143 INTERNATIONAL DATE LINE LIA GASCAR RUSIA KAZAKHSTAN RAN PAKISTAN INDIA SRI LANKA PAPUA NEW GUINEA MYANMAR MALAYSIA INDONESIA SOLOMON AUSTRALIA PHILIPPINES AFGHANISTAN CHINA JAPAN MONGOLIA TURKMENISTAN NEW ZEALAND INTERNATIONAL DATE LINE A MOZAMBIQUE AN YPT ETHIOPIA KENYA TANZANIA SOMALIA MADAGASCAR RUSIA KAZAKHSTAN LARUS RAINE TURKEY SAUDI ARABIA IRAQ IRAN PAKISTAN INDIA SRI LANKA PAPUA NEW GUINEA MYANMAR MALAYSIA INDONESIA SOLOMON AUSTRALIA PHILIPPINES AFGHANISTAN CHINA JAPAN MONGOLIA TURKMENISTAN SOUTH AFRICA NEW ZEALAND 4.1.1 4.1.2 (chinahighlight.com/ travelguide/china_time) Discuss countries that have two or more time zones with pupils. For example, Australia (GMT +8, GMT +9, and GMT +10) and Indonesia (GMT +7, GMT +8, and GMT +9). Scan the QR code to explore time all around the world. Time zone in Tokyo, Japan (GMT +9) Tuesday, 8 March 2022, 11:12 a.m. Time zone in Kuching, Malaysia (GMT +8) Tuesday, 8 March 2022, 10:12 a.m. Mexico City 8:12 p.m. Greenwich 2:12 a.m. 6 hours of difference 8 hours of difference 9 hours of difference Tokyo 11:12 a.m. Kuching 10:12 a.m. Based on the timeline, discuss the time difference between: a Kuching and Tokyo. b Mexico City and Kuching. Time differences between three cities from Greenwich What is GMT? GMT is Greenwich Mean Time, the local clock time at Greenwich Meridian 0° that passes through Greenwich, London in England. This standard time is the basis for the 24-hour time zone in the world. China uses only one time zone which is GMT +8. TIPS SCAN ME TIME ZONES WEBSITE Travel to the East
144 4.1.2 Tokyo, Japan is in the east of Malaysia. Therefore, the time in Tokyo is 1 hour ahead of Ipoh. Aceh, Indonesia is in the west of Tokyo, Japan. Therefore, the time in Aceh is 2 hours behind Tokyo. Guide pupils to find the time difference between two time zones for a few popular cities in the world. Emphasise the importance of identifying the location of a city or a country in the east or west to determine whether the time is ahead or behind. 3 The time difference between Ipoh and Tokyo is 1 hour . The time difference between Aceh and Tokyo is 2 hours . Indonesia, 1507 hours Aceh, Indonesia Sunday, 15 May 2022 Based on the above information, find the time difference between the cities: a Ipoh and Tokyo. b Aceh and Tokyo. Malaysia, 1607 hours Ipoh, Perak, Malaysia Sunday, 15 May 2022 Japan, 1707 hours Tokyo, Japan Sunday, 15 May 2022 hours minutes 1 7 0 7 − 1 6 0 7 1 0 0 hours minutes 1 7 0 7 − 1 5 0 7 2 0 0
4.1.2 145 Guide pupils to identify the location before subtracting the time to find the time difference. Surf https://timeanddate.com to get the time in two different cities in the world. 4 Calculate the time difference between Moscow and Vladivostok. The time difference between Moscow and Vladivostok is 7 hours . The time difference between Darwin and Alor Setar is 1 hour 30 minutes . Moscow, Russia 26 August 2022 4:35 a.m. Vladivostok, Russia 26 August 2022 11:35 a.m. Moscow 4:35 a.m. time difference? 11:35 a.m. Vladivostok Vladivostok time Moscow time Time difference hours minutes 1 1 3 5 − 0 4 3 5 7 0 0 0 11 5 Calculate the time difference between Darwin and Alor Setar. Thursday Friday Alor Setar 2310 hours 0010 hours 0040 hours Darwin 1 hour 30 minutes Darwin,Australia Friday, 24 June 2022 Alor Setar, Malaysia Thursday, 23 June 2022 Russia has 11 time zones. Subtract the time in Moscow from the time in Vladivostok because Moscow has a later time.
146 4.1.2 Change 10:00 p.m. to 24-hour system, which is 2200 hours. Guide pupils to determine the time in a 12-hour system or a 24-hour system correctly. Encourage pupils to use an analog clock face for simulation. The time in Tawau is 7 hours ahead of Dublin, Ireland on 6 December 2022. What is the time in Dublin if the time in Tawau is 1:45 p.m.? 6 The time in Kuala Lumpur is 5 hours ahead of Riyadh. State the time in Riyadh. Kuala Lumpur Tower, Malaysia 10:00 p.m. 22 February 2022 The time in Riyadh is 1700 hours or 5:00 p.m. . 1700 hours in a 12-hour system is 5:00 p.m. Subtract 5 hours from the time in Kuala Lumpur because the time in Riyadh is behind by 5 hours. State the time in city P and city Q. How much is the time difference between city P and city Q? Kingdom Centre, Riyadh, Saudi Arabia hours minutes 2 2 0 0 − 5 0 0 1 7 0 0 1 12 City A City P 1510 hours 2 hours ahead 3 hours behind City Q hours hours THINK SMART THINK SMART SMART
4.1.2 147 Ask pupils to refer to the time zone map to determine if the location is in the correct time zone. Find the time difference between Wellington and Kota Kinabalu. 1 2 The time in Los Angeles, The United States of America is Thursday, 27 January 2022, 1420 hours. The time in Kota Bharu is Friday, 28 January 2022, 0520 hours. Calculate the time difference between these two cities. 3 Zahidah has arrived at Ambon Airport, Maluku, Indonesia from Kuala Lumpur. Calculate the time difference between Kuala Lumpur and Maluku based on the picture. The time in Liverpool, England is 6 hours behind the time in Vientiane, Laos. State the time in Liverpool when the time in Laos is as shown in the picture. 5 6 The time in Arau, Perlis is ahead of the time in Buenos Aires, Argentina by 11 hours. State the time in Buenos Aires if the time in Arau is 1950 hours. 4 1915 hours 24 November 2022 1315 hours 24 November 2022 Vientiane,Laos Thursday, 17 February 2022 Wellington, New Zealand 10 May 2022 1355 hours Kota Kinabalu, Sabah, Malaysia 10 May 2022 0955 hours Calculate the time difference between the two places based on the information given above. Paris, France Maluku Kuala Lumpur LET’S DO IT
148 4.2.1 Remind pupils to solve problems using Polya’s method. • Malacca, 1545 hours. • Amman, 1045 hours. • Find the time difference in minutes. • Subtraction. • Convert the answer to minutes. 1545 hours – 1045 hours = 5 hours = 5 × 60 minutes = 300 minutes The time difference between both locations is 300 minutes. Ikhwan’s friend who is in Yangon, Myanmar also joined the same online class. The local time in Yangon at that time was 1415 hours. Calculate the time difference between Yangon and Amman. 1045 hours 1545 hours SOLVE THE PROBLEMS Plan the strategy Solve Check Solution 1 Ikhwan is in Malacca. He joins an online class organised by a university in Amman, Jordan on 23 February 2022 at 1545 hours Malaysia time. The local time in Amman is 1045 hours. How much is the time difference, in minutes, between both locations? Understand the problem 1 hour 60minutes 60minutes 60minutes 60minutes 60minutes 1 hour 1 hour 1 hour 1 hour Amman Malacca hours minutes 1 5 4 5 − 1 0 4 5 5 0 0
4.2.1 149 2 Guide pupils to understand day conversion by doing simulation. • London, 11:15 p.m. • Time in Putrajaya is 7 hours ahead of London. • Time in Putrajaya. London 11:15 p.m. 10 March 2022 1:15 a.m. 11 March 2022 3:15 a.m. 11 March 2022 5:15 a.m. 11 March 2022 Putrajaya 12:15 a.m. 11 March 2022 2:15 a.m. 11 March 2022 4:15 a.m. 11 March 2022 6:15 a.m. 11 March 2022 Johari Johari’s mother The time in Putrajaya is 6:15 a.m., 11 March 2022. Johari’s father is in Bangkok, Thailand. The time in Bangkok is 1 hour behind Putrajaya. Does his father's watch show 7:15 a.m. at that moment? Discuss. London 2315 hours 10 March 2022 The 7-hour time difference is because the time in Putrajaya is ahead of the time in London. 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 Check Solve Given Asked for Putrajaya Solution Johari returns to London for work. As soon as he arrives in London at 11:15 p.m., he sends a short text message to his mother who is in Putrajaya. The time in Putrajaya is 7 hours ahead of London. State the time in Putrajaya at that moment.
150 4.2.1 A football match is broadcast live from the National Stadium of Bukit Jalil, Kuala Lumpur. The pictures above show fans who are watching the match from their respective countries. a Why are the fans in Perth watch the match at the same time as in Kuala Lumpur? b State the time of the match in Naypyidaw, Myanmar and Jakarta, Indonesia. c Is it true that the fans in Osaka, Japan watch the match at 1945 hours? Prove it. d Calculate the time difference between Naypyidaw, Myanmar, and Osaka, Japan. Naypyidaw, Myanmar 1.5 hours behind National Stadium of Bukit Jalil, Kuala Lumpur 2045 hours 29 August 2022 Perth, Australia 2045 hours Jakarta, Indonesia 1 hour behind Osaka, Japan 1 hour ahead 3 −1 0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 G A R I SAN T A R I K H A N T ARABAN G S A MALI NIGAR NIGARIA GABON CONGO ZAMBIA MOZAMBIQUA ANGOLA NAMIBIA CHAD SUDAN MESIR HABSYAH KENYA TANZANIA SOMALIA MADAGASCAR ITANIA AGHRIBI RTUGAL SEPANYOL PERANCIS JERMAN PORLAND SWEDEN RUS I A KAZAKHSTAN NORWAY BALARUS UKRAINE TURKI ARAB SAUDI IRAQ IRAN +3½ +4½ +5½ +6½ +5¾ IRAN INDIA SRI LANKA MYANMAR SOLOMON AFGANISTAN CHINA JEPUN MONGOLIA TURKMENIA GREECE ITALI FINLAND UNITED KINGDOM RELAND D ALGERIA LIBYA AFRIKA SELATAN NEW ZEALAND Perth, Australia Kuala Lumpur, Malaysia Carry out a simulation to understand the situation. Use the clock face display to show the time difference between two cities. Solution Therefore, the fans in Perth watch the match at the same time as in Kuala Lumpur, which is at 2045 hours. a Perth is located in the same time zone as Kuala Lumpur.
4.2.1 151 Provide various problem-solving strategies such as using a timeline and a clock model. b The time in Naypyidaw is 1.5 hours behind the time in Kuala Lumpur. 1.5 hours = 1 hour 30 minutes Naypyidaw time = Kuala Lumpur time – Time difference = 2045 hours – 1 hour 30 minutes = 1915 hours The time of the match in Naypyidaw is at 1915 hours. The time in Jakarta is 1 hour behind the time in Kuala Lumpur. Jakarta time = Kuala Lumpur time – Time difference = 2045 hours – 1 hour = 1945 hours The time of the match in Jakarta is at 1945 hours. c The time in Osaka is 1 hour ahead of the time in Kuala Lumpur. Osaka time = Kuala Lumpur time + Time difference = 2045 hours + 1 hour = 2145 hours Incorrect. The fans in Osaka watch the the match at 2145 hours. d 1.5 hours + 1 hour = 2.5 hours = 2 hours + 0.5 hour = 2 hours + (0.5 × 60 minutes) = 2 hours 30 minutes The time difference between Naypyidaw, Myanmar and Osaka, Japan is 2 hours 30 minutes. Naypyidaw 1.5 hours 1 hour Kuala Lumpur How many hours difference? Osaka hours minutes 2 0 4 5 − 1 3 0 1 9 1 5 1 10 hours minutes 2 0 4 5 − 1 0 0 1 9 4 5 1 10 hours minutes 2 0 4 5 + 1 0 0 2 1 4 5
152 4.1.2, 4.2.1 OUR WORLD CLOCK CRAFT Kuala Lumpur 0900 hours London 0200 hours Brisbane 1100 hours Osaka 1000 hours Riyadh 0400 hours Solve the following problems. a Puan Winnie Mawan is from Miri, Sarawak. She works at a telecommunication company in Kawasaki, Japan. The current time in Kawasaki, Japan is 4:20 p.m. Meanwhile, the current time in Miri is 1520 hours. Find the time difference between these two cities. b Encik Emir works at the Turkey Embassy in Malaysia. He receives a short text message from his brother in Istanbul, Turkey while having his lunch at 12:30 p.m. The time in Kuala Lumpur is 5 hours ahead of the time in Istanbul. What is the local time in Istanbul at that time? c Father is having a conversation with his brother who is currently in Florida, The United States of America via a video call. The time in Kuala Lumpur is 12 hours ahead of Florida. i State the time in Florida when father’s watch shows 10:30 p.m., 5 February 2022. ii At what time will father contact his brother if he wants to talk to him at 0900 hours, Florida time? Surf https://www.timeanddate.com/time/map/ or other suitable websites to check the time for the selected cities in the Try It Out activity. TRY IT OUT Tools/Materials Participants Task Cardboards or manila cards, pens, scissors, small nuts, and screws. 5 pupils in a group. 1 Each pupil cuts the cardboard according to their creativity to create a clock face, hour hand, and minute hand. 2 Complete the clock face by writing the numbers in a 12-hour system or a 24-hour system. 3 Assemble the hour hand and minute hand using a small nut and screw. 4 Label one of the clock display according to the time in Kuala Lumpur. 5 Label another four clock displays according to the time in four other different cities. 6 Display the best top five world clock created in the class. LET’S DO IT
153 4.1.1, 4.1.2, 4.2.1 Ask pupils to refer to the time zone map to get the answers. Carry out 21st Century Learning activity such as Bus Stop to solve the question. 1 What is the total number of the world time zones? 2 Calculate the time difference between these two cities on 3 March 2022 according to the timeline below. 4 Solve the problems below. The time in Johannesburg, South Africa is 6 hours behind the time in Malaysia. At what time will the football fans in Malaysia start watching the live broadcast of the final match? b Maheshwaran works in Bern, Switzerland since January 2022. His family stays in Dungun, Terengganu. The time difference between Bern and Dungun is 7 hours. Maheshwaran makes a video call to his family starting at 1135 hours, the time in Bern. i At what time does the video call in Dungun start? ii They talk for 25 minutes. When does the video call in Bern end? c An international conference is broadcast live on 9 February 2022 from Putrajaya International Convention Centre (PICC) to a few countries. The conference starts at 0930 hours, Malaysia time. i The time in Putrajaya is 5 hours ahead of the time in Helsinki. State the time when the conference starts in Helsinki, Finland. ii Mrs Smith who is currently in London watched the delayed broadcast of the conference for 40 minutes. The time in London is 7 hours behind the time in Putrajaya. State the time Mrs Smith watched the delayed broadcast. Based on the information given, calculate the time difference between Lahad Datu and Medina. The clock shows the time in Seremban. The time in Seremban is 1.5 hours ahead of the time in town P. State the current time in town P. 3 Rio de Janeiro 11:30 p.m. Madrid 3:30 p.m. Greenwich 2:30 p.m. Mecca 5:30 p.m. Labuan 10:30 p.m. Gold Coast 12:30 a.m. Lahad Datu, Sabah Saturday, 16 April 2022 3:23 p.m. Medina, Saudi Arabia Saturday, 16 April 2022 10:23 a.m. AM FINAL FOOTBALL MATCH Venue: Johannesburg Time: 1700 hours LET’S PRACTISE 5 a
154 4.1.1, 4.1.2 Complete the crossword puzzle according to the sentences below. 1 7 8 2 3 9 4 11 5 12 6 10 horizontal 1 The time difference for each GMT is one . 2 The time difference in the world is because of the different time . 3 The time in Riyadh is 5 hours behind . 4 The time is behind if the location of the place is in the . 5 GMT acts as to determine 24 world time zones. 6 The world time zone is calculated from Meridian, London. vertical 7 Malaysia has time zone. 8 The time difference between and Greenwich is 9 hours. 9 The time is if the location is in the west. 10 The time in Malaysia is 8 hours of the time in Greenwich. 11 The time in Kuala Lumpur is hours ahead of the time in Karachi, Pakistan. 12 The time difference between Greenwich and Rome is hours. Scan the QR code to check your answers. Emphasise that the answers for time difference between two cities do not involve the daylight saving time. LET'S EXPLORE SCAN ME CROSSWORD PUZZLE AND ANSWERS
155 5.1.1 (i) Give pupils similar problems by changing the thickness or mass of a book. Ask pupils to work in pairs to solve the problems and present their answers to enhance their understanding. 1 The picture shows two books, A and B. The length and width of the books are the same but the thickness is different. The thickness of book A is 4 cm more than the thickness of book B. Calculate the mass, in kg, for book A. Do a mental calculation for a book with 1 cm thickness. Explain. • The thickness of book B, 2 cm. • The thickness of book A is 4 cm more than book B. • The mass of book B, 500 g. • Calculate the mass of book A in kg. The thickness of book A = 2 cm + 4 cm = 6 cm 5 0 0 g × 3 1 5 0 0 g 3 × 500 g = kg 3 × 500 g = 1.5 kg 1 500 g = 1.5 kg thickness 2 cm 2 cm + 2 cm 6 cm mass 50 0 g 50 0 g + 50 0 g 1 50 0 g 6 cm = 3 × 2 cm Books B A Thickness 2 cm 2 cm + 4 cm = cm Mass 500 g kg The mass of book A is 1.5 kg. 2 cm length width Book A Mass 500 g Book B LENGTH AND MASS 5 MEASUREMENT SOLVE THE PROBLEMS (1 500. ÷ 1 000) kg = 1.5 kg The thickness of book A is 3 times the thickness of book B. So, the mass of book A must be 3 times the mass of book B. Solution Understand the problem Solve Check Plan the strategy
156 5.1.1 (i) Vary the questions by changing the original mass of the metal rod to enhance pupils’ understanding. 2 Father cuts a 12 m metal rod into 3 parts of different lengths as shown in the table below. The mass of rod A is given. Find the mass of the longest metal rod. The mass of the longest metal rod. Divide 4.44 kg by 5 to check the answer. Find the mass of metal rod C. • A 12 m metal rod is cut into 3 parts, A, B, and C. • The length of metal rod A is 3 m and the mass is 2.664 kg. • The length of metal rod B is 5 m. • The length of metal rod C is 4 m. The longest metal rod, 5 m is metal rod B. The mass of metal rod B 5 × 0.888 kg = 5 × 0.888 kg = 4.44 kg 4 4 4 0.8 8 8 kg × 5 4.4 4 0 kg The mass of the longest metal rod is 4.44 kg. Metal rod A B C Length 3 m 5 m 4 m Mass 2.664 kg Step 1 3 m 2.664 kg 1 m 2.664 kg ÷ 3 = 0 . 8 8 8 kg 3 2 . 6 6 4 kg − 0 2 6 − 2 4 2 6 − 2 4 2 4 − 2 4 0 Find the mass for 1 m rod. Solution Step 2 Given Asked for Calculate
5.1.1 (i) 157 3 A weighing scale is used to observe the length of spring stretch when a weight is placed on it. The maximum length of spring stretch for this scale is 6 cm. When a weight of 500 g is hung on the scale, the length of spring stretches 3 cm. a State the length of spring stretch if a weight of 750 g is hung on the scale. b What is the maximum weight, in kg, that can be hung on the scale? Guide pupils to compare two measurement units using proportions. Discuss ways to check the answers. 1 . 5 cm 2 3 . 0 cm − 2 1 0 − 1 0 0 750 g 3 cm + 1.5 cm = 4.5 cm 500 g 3 cm 250 g 1.5 cm b 3 cm 500 g 6 cm 1 000 g 750 g = 500 g + 250 g Find the length of spring stretch for 250 g first. 2 × 500 g = 1 000 g = 1 kg The maximum weight that can be hung on the scale is 1 kg. The length of spring stretch is 4.5 cm if a weight of 750 g is hung on the scale. Weight Stretch length 500 g 3 cm 750 g maximum 6 cm a ÷ 2 × 2 × 2 ÷ 2 Solution Step 1 Step 2
158 5.1.1 (ii) Train pupils to check their answers using suitable methods. 1 My brother rides his motorcycle from home to his college every day. He uses 3 of petrol for every 100 km. The distance from home to college is shown in the picture. Calculate the total volume of petrol, in m, that he uses for a round trip. • 3 of petrol is used for every 100 km. • Distance from home to college: 12 km + 23 km + 16 km + 9 km = km The distance to college: 12 km + 23 km + 16 km + 9 km = 60 km The distance of the round trip: 60 km + 60 km = 120 km The total volume of petrol used for a round trip. The total volume of petrol used for a round trip is 3 600 m. 23 km 16 km 9 km 12 km 100 km 3 20 km 0.6 LENGTH AND VOLUME OF LIQUID ÷ 5 ÷ 5 home college Solution Step 1 3 + 0.6 = 3.6 = 3.6 × 1 000 m = 3 600 m 100 km + 20 km = 120 km Step 2 Given Asked for Solve 100 km 3 120 km 120 × 3 100 = 18 5 = 3.6 5 6 3 . 6 5 1 8 . 0 − 1 5 3 0 − 3 0 0 Check
5.1.1 (ii) 159 Guide pupils to solve problems step by step using tables or determining patterns. 2 Zarif’s mother made fresh mango juice. She poured into glass P until it was full and the remainder into glass Q. The level of each volume of juice in both glasses are labelled as shown in the picture. The volume of juice in glass Q is 150 m. Find the volume of mango juice in glass P. • The level of juice in glass P is 110 mm. • The level of juice in glass Q is 40 mm. • The volume of juice in glass Q is 150 m. • How much is the volume of juice in glass P? Level of juice Volume of juice 40 mm 150 m 40 mm ÷ 4 = 10 mm 150 m÷ 4 = m 11 × 10 mm = 110 mm 11 × m= m 3 7.5 m × 1 0 3 7 5.0 m 3 7.5 m × 1 3 7.5 m 11 × 37.5 m = (10 + 1) × 37.5 m = (10 × 37.5 m) + (1 × 37.5 m) 110 mm 40 mm P Q The volume of mango juice in glass P is 412.5 m. 3 7.5 m × 1 1 3 7 5 +3 7 5 0 4 1 2.5 m 1 3 7 5.0 m + 3 7 .5 m 4 1 2.5 m 1 1 40 mm 150 m 10 mm 37.5 m 3 7.5 m 4 1 50.0 m − 1 2 30 −28 2 0 −2 0 0 ÷ 4 ÷ 4 10 mm 37.5 m 110 mm 412.5 m × 11 × 11 Solution Solve Check Step 1 Step 2 Understand the problem Plan the strategy Calculate the volume of juice for 10 mm. Then use the proportion to figure out the volume of juice for 110 mm. 1
160 5.1.1 (iii) Get pupils to work in groups on a different recipe which involves mass and volume of liquid. Give suitable questions for each group to solve. Does she use 80 g of sugar and 800 g of ice cubes? Discuss. 1 My sister is preparing chocolate milk by referring to the recipe shown in the picture. What is the mass of chocolate pieces that she needs if 0.96 of fresh milk is used? 120 m of fresh milk 100 g of ice cubes 10 g of sugar 55 g of chocolate pieces Whipped cream (optional) (one glass) Chocolate Milk Recipe 440 g of chocolate pieces is needed if 0.96 of fresh milk is used. MASS AND VOLUME OF LIQUID 440 g ÷ 55 g = 8 8 × 120 m= 960 m = (960 ÷ 1 000) = 0.96 Solution Check • 120 m of fresh milk needs 55 g of chocolate pieces. • How many grams of chocolate pieces needed if 0.96 of fresh milk is used? 120 m 0.96 55 g ? g Understand the problem Plan the strategy Method 1 0.96 = 0.96 × 1 000 m = 960 m 120 m 55 g 960 m 960 × 55 g 120 = 440 g 1 8 960 m of fresh milk can make 8 glasses. 1 glass 55 g of chocolate pieces 8 glasses g of chocolate pieces 8 × 55 g of chocolate pieces = 440 g of chocolate pieces 960 m 120 m= 8 4 5 5 g × 8 4 4 0 g Solve Method 2
161 Solution Step 1 Step 2 5.1.1 (iii) 161 Does 4 blocks of butter give more than 1 of melted butter? Prove it. Guide pupils to construct correct number sentences to solve the problems. • A block of 250 g butter gives 271.74 m of melted butter. • 5 blocks of the same butter are melted and added to 2 000 m of evaporated milk. 5 × 271.74 m + 2 000 m = 5 × 271.74 m + 2 000 m= 3 358.7 m 1 358.7 m + 2 000 m = m 1 358.7 m + 2 000 m = 3 358.7 m Calculate the volume of the mixture of melted butter and evaporated milk. 1 piece 271.74 m 5 pieces m Natural salt 250 g Fresh Butter 3 3 2 2 7 1 . 7 4 m × 5 1 3 5 8. 7 0 m 3 3 5 8. 7 m − 2 0 0 0.0 m 1 3 5 8. 7 m 1 3 5 8. 7 m + 2 0 0 0.0 m 3 3 5 8. 7 m The volume of the cream soup mixture is 3 358.7 m. 2 7 1 . 7 4 m 5 1 3 5 8 . 7 0 m − 1 0 3 5 − 3 5 0 8 − 5 3 7 − 3 5 2 0 − 2 0 0 2 A block of 250 g butter gives you 271.74 m of melted butter. My sister is melting 5 blocks of butter and adding it to 2 000 m of evaporated milk to make cream soup. Calculate the volume of the cream soup mixture. Check Solve Given Asked for
162 Solution 5.1.1 (iii) Create a project which involves mass, volume of liquid, and length. Ask each group to present their project. • 150 g of black soil and 1 of water needed for 1 kg of waste materials. • Find the mass of black soil, in g, and litres of water for 2.5 kg of waste materials. Waste materials 1 .0 kg 1 .0 kg +0.5 kg 2.5 kg Black soil Water 1 .0 1 .0 +0.5 2.5 1 kg of waste materials 1 of water 2.5 kg of waste materials 2.5 of water 375 g of black soil and 2.5 of water are needed for 2.5 kg of waste materials. Solve using proportion. Check 3 Our teacher, Mr Peter Unggah asked our group to produce organic fertiliser as shown above. What is the mass of black soil and volume of water needed for 2.5 kg of waste materials? ORGANIC FERTILISER PROJECT Ingredients • 1 kg of waste materials (fruit peels, vegetable waste, dried leaves, grass) • 150 g of black soil • 1 of water Method 1 Combine all the waste materials, black soil, and water. 2 Mix and loosen the mixture a few times. 3 Let it decompose for three months. 1 kg or 1 000 g of waste materials need 150 g of black soil. 2.5 kg of waste materials = 2 500 g of waste materials 1 000 g of waste materials 150 g of black soil 2 500 g of waste materials 2 500 g × 150 g 1 000 g = 25 g ×15 = 375 g 2 5 g x 1 5 1 2 5 + 2 5 0 3 7 5 g 2 1 5 0 g 1 5 0 g + 7 5 g 3 7 5 g 1
5.1.1 (i) 163 163 , (ii), (iii) Solve these problems. Solve these problems. c A water tank can store 1 000 of water. The level of water in the tank is 1.5 m when full. Calculate the level of water, in cm, when the remaining volume of water is 350. The picture shows two metals, R and Q of the same type with different length and mass. i Find the mass of metal Q. ii Calculate the difference in mass of metal R and metal Q. i Based on the given recipe, how much volume of water and mass of anchovies are needed if 800 g of wheat flour is used? ii Find out the mass of wheat flour and the volume of water needed for 100 g of anchovies. d a A water bottle with the measurement shown is fully filled with 1 200 m of drinking water. After drinking, the level of water dropped to 8 cm. How much water was drunk? b Our family went to visit Pahang National Park. The distance from our house to Pahang National Park is 270 km. My father’s car consumes 9.4of petrol for every 100 km. Calculate the volume of petrol for a round trip. c Puan Selvi wants to make jelly. Based on the recipe, 2of water is used to dissolve 250 g of sugar and 20 g of jelly powder. Calculate the mass of jelly powder needed by Puan Selvi if she uses 5of water. ANCHOVIES FRITTER RECIPE 250 g of wheat flour 3 g of fine salt 180 mof water 50 g of anchovies (cleaned) Cooking oil for frying Carry out activity to solve problems such as Gallery Walk. Guide pupils to solve problems step by step using Polya method. a 5 kg of rice is fully filled in a container. The level of rice in the container is 20 cm. After a few days, the level of rice in the container is reduced to 4 cm. Calculate the mass, in g, of rice left. b Metal R 80 cm 10.2 kg Metal Q 0.6 m p kg 20 cm LET’S DO IT LET’S DO IT LET’S PRACTISE
164 Wooden sticks (20 cm), rubber bands (10 rings), transparent plastics, rulers, hooks, 3 containers filled with pebbles or sand (300 g, 500 g, and 1 000 g), 10 marbles, measuring cylinders, weighing scales, water bottles, 1of water, and tables. 4 pupils in a group. STATION 1 Marble mass (g) Volume of water (m) 0 200 STATION 2 Volume of water (m) Level of water (cm) 300 400 500 600 STATION 3 Weight (g) Length of stretched rubber bands (cm) 300 500 1 000 TEST AND REVIEW 164 5.1.1 (i), (ii), (iii) Prepare all the materials and apparatus needed for this activity in all three stations. Scan the QR code to get the tables. Guide pupils to make correct conclusion for each task. Tools/Materials Participants Task STATION 1 MASS AND VOLUME OF LIQUID 1 Fill the measuring cylinder with 200 m of water. 2 Weigh the mass of a marble and record it. 3 Put in the marbles one at a time carefully into the measuring cylinder. 4 Record the total mass of marbles and the volume of water after putting each marble. 5 Make conclusion about the mass of marbles and the volume of water. STATION 2 VOLUME OF LIQUID AND LENGTH 1 Measure 300 m of water and fill it in a bottle. 2 Measure the level of water in the bottle and record it. 3 Pour in another 100 m of water, measure the level of water and record it. 4 Repeat step 3 for 2 times. 5 Make conclusion about the volume of water and the level of water. STATION 3 MASS AND LENGTH 1 Tie rubber bands together in fives. 2 Insert the rubber bands through the wooden stick and hold. Measure the length of rubber bands. 3 Place a hook on the rubber bands and hang 300 g of pebbles or sand as shown in the picture. 4 Measure the length of stretched rubber bands. 5 Repeat steps 3 and 4 for the following weight of pebbles or sand: a 500 g b 1 000 g 6 Make a conclusion about the mass of weight and the length of stretched rubber bands. LET'S EXPLORE SCAN ME TABLE OF TASK
165 6.1.2 1 Draw a straight line. Mark two points as A and B. 2 Place the protractor’s baseline exactly on AB. Ensure that the centre of the protractor is exactly on point A. Read the inner scale from 0° to 50°. Mark and label it as C. 3 Remove the protractor. Join points A and C. Label the angle as 50° between straight lines AC and AB. Ask pupils to form other acute angles such as 20°, 45°, and 78°. Select a few pupils to present their works respectively. Teacher, how do we form an angle? Measure the value of an angle from a straight line using a protractor and mark the value. Then, draw a line to form the angle. An angle is formed when two lines meet. 50° ANGLE 6 SPACE LET’S FORM ANGLES
166 6.1.2 1 Draw a straight line of 6 cm long. Mark two points. Label it as D and E. 3 Remove the protractor. Draw a straight line from E to F. Label the angle as 90° between straight lines EF and ED. 1 Draw a straight line PQ. 2 Place the baseline and the centre of the protractor exactly on point Q. Read the outer scale from 0° to 108°. Mark and label as R. 3 Remove the protractor. Draw a straight line from Q to R. Label the angle as 108° between straight lines QR and QP. Place the baseline and the centre of the protractor exactly on point E. Read the outer scale from 0° to 90°. Mark and label it as F. Ask the pupils to do the activity in pairs to form other obtuse angles such as 100° and 165° angles and get them to check their work among themselves. D E 2 D P Q P Q R P Q R D E 90° You are given a ruler and a pencil. Explain how you can form a 90° angle. What is the type of angle for 50°, 90°, and 108°? 108° F E F 90° ANGLE 108° ANGLE
6.1.2 167 Alat/Bahan Steps Form angle ABC 1 Launch Geogebra software. Click Geometry. 2 Click Point on Object. 3 Plot three points. 4 Click Segment. Click point A and join with point B. Click point B and join with point C. 5 Click Angle. Next, click points C, B, and A. The value of angle ABC will appear on the diagram. 6 Click Move. Click and hold, move point A or B or C. See the changes in the value of angle ABC. Using a ruler and a protractor, form the angles below. a 10° b 25° c 40° d 68° e 87° f 95° g 130° h 115° i 142° j 174° Guide pupils to carry out the Try It Out activity in groups so that they can explore various angle values up to 180°. Scan the QR code to watch how to form angle ABC. Tools/Materials Geogebra software Participants In pairs TRY IT OUT LET’S DO IT LET’S DO IT SCAN ME FORM ANGLE TUTORIAL
168 6.1.1 Discuss various materials and suitable methods to draw shapes of regular polygons including the ones that have been learned such as tracing the surfaces of 3D objects. Think of other suitable materials that can be used to draw regular polygons and measure each of the angles. We can measure the angles too. Every angle must be 60°. We measure the sides, teacher. All sides must have equal length. cm inches Protractor Ruler Equilateral triangle grid paper Square grid paper Dotted grid paper DRAW AND MEASURE INTERIOR ANGLES OF REGULAR POLYGONS This shape is drawn on a dotted grid paper. What is the method to prove that this is an equilateral triangle? Excellent answers! We will learn to draw regular polygons and measure the interior angles. 11 AUGUST 2022
169 A B C 4 units 4 units 4 units 6.1.1 • Mark point A. • Count 4 units on the triangle grid to the right and mark as point B. • Join points A and B. • Label it as 4 units. • Count 4 units on the triangle grid from point A upwards. • Mark as point C. Join point A with point C. • Label it as 4 units. • Join point B with point C. • Label it as 4 units. • Place the centre of the protractor on point A. • Ensure that the baseline of the protractor overlaps line AB. • Read the value of the angle on line AC and label it. • Repeat to measure angles B and C. Let’s use this equilateral triangle grid paper to draw an equilateral triangle. Scan the QR code to print the materials. Ask pupils to draw equilateral triangles with length of sides of 4 units, 5 units, and 7 units in their mathematics exercise books and measure the angles. Remind pupils to measure the angles correctly as learned in Year 5. A B C 4 units 4 A 4 units B units 2 1 3 EQUILATERAL TRIANGLE 4 Method 1 C A B 60° 60° 60° 4 units 4 units 4 units SCAN ME EQUILATERAL TRIANGLE GRID PAPER
170 6.1.1 Remind pupils about perpendicular lines. Draw a straight line of 4 cm long. Mark as point A. Mark the centre of the line at 2 cm. Draw a perpendicular line. Measure 4 cm from point A until it touches the perpendicular line and mark it as point B. Label C and join points B and C. Measure angles A, B, and C. I can draw an equilateral triangle using a blank paper and a ruler. cm inches A B cm inches A cm inches A cm inches A 1 2 3 4 Method 2 B C A
6.1.1 171 Ask pupils to draw squares. Encourage pupils to draw in various ways such as using a blank paper and a ruler. Mark points A, B, C, and D at a distance of 5 units between one another. Join all the points. Make sure that all sides are of equal length. Measure the interior angles of each angle. Label the angles. Let’s draw a square. It must have four points of equal distance. A D B C A D B C A D B C Explain other methods to draw squares as well as to measure the angles. SQUARE 90° 1 2 3
172 6.1.1 Let’s draw a regular pentagon. Each angle of the pentagon is 108°. 2 4 Measure angle A, 108°. Draw a long straight line. 3 Measure angle B, 108°. Draw a long straight line. Measure 5 cm from B along the straight line drawn and label it as C. Measure 5 cm from A along the straight line drawn and label it as E. Draw a straight line of 5 cm long. Label it as A and B at each end of the line. 1 REGULAR PENTAGON cm inches A 5 cm B A 5 cm B A 5 cm B inches cm B A 5 cm B cm inches A 5 cm 5 cm 5 cm E C A B inches cm
173 Measure angle E, 108°. Draw a long straight line. Label it as D at the intersection of line EC. Erase extended lines at points C, D, and E. Label the angles and the length of the sides. 6 5 7 Surf the Internet to get the shapes of regular pentagon and five-pointed star. Print the shapes and give them to pupils. Ask pupils to draw regular pentagon using the given shapes and measure the angles. Measure angle C, 108°. Draw a long straight line. 6.1.1 A 5 cm 5 cm E C B A 5 cm 5 cm E C B cm inches A 5 cm 5 cm E C B A 5 cm 5 cm E C B D cm inches A 5 cm 5 cm E 108° 108° 108° 108° 108° C D B
174 6.1.1 Let’s draw a regular hexagon. Remember, the six sides must be of equal length! 1 Draw six equilateral triangles that can be joined to form a hexagon. Explore other methods to draw hexagon other than using the equilateral triangle grid paper. Discuss shapes of hexagon that can be found in daily life situations such as honeycomb. Can a regular hexagon be drawn on a square grid paper? Discuss. Count 4 units for the six sides. Mark six points and label them as P, Q, R, S, T, and U. Join all the points. P T U R 4 units 4 units 4 units 4 units 4 units Q S 1 2 3 4 5 6 4 units 2 Measure and label every interior angle. P Q T U R S 120° REGULAR HEXAGON Method 1 Method 2
6.1.1 175 I use a heptagon shape from MS Word software and print it out. 1 2 3 1 2 Click Shapes and select Heptagon from Basic Shapes. Click Shift on the keyboard and drag the mouse to enlarge the size of a regular heptagon. Print out the shape. Measure and label the interior angles of the regular heptagon. Get a picture of a seven-pointed star. Join the seven vertices of the star to draw a regular heptagon and measure every interior angle. Train pupils to draw a heptagon with suitable methods to obtain a regular heptagon shape that has an angle of 128.5°. REGULAR HEPTAGON 128.5° Method 1 Method 2 128.5°
176 6.1.1 2 Measure 4 cm from A and mark it as H. Measure 4 cm from B and mark it as C. 3 Measure and mark 4 cm from C and H. Label it as D and G. 4 Measure angle 135° at D and G. Mark and draw a straight line passing through the point. Guide pupils to draw and measure lines correctly to form a correct regular octagon. REGULAR OCTAGON 1 Draw a straight line of 4 cm long and label it as A and B at each end of the straight line. Measure angle 135° at A and B. Mark and draw a straight line passing through the point.
177 5 Measure and mark 4 cm from D and G. Label it as E and F. 6 Join E and F. Erase extended lines at points C, H, E, and F. Label every angle of the regular octagon. 6.1.1 Draw and measure the interior angles of the following regular polygons using grid papers, ruler, protractor, and other suitable materials. a Equilateral triangle e Regular heptagon c Regular hexagon b Square f Regular octagon d Regular pentagon Ask pupils to draw regular polygons up to eight sides based on their creativity. Get them to measure and label the interior angles. Charles and Raymond drew a regular polygon each. The number of sides of the regular polygon drawn by Charles is 2 times the number of sides of the regular polygon drawn by Raymond. What are the shapes of regular polygon that might be drawn by Raymond and Charles? THINK SMART THINK LET’S DO IT LET’S DO IT
178 6.2.1 Use various sizes of circle to stimulate pupils’ understanding about the centre of circle and the circumference. Wow, these logos are beautiful, teacher. Which logo will you choose for our robotics team? Yes, Ikram. All of these logos were designed from circles. Tomorrow, you will learn all about circles. Teacher, what does a circle have? O centre of the circle circumference of the circle a b RECOGNISE CIRCLES CENTRE OF A CIRCLE, DIAMETER, AND RADIUS This red dot is the centre of the circle. It is usually represented by the letter O. The curved line that forms this circle is called the circumference of a circle.
6.2.1 179 The red line is the diameter. The yellow line is the radius. The length of the radius from the centre of the circle is always equal. Can you relate radius with diameter? Explain. The centre of a circle is the point located in the middle of the circle. The circumference of a circle is the closed curve that forms the boundary of the circle. The diameter is a straight line that connects two points on the circumference and passes through the centre of the circle. The radius is a straight line that connects the centre of the circle with the circumference. O diameter radius Inform pupils that the length of all radii in a circle is equal. Guide pupils to relate radius with diameter. O centre of the circle circumference of the circle c d Ikram, based on the notes, which one is the diameter? Which one is the radius? circumference of the circle centre of the circle Monday 29 August 2022
180 6.2.2 Let’s draw a circle of 4 cm radius using the modified ruler. Prepare the modified ruler for each pupil. Train pupils to draw circles with various radius measurements neatly. 1 Use two pencils. Place one pencil point at the 0 cm hole (centre of the circle) and another one at the 4 cm hole (4 cm radius). 2 Move the pencil at the 4 cm hole to complete one round clockwise or anticlockwise. 3 Mark the centre of the circle and label it. Draw a radius and label it. Scan the QR code. Print the ruler and laminate it. Then, make a hole at every 1 cm and at every 0.5 cm. LET’S DRAW CIRCLES Method 1 Remember! Do not move the pencil point at 0 cm. SCAN ME MODIFIED RULER
6.2.2 181 There are many surfaces of round-shaped objects that can be traced to draw circles. 1 Draw a circle using the circumference of a medicine cup. 3 Fold the circle into four parts of equal size. 2 Cut out the circle. 4 Unfold it. Observe the folded intersection in the middle. 5 Mark the centre of the circle. Then, label the centre of the circle and the diameter. Ask pupils to bring any round-shaped containers for the circle drawing activity. Carry out the activity in small groups. Method 2 O diameter
182 6.2.1, 6.2.2 Guide and check pupils' work to ensure that they answer correctly. 1 Fill in the boxes based on the labels on the circle. 2 Complete the sentences below. a The of a circle is the point located in the of the circle. b The circumference of a is the that forms the boundary of a . c The is a straight line that connects the of a circle with the circumference. d The diameter is a that connects on the circumference that passes through the centre of the circle. 3 Draw the circles based on the given information. O PQ OT My radius is 3 cm. a b My radius is 5 cm. c My radius is 8 cm. 4 Draw a circle based on the information below and label it. O is the centre of the circle. OH is the radius of the circle. The length of OH is 3.5 cm. PT is the diameter of the circle. The length of PT is 7 cm. Draw another circle with a radius of one-third of the radius shown in the circle on the left. Label all the characteristics of the circle. THINK 12 cm SMART THINK LET’S DO IT LET’S DO IT O P T Q
183 Solution 6.3.1 1 Father plans to build a table in the garden. The surface of the table is a regular hexagon and will be placed in an area measuring 2 m long and 2 m wide. What is the plan for a suitable size of the table? Regular hexagon table surface: • it has six sides and vertices • all sides are of equal length • size does not exceed 2 m × 2 m • consider space for the chairs • The surface of the table is a regular hexagon. • The area is measured as 2 m × 2 m. • What is the plan for a suitable size of the table? • Draw a regular hexagon that does not exceed the length and width of 2 m. • Must have space for chairs around the table. 2 m chair 2 m table surface Discuss other surface shapes of regular polygons, which are suitable to make a table. In groups, ask pupils to draw plans for other regular polygons such as pentagon, heptagon, and octagon. Ask each group to present their work. SOLVE THE PROBLEMS Understand the problem Plan the strategy Solve Check
184 6.3.1 2 Zahid’s sister wants to bake a cake. She needs a sheet of paper to be used as cake mould parchment as shown in the picture. What is the method to make the parchment? • Circle-shaped cake mould. • The cake mould radius is 10 cm. The method to make a circle-shaped parchment. Simulate forming a circle. The radius of the circle is 10 cm. Vary length of radius and ask each pupil to simulate forming a circle like the method above. 10 cm Fold paper into four parts. Cut the paper using scissors along the curved line. • Using a modified ruler, place a pencil at 0 cm. Place another pencil at 10 cm. • Move the pencil at 10 cm to form a curved line. 1 Open the folds to see the result of the parchment. 3 Solution 2 4 Given Asked for Solve
185 6.1.1, 6.1.2, 6.2.1, 6.2.2, 6.3.1 1 Chee Cheong wants to make a circle from a piece of plank measuring 25 cm long and 25 cm wide. The radius of the circle is 8 cm. Help Chee Cheong to draw the circle. 2 A group of pupils were asked to design an area for resting. The area is of a regular octagon with the length of 5 m on each side. Draw the plan of the area. 3 Anding wants to make a photo frame of six equal sides. The perimeter of the photo frame is 120 cm. What is the length of each side of the photo frame? 4 Mr Awang wants to make a circle in the middle of a field. The radius of the circle is 0.3 m. Explain how Mr Awang will draw the circle. 1 Based on the information below, draw and label the interior angles for each regular polygon. a It has three sides of equal length. The length of each side is 5 cm. b Each interior angle of a polygon is 135°. The length of each side is 3 cm. c Each of the five sides measures 6.5 cm. All the interior angles are 108°. 2 Draw a regular polygon of four sides. Each side measures 5.3 cm. Label its interior angles. 3 Using writing utensils and a protractor, draw the following angles. a 40° b 65° c 89° d 125° e 160° f 173° 4 A circle consists of , , , and . 5 Draw circles based on the information given. a radius of 4 cm b radius of 4.7 cm c radius of 5.2 cm 25 cm 25 cm LET’S DO IT LET’S DO IT LET’S PRACTISE
186 6 Solve the following problems. a Mr Gopal is arranging bricks at his garden as a border for his regular pentagon-shaped mini flower garden. The length of one side of the regular pentagon’s border is 5 m. Sketch the shape. b Halina’s father plans to build a circle-shaped swimming pool. The radius of the swimming pool is 3 m. i Draw the plan of the swimming pool. ii Give a suggestion about the measurement of the pool area. c Mei Hwa’s mother wants to buy cake boards. She received many online orders of cakes with the size of 25 cm × 25 cm. What is the suitable measurement of the cake board she should buy? Why? 1 Design a geometrical pattern from any regular polygons up to eight sides and a circle. 2 Use the Cut-and-Paste technique or the colouring technique. 3 Present the work. 4 Each group chooses and proposes three types of geometrical patterns that are most interesting. 5 Three selected patterns will be announced as winners. 6.1.1, 6.2.2, 6.3.1 Tools/Materials Task A4 papers, grid papers, coloured papers, glue, water paint, crayons, coloured pencils, scissors, pencils, rulers, and protractors. Participants 4 pupils in a group. LET'S EXPLORE
187 7.1.1 Recall the horizontal distance and vertical distance of a point from the origin on the first quadrant of the Cartesian plane. Discuss the horizontal distance and vertical distance of other locations on the Cartesian plane based on scale given. 1 The Cartesian plane shows the location of Farid’s home and nearby places. a What is the horizontal distance of the mosque from Farid’s house in km? The distance for each grid on the Cartesian plane is 1 cm. 1 cm scale represents 1 km of the actual scale. State, in km, the horizontal distance and vertical distance of the restaurant from the fishing village. The horizontal distance of the mosque from Farid’s house is 5 km . b The actual vertical distance of the hotel from Farid’s house is 2 km . c The horizontal distance of the fishing village from Farid’s house, in km, is 5 km . Meanwhile, the vertical distance is 2 km . d The actual distance of the tourist spot from Farid’s house is horizontally and vertically. 0 1 2 3 4 5 5 km Mosque Farid’s house cm COORDINATES, RATIO, AND PROPORTION 7 DISTANCE BETWEEN TWO COORDINATES 1 Tourist spot Fish pond 1 2 3 4 5 6 2 3 y x O 4 5 6 Restaurant Fishing village N 1 cm 1 cm Farid’shouse Mosque RESTORAN RESTORAN RESTORAN RESTORAN RESTORAN Hotel 5 cm represents 5 km of the actual distance. Scale 1 cm represents 1 km RESTORAN RESTORAN
188 HOSPITAL HOSPITAL HOSPITAL HOSPITAL O 1 Residential B 1 2 3 4 5 6 2 3 y x 4 5 6 7 1 cm 4 cm 5 cm 1 cm N Scale 1 : 100 000 HOSPITAL HOSPITAL Residential D HOSPITAL HOSPITAL Hospital HOSPITAL HOSPITAL HOSPITAL HOSPITAL Petrol station 7.1.1 Explain that 100 000 cm is equal to 1 km. Explain that the scale on the Cartesian plane is used to represent the actual distance. Discuss the horizontal distance and vertical distance of two different locations on the Cartesian plane. 2 The Cartesian plane shows the location of residential A, B, C, D, hospital, and petrol station. 1 unit on the Cartesian plane represents 100 000 units of the actual distance. Thus, 1 cm on the Cartesian plane represents 100 000 cm or 1 000 m or 1 km of the actual distance. What is the actual horizontal distance and vertical distance, of Residential A from Residential C? By using the scale of 1 : 100 000, find the horizontal distance of P from Q on the Cartesian plane if the actual horizontal distance of P from Q is 7 000 m. The actual distance of Residential A from Residential C is 5 km horizontally and 4 km vertically . 5 km – 1 km 4 km 6 km – 1 km 5 km the difference of horizontal distance the difference of vertical distance 100 cm = 1 m 100 000 cm = 1 000 m = 1 km Find the horizontal distance and vertical distance, in km, of the hospital from Residential D. Residential Distance from origin Horizontal distance Vertical distance C 100 000 cm = 1 km 100 000 cm = 1 km A 600 000 cm = 6 km 500 000 cm = 5 km THINK SMART THINK SMART Residential A Residential C
7.1.1 189 3 The Cartesian plane shows the location of Khairil’s house, bus station, taxi station, MRT station, and airport. a What is the horizontal distance, in km, from Khairil’s house to the airport? The horizontal distance from Khairil’s house to the airport is 4 km . The distance from Khairil’s house to the bus station is 3 km horizontally and 2 km vertically . b What is the horizontal distance and vertical distance, in km, from Khairil’s house to the bus station? Carry out a suitable activity to determine the horizontal distance and vertical distance according to scale given. For instance, pupils’ seating arrangement in class. Horizontal distance = 5 units – 1 unit = 4 units (1, 4) (5, 4) Coordinate of Khairil’s house Coordinate of the airport Coordinate of Khairil’s house (1, 4) Coordinate of the bus station (4, 2) Horizontal distance = 4 units – 1 unit = 3 units Vertical distance = 4 units – 2 units = 2 units Refer to the scale, 4 units equals 4 km. 1 1 2 3 4 5 2 3 y x O 4 5 N 0 1 2 3 4 5 km Scale Bus station MRT station Airport Taxi station Khairil’s house State the horizontal distance and vertical distance, in km, from the taxi station to the MRT station.
190 7.1.1 a State, in km, the horizontal distance of Salim’s house from Feng’s house. b State, in km, the vertical distance of Shalini’s house from Feng’s house. c State the actual horizontal distance and vertical distance of Jack’s house from Feng’s house. Prepare a Cartesian plane for a student-centred activity for pupils to mark the nearby areas to their respective houses and find the actual horizontal distance and vertical distance based on the chosen scale. Scale 1 cm represents 1 km 1 Shalini’s house Jack’s house Salim’s house Feng’s house 1 2 3 4 2 3 y x O 4 5 1 cm 1 cm N 5 1 The Cartesian plane shows the location of Feng and his three friends’ houses. a Find the actual horizontal distance and vertical distance of: i Riang Island from Rajin Island. ii Seronok Island from Baik Island. b State the island which is located at a distance of 3 km horizontally and 2 km vertically from Baik Island. 2 The Cartesian plane shows the location of four islands. State the horizontal distance and vertical distance of rest area T from town H in km. 3 0 1 2 3 4 5 km Scale The Cartesian plane shows the rest area T and town H along a highway. 1 Rajin Island Baik Island Riang Island 1 2 3 4 2 3 y x O 4 5 1 cm 1 cm Scale 1 : 100 000 N Seronok Island 5 LET’S DO IT LET’S DO IT 1 2 3 4 5 2 3 y x O 4 5 Rest area T Town H N 1
191 Step 2 7.2.1 2 pupils represent 1 group. There is 1 boys’ group and 1 girls’ group. Enhance pupils’ understanding on the concept of ratio between two quantities by forming groups to simplify the ratio between two quantities. Emphasise how to say the correct ratio. For example, the ratio of one to one. 1 The picture shows pupils’ activities in the science laboratory. What is the ratio of the number of boys to the number of girls? The ratio of the number of boys to the number of girls is 2 : 2. 2 : 2 written in the simplest form is 1 : 1. The ratio of the number of boys to the number of girls is 1 : 1 . boys girls 1 group State the ratio of 5 : 5 in the simplest form. Rina and I will prepare the experiment report. Alright. We will carry out the experiment. 1 group RATIO BETWEEN TWO QUANTITIES Step 1 boys girls TIPS Ratio is the comparison of size or value of an object to the size or value of another object in the simplest form.
192 7.2.1 State the ratio of the number of mangoes to the number of mangosteens. 6 : 4 written in the simplest form is 3 : 2. The ratio of the number of mangoes to the number of mangosteens is 3 : 2 . State the ratio of 3 to 9 in the simplest form. 3 : 9 1 : 4 3 : 9 1 : 3 Adam Safiya Whose answer is correct? Discuss. Explain that simplifying ratio is the same as simplifying fraction. Emphasise that the value of ratio does not change even though it is simplified. Step 1 The ratio of the number of mangoes to the number of mangosteens is 6 : 4. The ratio of the number of mangoes to the number of mangosteens is 3 : 2. There are 3 groups of mangoes. There are 2 groups of mangosteens. 2 3 Method 1 6 and 4 can be divided by 2 without any remainder. The ratio of 1 to 4. 6 : 4 3 : 2 ÷ 2 ÷ 2 Method 2 THURSDAY 15 SEPTEMBER 2022 Step 2 Group in twos The ratio of 1 to 3.