on prime numbers before introducing composite numbers. 1 What about numbers that are not coloured? 7 ÷ 1 = 7 7 ÷ 7 = 1 9 ÷ 1 = 9 9 ÷ 9 = 1 9 ÷ 3 = 3 7 9 I am a prime number. I can only be divided by the number 1 and myself. Composite numbers are numbers that are not prime numbers, 0, and number 1. TIPS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50