Maths. 2nd Edition. Dr Fong Ho Kheong Gan Kee Soon Chelvi Ramakrishnan

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1 Maths 2nd Edition 6B Dr Fong Ho Kheong Gan Kee Soon Chelvi Ramakrishnan APPROVED BY MINISTRY OF EDUCATION for use from

2 Preface Maths (2nd Edition) is a comprehensive, activity-based programme designed to provide pupils with a firm foundation in Maths and to develop creative and critical thinking skills resulting in efficient problem solvers. Maths (2nd Edition) continues to make learning Maths fun and rewarding through the use of engaging illustrations and games that help to reinforce and consolidate learning. For the Teacher: Pie Charts Understanding Pie Charts Let s Learn! Use the engaging and highly scaffolded Let s Learn! to introduce concepts. Parallel questions allow for immediate assessment and consolidation of concepts learnt. 1 About 70% of the Earth s surface is water. The remaining 30% of the Earth s surface is land. We can show this fact in a table. Earth s Surface 100% Carry out investigative activities in Let s Explore! These allow pupils to apply concepts learnt. Work in pairs: 1 Draw the rectangle and square on a piece of paper and cut them out. Let s Explore! 3 cm 7 cm 3 cm 2 cm 2 With the rectangle and the square form these three types of composite figures Put On Your Thinking Caps! In the fi gure below, the area of the shaded part is 30% of the area of Circle P. It is also 20% of the area of Circle Q. What percentage of the figure is shaded? Express your answer correct to 2 decimal places. (Hint : Find the ratio of the area of the shaded part to the unshaded part.) Challenge pupils to solve non-routine questions by applying relevant heuristics and thinking skills in Put On Your Thinking Caps! P Q Indicates that appropriate use of calculators is allowed for the activities and practices to enhance the teaching and learning processes. National Education provides opportunities for teacher-pupil interaction on Singapore. For the Parent/Guardian: Make Maths come alive by using the tips found Home in Maths to apply mathematical concepts to common scenarios in and around the home. Home Maths Get your child to help you make konnyaku jelly by mixing konnyaku jelly powder, sugar and water. Show your child the recipe and ask him/her to fi nd the ratio of the amount of konnyaku jelly powder to that of sugar. Ask your child to find the amount of sugar needed to make twice the amount of konnyaku jelly. To make 24 jellies Ingredients: 10 g konnyaku jelly powder 210 g sugar 950 ml water Recipe: 1) Mix the konnyaku jelly powder and sugar together. Mix well. 2) Pour the mixture of konnyaku jelly powder and sugar into water gradually and stir till boiling. 3) Turn off the flame and continue stirring for 5 minutes, until the bubbles dissipate and the konnyaku jelly solution turns clear. 4) Pour the solution into moulds and chill to set.

3 For the Pupil: 5 Carry out this activity. Trace out the nets shown in 4 and identify the two coloured faces of each solid by shading these faces on the nets. Cut out the nets and fold them to form the solids. Did you shade the correct faces? 6 Try IT! Choose a solid from the ones you have learnt about previously. Use the drawing tool in your computer to draw a net of the solid you have chosen. Print out the net, cut it out and form the solid. Does the net you have drawn form the solid you wanted? Maths Journal Noraini was shown the two solids below. Enjoy Maths (2nd Edition) with your friends. Carry out this activity will lead you to discover games and activities that involve the use of Maths. Share with your teachers what you have learnt, create your own Maths questions, and become aware of your own mathematical thinking in. Use computers to carry out fun-filled activities in Try IT! Recall skills taught in earlier levels and link them to new concepts in the current chapter. Area And Perimeter Let s Learn! Area And Perimeter Of Composite Figures Let us revise area and perimeter of the following fi gures: square, rectangle, triangle and circle. Perimeter of closed fi gure with 1 A side of the square is 6 cm. straight sides = Sum of its sides 6 cm Let s Practise! 3b 1 Below are the nets of four solids. Name the solid formed by each net. a b Let s Practise! comprises diagnostic and practice questions that provide opportunities for further practice. Let s Wrap It Up! Let s Wrap It Up! summarises the concepts you have learnt in the current chapter, while Let s revise! provides a worked example that covers the key concepts for ease of revision. You have learnt to: calculate speed, distance and time given the other 2 quantities use the formula: Speed Distance Time Distance Speed Time Time Distance Speed fi nd the average speed given a word problem scenario read, interpret and write speed in different units: km/h, m/min, m/s and cm/s draw models to solve word problems in speed Let s revise! Jane took h to travel from Town A to Town B at an average speed of Think It Through Whole Number 1 Tim s age now is a multiple of 5. In one year s time, his age will be a multiple of 7 and in two years time, it will be a multiple of 11. If he is less than 60 years old, how old is Tim now? Solve the problem step by step. Step Tim s possible age a List the multiples of 5 which are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 less than 60 Review C 1 Write 2150 in words When the odd numbers from 1 to 99 are added up, what is the digit in the ones place? 3 a Round off the following to the nearest ten. i 512 ii 2786 Use graded worked examples and questions to understand problem-solving strategies for heuristics-based higher order problems. Cumulative reviews provide more practice to help you consolidate the concepts learnt in the previous topics; with higherorder questions marked with *. Have fun learning Maths with Googol and his pals!

4 Contents Speed Distance And Speed 2 Average Speed 12 Word Problems 20 Review H 28 Circles Radius, Diameter And Circumference 35 Area Of A Circle 47 Review I 58 Pie Charts Understanding Pie Charts 63 Review J 72

5 Area And Perimeter Area And Perimeter Of Composite Figures 78 Review K 90 Volume Of Solids And Liquids MPH(M) CB_6B_contents.indd 3 Volume Of Solids Volume Of Liquids Review L 122 Review M 129 Think It Through 135 5/28/08 8:49:46 AM

6 Speed Let s Learn! Distance And Speed 1 Mr Chen is driving from Town A to Town B. In 1 hour, he drove 65 km. Mr Gopal is also driving in the same direction. In 1 hour, he drove 95 km. Mr Chen is driving at a speed of 65 km per hour. Mr Gopal is driving at a speed of 95 km per hour. The speed tells how fast Mr Chen and Mr Gopal are travelling. 2 Chapter 7: Speed

7 We can write the speed of Mr Chen s car as 65 km/h. Similarly, we can write the speed of Mr Gopal s car as 95 km/h. The symbol / means per. So we read 65 km/h as 65 km per hour. We express speed as distance travelled per unit time. Do these. 2 a Jalil can cycle 8 km in one hour. His speed is 8 km/h. b c d Lalita can run 300 m in one minute. Her speed is 300 m/min. A marble rolls 9 cm in one second. Its speed is 9 cm/s. Mingwei throws a stone and it falls 2 m in one second. Its speed is 2 m/s. 3 a Bernard runs at a speed of 12.5 m/s. In 1 s, he runs 12.5 m. b A lorry travelled at a speed of 48 km/h. In 1 h, the lorry travelled 48 km. Chapter 7: Speed 3

8 4 Mr Ahmad drives his lorry at a speed of 45 km/h. At this speed, how far does Mr Ahmad travel in: a 2 hours? b 5 hours? 45 km/h means 45 km per hour. In 1 hour, Mr Ahmad travels 45 km. In 2 hours, Mr Ahmad travels km. D In 5 hours, Mr Ahmad travels km. S T Speed Time Distance D S T Distance Speed Time Home Maths Ask your child to calculate how long it takes you to travel from your offi ce to your home. Tell your child the time at which you left the offi ce and the time at which you reached home. 4 Chapter 7: Speed

9 5 A racing car is travelling at a speed of 175 km/h. How far can it travel in 3 hours? Method 1 1 h 175 km 3 h Speed 175 km/h 525 km The racing car can travel Method km in 3 hours. Speed 175 km/h Time 3 h Distance Speed Time km The racing car can travel 525 km in 3 hours. 6 A bullet fi red from a gun travels at a speed of 250 m/s. How far can the bullet travel in 2 seconds? Method 1 Speed 1 s 250 m 2 s 500 m 250 m/s The bullet can travel Method m in 2 seconds. Speed Time 250 m/s 2 s Distance m The bullet can travel 500 m in 2 seconds. Chapter 7: Speed 5