COURSEBOOK. 3rd Edition. Dr Lee Ngan Hoe Dr Koay Phong Lee Charlotte Collars Ong Bee Leng Tan Cheow Seng

Transcription

1 COURSEBOOK 6B rd Edition Dr Lee Ngan Hoe Dr Koay Phong Lee Charlotte Collars Ong Bee Leng Tan Cheow Seng

2 Can I use all these cubes Preface Shaping Maths (rd Edition) is an instructional package written according to the 0 Ministry of Education, Singapore, primary mathematics syllabus. The package is designed to meet the learning needs of pupils from Primary to 6. The Primary 6 package consists of two Coursebooks, two Activity Books and two Teacher s Planning Guides. Approach Shaping Maths (rd Edition) adopts a thematic approach towards the learning of mathematics in the upper primary levels. These themes reflect various aspects of pupils lives and help provide a concrete framework for the mathematical concepts that pupils learn in class. Pupils learning is then reinforced through the use of pictures and icons before they are introduced to the formal symbolic mode of mathematical representation. The themes also provide an environment for pupils to experience the interdisciplinary nature of learning. Continuing research in education has resulted in the introduction of new features in the third edition. Through these features, educators are further equipped with various strategies in addressing teaching and learning needs. These features include hands-on activities, group/pair work and open-ended questions to encourage exploration and in-depth thinking among pupils. This will equip pupils well for the challenges of the st century. Features Colourfully illustrated unit openers encourage rich and active pupil participation in learning and connections to everyday life through whole class discussion. Aini, Bala and Caili each use unit cubes to build a cuboid. Caili My cuboid is units long and units wide. cubic units What will be the height of my cuboid My cuboid is units long, units wide and units high. The volume of my cuboid is cubic units. units units units Aini to make a big cube Explain. Bala My cuboid is units long and units wide. cubic units The height of my cuboid is units. David Group Activity Use unit cubes to build a cuboid that is different from the cuboids built by Aini, Bala and Caili. Find the length, breadth and height of your cuboid. AB 6B, p >> Recall 7 8 Unit Friends of Shaping Maths The themes of the Coursebook revolve around Aini, Bala, Caili and David. The characters stimulate pupils interest and heighten their involvement in the learning process.

3 Question classification helps teachers spend their time more effectively by using the appropriate questions to get pupils to master the necessary skills. Town U and Town V were 50 apart. Mr Ahmad drove from Town U to Town V at a constant speed of 75 /h. At the same time, Mr Abdul drove from Town V to Town U at a constant speed of 90 /h. How far apart were they after h Mr Ahmad 75 /h, h Mr Abdul 90 /h, h Town U Town V 50 A car and a lorry started travelling at the same time from Town R to Town S. When the car arrived in Town S, the lorry had only travelled Reinforcement of current concepts of the journey. 5 The lorry needed 5 min more to complete the journey. The lorry travelled at a constant speed of 60 /h. Find the distance between the two towns. Car Town R Town S Lorry 60 /h 5 min Higher-order thinking skills/enrichment Town P and Town Q were 7 apart. Motorist X left Town P for Town Q at 0 5, travelling at a constant speed of 65 /h. At the same time, Motorist Y left Town Q for Town P, travelling at a constant speed of 70 /h. Both motorists took the same route. What time did they pass each other Motorist X 65 /h Motorist Y 70 /h Town P Town Q 7 Total distance covered by both motorists in h Total time taken to cover 7 Fun h after 0 5 is with Activity for pupils Maths Fun with Maths engages pupils in interactive maths activities that encourage exploration, discovery and active thinking. stopwatch x 00 m Relay What to do: STEP Select your team members and write their names in the first column of a table such as below. Example: My Notes Team members.. They passed each other at What you need: Distance (m) Speed Time taken (s) Distance (m/s) Time 00 m m Drawings of 00 Solid Figures Unit h AB 6B, p 5 >> Activity 5 Speed 0(M)SMCB6B_U pf.indd /6/7 5: PM Aini, Caili, Bala and David bought some gifts. Name the shapes of the solids that they bought. 00 m Dotted lines represent the hidden edges. 00 m Name of solid My Notes helps pupils consolidate and recall, and commit to memory key learning concepts. Drawing STEP Go to a running track. STEP Each member runs 00 m. Cube Cuboid STEP Record the time taken by each member. Find the average running speed of each member. Prism Who is the fastest runner in the team Cylinder Compare the average running speeds of your team members with those of the other teams. Predict the team that will win the 00 m relay. Explain your prediction. Pyramid A box of cookies A bar of chocolate A tin of biscuits 5 Nets A net is a a flat shape that can be folded to form a solid such as a cube. /6/7 5: PM The gift that I bought for my mother had triangular faces. Can you guess what I bought for her Below are drawings of pyramids. Guiding questions build the habit of checking to understand a problem. AB 6B, p 9 >> Let s Find Out Cone 0(M)SMCB6B_U pf.indd 5 A puzzle cube face base Distance travelled Speed base Time taken A B base C a) How many faces does each pyramid have b) What is the shape of each face of each solid c ) Draw a pyramid with a triangular base on a piece of paper. a cube A solid can have more than one net. AB 6B, p 90 >> My Maths Journal 67 06(M)SMCB6B_U pf.indd 67 8/6/7 5:5 PM Cubes and Cuboids A G p rou ity iv ct a) Build three cuboids. Use 6 -cm cubes to build each cuboid. Then find the missing numbers in the table below. Length (cm) Breadth (cm) Height (cm) A B C Base area (cm) 8 (cm) Breadth Height cm A cm Breadth Length Height Solid Figures 06(M)SMCB6B_U pf.indd 5 8/6/7 5:5 PM Review 6 cm A Johari cycled at a constant speed of 00 m/min. How far did he cycle in 5 min Give your answer in metres. Mr Tan completed a journey in 6 h at an average speed of 50 /h. Mr Yu completed the same journey at an average speed of 75 /h. How much less Part A time did Mr Yu spend than Mr Tan to complete the journey For each question, four options are given. One of them is the correct answer. Mrs Jones took 5 h to travel from Town P to Town Q. She took h to cover the first ( ) () half of her journey at an average speed of 00 /h. Find her average speed for () () 8 the second half of the journey. Express.005route as a to mixed number in its simplest form. take Muthu and his brother Raju the same school. Muthu s constant walking speed is 0 m/min faster than Raju s. When Muthu reaches their school in 5min, () ( ) 0 00 Raju has only walked of the distance. Find the distance between their house and 5 () () the school. Revision Review and Revision provide a formative assessment of pupils understanding and help to consolidate learning. 6 of a cuboid Length Breadth Height Length Unit Activities have been included to provide more individual, pair and group hands-on learning. These, along with the manipulatives required, are highlighted for ease of use. t Cuboid NEW! 5 My Summary min House We can write a number as a product of two or more factors. product B Length Breadth C cm Base area cm cm 9 0(M)SMCB6B_U pf.indd 9 8/6/7 :08 PM My Summary helps pupils to consolidate their learning at the end of the year. It also serves as a quick revision guide for pupils. factors ( ) 6 cm () 0 cm of 55 ()7 a.m. cmand drove at a constant speed() /h. cm 95 0 Mrs 9Foo started 0 her journey at h later, Mrs Chen started her journey from the same starting point as Mrs Foo 58took 0 h to catch up with Mrs Foo. What was Mrs Chen s constant driving speed and 580 We use to represent approximately equal to. Number 0(M)SMCB6B_Review A pf.indd 5 hundred ( ). l 600 () 7 l decimal place 560 the nearest whole number thousand 000 decimal places (M)SMCB6B_Revision pf.indd 75 Number 5 ARounded rectangular to tank measures 60 cm by 0 cm by 0 cm. How much water is needed to fill the tankthe to nearest of its capacity the nearest the nearest ten 56 Operation 8/6/7 :8 PM () 57.6 l () 90 l My Summary 09(M)SMCB6B_Summary pf.indd /6/7 0:5 PM Answer Sections with this icon involve the use of calculators. School Raju Muthu is made up of eight -cm squares. What is its perimeter The figure Number Notation and Place Value Height Find the remainder when 88 is divided by 5. /6/7 :59 PM

4 CONTENTS Speed Speed Average Speed 6 Solving Word Problems 9 7 Cubes and Cuboids 9 Solving Word Problems 5 Review A 5 Pie Charts Reading Pie Charts Solid Figures 5 Drawings of Solid Figures 5 Nets 57 Review B 68 Revision 75 My Summary 88

5 Speed David is behind me. He is slower than I am. I reached the finish line before Caili. I am faster than Caili. Who took the shortest time to complete the walk

6 I walked 50 m in 5 min. I walked 50 m in 6 min. Bala walked faster. He took a shorter time to walk 50 m. In min, Bala walked 50 m and Caili walked.7 m. Bala s walking speed was 50 m per minute. Caili s walking speed was.7 m per minute. Speed tells us how fast the children walked. It is the distance travelled per unit of time. Speed is the distance travelled per unit of time. Speed Distance travelled Time taken Did David walk more than m in min Explain. Did You Know In the 06 Olympics, gold medalist Usain Bolt of Jamaica ran 00 m in 9.8 s. Elaine Thompson of Jamaica ran 00 m in 0.7 s. Matej Toth of Slovakia walked 50 in h 0 min 58 s. Joseph Schooling of Singapore swam the 00 m butterfly in 50.9 s. Who can run faster, Usain Bolt or Elaine Thompson How do you know Do you think Usain Bolt can run 00 m in 9.6 s Explain. AB 6B, p >> Recall

7 Speed Bala and Caili shared a taxi home after the fun walk. The speedometer showed how fast the taxi was travelling. SMCB6B_U_ The taxi travelled at 60 kilometres per hour. We write 60 kilometres per hour as 60 /h. At this speed, how far would it travel in h At this speed, how far would it travel in h At this speed, how far would it travel in h Distance travelled Speed Time taken At this speed, how long would the taxi take to cover 80 h At this speed, how long would it take to cover 0 At this speed, how long would it take to cover 90 h h Time taken Distance Speed Unit Speed

8 The figure below shows the maximum speed of each car. Car A 8 /h Car B 7 /h Car C 90 /h Car D 89 /h Arrange the cars from the slowest to the fastest. Explain. Read the speed shown on each speedometer /h 0 0 /h 0 0 /h Car X Car Y Car Z a) Which car is travelling the fastest b) Explain the speedometer reading of Car X. c) Car Y travelled at this speed for h. How far did it travel at this speed David s toy robot walked 0 cm in 5 s. What was its speed After ascending, an aeroplane travels a distance of 800 at a speed of 900 /h before descending. Find the time it takes to travel at this speed. We can calculate speed, distance and time using the following: D S T 5 A toy train is moving at 70 cm/s. At this speed, what is the distance it will cover in 5 s AB 6B, p 5 >> Activity 5

9 Average Speed Osman swims 50 m in min. Does Osman swim at the same speed throughout Explain. Osman swims a total of 50 m in min. He swims an average of His average speed is m in min. m/min. Average speed Total distance travelled Total time taken Roderick cycled 7 in h. What was his average cycling speed in /h A remote-controlled car covers 50 m in s. Find its average speed in m/s. 50 Its average speed is m/s. s 50 m s m 6 Unit Speed