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Basic Essential Additional Mathematics Skills
Curriculum Development Division
Ministry of Education Malaysia
Putrajaya
2010
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First published 2010
Curriculum Development Division,
Ministry of Education Malaysia
Aras 4-8, Blok E9
Pusat Pentadbiran Kerajaan Persekutuan
62604 Putrajaya
Tel.: 03-88842000 Fax.: 03-88889917
Website: http://www.moe.gov.my/bpk
Copyright reserved. Except for use in a review, the reproduction or utilization of this
work in any form or by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, and recording is forbidden without prior
written permission from the Director of the Curriculum Development Division, Ministry
of Education Malaysia.
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TABLE OF CONTENTS
Preface i
Acknowledgement ii
Introduction iii
Objective iii
Module Layout iii
BEAMS Module:
Unit 1: Negative Numbers
Unit 2: Fractions
Unit 3: Algebraic Expressions and Algebraic Formulae
Unit 4: Linear Equations
Unit 5: Indices
Unit 6: Coordinates and Graphs of Functions
Unit 7: Linear Inequalities
Unit 8: Trigonometry
Panel of Contributors
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ACKNOWLEDGEMENT
The Curriculum Development Division,
Ministry of Education wishes to express our
deepest gratitude and appreciation to all
panel of contributors for their expert
views and opinions, dedication,
and continuous support in
the development of
this module.
ii
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Additional Mathematics is an elective subject taught at the upper secondary level. This
subject demands a higher level of mathematical thinking and skills compared to that required
by the more general Mathematics KBSM. A sound foundation in mathematics is deemed
crucial for pupils not only to be able to grasp important concepts taught in AdditionalMathematics classes, but also in preparing them for tertiary education and life in general.
This Basic Essential Additional Mathematics Skills (BEAMS) Module is one of the
continuous efforts initiated by the Curriculum Development Division, Ministry of Education,
to ensure optimal development of mathematical skills amongst pupils at large. By the
acronym BEAMS itself, it is hoped that this module will serve as a concrete essential
support that will fruitfully diminish mathematics anxiety amongst pupils. Having gone
through the BEAMS Module, it is hoped that fears induced by inadequate basic
mathematical skills will vanish, and pupils will learn mathematics with the due excitement
and enjoyment.
INTRODUCTION
OBJECTIVE
The main objective of this module is to help pupils develop a solid essential mathematics
foundation and hence, be able to apply confidently their mathematical skills, specifically
in school and more significantly in real-life situations.
iii
MODULE LAYOUT
This module encompasses all mathematical skills and knowledge
taught in the lower secondary level and is divided into eight units as
follows:
Unit 1: Negative Numbers
Unit 2: Fractions
Unit 3: Algebraic Expressions and Algebraic Formulae
Unit 4: Linear Equations
Unit 5: Indices
Unit 6: Coordinates and Graphs of Functions
Unit 7: Linear Inequalities
Unit 8: Trigonometry
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Each unit stands alone and can be used as a comprehensive revision of a particular topic.
Most of the units follow as much as possible the following layout:
Module Overview
Objectives
Teaching and Learning StrategiesLesson Notes
Examples
Test Yourself
Answers
The Lesson Notes, Examples and Test Yourself in each unit can be used as
supplementary or reinforcement handouts to help pupils recall and understand the basic
concepts and skills needed in each topic.
Teachers are advised to study the whole unit prior to classroom teaching so as to familiarize
with its content. By completely examining the unit, teachers should be able to select any part
in the unit that best fit the needs of their pupils. It is reminded that each unit in this module is
by no means a complete lesson, rather as a supporting material that should be ingeniously
integrated into the Additional Mathematics teaching and learning processes.
At the outset, this module is aimed at furnishing pupils with the basic mathematics
foundation prior to the learning of Additional Mathematics, however the usage could be
broadened. This module can also be benefited by all pupils, especially those who arepreparing for the Penilaian Menengah Rendah (PMR) Examination.
iv
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Advisors:
Haji Ali bin Ab. Ghani AMN
DirectorCurriculum Development Division
Dr. Lee Boon HuaDeputy Director (Humanities)
Curriculum Development Division
Mohd. Zanal bin Dirin
Deputy Director (Science and Technology)Curriculum Development Division
Editorial Advisor:
Aziz bin SaadPrincipal Assistant Director
(Head of Science and Mathematics Sector)Curriculum Development Division
Editors:
Dr. Rusilawati binti OthmanAssistant Director
(Head of Secondary Mathematics Unit)Curriculum Development Division
Aszunarni binti Ayob
Assistant DirectorCurriculum Development Division
Rosita binti Mat ZainAssistant Director
Curriculum Development Division
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Abdul Rahim bin BujangSM Tun Fatimah, Johor
Ali Akbar bin AsriSM Sains, Labuan
Amrah bin BahariSMK Dato Sheikh Ahmad, Arau, Perlis
Aziyah binti Paimin
SMK Kompleks KLIA, , Negeri Sembilan
Bashirah binti SelemanSMK Sultan Abdul Halim, Jitra, Kedah
Bibi Kismete binti Kabul KhanSMK Jelapang Jaya, Ipoh, Perak
Che Rokiah binti Md. IsaSMK Dato Wan Mohd. Saman, Kedah
Cheong Nyok TaiSMK Perempuan, Kota Kinabalu, Sabah
Ding Hong EngSM Sains Alam Shah, Kuala Lumpur
Esah binti DaudSMK Seri Budiman, Kuala Terengganu
Haspiah binti BasiranSMK Tun Perak, Jasin, Melaka
Hon May WanSMK Tasek Damai, Ipoh, Perak
Horsiah binti AhmadSMK Tun Perak, Jasin, Melaka
Kalaimathi a/p RajagopalSMK Sungai Layar, Sungai Petani, Kedah
Kho Choong Quan
SMK Ulu Kinta, Ipoh, Perak
Lau Choi FongSMK Hulu Klang, Selangor
Loh Peh ChooSMK Bandar Baru Sungai Buloh, Selangor
Mohd. Misbah bin Ramli
SMK Tunku Sulong, Gurun, KedahNoor Aida binti Mohd. ZinSMK Tinggi Kajang, Kajang, Selangor
Noor Ishak bin Mohd. SallehSMK Laksamana, Kota Tinggi, Johor
Noorliah binti AhmatSM Teknik, Kuala Lumpur
Nor Aidah binti JohariSMK Teknik Setapak, Selangor
Writers:
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Layout and Illustration:
Aszunarni binti Ayob Mohd. Lufti bin Mahpudz
Assistant Director Assistant Director Curriculum Development Division Curriculum Development Division
Writers:
Nor Dalina binti IdrisSMK Syed Alwi, Kangar, Perlis
Norizatun binti Abdul SamidSMK Sultan Badlishah, Kulim, Kedah
Pahimi bin Wan SallehMaktab Sultan Ismail, Kelantan
Rauziah binti Mohd. AyobSMK Bandar Baru Salak Tinggi, Selangor
Rohaya binti ShaariSMK Tinggi Bukit Merajam, Pulau Pinang
Roziah binti Hj. ZakariaSMK Taman Inderawasih, Pulau Pinang
Shakiroh binti AwangSM Teknik Tuanku Jaafar, Negeri Sembilan
Sharina binti Mohd. Zulkifli
SMK Agama, Arau, Perlis
Sim Kwang YawSMK Petra, Kuching, Sarawak
Suhaimi bin Mohd. TabieeSMK Datuk Haji Abdul Kadir, Pulau Pinang
Suraiya binti Abdul HalimSMK Pokok Sena, Pulau Pinang
Tan Lee FangSMK Perlis, Perlis
Tempawan binti Abdul AzizSMK Mahsuri, Langkawi, Kedah
Turasima binti MarjukiSMKA Simpang Lima, Selangor
Wan Azlilah binti Wan NawiSMK Putrajaya Presint 9(1), WP Putrajaya
Zainah binti KebiSMK Pandan, Kuantan, Pahang
Zaleha binti Tomijan
SMK Ayer Puteh Dalam, Pendang, Kedah
Zariah binti HassanSMK Dato Onn, Butterworth, Pulau Pinang
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UNIT 1
NEGATIVE NUMBERS
B a s i c E s s e n t i a l
A d d i t i o n a l M a t h e m a t i c s S k i l l s
Curriculum Development Division
Ministry of Education Malaysia
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TABLE OF CONTENTS
Module Overview 1
Part A: Addition and Subtraction of Integers Using Number Lines 2
1.0 Representing Integers on a Number Line 3
2.0 Addition and Subtraction of Positive Integers 3
3.0 Addition and Subtraction of Negative Integers 8
Part B: Addition and Subtraction of Integers Using the Sign Model 15
Part C: Further Practice on Addition and Subtraction of Integers 19
Part D: Addition and Subtraction of Integers Including the Use of Brackets 25
Part E: Multiplication of Integers 33
Part F: Multiplication of Integers Using the Accept-Reject Model 37
Part G: Division of Integers 40
Part H: Division of Integers Using the Accept-Reject Model 44
Part I: Combined Operations Involving Integers 49
Answers 52
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
1
Curriculum Development Division
Ministry of Education Malaysia
MODULE OVERVIEW
1. Negative Numbers is the very basic topic which must be mastered by everypupil.
2. The concept of negative numbers is widely used in many AdditionalMathematics topics, for example:
(a) Functions (b) Quadratic Equations
(c) Quadratic Functions (d) Coordinate Geometry
(e) Differentiation (f) Trigonometry
Thus, pupils must master negative numbers in order to cope with topics inAdditional Mathematics.
3. The aim of this module is to reinforce pupils understanding on the concept ofnegative numbers.
4. This module is designed to enhance the pupils skills in using the concept of number line; using the arithmetic operations involving negative numbers; solving problems involving addition, subtraction, multiplication and
division of negative numbers; and applying the order of operations to solve problems.
5. It is hoped that this module will enhance pupils understanding on negativenumbers using the Sign Model and the Accept-Reject Model.
6. This module consists of nine parts and each part consists of learning objectiveswhich can be taught separately. Teachers may use any parts of the module as
and when it is required.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
2
Curriculum Development Division
Ministry of Education Malaysia
TEACHING AND LEARNING STRATEGIES
The concept of negative numbers can be confusing and difficult for pupils to
grasp. Pupils face difficulty when dealing with operations involving positive and
negative integers.
Strategy:
Teacher should ensure that pupils understand the concept of positive and negative
integers using number lines. Pupils are also expected to be able to performcomputations involving addition and subtraction of integers with the use of the
number line.
PART A:
ADDITION AND SUBTRACTION
OF INTEGERS USING
NUMBER LINES
LEARNING OBJECTIVE
Upon completion of Part A, pupils will be able to perform computationsinvolving combined operations of addition and subtraction of integers using a
number lines.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
3
Curriculum Development Division
Ministry of Education Malaysia
PART A:
ADDITION AND SUBTRACTION OF INTEGERS
USING NUMBER LINES
1.0 Representing Integers on a Number Line
Positive whole numbers, negative numbers and zero are all integers. Integers can be represented on a number line.
Note: i) 3 is the opposite of +3
ii) (2) becomes the opposite of negative 2, that is, positive 2.
2.0 Addition and Subtraction of Positive Integers
3 2 1 0 1 2 3 4
LESSON NOTES
Rules for Adding and Subtracting Positive Integers
When adding a positive integer, you move to the right on anumber line.
When subtracting a positive integer, you move to the lefton a number line.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
Positive integers
may have a plus sign
in front of them,
like +3, or no sign in
front, like 3.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
4
Curriculum Development Division
Ministry of Education Malaysia
(i) 2 + 3
Alternative Method:
EXAMPLES
Adding a positive integer:
Start by drawing an arrow from 0 to 2, and then,
draw an arrow of 3 units to the right:
2 + 3 = 5
5 4 3 2 1 0 1 2 3 4 5 6
Start
with 2
Add a
positive 3
Adding a positive integer:
Start at 2 and move 3 units to the right:
2 + 3 = 5
Make sure you start from
the position of the first
integer.
5 4 3 2 1 0 1 2 3 4 5 6
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
5
Curriculum Development Division
Ministry of Education Malaysia
(ii) 2 + 5
Alternative Method:
Adding a positive integer:
Start by drawing an arrow from 0 to2, and then,draw an arrow of 5 units to the right:
2 + 5 = 3
5 4 3 2 1 0 1 2 3 4 5 6
Add a
positive 5
Make sure you start from
the position of the firstinteger.
5 4 3 2 1 0 1 2 3 4 5 6
Adding a positive integer:
Start at2 and move 5 units to the right:
2 + 5 = 3
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
(iii) 25 =3
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a positive integer:
Start by drawing an arrow from 0 to 2, and then,
draw an arrow of 5 units to the left:
25 =3
Subtract a
positive 5
Subtracting a positive integer:
Start at 2 and move 5 units to the left:
25 =3
5 4 3 2 1 0 1 2 3 4 5 6
Make sure you start from
the position of the first
integer.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
(iv) 32 =5
Alternative Method:
Subtracting a positive integer:
Start by drawing an arrow from 0 to3, and
then, draw an arrow of 2 units to the left:
32 =5
5 4 3 2 1 0 1 2 3 4 5 6
Subtract a
positive 2
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a positive integer:
Start at3 and move 2 units to the left:
32 =5
Make sure you start from
the position of the firstinteger.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
8
Curriculum Development Division
Ministry of Education Malaysia
3.0 Addition and Subtraction of Negative Integers
Consider the following operations:
41 = 3
42 = 2
43 = 1
44 = 0
45 =1
46 =2
Note that subtracting an integer gives the same result as adding its opposite. Adding orsubtracting a negative integer goes in the opposite direction to adding or subtracting a positive
integer.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
4 + (5) =1
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 44 + (6) =2
4 + (1) = 3
4 + (2) = 2
4 + (3) = 1
4 + (4) = 0
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
9
Curriculum Development Division
Ministry of Education Malaysia
Rules for Adding and Subtracting Negative Integers
When adding a negative integer, you move to the left on anumber line.
When subtracting a negative integer, you move to the righton a number line.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
10
Curriculum Development Division
Ministry of Education Malaysia
(i) 2 + (1) =3
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start at2 and move 1 unit to the left:
2 + (1) =3
EXAMPLES
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start by drawing an arrow from 0 to2, and
then, draw an arrow of 1 unit to the left:
2 + (1) =3
Add a
negative 1
Make sure you start from
the position of the first
integer.
This operation of
2 + (1) =3
is the same as
21 =3.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
11
Curriculum Development Division
Ministry of Education Malaysia
(ii) 1 + (3) =2
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start at 1 and move 3 units to the left:
1 + (3) =2
Add a
negative 3
5 4 3 2 1 0 1 2 3 4 5 6
Adding a negative integer:
Start by drawing an arrow from 0 to 1, then, draw an arrow of
3 units to the left:
1 + (3) =2
Make sure you start from
the position of the first
integer.
This operation of
1 + (3) =2
is the same as
13 =2
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
12
Curriculum Development Division
Ministry of Education Malaysia
(iii) 3(3) = 6
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a negative integer:
Start at 3 and move 3 units to the right:
3(3) = 6
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a negative integer:
Start by drawing an arrow from 0 to 3, and
then, draw an arrow of 3 units to the right:
3(3) = 6
Subtract a
negative 3
This operation of
3(3) = 6
is the same as
3 + 3 = 6
Make sure you start from
the position of the first
integer.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
13
Curriculum Development Division
Ministry of Education Malaysia
(iv) 5(8) = 3
Alternative Method:
5 4 3 2 1 0 1 2 3 4 5 6
Subtracting a negative integer:
Start at5 and move 8 units to the right:
5(8) = 3
5 4 3 2 1 0 1 2 3 4 5 6
Subtract a
negative 8
This operation of
5(8) = 3
is the same as
5 + 8 = 3
Subtracting a negative integer:
Start by drawing an arrow from 0 to5, and
then, draw an arrow of 8 units to the right:
5(8) = 3
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
14
Curriculum Development Division
Ministry of Education Malaysia
Solve the following.
1. 2 + 4
2. 3 + (6)
3. 2(4)
4. 35 + (2)
5. 5 + 8 + (5)
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3 4 5 6
TEST YOURSELF A
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
TEACHING AND LEARNING STRATEGIES
This part emphasises the first alternative method which include activities and
mathematical games that can help pupils understand further and master the
operations of positive and negative integers.
Strategy:
Teacher should ensure that pupils are able to perform computations involving
addition and subtraction of integers using the Sign Model.
PART B:
ADDITION AND SUBTRACTION
OF INTEGERS USING
THE SIGN MODEL
LEARNING OBJECTIVE
Upon completion of Part B, pupils will be able to perform computations
involving combined operations of addition and subtraction of integers usingthe Sign Model.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
PART B:
ADDITION AND SUBTRACTION OF INTEGERS
USING THE SIGN MODEL
In order to help pupils have a better understanding of positive and negative integers, we have
designed the Sign Model.
Example 1
What is the value of 35?
NUMBER SIGN
3 + + +
5
WORKINGS
i. Pair up the opposite signs.
ii. The number of the unpaired signs is
the answer.
Answer 2
+ + +
LESSON NOTES
EXAMPLES
The Sign Model
This model uses the + and signs. A positive number is represented by + sign. A negative number is represented by sign.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
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Example 2
What is the value of 53 ?
NUMBER SIGN
3 _ _ _
5
WORKINGS
There is no opposite sign to pair up, sojust count the number of signs.
_ _ _ _ _ _ _ _
Answer 8
Example 3
What is the value of 53 ?
NUMBER SIGN
3
+5 + + + + +
WORKINGS
i. Pair up the opposite signs.
ii. The number ofunpaired signs is the
answer.
Answer 2
_
+ + +
_
+
_
+
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
18
Curriculum Development Division
Ministry of Education Malaysia
Solve the following.
1. 4 + 8 2. 84 3. 127
4. 55 5. 574 6. 7 + 43
7. 4 + 37 8. 62 + 8 9. 3 + 4 + 6
TEST YOURSELF B
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
PART C:
FURTHER PRACTICE ON
ADDITION AND SUBTRACTION
OF INTEGERS
TEACHING AND LEARNING STRATEGIES
This part emphasises addition and subtraction of large positive and negative integers.
Strategy:
Teacher should ensure the pupils are able to perform computation involving addition
and subtraction of large integers.
LEARNING OBJECTIVE
Upon completion of Part C, pupils will be able to perform computationsinvolving addition and subtraction of large integers.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
PART C:
FURTHER PRACTICE ON ADDITION AND SUBTRACTION OF INTEGERS
In Part A and Part B, the method of counting off the answer on a number line and the Sign
Model were used to perform computations involving addition and subtraction ofsmallintegers.
However, these methods are not suitable if we are dealing with large integers. We can use the
following Table Model in order to perform computations involving addition and subtraction
of large integers.
LESSON NOTES
Steps for Adding and Subtracting
Integers
1. Draw a table that has a column for + and a columnfor.
2. Write down all the numbers accordingly in thecolumn.
3. If the operation involves numbers with the samesigns, simply add the numbers and then put the
respective sign in the answer. (Note that we
normally do not put positive sign in front of a
positive number)
4. If the operation involves numbers with differentsigns, always subtract the smaller number from
the larger number and then put the sign of the
larger number in the answer.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
Examples:
i) 34 + 37 =+
34
37
+71
ii) 6520 =+
65 20
+45
iii)
73 + 22 =
+
22 73
51
iv) 228338 =+
228 338
110
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
We can just write the answer as
45 instead of +45.
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.
Add the numbers and then put the
positive sign in the answer.
We can just write the answer as
71 instead of +71.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
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v) 428316 =+
428316
744
vi) 863 127 + 225 =+
225 863
127
225 990
765
vii) 234 675 567 =+
234 675
567
234 1242
1008
Add the numbers and then put the
negative sign in the answer.
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
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viii) 482 + 236 718 =+
236 482
718
236 1200
964
ix) 765 984 + 432 =
+
432 765
984
432 1749
1317
x) 1782 + 436 + 652 =+
436
652
1782
10881782
694
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
Add the two numbers in the
column and bring down the number
in the + column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
Add the two numbers in the +
column and bring down the numberin the column.
Subtract the smaller number from
the larger number in the third row
and put the sign of the larger
number in the answer.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
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Solve the following.
1. 4789 2. 5448 3. 33125
4. 352556 5. 345437456 6. 237 + 564318
7. 431 + 366778 8. 652517 + 887 9. 233 + 408689
TEST YOURSELF C
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
TEACHING AND LEARNING STRATEGIES
This part emphasises the second alternative method which include activities to
enhance pupils understanding and mastery of the addition and subtraction of
integers, including the use of brackets.
Strategy:
Teacher should ensure that pupils understand the concept of addition and subtraction
of integers, including the use of brackets, using the Accept-Reject Model.
PART D:
ADDITION AND SUBTRACTION
OF INTEGERS INCLUDING THE
USE OF BRACKETS
LEARNING OBJECTIVE
Upon completion of Part D, pupils will be able to perform computations
involving combined operations of addition and subtraction of integers, includingthe use of brackets, using the Accept-Reject Model.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
PART D:
ADDITION AND SUBTRACTION OF INTEGERS
INCLUDING THE USE OF BRACKETS
To Accept or To Reject? Answer
+ ( 5 ) Accept +5 +5
( 2 ) Reject +2 2
+ (4) Accept 4 4
(8) Reject 8 +8
LESSON NOTES
The Accept - Reject Model
+ sign means to accept.
sign means to reject.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
27
Curriculum Development Division
Ministry of Education Malaysia
i) 5 + (1) =
Number To Accept or To Reject? Answer
5+ (1)
Accept 5Accept 1
+51
+ + + + +
5 + (1) = 4
We can also solve this question by using the Table Model as follows:
5 + (1) = 51
+
5 1
+4
EXAMPLES
This operation of
5 + (1) = 4
is the same as
51 = 4
Subtract the smaller number fromthe larger number and put the sign
of the larger number in the
answer.
We can just write the answer as 4
instead of +4.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
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Curriculum Development Division
Ministry of Education Malaysia
ii) 6 + (3) =
Number To Accept or To Reject? Answer
6+ (3)
Reject 6Accept3
63
6 + (3) = 9
We can also solve this question by using the Table Model as follows:
6 + (3) =63 =
+
6
3
9
This operation of
6 + (3) =9
is the same as
63 =9
Add the numbers and then put the
negative sign in the answer.
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Basic Essential Additional Mathematics Skills (BEAMS) Module
Unit 1: Negative Numbers
iii) 7(4) =
Number To Accept or To Reject? Answer
7(4)
Reject 7Reject4
7+4
+ + + +
7(4) = 3
We can also solve this question by using the Table Model as follows:
7(4) =7 + 4 =
+
4 7
3
This operation of
7(4) =3
is the same as
7 + 4 =3
Subtract the smaller number from
the larger number and put the sign
of the larger number in the
answer.