192 Mathematics Grade 5 A cubical tank contains 2.744 l of water. It is filled to its brim. Find the area of the base of the tank in cm2 . (1 l = 1000 cm3 ) Capacity of tank = 2.744 l × 1000 ? = cm3 Length of one edge = 3 = cm Area of base = cm × cm = cm2 The area of the base of the tank is cm2 . A cubical container is 3 4 full of water. The volume of water in the container is 6 l. What is the base area of the container in cm2 ? 3 4 of capacity of container 6 l 1 4 of capacity of container 6 l ÷ 3 = l Capacity of container 4 4 = × l = l = cm3 Length of one edge = 3 = cm Area of base = × = cm2 The base area of the container is cm2 .
CHAPTER 8 Volume of cubes and cuboids 193 Practice Solve the following word problems. 1. How much more water is needed to fill up each of the following tank? Give your answer in litres. (1l = 1000 cm³) 2. A cubical container measuring 15 cm by 20 cm by 10 cm is 2 5 filled with oil. (a) What is the volume of oil in the container? (b) How much more oil is needed to fill the container to its brim? Give your answer in litres. (1l = 1000 cm³) 30 cm 25 cm 20 cm 14 cm
194 Mathematics Grade 5 A juice carton is 8 cm long, 5 cm wide and 20 cm tall. What is the capacity of the juice carton in litres? The capacity of carton = Length × Breadth × Height = 8 cm × 5 cm × 20 cm = 800 cm3 1000 cm3 = 1 l 800 cm3 = 1 1000 × 800 l = 0.8 l The capacity of the juice carton is 0.8 litre. A swimming pool is 10 metres long and 4 metres wide. It contains 200 m³ of water. How deep is the pool? Depth of the pool = Volume Length × Breadth = 200 10 × 4 = 200 40 = 5 m The pool is 5 m deep. Solving word problems involving volume and capacity G 10 m 4 m ? Remember: Volume = Length x Breadth x Height Height = Volume ÷ (Length x Breadth) 5 1 watch me
CHAPTER 8 Volume of cubes and cuboids 195 Practice Solve the following word problems. 1. A pool is 6 m long, 3 m wide and 2 m deep. How much water can the pool contain? Give your answer in m³. 2. A rectangular cake is 20 cm long, 20 cm wide and 4 cm thick. If the cake is cut into 25 slices of equal size, what will the volume of each slice of cake be? 3. A tub that is 120 cm long, 75 cm wide and 32 cm tall is full of water. If 96 l of water is drawn from the tub, how many l of water will be left in it?
196 Mathematics Grade 5 4. A rectangular oil tank measuring 16 m by 50 m by 3 m is filled to its full capacity, what will the volume of the oil in the tank be? Give your answer in litres. 5. A plot of land has an area of 220 m2 . The landowner aims to raise the ground level by 1 m. How much soil does he need to raise the ground to his intended level? 6. A fish tank is 90 cm wide, 1.5 m long and 60 cm tall. If you need to fill up the tank with water using a 10 l pitcher, how many times will you have to fill up the pitcher?
CHAPTER 8 Volume of cubes and cuboids 197 Let's look at the figures below. Tap A Tap B 3 l of water flows from Tap A into this tank in a minute. 5 l of water flows from Tap B into this tank in a minute. The flow rate tells how fast a liquid is flowing. Water flows from Tap A into the tank at 3 l per minute. We can write the flow rate of Tap A as 3 l / min. Water flows from Tap B into the tank at 5 l per minute. The flow rate of Tap B is 5 l / min. Water flows into a container at 6 litres per minute. How much water will there be in the container after 2 minutes? In 1 minute, there will be 6 litres of water. In 2 minutes, there will be 2 × 6 = 12 litres of water. There will be 12 litres of water in the container after 2 minutes. How much water will there be after 5 minutes? × l = l There will be litre of water after 5 minutes. H Flow rate 1 min 5 l 2 min 2 × 6 l = 12 l
198 Mathematics Grade 5 Water flows through a tap at 9 l / min. How much water flows in 12 minutes? 1 min 9 l 2 min × l = l l of water flows in 12 minutes. 500 ml of water flows through a tap in 4 minutes. What is the flow rate in ml / min? 4 min 500 ml 1 min 500 ml ÷ 4 = 125 ml The flow rate is 125 ml / min. 1155 ml of water flows through a tap in 7 minutes. What is the flow rate in ml / min? 7 min ml 1 min ml ÷ = ml The flow rate is ml / min. The capacity of a tank is 255 l . It takes 5 hours to fill the tank with water from a tap to its brim. What is the flow rate of the tap? 5 h l 1 h l ÷ = l The flow rate of the tap is l /h.
CHAPTER 8 Volume of cubes and cuboids 199 Practice Solve the following word problems. 1. Water is flowing through a tap at 18 l/ min. Find the total volume of water flowed after (a) 5 minutes. (b) 30 minutes. 2. A cubic tank has an edge of 12 cm. It takes 6 minutes to fill in the tank with water from a tap to its brim. What is the flow rate of the tap? 3. A rectangular tank measuring 40 cm by 30 cm by 20 cm is completely filled with water. A tap drains the water at 8 l per minute. How long does it take to empty the tank? (1 l = 1000 cm³)
Chapter 9 You should be able to • presenting and interpreting data in a table • read and understand data tables and from line graphs • draw line graphs using given data • solve word problems related to line graphs Learning Outcomes Do you know how to extract information from line graphs and pie charts? https://qr.pelangibooks.com/?u=MOMG5C9mo1 https://qr.pelangibooks.com/?u=MOMG5C9mo2 https://qr.pelangibooks.com/?u=MOMG5C9mo3 Maths Online Introduction to statistics Maths Online Maths Online Maths Online 2 3
CHAPTER 9 Introduction to statistics 201 A Collecting and organising data An interview is conducted in a class of 40 pupils. They are asked to name their favourite types of fruit. The following is the data collected from the interview. We can organise the data in a table. There are many ways of collecting data such as conducting interviews, handing out questionnaires and taking measurements. The method used to collect data depends on the type of data and the amount of data needed. Guava 5 Papaya 10 Orange 8 Watermelon 12 Apple 5 Guava |||| Papaya |||| |||| Orange |||| ||| Watermelon |||| |||| || Apple |||| watch me
Mathematics 202 Grade 5 1. May recorded the favourite sports among her classmates. Can you help her to organise the data in a table? Swimming |||| |||| || Football |||| Basketball |||| Badminton |||| || Tennis ||| Practice Swimming Football Basketball Badminton Tennis 2. Collect data on the hobbies of your classmates. Then, organise the data in a table to identify the most popular hobby among your classmates.
CHAPTER 9 Introduction to statistics 203 B Tables The following table shows the number of people who visited a zoo on each day of a week. What do we learn from the table? We can also present data in the form of a table. Tabulated data enables us to examine the details and make comparisons easily. Day Number of visitors Male Female Total Monday Tuesday Wednesday Thursday Friday Saturday Sunday 99 101 100 126 102 188 198 108 78 120 142 151 168 178 207 179 220 268 253 356 376 Total 914 945 1859 (a) people visited the zoo during the week. (b) The most number of people visited the zoo on . (c) The least number of people visited the zoo on . (d) The total number of female visitors during the week was . (e) male visitors were at the zoo during the week. (f) There were more female visitors than male visitors at the zoo during the week. (g) recorded the least number of female visitors at the zoo. (h) recorded the least number of male visitors at the zoo. watch me
Mathematics 204 Grade 5 Practice 1. The table shows the prices of some types of vegetables in a grocery shop. Study it and answer the following questions. Item Price (Rp/kg) Cabbage Carrot Broccoli Onion Potato 7.600,00 5.000,00 16.000,00 10.500,00 15.200,00 (a) What is the price of 1 kilogram of carrots? (b) What is the price of 2 kilograms of broccoli? (c) If you purchase 1 kilogram of each item, how much will they cost? (d) If you use a 50 000 rupiah note to pay for 2 kilograms of carrots and 1 kilogram of potatoes, how much change will you receive? (e) Which type of vegetable costs twice as much as the cabbage?
205 CHAPTER 9 Introduction to statistics 2. Miss Dorris drew a table to show the number of Primary 5 pupils who passed the final exam. Help Miss Dorris to complete the table below. Class Number of boys Number of girls Total number of pupils 5A 8 11 5B 11 9 20 5C 16 32 5D 19 6 Total Study the table and answer the following questions. (a) How many pupils who passed the final exam are from Class 5D? (b) Which class recorded the greatest number of pupils passing the final exam? (c) Did more boys or girls pass the final exam? How many more? (d) Express the number of pupils in 5C passing the final exam as a fraction of the total number of pupils passing the final exam. Give your answer in its simplest form.
Mathematics 206 Grade 5 C Line graphs A line graph is a graph on which points representing data are joined by line segments to show the change in the value of data collected over a certain period of time. Month January February March April May June Number of cars sold 150 200 350 250 300 200 The table below shows the sales of imported cars of a company from January to June. (a) In which month were there 350 cars sold? Therefore, there were 350 cars sold in March. (b) In which month were there 150 cars sold? There were 150 cars sold in . To find the answer, Step 1: Find the amount of 350 along the scale. Step 2: Move right until you meet the graph. Step 3: Move down until you meet the scale. Number of cars sold 100 200 300 400 350 Jan Feb Mar Apr May Jun Sales of imported cars Month watch me
207 CHAPTER 9 Introduction to statistics The line graph below shows the temperature change of a cup of a coffee in an hour. Study the graph and answer the following questions. (a) The temperature of the cup of coffee at first was °C. (b) The temperature of the cup of the coffee at the end was °C. (c) How long did it take for the temperature of the cup of coffee to drop until 55°C ? minutes (d) What was the decrease in temperature of the cup of coffee between 8.40 a.m to 8.50 a.m? °C. (e) What was the room temperature? °C. Temperature (°C ) 10 20 30 40 50 60 70 80 90 100 8.00 8.10 8.20 8.30 8.40 8.50 9.00 Temperature change of a cup of coffee Time (a.m )
Mathematics 208 Grade 5 The line graph below shows mass of Azlan at the end of each month over a period of six months. Study the graph and answer the following questions. (a) Azlan's mass at the end of July was kg. (b) Azlan was 60 kg at the end of . (c) Azlan was the heaviest at the end of . (d) Azlan was the lightest at the end of . (e) The difference between Azlan's smallest mass and greatest mass was kg. (f) The increase in Azlan's mass from the end of July to the end of August was kg. (g) Azlan's mass was the same at the end of the months of and . Mass (kg) 10 20 30 40 50 60 70 80 Jun Jul Aug Sep Oct Nov Dec Azlan’s mass Month
209 CHAPTER 9 Introduction to statistics Practice 1. The line graph shows the monthly gas consumption of Jordan’s family in a certain year. Study the line graph and answer the following questions. Gas used (kWh) Jan 50 100 150 200 250 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Monthly gas consumption Month (a) Which month had the highest gas consumption? (b) What was the gas comsumption in July? (c) In which months did the gas consumption exceed 150 kWh? (d) In which month did Jordan's family leave for the summer holiday?
Mathematics 210 Grade 5 2. The line graph below shows the temperature recorded in City R from 6 a.m. to 12 midnight. The temperature is taken every three hours and measured in degree Celsius (°C). Study the graph and answer the following questions. (a) What was the difference between the highest temperature and the lowest temperature recorded? (b) At what time was the temperature 25°C? (c) At what time was the hottest during the day? (d) How many °C did the temperature rise between 9 a.m. and 3 p.m.? (e) How many °C did the temperature fall between 6 p.m. and 12 midnight? 6 a.m. 9 a.m. 12 noon 6 p.m. 9 p.m. 12 midnight 3 p.m. 5 10 15 20 25 30 35 40 Temperature recorded in City R Time Temperature (°C )
CHAPTER 9 Introduction to statistics 211 D Pie charts Pie charts are used to present information when the proportions of a whole are more important than the individual quantities. The total number of the pupils in Grade 5 is one whole. All the Grade 5 pupils of School Y took part in a survey to find out their favourite hot drinks. The results of the survey are shown in the table below. Type of hot drink Chocolate Coffee Tea Milk Number of pupils 120 30 75 75 There are 300 pupils in Grade 5. Let’s express the quantity of each type of drink as a fraction. Chocolate = 120 300 = 2 5 Coffee = 30 300 = 1 10 Tea = 75 300 = 1 4 Milk = 75 300 = 1 4 Therefore, 2 5 of the pupils like chocolate drink. 1 10 of the pupils like coffee. 1 4 of the pupils like tea. 1 4 of the pupils like milk. The results are presented in the pie chart below. A pie chart is a type of chart that is in the shape of a circle. Notice that the type of drink with the greatest quantity is represented by the largest part in the pie chart. In pie charts, it is easy to see the relative sizes of data. Hot chocolate Milk Tea Coffee 2 5 1 1 4 4 1 10 watch me
Mathematics 212 Grade 5 Therefore, 40% of the pupils like chocolate drink. 10% of the pupils like coffee. 25% of the pupils like tea. 25% of the pupils like milk. We can present the data in a pie chart as shown below. Each part of the pie chart represent the quantity of each type of drink as a number, a fraction or a percentage. We can also express the number of pupils that choose each type of drink in the survey as a percentage. Chocolate 2 5 × 100% = 0.4 × 100% = 40% Coffee 1 10 × 100% = 0.1 × 100% = 10% Tea 1 4 × 100% = 0.25 × 100% = 25% Milk 1 4 × 100% = 0.25 × 100% = 25% Notice that the size of the parts remain the same even though they are presented in percentage. Hot chocolate 40% 10% 25% 25% Milk Tea Coffee
213 CHAPTER 9 Introduction to statistics The pie chart below shows different types of ice creams sold by an ice cream vendor. 36 yam-flavoured ice creams were sold. (a) What percentage of the ice creams sold are vanilla flavoured? 2 5 × 100% = 0.5 × 100% = 50% 50% of the ice cream sold are vanilla flavoured. (b) What fraction of the ice creams sold are strawberry flavoured? 25% = 25 100 = 1 4 1 4 of the ice creams sold are strawberry flavoured. (c) What percentage of the ice creams sold are corn flavoured? 3 20 × 100% = 15% 15% of the ice creams sold are yam flavoured. 100% – 50% – 25% – 15% = 10% 10% of the ice creams sold are corn flavoured. (d) How many ice creams were sold in total? Yam-flavoured ice creams = 3 20 3 units = 36 1 unit = 36 ÷ 3 = 12 ice creams 20 units = 20 × 12 = 240 ice creams 240 ice creams were sold in total. Vanilla 25% Strawberry Yam Corn 1 2 3 20 1 4 5 1
Mathematics 214 Grade 5 1. A survey is carried out on 500 pupils of Grade 5 to find out their future career choices. The results are shown in the pie chart below. Answer the following questions. Future career choices of Grade 5 pupils Engineer 26% Doctor 30% Teacher 10% Lawyer 12% Farmer 8% Nurse 14% (a) What is the most popular choice of future career among them? (b) What career is preferred by the least number of pupils? (c) How many pupils wish to become a doctor? (d) How many more pupils are there who prefer to be a nurse than to be a teacher? Practice
215 CHAPTER 9 Introduction to statistics 2. The pie chart below shows the number of pupils who attend classes learning different musical instruments at a music school. 96 pupils are at the music school (a) What percentage of the pupils are taking violin lessons? (b) How many pupils are taking violin lessons? (c) Find the number of pupils taking piano lessons. (d) What fraction of the pupils at the music school are taking cello lessons? Cello 12 Violin Piano 3 8
Mathematics 216 Grade 5 3. The pie chart below shows the body mass composition of an average male adult. Body mass composition of an average male adult (a) What percentage of the human body mass is made up of muscles? (b) The percentage of the bone mass is equal to the percentage of the fat mass in a human body. Find the mass of the bone of a 72-kg male. (c) The body fat of the human body is made up of essential fat and storage fat. The storage fat is four times the essential fat. How many percent more of storage fat than essential fat are there in the human body? (d) Oliver is 105 kg. How many kg of his mass is made up of muscles and other elements? Fat Other elements 25% Bone Muscles 9 20
21st Century Learning Components: Chapter Opener : provides an engaging introduction to the topics and concepts in the upcoming chapter Learning Outcomes : states the learning objectives in each chapter Maths Online : lists suitable websites that offer learning activities using information technology Practice : provides exercises to reinforce pupils’ grasp of new concepts learnt Watch Me : directs pupils to the carefully selected videos online for further reinforcement and mastery of concepts Activity Corner : offers suggestions for hands-on activities Let’s Think! : challenges pupils to answer non-routine questions Maths Tips : presents informative passages and points out important tips for pupils to take note of Stem Activity : provides an activity that engages in the application of knowledge of scientists, mathematicians and engineers Quick Quiz : provides printable online maths quizzes for pupils to boost their maths knowledge Maths Battle : contains different types of online activities and games that promote peer interaction and collaborative learning MINDS-ON MATHS is a series of textbooks with accompanying workbooks, specially designed to meet the requirements of the latest Indonesian Maths syllabus. The Singapore Maths Method which is proven to be one of the most effective teaching approaches in the world is adopted for content enhancement. This series encourages active learning and practices so that pupils’ mathematical fluency can be developed through questions and activities infused with heuristic and modelling techniques, critical thinking, logical reasoning and metacognitive skills. SPECIAL FEATURES MINDS-ON MATHS comprises: Textbook Workbook Teacher’s Guide Digital Handbook JBRB211035 ISBN 978-981-17099-0-6
