Model Drawing - SAP Education · 02_Model Drawing Upper Pri_2017_TP B&W.pdf 1 22/9/2017 9:37:11 AM SAMPLE. ALL RIGHTS RESERVED ... Wendy had twice as many stamps as Queenie. After

For Upper Primary Levels

Model DrawingSolving Mathematics Problems with Bar Models

Name:

Class:

· Covers 7 core topics from Primary 4 to 6

· More than 140 practice questions

· Full worked solutions with explanatory notes and clearly illustrated model diagrams

Written by:

Teachers fromWalter Education CentreProject Editor:

Alan Tan

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02_Model Drawing Upper Pri_2017_TP B&W.pdf 1 22/9/2017 9:37:11 AM

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www.sapgrp.com

ALL RIGHTS RESERVEDAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publishers.

ISBN-13 978-981-4754-50-7 ISBN-10 981-4754-50-1

Printed in Singapore

Conquer Model Drawing for Upper Primary Levels

New Edition 2018

© Singapore Asia Publishers Pte Ltd teachers@work is an imprint of Singapore Asia Publishers Pte Ltd

Published and Distributed by: Singapore Asia Publishers Pte Ltd219 Henderson Road #10-04 Henderson Industrial Park Singapore 159556 Tel : +65 6276 8280 Fax : +65 6276 8292 Email: [email protected]: www.sapgrp.comFacebook: Singapore-Asia-Publishers

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Printed under licence in Australia by Five Senses Education Pty Ltd

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PrefacePrefaceConquer Model Drawing is a series of two books – Lower Primary and Upper Primary – specially conceived and developed to encapsulate the essence of mathematical modelling and harness students’ cognitive skills to solve word problems. The books cover all topics in the curriculum: Numbers, Measurements, Fractions, Decimals, Ratio, Average, Percentage and Speed.

In Primary Mathematics, applications and modelling are problem solving processes that allow students to connect mathematics learned to the real world, thereby enhancing the understanding of key concepts and methods as well as developing mathematical competencies. Why draw a model?Modelling, in particular, is the process of formulating and improving a mathematical model to solve real-world problems. Through mathematical modelling, students learn to deal with ambiguity, make connections, select and apply appropriate mathematics concepts and skills, identify assumptions and reflect on the solutions, and make informed decisions based on given or collected data. In other words, a student learns to read a problem, assess the known and unknown, draw a model to represent the problem, and in the process, simplify the problem to see a solution. GradedThe topics, and therefore, the questions, are graded for effective progressive learning. Examples appended with clear notes and instructions serve to help students understand the concept behind each model drawing. Exercises are designed to teach the use of these models for problem solving,

Free additional examples and exercises related to particular concepts and topics are also available at onlineresources.sapgrp.com.

SolutionsThe step-by-step solutions provide a comprehensive learning experience for students, enabling them to master the mathematical skill of model drawing.

The Editorial Team

resources availablewww.onlineresources.sapgrp.com

EnhancedLearning resources availablewww.onlineresources.sapgrp.com

EnhancedLearning

Enhanced Learning

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LeveL 4 Unit 1 Whole Numbers – Order of Four Operations (1)............................. 1

LeveL 5 Unit 2 Whole Numbers – Order of Four Operations (2) ............................ 9

LeveL 4 Unit 3 Fractions (1) .................................................................................... 17

LeveL 5 Unit 4 Fractions (2) .................................................................................... 25

LeveL 6 Unit 5 Fractions (3)..................................................................................... 33

LeveL 4 Unit 6 Decimals (1) .................................................................................... 39

LeveL 5 Unit 7 Decimals (2) .................................................................................... 47

LeveL 5 Unit 8 Ratio (1) .......................................................................................... 55

LeveL 6 Unit 9 Ratio (2) ........................................................................................... 63

LeveL 5 Unit 10 Average ........................................................................................... 71

LeveL 5 Unit 11 Percentage (1) ................................................................................. 79

LeveL 6 Unit 12 Percentage (2) .................................................................................. 87

LeveL 6 Unit 13 Speed ............................................................................................... 97

SoLUtionS ...........................................................................................................S1 – S48

ContentsContents

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Conquer Model Drawing for Upper Primary Levels© Singapore Asia Publishers Pte Ltd

Unit 1 Whole Numbers – Order of Four Operations (1)�

Example 1Wendy had twice as many stamps as Queenie. After Queenie used up 30 stamps, Wendy had 6 times as many stamps as Queenie. How many stamps did Wendy have?

Solution:

Wendy

1 unitQueenie

1 unit 1 unit

Before

Wendy 1 u

Queenie

After

1 u 1 u 1 u 1 u 1 u

1 u30 stamps

First, find the number of stamps represented by 1 u:2 u → 30 stamps1 u → ? stamps30 ÷ 2 = 15Since 1 u represents 15 stamps, we find the number of stamps Wendy had:1 u → 15 stamps6 u → ? stamps15 × 6 = 90Wendy had 90 stamps.

LEVEL 4

Whole Numbers – Order of Four Operations (1)1

UnitUnit

Word Problems

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Example 2At first, Kara and Carlo had the same number of stickers. After Kara bought 28 more stickers and Carlo lost 10 stickers, Kara had thrice as many stickers as Carlo. How many stickers did Kara have at first?

Solution:

Kara

1 unitCarlo

1 unit

Before

Kara

Carlo

After

10

28

Kara

Carlo

1 unit 1 unit 1 unit

1 unit

10 + 28

First, find the number of stickers represented by 2 units:10 + 28 = 38Then, find the number of stickers represented by 1 unit:2 units → 38 stickers1 unit → ? stickers38 ÷ 2 = 19Now, find the number of stickers Kara had in the end:1 unit → 19 stickers3 units → ? stickers19 × 3 = 57Lastly, take away the number of stickers she bought:57 – 28 = 29Kara had 29 stickers at first.


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Unit 1 Whole Numbers – Order of Four Operations (1)�Conquer Model Drawing for Upper Primary Levels

© Singapore Asia Publishers Pte Ltd

Solve the following word problems using models.� Sue and Dave had some seeds. If Sue gave away 5900 seeds

and Dave gave away 846 more seeds than Sue, how many seeds did Dave give away?

� Mr Lee sold 15 900 seashells and Mr Tan sold 9145 fewer seashells than Mr Lee. How many seashells did they sell altogether?

Practice Time!Working


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Working


� Christy had 10 890 pieces of coloured paper. If she had 4912 more pieces than Kenny, how many pieces of coloured paper did they have altogether?

� Simon baked 30 179 cakes in January and 8675 more cakes in February than in January. How many cakes did he bake in all?


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Working


� Jolin, Pearlie and Carol made some paper stars. Jolin made 4950 paper stars. Pearlie made 2150 more paper stars than Jolin but 1500 fewer paper stars than Carol. How many paper stars did they make altogether?

6 Susan had 5195 safety pins. She gave 956 safety pins to John and 565 more safety pins to Joshua than to John. How many safety pins did Susan have left?


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Unit 1 Whole Numbers – Order of Four Operations (1)6

Working


7 Fiona has 2110 seashells. Christine has twice as many seashells as Fiona. How many seashells must Christine give to Fiona so that they will have the same number of seashells?

8 Mr Teo and Mr Chan had 25 565 stamps. If Mr Teo gave 3500 stamps to Mr Chan, Mr Chan would have 4 times as many stamps as Mr Teo. How many stamps did Mr Chan have at first?


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9 Paul had 750 pegs. Shaun had twice as many pegs as Paul. Alice had thrice as many pegs as Shaun. Find the number of pegs they had in all.

�0 Carol, Dora and Eve planted 11 753 roses altogether. Carol planted half as many roses as Dora and Eve planted half as many roses as Carol. How many more roses did Dora plant than Eve?


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Working


�� At first, there were same number of boys and girls at a birthday party. During the party, 18 more boys joined in and 9 girls left. There were now four times as many boys as there were girls. How many children were at the party in the end?

�� There are 2468 goldfish in Tank A and 956 fewer goldfish in Tank B than in Tank A. Some goldfish are transferred from Tank A to Tank B and there are now 3 times as many goldfish in Tank B as there are in Tank A. How many goldfish are transferred from Tank A to Tank B?


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S�Conquer Model Drawing for Upper Primary Levels© Singapore Asia Publishers Pte Ltd

Unit 1: Whole Numbers – Order of Four Operations (1)

1.

?

Dave

5900

Sue

846

5900 + 846 = 6746 Dave gave away 6746 seeds.

2.

?

Mr Tan

15 900

Mr Lee

9145

?

First, find the number of seashells Mr Tan sold: 15 900 – 9145 = 6755

Then, find the number of seashells they sold altogether:

MrLee→15900seashells MrTan→6755seashells

15 900 + 6755 = 22 655 They sold 22 655 seashells altogether.

3.

?

Kenny

10 890

Christy

4912

?

First, find the number of pieces of coloured paper Kenny had:

10 890 – 4912 = 5978

Then, find the number of pieces of coloured paper they had altogether:

Christy→10890pieces Kenny→5978pieces

10 890 + 5978 = 16 868 They had 16 868 pieces of coloured paper

altogether.

4.

?

February

30 179

January

?

8675

First, find the number of cakes Simon baked in February:

30 179 + 8675 = 38 854 Then, find the number of cakes Simon baked in

all: January→30179cakes February→38854cakes 30 179 + 38 854 = 69 033 He baked 69 033 cakes in all.

5.

4950

Jolin

?Pearlie

Carol

2150

1500

Jolin→4950paperstars Pearlie→4950+2150=7100paperstars Carol→7100+1500=8600paperstars 4950 + 7100 + 8600 = 20 650 They made 20 650 paper stars altogether.

6.

?

Joshua

956

John

?

565

First, find the number of safety pins Joshua received from Susan:

956 + 565 = 1521 Then, find the total number of safety pins John

and Joshua received from Susan: John→956safetypins Joshua→1521safetypins 956 + 1521 = 2477

Lastly, find the number of safety pins Susan had left after giving away to John and Joshua:

5195 – 2477 = 2718 Susan had 2718 safety pins left.

Unit 1

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Model Drawing - SAP Education · 02_Model Drawing Upper Pri_2017_TP B&W.pdf 1 22/9/2017 9:37:11 AM SAMPLE. ALL RIGHTS RESERVED ... Wendy had twice as many stamps as Queenie. After