A bridge between the latest mathematicssyllabuses for primary and senior secondary levels

S1 - S3

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Student’s Resources

Coping with Teaching Pace• The length and arrangement of each chapter are designed to cope with the teaching pace

and enhance the interaction among students and teachers.

Catering for Learner Differences• Contents are divided into ‘Foundation Part’ and ‘Non-foundation Part’ according to the

syllabus. The latter are highlighted with blue frames, and for easy

identification.

• A great variety of questions are carefully graded from elementary level to advanced level.

Teaching and Learning with I.T.• Mathematics is introduced in a vivid and vigorous way by making good use of different

software together with new teaching and learning approach.

Warming up for School-based Assessments• To cope with the change in assessing students’ abilities from all aspect through public

examinations as well as school-based assessments in senior secondary level, ‘School-

based Assessment Training Camp’ with selected materials based on junior secondary

mathematics syllabus is provided in every Course Book A, to assist teachers in training

the inquiring, communication and problem-solving skills of students starting as early as

Secondary 1.

• Open-ended questions and questions which cultivate students’ judgment and communication

skills are distributed in different exercises where appropriate.

• Chapter 0 in each Course Book A which introduces thinking skills in problem solving through

simple examples and side notes can help in enhancing students’ problem-solving skills.

Traditional / Loose-leaf Binding• Course Books are available in both traditional binding and loose-leaf binding. For loose-

leaf binding, each chapter is bound as a bundle for easy carrying and to facilitate the

preparation of school-based curriculum.

TextbookNew Arrangement• This series of mathematics textbooks is written in

accordance with the latest mathematics syllabus

(Secondary 1-5) for key stage 3, published by the

Curriculum Development Council in 1999.

• Thorough consideration has been given to the

contents arrangement for the bridge between the new

mathematics syllabuses for pre- and post-key stage 3,

including the Mathematics Curriculum Guide (P1-P6)

which has taken effect since 2002, and the Mathematics

Curriculum and Assessment Guide (Secondary 4-6)

which will take effect in 2009.

Exploratory Approach• Through the activities which motivate students to

explore, to think, to create and establish the abilities

in mathematical reasoning and problem solving, this

series of mathematics textbooks aims at cultivating

students into active learners and knowledge builders

on their own initiative.

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Extension• Questions to facilitate immediate feedback

to students on their understanding of the

knowledge just acquired.

Non-foundation part• Based on the syllabus, textbook contents are divided into

Foundation Part and Non-Foundation Part. Contents of

Non-Foundation Part are highlighted with blue frame,

and . For easy identification in the

table of contents, or are used to indicate part

of the section or the whole one belongs to Non-Foundation

Part respectively.

Learning Objectives• Learning Objectives of each chapter are

clearly listed.

Title Page Question• Interesting comics are used to introduce

topic-related problems, of which the

techniques required in solving these

problems are embodied in each chapter.

Preview• Brief notes to recall students’ memories

of readily acquired knowledge before

learning something new.

Class Activity• Activities to explore new concepts

and techniques through which

students can actively participate in

constructing knowledge.

Now I See• A concise summary to conclude the

concepts and techniques discussed

in the Class Activity.

Example and Classwork• One-to-one Example and Classwork

to consolidate the relevant knowledge

acquired.

Structure and features ofNew Trend Mathematics (Second Edition)

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Revision Exercise• Questions classified under

Level 1, Level 2 and MC

Question to help students in

consolidating the knowledge

acquired.

Exercise• Questions are classified under Level 1 and Level 2 according

to the level of difficulty.

• Open-ended questions without

definite answers are labelled

with .

• Questions which emphasize

judgement and communication

skills are labelled with .

Skills Upgrading Corner• Questions which require more advanced

problem-solving skills to help students

strengthen their abilities in applying

knowledge and skills.

Chapter Summary• A concise summary of the

main points in each chapter.

Check Yourself• Questions to assess students’

understanding of each chapter.

• Some of the question formats in

Territory-wide System Assessment

(TSA) in Mathematics are adopted

here to let students familiarize with

such formats.

Problem-solving and Exploring• Hint for the Title Page Question guides

students to solve the title page questions

step by step.

• Additional Question trains students’

problem-solving skills. Some of them

are daily-life questions which enable

students to experience the practicality of

mathematics.

I.T. Tools• I.T. Tools are provided in the Student’s CD

to assist further exploration of the contents

indicated with .

I.T. Corner• Demonstration to show how to create simple I.T. tools

for learning and exploring mathematical concepts.

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Integrated Exercise• Two Integrated Exercises are provided in

each course book with questions classified

under Level 1, Level 2 and MC Question.

They aim at training students’ ability in

applying the knowledge acquired from

several chapters.

Appreciating Mathematics,Origins of Mathematics andExploration with Fun• Appreciating Mathematics and Origins of

Mathematics let students appreciate the cultural

aspect and aesthetic nature of mathematics.

Exploration with Fun enables students to discover

knowledge through observation and analysis.

Some of them are Enrichment topics which extend

students’ exposure in mathematics.

School-based Assessment Training Camp• Interesting tasks provided in each Course Book A to focus

on the training in the abilities in applying knowledge and

skills, problem-solving skills and communication skills.

Cross-subject Applications• Cross-subject information to facilitate the

use of mathematics as a tool to study

other subjects.

10

11

Revision Cards• Handy cards to include brief notes and

corresponding examples for each topic to let

students do revision anytime, anywhere.

Revision Test• A test to match with each Course Book

and serve as a self-assessment before the

examination of each term.

• Each chapter includes Warm-up Exercise and Build-up

Exercise. To cater for learner differences, Fundamental

Question, Consolidation Question and Challenging Question

are provided in each Build-up Exercise.

• I.T. Activity

• Exercise

• Revision Exercise

Activity Book & CD (I.T.)Student’s Resource PackEach Course Book A is provided with a free Student’s Resource

Pack, which includes:

Fundamental Mathematics (S1)• Revision on some basic topics learned in primary schools.

• Provide a chance to learn some topics which are either

deleted from the latest Mathematics syllabus for primary

schools or turned into Enrichment topics under the syllabus,

but are useful before learning something new in S1.

• A compact resource to serve as a summer holiday exercise

(for P6 to S1) as well as a bridging course in language.

Summer Holiday Exercise (S2 & S3)• Revision on the knowledge acquired in S1 and S2 before

studying new topics in S2 and S3 respectively.

Supplementary Exercise

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• I.T. Tools and Dynamic 3D Figures

• Chapter Summary

• Glossary

• Programs for Calculators

• Diagrams in Appendices

• Graph Paper

• Cabri Software Demo

• Smart Problem Solver introducing some problem-solving

skills with related questions and solutions.

• The system provides a large number of multiple choice questions.

• Students may do the class exercises assigned by teachers or self tests via the system after school. They

may also do the class tests assigned by teachers in the class.

• The system automatically corrects tests/exercises with suggested solutions provided. For any question

answered, chances are given to students to try another question of the similar type for practice.

• The system can effectively cater for learner differences. Questions for students to choose from are

generated according to the level of achievement of each individual student.

• The contents in the system are available in Chinese and English to facilitate bridging between languages.

• Students can login to this system anytime through the internet.

• Activities and Games

• Puzzles

• History

Student’s CD (I.T.) Self-Assessment System –For Students (I.T.)

Online Resources –Student’s Area (I.T.)

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Teacher’s Resources• Teaching Strategy for the Title Page Question

• Suggested Teaching Period

• Section Objective

• Teaching Suggestion

• Teaching Note

• Classification of Questions

• Additional Example and Solution

• Suggested Answer

• Guideline for I.T. Tool

• Guideline for Class Activity

• Highlight of the Related Exercise to the

Example

• Highlight of the contents involving higher-order

thinking skills

• Highlight of the basic competencies of learning

units for Territory-wide System Assessment in

Section Objective and Check Yourself

Textbook – Teacher’s Edition

Chapter 1N

ew Tren

d M

athem

atics1

3

2

4

Excuse me, young man. Can you tell me your dreams?

Excuse me, young man. Can you tell me your dreams?

Excuse me, young lady. Can you tell me your dreams?

Because I want to give accurate injections to my patients.

I want to take part in Hong Kong's Darts Competition when I grow up.

I want to take part in the World's Darts Competition when I grow up.

I want to become a nurse.

Then, whyare you here?

S 1 A

The following figure shows a dartboard with 4 regions. The scores of the respective regions are +5, +2, −1 and −4 as shown. How can Patrick obtain a total score of 0 by throwing 3 darts onto the dartboard? (There may be more than one answer.)

Directed Numbers

Learning Objectives

• understand and apply the concept of negative numbers.• know the concept of the order of numbers on a number line.• handle the operations of directed numbers.

After completing this chapter, you will be able to

(2n

d E

ditio

n)

−4

−1

+2

+5

The following table shows all the possibilities of getting a total of zero mark:

∴ When 3 darts thrown by Patrick hit the regions +5, −1, −4 or +2, +2, −4 or +2, −1, −1, Patrick will get a total of 0 mark.

+5 marks Total

1 0

0 0

0 0

−4 marks

1

1

0

−1 mark

1

0

2

+2 marks

0

2

1

TEACHING STRATEGY FORTHE TITLE PAGE QUESTION• Students should already have the intuitive

experience of cancelling positive and negative numbers against each other.

• Encourage students to use problem-solving strategies introduced in Chapter 0.

• Ask abler students to l ist out all possible combinations.

New Trend Mathematics (2nd Edition) S2A

1.2

[ Basic technique required for this chapter.]

Rounding off

Example: (a) Rounding off 34 to the nearest ten is 30.

(b) Rounding off 7.5 to the nearest integer is 8.

(c) Rounding off 1.629 to 1 decimal place is 1.6.

(d) Rounding off 0.238 4 to 2 decimal places is 0.24.

1.1 Estimation

A What is estimation?In the process of learning mathematics, we are generally asked to findaccurate answers. However, in real-life situations, we sometimes takean approximate value instead due to the absence of measuring tools orother reasons (to be discussed later).

1.1

Aim: To strengthen the awareness of estimation.

7 friends go to Italian Restaurant for their lunch together. The menu is as follows:

Pizza

Spaghetti / Baked riceSoft drink

Fresh orange juice

Large $94/eachMedium $76/each

Small $58/each

$29/dish

$22/jar$8.5/glass

$16.5/glass

Italian RestaurantMenu

No service charge

� i.e. Rounding off to the nearest unit.

❀ TEACHING SUGGESTION ❀• Suggest to use simple examples at the

early stage, and avoid looking for highprecision during estimation.

• To help students apply est imation indai ly l i fe, pract ical examples can bewidely used for illustration.

• Since estimation calls on a set of skillsand mentality, it should be emphasizedi n o t h e r t o p i c s o f m a t h e m a t i c s i fpossible.

( In th is chapter , a l l answers involv ingestimations are provided with exact valuesfor reference.)

Suggested teaching period: 2.0

✵ SECTION OBJECTIVE ✵• To learn that in some cases, conclusions

can be drawn without accurate values.Hence, to appreciate the advantages ofestimation.

• To determine under what circumstancesshould estimation or accurate values beused.

• Involving the basic competency undercode KS3-NA2-1.

✥ GUIDELINE FOR CLASS ACTIVITY ✥• Calculators are not allowed in this Class Activity.

• There should be no restrictions on the estimationstrategies used by students.

• Teachers may ask some students to present theirstrategies used, and the others to point out thepros and cons.

• Either provide students with answers in exactvalues for comparison or ask them to find theexact values themselves.

• After completing the Class Activity, teacher maypoint out that answers of high precision are notnecessary in many real-life situation.

New Trend Mathematics (2nd Edition) S1A

2.16

2B

1. If x = 4 , find the values of the following expressions.

(a) x + 8 (b) 5x (c) 24 ÷ x(d) 30 5− x (e) 3 4( )x + (f) x2 5−

2. If y = −2 , find the values of the following expressions.

(a) 6 − y (b) 4 2y (c) − ÷32 y

(d) ( )3 2+ y (e) ( )( )y y− +1 2 (f) yy

+12

3. Find the value of each of the following expressions by substituting the values given in the brackets [ ]into the expression.

(a) 3 7( )x y+ − [ x = 2 , y = 3]

(b) ( )( )4 3 2 2 3 4x y y x+ + − + [ x = 12

, y = 4 ]

(c) 1

22 2x y+[ x = 2 , y = 3]

4. The following table shows the respective values represented by a to j. Find the values of the followingexpressions.

a b c d e

1 2 3 4 5

f g h

6 7 8

i

9

j

0

Letter

Value

(a) ac bd+ (b) e fh+ (c) i d c( )+ 2

(d) ( )( )d b f c− + (e) ah g2 (f) g h j2 2 2+ +

(g) 2 3 5( )i b b− ÷ (h) f h j( )5 22− (i) ( )a b c d e f ghi+ + + + + ÷

5. In each of the following expressions, determine whether it is an algebraic expression or a formula.

(a) y x= 2 (b) 6 2ab (c) A h= l

(d) E mc= 2 (e) πr h2 (f) 6 3 2− r

6. The length of each side of a square is x cm. If the perimeter of thesquare is S cm, write down the formula for the perimeter of thesquare.

x cm

I

I

I

I

10

12

24

20

11

6

1

8

0

16 16

−5

8

91

122

11

18

5

448

1 920

90

113

118

124

II

III

Formula

Formula

Algebraic expression

Algebraic expression

Formula

Algebraic expression

S x= 4

Classification of questions

I

II

Finding values by substitution

TypeSymbol

Distinguishing between algebraicexpressions and formulae

III

IV

Setting up formulae

Applications of substitution

4.23

Linear Equations in One Unknown 4

[ This is a quiz to remind you of the basic concepts you have learned inthis chapter. Each question tests a concept under the section listed onthe right. Failure in any part of a question indicates a need to do arevision on the section listed. ]

1. (a) x = 7 is / is not a solution of equation 15 2 7− =x .

(b) Solvex3

4 9+ = .

2. Solve the following equations.

(a) − + =6 5 3x x (b) 6 8 14 8x x− = +

3. Solve the following equations.

(a) − − = −2 9 2 6( )x x (b) 7 9 12 2 11( ) ( )x x+ − + = −

4. Solve the following equations.

(a) 122

2 113

− = +x x (b) 2 103

9 5x x− − =

5. Calvin’s marbles is half of Daisy’s. If Daisy gives 14 marbles toCalvin, they will have the same number of marbles. Let Calvin havex marbles originally.

(a) Set up an equation of x.

Equation:

(b) How many marbles does each of them have originally?

4

Solve the following equations. (1 − 4)

1. (a) 3 5 10x x− = (b) − − = +8 9 4 3x x (c) 14 11 15 12− = −x x

2. (a) y y+ = −6 2 5( ) (b) 4 3 5 6 0( ) ( )− − − =y y (c) 2 3 3 2 1 13 0( ) ( )y y+ + − + =

Section

4.1

4.2A

4.2B

4.2C

4.3B

15

−3 −2

6 10

2 −1

2 14 14x x− = +

Daisy: 56, Calvin: 28

−5

16

−1

18

1

−2

§4.2

§4.2

Involving KS3-NA12-2

Involving KS3-NA12-2

Involving KS3-NA12-2

Involving KS3-NA12-2

Involving KS3-NA12-1 and KS3-NA12-2

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9.17

2. (a) Mark the following points on the rectangular coordinate

plane.

X(−3, −4) Y(5, 1) Z(−3, 1)

O

y

x

−1−2−3−4−5

12345

3 4 5 621−1−2−6 −5 −4 −3

Z Y

X

(b) Join the points according to the order X, Y, Z and X.

(c) Find the area of ∆XYZ.

Solution XZ = − −

=

[ ( )]1 4

5

units

units

YZ = − −

=

[ ( )]5 3

8

units

units

The area of ∆XYZ = × ×

=

12

5 8

20

square units

square units

3. The figure shows ∆ABC.y

xO

B (9, 9)

C (4, 0) D

A (−3, 0)

(a) Find the length of AC.

Solution AC = − −

=

[ ( )]4 3

7

units

units

(b) Find the height BD of ∆ABC.

Solution BD = −

=

( )9 0

9

units

units

(c) Find the area of ∆ABC.

Solution The area of ∆ABC = × ×

=

12

7 9

31 5.

square units

square units

Chapter 9 Introduction toCoordinates

• Teaching Note

• Suggested Answer

• Suggested solutions for all the exercises in

Supplementary Exercise

• Teaching Schedule

• Suggested Solution to Question in Textbook

• Ideas for Mathematics Teaching : ‘Problem Solving’,

‘Group Discussion’, ‘Project-based learning’,

‘Information technology based exploration’ and

‘Open-ended questions’ are highlighted in this part.

Suggested assessment rubrics and examples for

each idea are also provided for reference.

• The CD provides a question bank

program under which the multiple

choice and conventional questions in

Question Bank, and the conventional

questions in Supplementary Exercise

can be found.

• Teachers can create new questions

or edit the existing ones through the

program.

• Test papers in printed form can be

generated conveniently.

• Contents of the Student’s CD

• Teaching Schedule (MS Word)

• Example and Additional Example (MS PowerPoint)

• Diagram Bank

• Full Solution to Question in Textbook (MS Word)

• Supplementary Exercise and Solution Guide (MS Word)

• A link to online resources including Teaching Support and

Download Area under Teacher’s Area, Self-Assessment

System and the web site of Chung Tai Educational Press

Teacher’s Reference

Activity Book –Teacher’s Edition

Supplementary Exercise Solution Guide

Question Bank –Printed Copy & CD (I.T.)

Teacher’s CD (I.T.)

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• Teachers may preset class tests in the system through the internet.

• To enhance the diversity of questions in the system, teachers can add their own questions to the system.

• All past records of students can be viewed via the system to help teachers follow up the progress of students easily.

• Different analyses are provided to help teachers get an insight of students’ performance according to chapters in the

Textbook, dimensions or overall syllabus. By knowing the extent of learner differences through the system, teachers may

make appropriate adjustments in teaching.

• Smart Search engine allows teachers to quickly search for student whose performance is above or below average.

• Teachers may add some special classes in the system for abler and less able students to cater for learner differences.

• Teaching Support is an online platform to integrate useful resources

for the preparation of lessons, which includes Experience Sharing

in Teaching, Common Mistakes Made by Students, Extra Teaching

Resources and links to some supporting materials.

• Download Area allows teachers to download our supporting

materials including Supplementary Exercise, Supplementary

Exercise Solution Guide, Teaching Schedule, Full Solution to

Question in Textbook etc.

• Extracts from the latest seminars / workshops and PowerPoint

presentations.

Self-Assessment System – For Teachers (I.T.)

Online Resources –Teacher’s Area (I.T.)

Student’s Resources

Teacher’s Resources

● Textbook ● Activity Book and CD (I.T.)

● Textbook - Teacher’s Edition● Activity Book - Teacher’s Edition

● Student’s Resource Pack Fundamental Mathematics (coming

with Course Book S1A) / Summer Holiday Exercise (coming with Course Books S2A and S3A), Revision Cards and Revision Tests

● Student’s CD (I.T.)● Supplementary Exercise

● Self-Assessment System - For Students (I.T.)

● Online Resources - Student’s Area (I.T.)

● Supplementary Exercise Solution Guide

● Teacher’s Reference

● Question Bank - Printed Copy and CD (I.T.)

● Teacher’s CD (I.T.) ● Self-Assessment System - For Teachers (I.T.)

教師資源中心

A rich variety of resources in this junior secondary mathematics textbooks series aim at:

● Online Resources - Teacher’s Area (I.T.) Teaching Support, Download Area

A rich variety of resources in this junior secondary mathematics textbooks series aim at:● Bridging between the latest mathematics syllabuses

for primary and senior secondary levels● Facilitating school-based curriculum● Supporting school-based assessment● Catering for learner differences● Providing solutions for the transition between

Chinese and English as a medium of instruction S1 - S3