43 What are the missing numbers? 1.3.1 51 51 ÷ 1 = 51 51 ÷ 3 = 17 51 ÷ 17 = 3 51 ÷ 51 = 1 53 53 ÷ 1 = 53 53 ÷ 53 = 1 3 Are 51 and 53 composite numbers? Explain. 51 is a composite number. 53 is a prime number. 4 5 Complete the flow charts. I have classified numbers from 59 until 73 accordingly. Discuss composite numbers between 75 up to 100. 53 can be divided by numbers 1 and 53 without any remainder. 53 is a prime number. 59 61 71 62 69 60 64 70 66 Number Prime number Composite number 51 can be divided by numbers 1, 3, 17, and 51 without any remainder. 51 is a composite number. can be divided by number1. 85 is . 85 can also be divided by numbers and . a b 85 can be divided by number1. can be divided by numbers 3 and 29. can be divided by itself. 85 can be divided by itself.
44 79 67 61 23 100 88 52 81 78 47 15 16 2 53 1 1 97 31 17 73 43 19 89 82 56 90 86 37 23 41 3 24 85 56 4 91 54 99 80 95 52 30 10 80 1 Are 47 and 74 prime numbers or composite numbers? Give reasons for your answer. 2 Identify and classify prime numbers and composite numbers. 49 71 39 61 88 46 56 91 19 27 9 94 15 13 1 Scan the QR code and print out the number template. 2 Colour all the composite numbers in red and prime numbers in yellow. 3 Collect and compile pupils’ work as a scrapbook. 3 List all composite numbers which has digit 3 at the ones place value, up to 100. 1.3.1 TRY IT OUT Tools/Materials Number templates and coloured pencils. Task LET’S DO IT SCAN ME NUMBER TEMPLATES
45 1 Rizal and Sharvina show their first number cards. Rizal forms a number pattern in ascending order by sixes. Sharvina forms a number pattern in ascending order by eights. At which position in their number patterns will the numbers be the same? The third number in Sharvina’s number pattern is the same as the fifth number in Rizal's number pattern. Build Rizal and Sharvina’s number patterns. Rizal’s number pattern fifth number Sharvina’s number pattern third number Explain and emphasise the steps in problem-solving using Polya's model. Rizal 4 095 180 ascending order by sixes Sharvina 4 095 188 ascending order by eights 4 095 180 + 24 4 095 204 1 Rizal’s number patttern Sharvina’s number patttern + 8 4 095 188, 4 095 196, 4 095 204, 4 095 212, ... + 8 + 8 4 095 180, 4 095 186, 4 095 192, 4 095 198, 4 095 204, ... + 6 + 6 + 6 + 6 Rizal Sharvina 4 095 180 4 095 188 Rizal’s fifth number and Sharvina's third number are the same. 1 4 095 188 + 16 4 095 204 1 SOLVE THE PROBLEMS Understand the problem Plan the strategy Solve Check Solution 1.4.1
46 1.4.1 2 The picture shows a number wheel. Jamal turns the wheel and gets a composite number. Rishi gets a prime number. The difference between the two numbers is 14. What number did Jamal get for that turn? • Jamal gets a composite number. • Rishi gets a prime number. • The difference between the two numbers is 14. • What number did Jamal get? Classify composite and prime numbers. Composite number 77 87 91 Prime number 53 67 73 Jamal got 87 for that turn. Jamal gets 77. Rishi gets 53. Difference 77 – 53 = 24 First Try Second Try Jamal gets 87. Rishi gets 73. Difference 87 – 73 = 14 Yanti gets a composite number and Dayang gets a prime number when they turn the same number wheel. The product of their numbers is 4 823. What is the sum of the numbers? Jamal might get 77, 87, or 91. Use the trial and error method. Guide pupils to find keywords in the question. Rishi might get 53, 67, or 73. 87 67 77 53 73 91 Understand the problem Plan the strategy Solve Solution
47 The total number of palm oil exported to countries Y and Z is 1 537 506 tonnes. • Country X, 214 466 tonnes. • Country Y, 1 229 434 tonnes. • Country Z has 93 606 tonnes more than country X. • Find the total number of palm oil exported to countries Y and Z. Draw a diagram. 214 466 + 93 606 + 1 229 434 = 1 537 506 Provide more questions on constructing number sentences orally using question cards. 3 1.4.1 Understand the problem Plan the strategy Solve Check Country Z Country Y 1 229 434 214 466 93 606 214 466 Country X 214 466 + 93 606 + 1 229 434 = 1 1 3 0 8 0 7 2 + 1 2 2 9 4 3 4 1 5 3 7 5 0 6 1 1 1 2 1 4 4 6 6 + 9 3 6 0 6 3 0 8 0 7 2 2 17 4 10 1 5 3 7 5 0 6 − 1 2 2 9 4 3 4 3 0 8 0 7 2 2 10 7 10 6 12 3 0 8 0 7 2 − 9 3 6 0 6 2 1 4 4 6 6 How many tonnes of palm oil are exported to countries Y and Z in total? Palm oil export to country X is 214 4666 tonnes and 1 229 434 tonnes to country Y. The export to country Z is 93 606 tonnes more than country X. Solution
48 4 An electronics factory produces 2.46 million units of light-emitting diode (LED). All the units are packed equally into 80 boxes .The electronics factory delivers 2 boxes to Azlan Electric Shop. How many units of LED are received by the shop? • 2.46 million units of LED. • Packed equally into 80 boxes. • 2 boxes are sent to Azlan Electric Shop. The number of units of LED received by Azlan Electric Shop is 61 500 units. 2.46 million ÷ 80 × 2 = 61 500 Number of units of LED received by Azlan Electric Shop. 2.46 million ÷ 80 × 2 = 2.46 million ÷ 80 × 2 = 2.46 million = 2.46 × 1 000 000 = 2 460 000 Vary questions on mixed operations of multiplication and division involving brackets. Check the answer using a calculator. 3 0 7 5 0 × 2 6 1 5 0 0 1 1 30 7 50 80 2 460 000 −2 40 60 − 0 60 0 −56 0 4 00 −4 00 00 − 0 0 1.4.1 Solution Given Asked for Calculate Number sentence
49 0.03 million + 30 × 580 = (0.03 × 1 000 000) + 30 × 580 = 30 000 + 30 × 580 = 30 000 + 17 400 = 47 400 Carry out activities in pairs to create number sentences based on problems given to reinforce pupils' understanding. 5 A company delivered 0.03 million seats to a new stadium. Then, it sent another 30 containers of seats to the stadium. Each container carried 580 seats. What is the total number of seats delivered to the new stadium? Delivered 0.03 million seats. 30 containers carried 580 seats each. Total number of seats delivered to the new stadium. The total number of seats delivered to the new stadium is 47 400 seats. 0.03 million + 30 × 580 = 0.03 million + 30 × 580 = 47 400 I check the answer using this number sentence. (47 400 – 30 000) ÷ 30 = 580 580 30 1 7 400 − 1 5 0 2 40 −2 40 00 − 0 0 2 580 × 30 1 7 400 30 000 + 1 7 400 4 7 400 4 7 400 – 30 000 1 7 400 1.4.1 Solution Given Check Asked for Calculate Number sentence
50 Pupils can use a calculator to check their answers. 6 Teguh Berjaya Company gains a profit of RM3.4 million. The company has 5 subsidiaries. Each subsidiary receives a bonus of RM0.26 million from the profit. What is the balance of the profit? • Profit of Teguh Berjaya Company is RM3.4 million. • 5 subsidiaries. • Each subsidiary receives a bonus of RM0.26 million. Balance of profit. RM3.4 million – 5 × RM0.26 million = RM3.4 million – 5 × RM0.26 million = RM2.1 million The balance of profit of Teguh Berjaya Company is RM2.1 million. 1 3 RM 0.2 6 million × 5 RM 1 .3 0 million RM 3.4 million – RM 1 .3 million RM 2. 1 million 1.4.1 Solution RM 3.4 million – RM 2. 1 million RM 1 .3 million RM 0 . 2 6 million 5 RM 1 . 3 0 million − 0 1 3 − 1 0 3 0 − 3 0 0 Given Asked for Calculate Number sentence Check
51 Give other examples for pupils to try various strategies to solve problems, such as simulation. 1 8 million pieces of clothes distributed equally to 4 stores. Total number of clothes in store R P 1 8 million ÷ 4 R 1 8 million ÷ 4 Has 0.004 million pieces of unsold clothes T 1 8 million ÷ 4 1 8 million ÷ 4 + 0.004 million = 1 8 million ÷ 4 + 0.004 million = 125 000 ÷ 4 + 4 000 = 31 250 + 4 000 = 35 250 1 8 million ÷ 4 + 0.004 million = 35 250 The number of clothes in store R is 35 250 pieces. Add the number of clothes received and the number of unsold clothes. 1 8 million ÷ 4 and 0.004 million Convert 1 8 million to a decimal of a million and solve it. • 4 stores P, Q , R, and T. • 1 8 million pieces of clothes distributed equally to 4 stores. • Store R has 0.004 million pieces of unsold clothes. • What is the number of clothes in store R now? 1.4.1 Solution 7 A businessman owns 4 clothing stores P, Q , R, and T. He distributes 1 8 million pieces of clothes equally to his 4 stores. Store R has 0.004 million pieces of unsold clothes. What is the number of clothes in store R now? Q 1 8 million ÷ 4
52 Check the answer based on this number sentence. 2 352 × 1 000 − 1.602 million = Guide pupils to record important information concisely. 8 A telecommunication company received 1.602 million prepaid cards worth RM5 each and 3 4 million prepaid cards worth RM10 each. All the cards will be distributed equally to 1 000 telephone shops. How many prepaid cards are allocated for one shop? (1.602 million + 3 4 million) ÷ 1 000 = (1.602 million + 3 4 million) ÷ 1 000 = 2 352 Step 1 1.602 million = 1.602 × 1 000 000 = 1 602 000 3 4 million = 3 4 × 1 000 000 = 0.75 × 1 000 000 = 750 000 The number of prepaid cards allocated for one shop is 2 352 units. How many prepaid cards are allocated for one shop? Step 2 1 1 602 000 + 7 50 000 2 352 000 Step 3 1.4.1 Solution 2 352 000 = 1 000 2 352 Types of prepaid cards Number of cards RM5 1.602 million RM10 3 4 million Total cards Distributed equally to 1 000 telephone shops
53 Using story cards, provide more exercises on forming number sentences orally based on problems given. 1 10 million 0.002 million Malay language English language Number of newspapers printed daily. Underline the important information. February 2020 had 29 days because 2020 was a leap year. ( 1 10 million + 0.002 million) × 29 = 2 958 000 ( 1 10 million + 0.002 million) × 29 = ( 1 10 million + 0.002 million) × 29 = (100 000 + 2 000) × 29 = 102 000 × 29 = 2 958 000 The total number of newspapers printed in February 2020 was 2 958 000. 1 1 02 000 × 29 9 1 8 000 +2 040 000 2 958 000 2 958 000 ÷ 29 – 0.002 million = 102 000 – 2 000 = 100 000 = ( 100 000 1 000 000) million = 1 10 million 1.4.1 Solution 9 A publishing company prints 1 10 million Malay language newspapers and 0.002 million English language newspapers daily. What was the total number of newspapers printed in February 2020? Check SUN MON TUE WED THU FRI SAT 8 15 22 7 14 21 28 29 6 13 20 27 5 12 19 26 4 11 18 25 3 10 17 24 1 2 9 16 23 FEBRUARY 2020
54 Give problem-solving questions on basic operations, that is addition, subtraction, multiplication, and division involving unknown to strengthen pupils’ mastery of skills. 10 p primary school pupils and 0.85 million secondary school pupils took part in an online health quiz. The total number of participants is 1.05 million. Calculate the value of p in a whole number. p + 0.85 million = 1.05 million p = 1.05 million – 0.85 million p = 0.2 million p = 0.2 × 1 000 000 p = 200 000 p 0.85 million 1.05 million p + 0.85 million = 1.05 million There are m number of primary school boys. The difference in the number of secondary school boys and primary school boys who took part in the health quiz is 0.515 million. The number of secondary school boys is 0.6 million. Find the value of m. 200 000 + 0.85 million = ( 200 000 1 000 000) million + 0.85 million = 0.2 million + 0.85 million = 1.05 million 200 000 + 0.85 million = 1.05 million The value of p is 200 000. 1.4.1 Check Solution • p primary school pupils • 0.85 million secondary school pupils • Total number of participants is 1.05 million. • Find the value of p in a whole number.
55 Give examples that involve unknown to strengthen pupils’ mastery of skills. m – 13 × 0.086 million = 1 482 000 m – 13 × 0.086 million = 1 482 000 2.6 million – 13 × 0.086 million = 1 482 000 m – 13 × 86 000 = 1 482 000 m – 1 118 000 = 1 482 000 m = 1 482 000 + 1 118 000 m = 2 600 0000 m = 2.6 million 0.086 million m pairs of sport shoes 1 482 000 pairs of sport shoes are not yet distributed 2.6 million – 13 × 0.086 million = The value of m is 2.6 million. 1.482 million = 1.482 × 1 000 000 = 1 482 000 1 86 000 × 1 3 1 258 000 + 860 000 1 1 1 8 000 2 1 0.086 million × 1 3 1 1 0 258 +00 860 1.1 1 8 million 9 5 10 10 2.6 0 0 million – 1. 1 1 8 million 1.4 8 2 million 1.4.1 Check Solution • Produces m pairs of sport shoes. • Distributes 0.086 million pairs of sport shoes to each warehouse in 13 states. • 1 482 000 pairs are not yet distributed. • Calculate the value of m in decimal of a million. 11 Zing Shoe Factory produces m pairs of sport shoes. The factory distributes 0.086 million pairs to each warehouse in 13 states. 1 482 000 pairs of shoes are not yet distributed. Calculate the value of m in decimal of a million.
56 1.4.1 2 The following are eight number cards. 1 Mary is asked to find the difference between the largest composite number and the smallest prime number. a What is her answer? b State whether her answer is a prime number or a composite number. 3 A manufacturer of COVID-19 vaccine distributes 4 7 10 million doses of vaccine to Country X. Country Y receives 1.06 million doses lesser than Country X. What is the total number of doses of vaccine distributed by the manufacturer? 4 ABZ Printing Company prints 0.063 million books. All the books are packed equally into 90 boxes. The company delivers 4 boxes to Alma Book Store. How many books are delivered to Alma Book Store? 5 Karim Electronic Company sends 2 7 10 million earphones to wholesaler A and 6 boxes of earphones to wholesaler B. Each box has 0.009 million earphones. How many earphones are sent to wholesalers A and B in total? 97 83 47 36 73 79 90 96 Wan writes a number pattern on a whiteboard. What is the seventh number in the number pattern? Number pattern MONDAY 7 MARCH 2022 6 008 351, 6 009 351, 6 010 351, 6 011 351, ... LET’S DO IT
1.4.1 57 6 The table shows the number of blue pens and black pens in boxes M and N. A multinational company donated a box of M and 8 boxes of N to several schools in Johor in conjunction with World Children's Day. Calculate the difference in the number of blue pens and black pens donated by the company. Honey dates A Honey dates B 7 Factory Q produces 0.05 million containers of baulu cakes. The cakes are distributed equally to supermarket T and 9 other supermarkets. Supermarket T sold 2 900 containers of the cakes. What is the number of containers of unsold cakes in supermarket T? 0.45 million boxes 1 2 million boxes Box M N Pen Blue Black Number of pens 2 5 million 0.04 million 8 In conjunction with the holy month of Ramadan, the number of boxes of honey dates A and honey dates B marketed weekly are as follows: What is the total number of boxes of honey dates A and honey dates B marketed in 4 weeks? 9 An oil company produces 1 3 8 million gallons of petrol. 0.017 million gallons are stored and the rest are distributed equally to 97 petrol stations. Does each station receive 0.014 million gallons? Prove it.
58 1.1.1, 1.1.2, 1.1.3, 1.1.4, 1.1.5, 1.2.1, 1.3.1 1 Write the numbers in numerals or words. a 3 518 042 b 1 090 256 c 4 007 980 d 5 040 019 e eight million seven hundred nine thousand one hundred and eighty-one f nine million two hundred fifty-three thousand g two million fifty thousand eight hundred and six 2 Five number cards are arranged in a certain pattern as below. 8 007 056 8 007 068 8 007 080 x y 11 8 24 29 35 41 67 80 a State the pattern. b What are the values of x and y? 3 Classify the following numbers into composite numbers and prime numbers. 4 Write the numbers in words or numerals. a 1 3 4 million b one-eighth of a million c five and seven-tenths of a million 5 Convert decimal of a million or fraction of a million into whole numbers. a 0.2 million b 1.095 million c 1 5 million d 43 8 million e 6 9 10 million 6 Complete the following table. 7 Solve these. a 8 500 000 + 790 680 = b 1 1 2 million + 1.192 million = c 8.01 million – 4 1 10 million – 2 650 000 = d 14 × 0.46 million = 8 Calculate. State answers in decimal of a million. a 7 × 1 1 10 million = b 9.225 million ÷ 3 = 9 a 8.551 million ÷ 17 = b 6 1 4 million ÷ 25 = Whole number 3 500 000 Decimal of a million 0.6 million 2.8 million Fraction of a million 3 4 million 95 8 million State the answer in a whole number. State the answer in fraction of a million. LET'S PRACTISE
59 1.2.1, 1.4.1 10 Calculate. a 0.8 million – 440 000 + 1 2 5 million = b 6 3 10 million ÷ 9 × 7 = Give the answer in decimal of a million. State the answer in fraction of a million. c 1.05 million + 8 × 9 10 million = d 4 × (1.36 million – 1 4 million) = e 3.7 million + 1 1 2 million ÷ 6 = f (5.03 million – 2 3 4 million) ÷ 8 = 11 Find the value of k. a k – 0.7 million + 1.02 million = 590 000 b k ÷ 2 × 5 = 0.01 million c k + 1.2 million × 4 = 7 3 4 million d 8.007 million – k ÷ 6 = 7.9 million e (k + 0.013 million) × 24 = 408 000 f (6 3 8 million – k) ÷ 10 = 0.46 million 12 Solve the following problems. a A battery factory produces 4.082 million batteries of AA size. The factory produces size C batteries which are 1 4 5 million lesser than the number of AA size, and 860 000 batteries of size D. What is the total number of size C and D batteries produced? b A library has 1 1 4 million books. Damaged books are kept in 3 boxes. Each box has 0.003 million books. How many books are in good condition? c 5 printing machines are used to print 3 7 8 million pamphlets. Each machine can print equal numbers of pamphlets. How many pamphlets can be printed by 7 printing machines of the same type? d A factory produced 2 5 million table tennis balls. 0.04 million balls are separated for orders while the remaining balls are distributed equally to 100 sports store. Is the number of table tennis balls distributed to the stores less than 4 000 balls? Prove it. e In conjunction with the festive season, Siti Cake Shop received orders for peanut and dahlia biscuits. The table shows the number of orders received by each supermarket. What is the total number of jars of peanut biscuits and dahlia biscuits ordered by 15 supermarkets? Biscuit Peanut Dahlia Number of jars 0.06 million 1 8 million
60 1.1.5, 1.2.1, 1.3.1, 1.4.1 Move 19 spaces to the right Move 16 spaces to the right Move 8 spaces to the right Move 10 spaces to the right Move 13 spaces to the right RULES TO MOVE MARKER FOR CORRECT ANSWER 1 8 7 10 million – 5.084 million = 2 9 × 3 10 million = 3 2 7 8 million ÷ 20 × 6 = 4 6 × (0.98 million – 1 4 million) = 5 0.4 million + 1 1 5 million ÷ 4 = 6 9.2 million – k ÷ 4 = 8.9 million. Calculate the value of k. 7 In a patriotic song competition, Fella gets 2 3 5 million votes while Razif gets twice the number of votes. What is their total number of votes? 1 4 1 2 million + 2.9 million = 2 6 3 8 million ÷ 15 = 3 3.92 million – 120 000 + 3 2 5 million = 4 4.09 million + 5 × 1 4 million = 5 (5 million – 2 9 10 million) ÷ 7 = 6 (k + 0.1 million) × 19 = 2 394 000. Find the value of k. 7 Country A had 4 3 5 million patients of COVID-19. The number showed a weekly rise of 0.007 million patients. What was the total number of patients by the third week? Prime Number Room Composite Number Room Tools/Materials Participants How to play 16 question cards, dice, papers, pens, 100-squared grid, and 4 markers of different colours 5 pupils (4 players and a referee) 1 Choose a marker and determine turns. 2 The first player rolls the dice and move the marker according to the number shown on Vary questions for the activity in Let’s Explore to prevent pupils from memorizing answers. Scan the QR code. Print out the game board and rules for marker movements. the dice. 3 Determine whether the marker lands on a prime number square or a composite number square. 4 If it lands on a prime number square, choose a question from the prime number room. If it lands on a composite number, choose from the composite number room. 5 Write down calculations and answers on a piece of paper. 6 The referee checks each answer. If the answer is correct, the player moves the marker based on rules given. If incorrect, the marker remains. 7 Take turns until the fourth round of play. 8 The player with the largest number, wins. 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 LET'S EXPLORE SCAN ME GAME BOARD AND RULES FOR MARKER MOVEMENTS
6161 2.1.1 Conduct simulation to explain the concept of dividing a proper fraction with a whole number. Scan the AR for the explanation on the concept of dividing proper fractions with whole numbers. What is the fraction of one part after 4 5 puddings are cut into 2 equal parts? 4 5 ÷ 2 = 4 5 ÷ 2 = 2 5 The fraction of one part will be 2 5. 1 All will be 4 10 . The simplest form of 4 10 is 2 5 . Alright, mother. 4 5 is cut into 2 equal parts. There are 4 parts of 1 10 . 4 10 1 10 4 ÷ 2 10 ÷ 2 2 5 2 5 DIVIDING PROPER FRACTIONS WITH WHOLE NUMBERS FRACTIONS, DECIMALS, AND PERCENTAGES 2 DIVISION OF FRACTIONS Anis, please cut 4 5 parts of this pudding into 2 equal parts. = 1 5 4 5 ÷ 2
62 2.1.1 Make sure pupils do not cancel numerator with a numerator or denominator with a denominator while performing the cancellation. Divide 3 4 of the pizza into 6 equal parts. What is the fraction of each part? 3 3 4 ÷ 6 = 8 9 ÷ 4 = Inverse operation and divisor. Perform cancellation. 6 = 6 1 Each part will be 1 8 . 3 4 of the pizza is divided into 9 equal parts. What is the fraction of one part? Discuss. 3 4 ÷ 6 = 3 4 ÷ 6 1 = 3 4 × 1 6 = 3 4 × 1 6 = 1 8 1 2 3 4 ÷ 6 = 1 8 2 1 4 1 4 1 4 1 8 8 9 ÷ 4 = 8 9 ÷ 4 = 8 9 = 8 9 ÷ 4 = SCAN ME CONCEPT OF DIVIDING FRACTIONS
2.1.1 63 Remind pupils to identify numerators and denominators that can be cancelled first. Emphasise that inverses only involve divisor and operation. I'm going to cut 2 1 4 m of this ribbon into 3 strips of equal length. What is the length, in fractions, of each ribbon strip? Is the answer for 2 2 5 ÷ 20 the same as 20 ÷ 2 2 5 ? Explain. 1 2 2 5 ÷ 20 = 2 2 5 ÷ 20 = 3 25 2 1 4 m ÷ 3 = m 2 1 4 m ÷ 3 = m DIVIDING MIXED NUMBERS WITH WHOLE NUMBERS • Convert the mixed numbers, 2 1 4 to improper fraction, 9 4 . • Inverse 3 1 to 1 3 . • Perform cancellation (if needed). • Multiply numerator with numerator. • Multiply denominator with denominator. • State the answer in the simplest form. TIPS 2 1 4 ÷ 3 = 9 4 ÷ 3 1 = 9 4 × 1 3 = 3 4 1 3 2 2 5 ÷ 20 = 12 5 ÷ 20 1 = 12 5 × 1 20 = 3 25 5 3 The length of each ribbon strip is 3 4 m. 2 1 m 1 m 1 strip 1 strip 1 strip 1 4 m 3 4
64 DIVIDING PROPER FRACTIONS WITH PROPER FRACTIONS 2.1.1 Use the method of folding paper and shading a diagram to divide two proper fractions. The number of attempts is 2. I have 1 2of water. I use 1 4of the water for every attempt to see the distance of the water rocket's movement. 2 How many 1 6 are there in 2 3 ? How many attempts can be made? 1 2 ÷ 1 4 = 1 2 ÷ 1 4 = 2 2 3 ÷ 1 6 = 2 3 = 1 2 3 1 6 1 2 1 4 1 2 ÷ 1 4 = 1 2 × 4 1 = 2 1 = 2 2 1
65 DIVIDING MIXED NUMBERS WITH PROPER FRACTIONS 2.1.1 1 How many 1 4 kg are there in 1 1 2 kg? Divide the diagrams into 4 equal parts. Method 1 Method 2 1 1 2 kg ÷ 1 4 kg = 1 1 2 ÷ 1 4 = 3 2 × 4 1 = 6 1 1 2 kg ÷ 1 4 kg = 6 There are 6 parts of 1 4 kg in 1 1 2 kg. 1 2 1 2 1 2 1 1 2 1 4 1 4 1 4 1 4 1 4 1 4 1 1 2 3 2 There are 6 parts of 1 4. 2 6 2 9 ÷ 7 8 = Whose answer is correct? Why? 1 4 kg 2 1 1 1 2 kg Sara’s answer 6 2 9 ÷ 7 8 = 56 9 ÷ 7 8 = 9 56 × 8 7 = 9 49 1 7 6 2 9 ÷ 7 8 = 56 9 ÷ 7 8 = 56 9 × 8 7 = 64 9 = 7 1 9 8 1 Hanis’ answer Give other examples of dividing two fractions with the same denominator. For example: 2 1 5 ÷ 1 5 = 11 5 × 5 1
66 2.1.1 Encourage pupils to check the answer by filling in the unknown value in a number sentence and solve it. Complete , , and with digits 1, 2, or 3 so that the number sentence will be true. 3 1 7 ÷ = 1 14 What is the value in ? 4 ÷ 3 4 = 8 4 5 Calculate the value in . 1 ÷ = 1 2 The value in is 2. The value in is 63 5 . Let’s check the answer. 1 7 ÷ 2 = 1 7 ÷ 2 1 = 1 7 × 1 2 = 1 14 Simple example. 6 ÷ 2 = 3 2 = 6 ÷ 3 1 7 ÷ = 1 14 = 1 7 ÷ 1 14 = 1 7 × 14 1 = 2 1 7 ÷ 2 = 1 14 2 1 Simple example. 6 ÷ 2 = 3 6 = 3 × 2 THINK SMART THINK SMART SMART ÷ 3 4 = 8 4 5 ÷ 3 4 = 44 5 = 44 5 × 3 4 = 33 5 = 6 3 5 11 1 63 5 ÷ 3 4 = 8 4 5 Relate division with multiplication.
2.1.1 67 1 Calculate. Calculate. 3 Solve these. 4 Find the value in . 5 Calculate. 6 Complete these. a 1 5 ÷ 5 = × = a 1 2 ÷ 1 6 = d 4 1 6 ÷ 5 9 = ÷ 9 10 = 1 5 6 d ÷ 4 = 2 5 b 5 8 ÷ 2 7 = e 10 2 5 ÷ 4 5 = c 7 9 ÷ 2 3 = f 1 5 7 ÷ 3 4 = b 6 7 ÷ 9 = × = c 2 1 3 ÷ 28 = × = d 9 3 4 ÷ 30 = × = a How many 1 5 are there in 2 9 ? How many 5 6 are there in 1 7 10 ? c There are 42 parts of 1 4 m in 10 1 2 m of fabric. Is the statement true? Prove it. a What is 1 2 ÷ 3? b How many 3 7 are there in 3 5 ? Divide 7 1 9 by 2 3. d Is 1 1 4 ÷ 3 10 the same as 3 10 ÷ 1 1 4 ? Prove it. a b as 3 4 ÷ 2 5 8 1 1 2 ÷ 3 3 1 8 ÷ 2 1 2 Provide more exercises for drilling by giving simple questions and questions that are in progressive forms. LET’S DO IT 3 1 2 ÷ 1 3 3 1 4 ÷ 1 2 1 1 2 ÷ 2 a 1 8 ÷ = 1 6 c 1 1 2 ÷ = 2 b c b as as as
68 2.2.1 Pupils can check the answers using other methods such as by using a calculator. 1 The diagram shows the positions of R, S, and T. The distance of ST is 0.3 times the distance of RS. What is the distance, in km, from S to T? 0.3 × 0.4 km = km 0.4 = 4 × 10 10 × 10 = 40 100 0.3 = 3 × 10 10 × 10 = 30 100 Shade 0.4 Shade 0.3 The distance from S to T is 0.12 km. There are 12 overlapping squares. 12 100 = 0.12 0.3 × 0.4 = 3 10 × 4 10 = 3 × 4 10 × 10 = 12 100 = 0.12 0.3 × 0.4 km = 0.12 km 2 81.2 × 4.9 = 81.2 × 4.9 = 397.88 8 1.2 × 4.9 7 3 0 8 + 32 4 8 0 39 7.8 8 1 1 1 decimal place 1 decimal place 2 decimal places 0.3 × 0.4 1 2 + 0 0 0 0.1 2 1 MULTIPLICATION OF DECIMALS BASIC OPERATIONS The position of decimal point of the product depends on the total number of decimal places of the number multiplied. Method 1 Method 2 Method 3 TIPS R 0.4 km S T
2.2.1 69 Encourage pupils to use various methods of calculation such as lattice multiplication. 4.5 × 260.13 g = g The mass of the ostrich egg is 1 170.585 g. Write 0 and the decimal point before 2. Do method 2 and method 3 give the answer of 0.234? 4.5 × 260.13 g = 1 170.585 g Calculate the mass of the ostrich egg. 0.6 × 0.39 = 1 decimal place The mass of a 3 decimal places kiwi egg is 260.13 g. The mass of an ostrich egg is 4.5 times the mass of a kiwi egg. 1 . 3 × 6 . 2 = 8.06 or 6 . 2 × 1 . 3 = 8.06 2 6 0.1 3 × 4.5 1 3 0 0 6 5 + 1 0 4 0 5 2 0 1 1 7 0.5 8 5 3 1 Method 1 0.3 9 × 0.6 0.2 3 4 2 5 0.3 9 × 0.6 2 3 4 + 0 0 0 0 2 5 2 1 THINK SMART THINK SMART SMART Rearrange the position of numbers 1, 2, 3, and 6 to complete the number sentence below. . × . = 8.06 2 decimal places 3 4 0.6 × 0.39 = 6 10 × 39 100 = 6 × 39 10 × 100 = 234 10 × 100 = 234 1 000 = Method 2 Method 3
70 0.5 0.5 0.5 0.5 0.5 0.5 0.5 2.2.2 Convert divisor and dividend to whole numbers by multiplying by 10, 100, or 1 000 depending on the number of decimal places of the divisor. The number of bottles that will be needed is 5. How many bottles will be needed? 2.5 ÷ 0.5 = 2.5 ÷ 0.5 = 5 Method 1 0.5 2.5 × 10 × 10 Step 1 5 5 25 –25 0 Step 2 2.5 ÷ 0.5 = 25 10 ÷ 5 10 = 25 10 × 10 5 = 5 1 1 1 5 Is the calculation shown here correct? Discuss. I will pour 2.5of the orange juice equally into a few bottles. Each bottle contains 0.5. 2 0.3 ÷ 0.15 = 0.3 0.1 5 0.5 3 1.5 – 0 1 5 – 1 5 0 DIVISION OF DECIMALS 0.5 0.5 0.5 2.5 × 10 × 10 Method 2 Method 3 1 0 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.5 2.0 2.5 0.5 0.5 0.5 0.5 0.5
2.2.2 71 Step 2 Show other calculation methods to get the answers. For example, 0.1 ÷ 0.002 = 1 10 ÷ 2 1 000 . 3 How much more is the price of a pen that costs RM6.00 compared to a pen that costs RM0.80? 4 I can get a total of 50 tea bags from 0.1 kg of tea leaves. RM6.00 ÷ RM0.80 = RM6.00 ÷ RM0.80 = 7.5 The price of a pen that costs RM6.00 is 7.5 times more compared to a pen that costs RM0.80. 7.5 80 60 0.0 – 56 0 4 0 0 – 4 0 0 0 If the weight of 1 tea bag is 0.005 kg, how many tea bags will I get from 0.1 kg of tea leaves? Discuss. A tea bag 0.002 kg Step 1 0.80 6.00 × 100 × 100 Step 1 0.002 0.1 00 × 1 000 × 1 000 Step 2 50 2 1 00 – 1 0 00 – 0 0 My price is RM6.00. I am only RM0.80. 0.1 kg ÷ 0.002 kg = 50 Delicious Tea How many tea bags of 0.002 kg can you get from 0.1 kg of tea leaves? 0.1 kg ÷ 0.002 kg = 0.1 kg of tea RM6.00 EACH RM0.80 EACH 0.1 kg
72 2.2.1, 2.2.2 0.093 ÷ = 0.012 6 Solve it. 1 Calculate. a 0.7 × 0.3 = b 0.9 × 1.1 = c 4.8 × 2.5 = d 8.91 × 1.6 = e 3.7 × 50.08 = f 2.8 × 0.14 = 2 Calculate. a 9.5 ÷ 1.9 = b 0.8 ÷ 0.02 = c 3.417 ÷ 3.4 = 0.33 ÷ 0.006 = e 36.848 ÷ 5.6 = f 7.2 ÷ 0.75 = Provide various forms of questions such as calculating the product or the quotient. Conduct 21st Century Learning activity such as Showdown to answer questions to enhance pupils' understanding. Step 2 . 4 26.8 – – 0 5 × 0.4 = 2.68 × 0.4 = 2.68 = 2.68 ÷ 0.4 Find the value of . Simple example. × 3 = 6 = 6 ÷ 3 Simple example. 6 ÷ = 3 6 ÷ 3 = 2.88 7.2 0.5 0.6 0.093 ÷ = 0.012 0.093 ÷ 0.012 = Step 2 . 12 93.0 0 – – – 0 Step 1 0.4 2.68 × 10 × 10 Step 1 0.012 0.093 × 1 000 × 1 000 3 Solve these. The number in are the product of the two numbers below it. are the dividends. Find the values in and . d LET’S DO IT
2.3.1 73 Carry out paper-folding activities to enhance the understanding of percentages. The % symbol must be written when writing percentages. Complete the values of percentages. Represent the cakes with a 100-squared grid. 1 Alia sold a cake in the morning. Then, she sold another half in the evening. Altogether, Alia sold 1.5 cakes. 1.5 = % 1.5 = 150 % 1 = 100 100 = 100% 1 2 = 0.5 = 5 × 10 10 × 10 = 50 100 = 50% 1.5 = 1 + 0.5 = 100% + 50% = 150% Method 1 1.5 = 1 5 10 = 15 10 = 15 10 ×100% = 150% 1.5 = 1.50 × 100% = 150% Convert 1.5 to percentage. 2 CONVERT DECIMALS TO PERCENTAGES Method 2 Method 3 100% % % % % 1.0 1.7 2.0 2.2 3.0
74 2.3.1 Ask pupils to convert decimals to percentages or vice versa. 175% = 910% = Complete the table. 175% = 1.75 Are the two answers the same? Discuss. 3 State 175% in decimal. 4 State 910% in decimal. 100% 25% 25% 25% 75% 100% Method 1 Method 1 Method 2 175% = 100% + 75% = 100 100 + 75 100 = 1.00 + 0.75 = 1.75 910% = 910 = Decimals 1.08 6.7 Percentages 345% 206% 910% = 910 × 1 100 = = 175% = 175 100 = 175 ÷ 100 = 1.75 Method 2 LET’S DO IT
75 DELICIOUS GRAINS DELICIOUS GRAINS 2.3.2 Remind pupils to write the percentage symbol in their answers. Encourage pupils to eat a balanced diet every day. 1 a Calculate the total percentage of vitamin B6, calcium, and iron for a serving of 30 g of grains with 125 mof skimmed milk as below. 2 67% – 18% – 9% = 67% – 18% – 9% = 40% b What is the difference in percentage between calcium and iron? 46% + 24% + 16% = 46% + 24% + 16% = 86% 24% – 16% = 24% – 16% = 8% % Content of Vitamins and Minerals % per 30 g serving Vitamin B6 --------- 46% Calcium ----------- 24% Iron ---------------- 16% Try to add 18% and 9% first. Then, deduct the total from 67%. Is the answer the same? Discuss. x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 4 6% 2 4% + 1 6% 8 6% The total percentage of vitamin B6, calcium, and iron is 86%. The difference in percentage between calcium and iron is 8%. Step 2 4 9% – 9% 4 0% Step 1 5 17 6 7% – 1 8% 4 9% 1 14 2 4% – 1 6% 8% ADDITION AND SUBTRACTION OF PERCENTAGES
76 2.3.2 The percentage of wool used is %. Vertical 2 84% + 39% + 60% = 4 217% + 304% = 6 320% – 95% = 8 406% – 248% – 77% = 4 1 3 8 5 7 6 2 Solve this cross-number puzzle. 3 What is the percentage of wool used in this winter jacket compared to synthetic fiber? 10% 80% more Synthetic fiber 10% Wool Made of Wool is 80% more than synthetic fiber. 10% of synthetic fiber. 1 0% + 8 0% % Build cross-number puzzles involving various questions of addition and subtraction of percentages. Encourage pupils to come out with their own questions in groups. Horizontal 1 50% + 28% = 3 76% + 25% + 93% + 8% = 5 101% – 36% = 7 800% – 47% – 209% = LET’S DO IT
77 2.3.3 Carry out a quiz to convert percentages to decimals or fractions. For example, 130% = 1.3 or 130% = 1 3 10 . 1 What is the length of 90% of 2.5 m of the rope? 90% of 2.5 m = 90% × 2.5 m 90% × 2.5 m = m 90% × 2.5 m = 90 100 × 2.5 m = 9 × 2.5 10 m = 22.5 10 m = 2.25 m 90% × 2.5 m = 90 100 × 2.5 m = 0.9 × 2.5 m = 2.25 m 90% × 2.5 m = 2.25 m The length of 90% of 2.5 m of the rope is 2.25 m. 2 Calculate the volume of 240% of 1.8 of juice. 240% × 1.8= Given 200% × 5.5 = 11, % × 2.75 = 11 What is the value in ? The length of my rope is 2.5 m. The length of this rope is 90% of your rope, James. Method 1 Method 2 4 2.5m × 0.9 2.2 5m THE VALUE OF QUANTITY AND THE VALUE OF PERCENTAGES THINK SMART THINK SMART SMART 240% of 1.8of juice is . 240% × 1.8= 240 100 × 1.8 = × 1.8 = × =
78 2.3.3 Emphasise that the symbol % must be written for the value of percentages. 3 Based on the table, calculate the jumping distance of the second attempt compared to the first attempt in percentage. What is the percentage of 1.75 acres compared to 1.4 acres? 1.68 m compared to 1.6 m = % 1.75 1.4 × 100% = 1.75 1.4 × 100% = 1.75 × 100 1.4 % = 175 1.4 % = % 1.68 m compared to 1.6 m is 105 %. 1.75 acres compared to 1.4 acres is %. Step 1 1.68 1.6 × 100% = 1.68 × 100 1.6 % = 168 1.6 % Step 3 1 05 16 1 680 – 1 6 08 – 0 80 – 80 0 4 4.05 kg 0.9 kg × 100% = % 5 . 9 40.5 – – Initially, I wanted to plant 1.4 acres of green plants. In the end, I managed to plant 1.75 acres. Is the answer 450% or 4.5%? 1.68 1.6 × 100% = % Step 2 1.6 1 6 8.0 × 10 × 10 0.9 4.05 × 10 Attempt Jumping distance (m) First 1.6 Second 1.68 × 10
2.3.3 79 1 Calculate the value of quantities for each of the following. 2 Calculate the percentage. 3 Solve these. c 20.77 m compared to 6.2 m. d 0.72 hour compared to 0.45 hour. What is the percentage of pocket money which was successfully saved compared to the targeted amount? The mass of Amir’s red beans is % compared to the mass of Ben’s red beans. Guide pupils to determine the correct method to get the answer. a Target of pocket money to be saved on Monday RM1.50 Pocket money which was successfully saved RM1.80 b Q P 8.64 3.6 I am Amir. I am Ben. a State the length, in m, for 230% of 6.5 m clothes. b What is the percentage of 10.2 kg of old newspapers collected compared to the 8.5 kg target at the beginning? c a 80% of 4.8 kg b 50% of 7.6 c 360% of 29.5 m e 125% of 1.6 hours d 470% of 54.32 km f 500% of 20.2 minutes The volume of water in container Q is % compared to the volume of water in container P. LET’S DO IT 0.6 kg 1.2 kg
80 2.4.1 Emphasise that when subtracting decimals in vertical form, the decimal points must be aligned. Carry out question and answer session on converting fractions to decimals or vice versa to enhance pupils’ competency in calculation. 1 The volume of the three water containers P, Q, and R is as shown in the picture. How much more is the volume of water, in, in containers P and Q compared to container R? 1 + 3 4 – 0.8= 1 + 3 4 – 0.8= 0.95 or 19 20 The volume of water in containers P and Q is 0.95or 19 20more than in container R. 1 + 3 4 – 0.8 = 1 + 3 × 5 4 × 5 – 8 × 2 10 × 2 = 20 20 + 15 20 – 16 20 = 35 20 – 16 20 = 3 4 = 0.75 0.8 = 8 10 My answer in decimal is 0.95. My answer in fraction is 19 20. Step 1 Step 2 1.00 + 0.75 1.75 1.75 − 0.80 0.95 0 17 1 3 4 0.8 Is 1 + 3 4 – 0.8 = the same as 1 + 0.75 – 4 5 = ? Discuss. MIXED OPERATIONS ADDITION AND SUBTRACTION P Q R Solve the operations from left to right. 19 20 TIPS Calculation 1 Calculation 2
81 0.85 + 1.50 2.35 1 Step 2 2.4.1 Guide pupils to master the conversion of fractions to decimals and vice versa for faster calculations. For examples, 1 2 = 0.5, 0.2 = 1 5, 4 5 = 0.8. What is the current mass, in kg, of sugar? 3 20 1 5 – (9.5 + 7) = 4 kg – 3.15 kg + 1 1 2 kg = kg 4 kg – 3.15 kg + 1 1 2 kg = 2.35 kg The current mass of sugar is 2.35 kg. 20 1 5 – 10.2 = 20.2 – 10.2 = 10 20 1 5 – 16.5 = 20.2 – 16.5 = 3.7 4 kg of sugar 1 1 2 kg of sugar added in. Step 1 Step 1 Step 2 Step 1 Step 2 Card 1 Card 2 Which calculation is correct? 3.15 kg of sugar used to make kuih. 9.5 + 7.0 1 6.5 4.00 – 3.1 5 0.85 3 10 9 10 2 1 9.5 + 7 1 0.2 1 1 2 = 1 + 1 2 = 1 + 0.5 = 1.5
82 2.4.1 Emphasise that a ÷ b can be written as a b . How many smaller packets will be produced? 4 × 1 1 5 kg ÷ 0.16 kg = 4 × 1 1 5 kg ÷ 0.16 kg = 30 30 smaller packets will be produced. Try to divide 1 1 5 kg by 0.16 kg and multiply the quotient with 4. Is your answer the same? Discuss. These 4 sacks of grains will be repacked with equal mass into smaller packets of 0.16 kg. Step 1 Step 2 Step 3 1 2 3 4 × 8 ÷ 1.5 = 3 4 × 8 ÷ 1.5 = 4 Step 2 Step 3 30 16 480 −48 00 − 0 0 0.16 4.80 × 100 × 100 Method 1 Method 2 3 4 × 8 = 6 1 2 4 15 60 −60 0 3 4 × 8 ÷ 1.5 = 3 4 × 8 1.5 = 2 × 10 0.5 × 10 = 20 5 = 4 1 1 2 0.5 Step 1 1.2 × 4 4.8 1 1 5 = 1 + 1 5 = 1.0 + 0.2 = 1.2 MULTIPLICATION AND DIVISION × 10 × 10 1.5 6.0
2.4.1 83 What is the height of robot R? 0.75 m ÷ 3 × 1 2 = m 0.75 m ÷ 3 × 1 2 = 0.125 m The height of robot R is 0.125 m. 3 The height of robot P is 3 times the height of robot Q, while the height of robot R is 1 2 of the height of robot Q. 4 14.6 ÷ 1 4 × 6 = 14.6 ÷ 1 4 × 6 = 350.4 14.6 ÷ 1 4 = 14.6 × 4 1 = 14.6 × 4 = 58.4 Can we multiply first then divide? Discuss. Provide various questions according to pupils’ levels of performance. Remind pupils to solve the operations from left to right. Step 1 Step 1 Step 2 0.25 3 0.7 5 −0 0 7 − 6 1 5 − 1 5 0 58.4 × 6 350.4 5 2 0.75 m P Q R 0.25 × 1 2 = 0.125 0.125 1 Step 2 1 2 1 4.6 × 4 58.4
84 2.4.1 6 × 0.28 6 × 0.28+ 10 3 4 = 6 × 0.28+ 10 3 4 = 12.43 The total volume of the orange drink is 12.43. 1.68 + 10 3 4 = 1.68 + 10.75 = 12.43 Carry out simulation to explain the concept of addition and multiplication to enhance pupils’ understanding. Emphasise that multiplication must be solved first in mixed operations involving addition and multiplication. 2 What is the total volume, in, of the orange drink? 9.5 m + 3 × 4.2 m = m 9.5 m + 3 × 4.2 m = 22.1 m The total length of thread used is 22.1 m. 1 9.5 m of black thread and 3 rolls of red thread which is 4.2 m each are used for cross-stitching. What is the total length of thread used? 6 bottles of orange concentrate with the volume of 0.28 each is mixed into a container with 10 3 4 of water to make the orange drink. I LOVE MALAYSIA Step 2 Step 2 9.5 + 1 2.6 22.1 Step 1 4.2 × 3 1 2.6 1 1 Step 1 0.28 × 6 1.68 1 4 ADDITION AND MULTIPLICATION Cross-stitch 1.68 + 1 0.7 5 1 2.43 1 1 10 3 4
2.4.1 85 Show various calculation methods to enhance pupils’ understanding. 3 Calculate the total mass, in g, of vitamins C and D tablets. (15 × 0.1 g) + (60 × 1 5 g) = g (15 × 0.1 g) + (60 × 1 5 g) = 13.5 g 4 16 × (5.5 + 3 1 4) = 16 × (5.5 + 3 1 4) = 140 Solve the operation in brackets first. 5.5 = 5 5 ÷ 5 10 ÷ 5 = 5 1 2 Step 1 Step 1 Step 3 0. 1 × 1 5 0 5 + 0 1 0 1.5 1.5 + 1 2.0 1 3.5 5.5 + 3 1 4 = 5 1 × 2 2 × 2 + 3 1 4 = 5 2 4 + 3 1 4 = 8 3 4 State the value of in decimals. 10 × ( 1 4 + ) = 10 Step 2 16 × 8 3 4 = 16 × 35 4 = 140 1 4 Step 2 60 × 1 5 = 12 12 1 0 in the front can be omitted. 35 × 4 1 40 2 THINK SMART THINK SMART SMART The mass of 1 vitamin C tablet 0.1 g 15 tablets 60 tablets The mass of 1 vitamin D tablet 1 5 g The total mass of vitamins C and D tablets is 13.5 g. 60 TABLETS
86 2.4.1 Instil the importance of cleanliness and health. Emphasise that multiplication must be solved first before subtraction. 2 3 4 × 84 – 1.295 = 3 9.35 × 3 5 – 5 = 3 4 × 84 – 1.295 = 61.705 – 5 = What is the balance, in kg, of soda bicarbonate in the bottle? 1 10 kg – 3 × 0.005 kg = kg 1 10 kg – 3 × 0.005 kg = kg The balance of soda bicarbonate in the bottle is 0.085 kg. There is 1 10 kg of soda bicarbonate in the bottle. I put 3 tablespoons of soda bicarbonate into the water to wash away pesticide residues on the apple skin. The mass of each tablespoon of soda bicarbonate is 0.005 kg. 1 Step 1 Step 2 Step 1 Step 2 3 4 × 84 = 63 1 21 Step 1 9.35 × 3 5 = 63.000 − 1.295 6 1.7 05 9 9 2 101010 0.005 × 3 0.0 1 5 1 SUBTRACTION AND MULTIPLICATION 0.1 00 − 0.0 1 5 0.085 Step 2 01010 3 9 tablespoons of soda bicarbonate 0.085 1 10 = 0.1 SODA BICARBONATE 100 g
2.4.1 87 Encourage pupils to talk about daily life situations that involve mixed operations to enhance their understanding. Talk about the benefits of hydroponic cultivation towards the environment. 4 The picture shows the difference in length for two pieces of flannel used for hydroponic cultivation. Find the length, in m, of 5 pieces of the yellow flannel. 5 × (2.07 m – 1 2 m) = m 5 × (2.07 m – 1 2 m) = 7.85 m The length of 5 pieces of the yellow flannel is 7.85 m. 5 (9.2 – 7) × ( 4 5 – 0.6) = (9.2 – 7) × ( 4 5 – 0.6) = 0.44 Solve the operation in brackets first. Step 1 Step 2 1 2 = 0.5 2.0 7 − 0.50 1.5 7 1 10 1.5 7 × 5 7.85 2 3 Step 1 9.2 – 7.0 2.2 Step 2 4 × 2 5 × 2 = 8 10 = 0.8 0.8 – 0.6 = 0.2 Step 3 2.2 × 0.2 4 4 + 0 0 0 0.4 4 60.6 – 30 × 5 6 = 30.6 × 5 6 = 25.5 5.1 1 Is this calculation correct? Discuss. 2.07 m 1 2 m
88 Emphasise that 3 ÷ 1.5 can be written as 2.4.1 3 1.5 equals 30 15. Vary questions on division involving whole numbers and decimals to enhance the concept. 2.5 hours + 4 1 2 hours ÷ 3 = hours 2.5 hours + 4 1 2 hours ÷ 3 = 4 hours The total duration of the morning session and slot 1 in the afternoon session is 4 hours. 4 1 2 ÷ 3 = 4.5 ÷ 3 = 1.5 2 3 ÷ 1.5 + 1 10 = 1 Calculate the total duration of the morning session and slot 1 in the afternoon session based on the diagram. Step 1 2.5 + 1.5 = 4 Step 2 Method 1 Step 1 Step 2 4 1 2 ÷ 3 = 9 2 ÷ 3 1 = 9 2 × 1 3 = 3 2 = 1 1 2 1 3 2.5 + 1.5 = 4 1 1 2 = 1.5 Which calculation is correct? Discuss. ADDITION AND DIVISION 1.5 3 4.5 −3 1 5 − 1 5 0 0.5 3 1.5 −0 1 5 − 1 5 0 0.5 + 0.1 0.6 1.5 3.0 2 15 30 −30 0 2 + 1 10 = 2.0 + 0.1 = 2.1 Calculation 1 Calculation 2 1 10 Solve the division first. Success Motivation Camp MORNING SESSION AFTERNOON SESSION SLOT 1 SLOT 2 SLOT 3 2.5 hours 4 1 2 hours Method 2
2.4.1 89 Ask pupils to create stories based on the number sentences to enhance their understanding. The above picture shows a convenience shop M which is located in the middle of restaurants R and T. What is the distance, in km, from restaurant R to convenience shop M? (0.75 km + 1 5 km) ÷ 2 = km (0.75 km + 1 5 km) ÷ 2 = 0.475 km The distance from restaurant R to convenience shop M is 0.475 km. 4 (2.4 + 6) ÷ (1 + 2 5 ) = 3 Step 1 0.75 + 0.20 0.95 1 × 2 5 × 2 = 2 10 = 0.2 Step 1 2.4 + 6.0 Step 2 Step 3 ÷ = × = 1 + 2 5 = + = 10 + 1 5 ÷ = 1 1 State the value of in decimals. THINK SMART THINK SMART SMART Restaurant R Convenience shop M Restaurant T 0.75 km 1 5 km BUKA KEDAI SERBANEKA Bookstore Step 2 0.4 7 5 2 0.950 −0 0 9 − 8 1 5 − 1 4 1 0 − 1 0 0
90 2.4.1 Instil moral values such as gotong-royong and helping each other. Emphasise that the division must be solved first. How much more time is taken for the gotong-royong, in hours, on site P compared to one mini site? The time taken for the gotong-royong on site P is 1 3 8 hours more than one mini site. 2.25 hours – 3 1 2 hours ÷ 4 = hours 2.25 hours – 3 1 2 hours ÷ 4 = 1 3 8 hours In a gotong-royong programme, 2.25 hours is allocated for site P and 3 1 2 hours for all the mini sites. The time taken for each mini site is the same. 2 1 1 2 ÷ 0.25 – 5 = Site P mini site Gotong-royong plan Solve division first. 3 1 2 ÷ 4 = 7 2 ÷ 4 = 7 2 ÷ 4 1 = 7 2 × 1 4 = 7 8 Step 1 Convert 2.25 to fraction. 2.25 = 2 25 ÷ 25 100 ÷ 25 = 2 1 4 = 9 4 Step 2 Step 3 9 × 2 4 × 2 − 7 8 = 18 8 − 7 8 = 11 8 = 1 3 8 1 6 – 5 = Step 2 Step 3 6 25 1 50 − 1 50 0 Remember! 1 1 2 = 1.5 SUBTRACTION AND DIVISION Step 1 × 100 × 100 0.25 1.50
2.4.1 91 Modify the questions to suit pupils' level of performance. What is the length of cable, in m, for each group of pupils? (5.7 m – 1 1 2 m) ÷ 3 = (5.7 m – 1 1 2 m) ÷ 3 = 1.4 m 4 ( 5 8 – 0.35) ÷ (10 – 9 1 2) = I cut 1 1 2 m from 5.7 m of cable. I give the remaining cable in equal length to 3 groups of pupils to make this electric circuit. What is the value of a? (6.25 – 4 1 4) ÷ (a – 3) = 1 Step 2 1.4 3 4.2 −3 1 2 − 1 2 0 3 Convert 5 8 to decimal. Step 1 0.625 − 0.350 Step 2 (10 – 9 1 2) = 9 – 9 1 2 = Step 3 ÷ = × = The length of cable for each group of pupils is 1.4 m. Step 1 5.7 − 1.5 4.2 0.625 8 5.000 −0 5 0 −4 8 20 − 1 6 40 −40 0 THINK SMART THINK SMART SMART 1 1 2 = 1.5 2 2
92 2.4.1 Tools/Materials Participants Task Manila cards, 100-squared grids, pens, coloured pencils, rulers, and task cards. 4 pupils in a group 1 Each group chooses a skill that they have learned such as fractions, decimals, or percentages. 1 Solve these. 2 Calculate. c 8.5 hours + 3 × 1 2 hours = e 8.5 – 4 × 1 1 2 = b 4 × 1.39 kg ÷ 1 2 kg = a 10 – 2.6 ÷ 1 2 = c (40 1 2 – 8.5) × (7 – 4.15) = b (32.25 – 1 4 ) ÷ 4 = d (45.2 + 15) ÷ (1 + 1 4 ) = d 7 × (0.25 day + 5 3 4 days) = f 2 ÷ 0.8 × 3 5 = a 2 m + 1.7 m – 3 5 m = The initial target of the sale of recycled items is RM20. In the end, the sale reached RM50. RM50 of RM20 = % 50 20 × 100% = 250% Picture Story Object Symbol Percentage 2 Divide the manila card into four parts. Each pupil is given a task to complete their part. Write the title as “Think Board”. 3 Present your group work and display it on the noticeboard. 4 Do corrections from the comments given. Carry out group activities so that each pupil has a chance to fill in each part of the Think Board. Guide pupils to prepare materials for the Try It Out activity. Title LET’S DO IT Example of “Think Board” TRY IT OUT