Objective

1.1 Concept of Directed Numbers

• Understand the concept of directed numbers intuitively.
• Notice the use of directed numbers in our daily life.

1.2 The Number Line

• Understand the concept of number line and learn the ordering on a number line.

1.3 Operations of Directed Numbers

• Addition and Subtraction of Directed Numbers
• Multiplication and Division of Directed Numbers
• Mixed Operations of Directed Numbers

• Illustrate the addition and subtraction of directed numbers by a number line.
• Explore the rules for multiplication and division of directed numbers.
• Learn mixed operations of directed numbers.

Objective

2.1 Algebraic Language

• Basic Algebraic Knowledge
• Algebraic Expressions

• Introduce the basic concept of Algebra and state the similarities and differences between Algebra and Arithmetic.
• Learn and simplify simple algebraic expressions.
• Learn the conversion between word phrases and algebraic expressions, and understand the advantages of expressing statements in algebraic expressions.

2.2 Method of Substitution and Formulae

• Value of Algebraic Expression and Method of Substitution
•  Formulae

• Find the values of algebraic expressions by the method of substitution.
• Recognize some common formulae and apply the method of substitution to find the unknowns of a formula.

2.3 Algebraic Equations

• Introduction to Algebraic Equations
• Setting up Algebraic Equations to Solve Problems

• Establish the concept of Algebraic Equations.
•Set simple algebraic equations to solve daily life problems.

2.4 Number Patterns

• Introduction to Sequences
• Some Common Sequences

Represent a sequence by an algebraic expression (its general term).

2.5 Basic Concept of Functions

Based on the method of substitution, introduce the basic concept of functions: ‘input – processing - output’.

Objective

3.1 Concept of Positive Integral Indices

• Introduce the three terms 'base', 'index' and 'power'.
• Deduce two laws of positive integral indices

3.2 Monomials

• Understand the meaning of monomials.
• Understand the meaning of coefficients and degrees.

3.3 Polynomials

• Basic Concept of Polynomials
• Like Terms and Unlike Terms
• Polynomials in One Variable
• Value of a Polynomial

• Understand the meaning of polynomials and constant terms.
• Understand the meaning of the degree of a polynomial.
• Understand the meaning of like terms and unlike terms.
• Introduce polynomials in one variable.
• Learn to find the values of polynomials by substitution.

3.4 Addition and Subtraction of Polynomials

• Learn the addition and subtraction of polynomials.

3.5 Multiplication of Polynomials

• Learn the multiplication of polynomials.

Objective

4.1 Simple Linear Equations in One Unknown

• Understand linear equations in one unknown and recall the principle of balance to solve equations.
• Introduce the technique of transposing terms to solve equations.

4.2 More about Solving Equations

• Combining Like Terms
• Cancelling Denominators

 •Introduce two advanced techniques of solving equations in one unknown:
• combining like terms
• cancelling denominators

4.3 Using Equations to Solve Problems

•Set up linear equations in one unknown to solve daily life problems.

4.4 Literal Equations

• Understand the meaning of literal equations.
• Solve simple literal equations.

Objective

5.1 Estimation

• Concept of Estimation
• Reasons for Estimation
• Estimation of π

• Introduce the concept of estimation.
• Know the reasons for estimation.
• Appreciate the contribution of ancient Chinese mathematicians in estimating the value of π.

5.2 Estimation Strategies

• Reformulation Strategy
• Compensation Strategy
• Translation Strategy
• More about Estimation Strategies

• Learn to use different estimation strategies.

Objective

6.1 Meaning of Percentages

• Review the basic concept of percentages.
• Understand the relationship between fractions and percentages, and review the conversions between fractions and percentages as well as decimals and percentages.

6.2 Simple Problems on Percentages

• Finding the Percentage of a Part
• Using Percentage to Find a Part
• Using Percentage to Find the Whole

• Understand the relationship between partial quantities and the whole quantities by using percentages.
• Solve problems involving percentages, including application of equations.

6.3 Percentage Increase and Decrease

• Percentage Increase
• Percentage Decrease

• Learn to express an increase or a decrease by percentages.
• Apply the formula of percentage increase or percentage decrease to solve problems.

6.4 Discount

• Introduce the terms discount, discount per cent, marked price and selling price, and their relationship.
•Learn the skill of solving problems involving discount.

6.5 Profit and Loss

• Profit
• Loss

• Introduce the terms profit, loss, profit per cent and loss per cent, and their relationship.
•Learn the relationship between profit / loss, selling price and cost price.
•Master the skills in solving problems involving profit and loss

Objective

7.4 Plane Figures

• Triangles
• Polygons
• Circles

•Introduce the concept of triangles and their representations.
•Learn the classification of triangles by their sides and angles.
•Understand that the sum of all the interior angles of a triangle is 180°.
•Introduce the concept of polygons and the method of naming.
•Learn the classification of polygons by their angles and sides.
•Introduce the concept of circles.

7.5 Construction of Figures

• Construction of Parallel Lines and Perpendicular Lines
• Construction of Circles and Line Segments
• Construction of Triangles

•Know the tools for drawing geometric figures.
•Investigate how to draw a line parallel or perpendicular to a given line.
•Investigate how to draw circles, copy line segments and draw triangles with given lengths and / or angles.

7.6 Three-Dimensional Figures

• Introduction to Solids
• Polyhedra

•Introduce the two types of solids: polyhedra and non-polyhedra.
•Understand the characteristics of polyhedra and realize different regular polyhedra.

7.7 Cross-sections of Solids

•Introduce the concept of cross-sections of solids.
•Learn to draw the cross-sections of simple solids.
•Distinguish solids with uniform cross-sections.

7.8 2-D Representations of Simple Solids

• Isometric Grid
• Oblique Grid

• Draw 2-D representations of simple solids using oblique grid and isometric grid papers.
•Develop the spatial sense by drawing 2-D representations of solids.

Objective

8.1 Approximate Nature of Measurement

• Realize that all measurements are approximations only.
• Understand the concepts of the lower and the upper limits of actual values, and realize their relationships with measured values and the scale intervals of the measuring tools.

8.2 Measure and Record the Results

• Choosing an Appropriate Measuring Tool
• Choosing an Appropriate Unit for Measurement
• Degree of Accuracy Required

• Learn to choose appropriate measuring tools and units for measurements.
• Decide the degree of accuracy required for measurements.

8.3 Indirect Measurement

• Using Formulae
• Estimation Strategies in
  Measurement

• Use formulae to find the measurements that cannot be measured directly.
• Learn different estimation strategies in measurements, including benchmark strategy and decomposition-recomposition strategy.

8.4 Methods of Reducing Errors in Measurement

• Learn how to reduce errors in measurements.

Objective

9.1 Areas of Simple Polygons

• Learn to use different methods to find the areas of simple polygons.

9.2 Prisms

• Review on Volume
• Volumes of Prisms
• Total Surface Areas of Prisms

• Understand the basic concept of volume.
• Use the formula to calculate the volumes of cuboids.
• Understand that prisms are solids with uniform cross-sections, and learn to use the formula to calculate their volumes.
• Understand the concept of the total surface areas of prisms, and learn to use the formula to do calculations.

9.3 Accumulated Error

• Realize the accumulated errors in the result when measured values are substituted into formulae to calculate another measurement.

Objective

10.1 Symmetry

• Reflection Symmetry
• Rotational Symmetry

• Realize reflectional symmetry in plane figures, and learn to determine the number of axis (axes) of symmetry.
• Realize rotational symmetry in plane figures, and learn to determine the centre of rotation and the order of symmetry.

10.2 Transformation

• Translation
• Rotation
• Reflection
• Enlargement / Reduction

• Realize and understand the concepts of 4 types of transformation, including translation, rotation, reflection and enlargement/reduction.
• Learn to draw the images of figures after transformation.

10.3 Designing Tile Patterns

• Learn to form tiles of different patterns by transformation.

Objective

11.1 Congruence

• Understand the concept of congruent figures.

11.2 Congruent triangles and their Properties

• Recognize the properties of congruent triangles (corresponding angles equal and corresponding sides equal), and apply them to solve problems.

11.3 Conditions for Congruent Triangles

• Recognize the 5 conditions for congruent triangles and apply them to determine whether two triangles are congruent.
• Learn that the shape and size of a triangle can be fixed by any one of the 5 conditions for congruent triangles.

11.4 Similarity

• Understand the concept of similar figures.

11.5 Similar Triangles and their Properties

• Recognize the properties of similar triangles (corresponding angles equal and corresponding sides proportional), and apply them to solve problems.

11.6 Conditions for Similar Triangles

• Recognize the 3 conditions for similar triangles and apply them to determine whether two triangles are similar.

Objective

12.1 Introduction to Ordered Pairs

• Learn the meaning of ordered pair.

12.2 Rectangular Coordinate System

• Learn rectangular coordinate system.
• Learn to represent a point on a rectangular coordinate plane by an ordered pair.

12.3 Distance between Two Points

• Learn to calculate the distance between two points on a vertical or horizontal line on a rectangular coordinate plane.

12.4 Areas of Plane Figures

• Learn to calculate the areas of simple plane figures on a rectangular coordinate plane.

12.5 Transformations of Points on the Coordinate Plane

• Translation
•  Reflection
• Rotation through the Multiples of 90° about the Origin

• Study the images of points on a rectangular coordinate plane after different types of transformations, including:
1. Translation to the left/right, upwards/downwards
2. Reflection of the axes/ lines parallel or perpendicular to the axes
3. Rotation through the multiples of 90° about the origin.

12.6 Polar Coordinate System

• Learn to describe locations of points by another coordinate system.

Objective

13.1 Introduction to Statistics

• Recognize different stages involved in Statistics.

13.2 Collection of Data

• Learn to use different methods to collect data.

13.3 Classification of Data

• Learn to distinguish the two types of data – discrete data and continuous data.

13.4 Organization of Data

• Learn to use the frequency distribution table to organize data.
• Understand the principle in grouping data.

Objective

14.1 Simple Statistical Diagrams

• Bar Charts
•  Broken–Line Graphs
• Pie Charts

• Learn to construct and interpret simple statistical diagrams including bar charts, broken-line graphs and pie charts.

14.2 Stem–and–Leaf Diagrams

• Stem–and–Leaf Diagrams
• Back–to–Back Stem–and–Leaf Diagrams

• Learn to construct stem-and-leaf diagrams and study their properties.
• Learn to compare two data sets using back-to-back stem-and-leaf diagrams.

14.3 Histograms

• Grouping of Continuous Data
• Drawing Histograms

• Realize how to group continuous data, and learn the related terminology.
• Learn to construct histograms and recognize their properties.
• Understand the differences between bar charts and histograms.

14.4 Scatter Diagrams

• Learn to construct scatter diagrams and use them to determine whether two sets of data are related.

14.5 Constructing Statistical Diagrams with Computer Software

• Learn to construct simple statistical diagrams using Microsoft Excel.