Lesson Notes
Numbers to 20
Learn to count, compare, and understand numbers from 1 to 20
Basic addition and subtraction
Understanding the basic concepts of addition and subtraction
Numbers to 100
Extending number understanding to 100, including place value
Addition and subtraction (I)
Performing addition of two numbers (at most two digits, possibly with carry)
3-D shapes
Introduction to basic 3D shapes and their properties
2-D shapes
Introduction to basic 2-D shapes and their properties
Money (I)
Recognizing Hong Kong coins and learning to use money in daily life
Length and distance (II)
Recognizing centimetre (cm) as a unit of measurement
Simple Sudoku game
Problem-solving with simple sudoku puzzles
Inquiry and investigation
Discovering and constructing mathematical knowledge through inquiry
Basic division
Introduction to division as sharing and grouping
3-digit numbers
Recognise 3-digit numbers (count, read, write, odd/even)
Addition and subtraction (II)
Perform addition of not more than three numbers (each up to 3 digits, with carry)
4-digit numbers
Recognise 4-digit numbers (count, read, write, odd/even)
Addition and subtraction (III)
Perform subtraction of two numbers (up to 3 digits, with borrowing)
Directions and positions (II)
Recognise the four main directions: east (E), south (S), west (W), north (N)
Inquiry and investigation
Through various activities, discover and construct knowledge; improve ability to inquire, communicate, reason, and conceptualise math concepts
Time-recording and timing devices
Recognise time-recording and timing devices in modern and ancient times
Basic computation
Divisibility tests, prime factorization, GCD/LCM, and mixed operations with integers, fractions, and decimals
Directed numbers
Understanding positive and negative numbers, comparing magnitudes, and performing operations with directed numbers
Approximate values and numerical estimation
Rounding to significant figures, place values, decimal places, and estimation strategies
Rational and irrational numbers
Understanding nth roots, rational/irrational numbers, and operations with quadratic surds
Using percentages
Solving problems involving percentage changes, discount, profit/loss, and compound interest
Rates, ratios and proportions
Understanding and applying rates, ratios, and direct/inverse proportions in real-life contexts
Algebraic expressions
Representing phrases algebraically, working with sequences, and introducing function concepts
Linear equations in one unknown
Formulating and solving linear equations to solve word problems
Linear equations in two unknowns
Graphing linear equations and solving simultaneous equations using various methods
Laws of integral indices
Understanding and applying laws of indices in algebraic expressions and equations
Polynomials
Operations with polynomials including addition, subtraction, multiplication, and division
Identities
Working with algebraic identities and factorization techniques
Formulae
Manipulating and using formulae to solve mathematical and real-life problems
Linear inequalities in one unknown
Solving and representing linear inequalities on number lines
Errors in measurement
Understanding absolute and relative errors in measurements and calculations
Arc lengths and areas of sectors
Calculating arc lengths and areas of sectors using appropriate formulae
3-D figures
Understanding properties of three-dimensional shapes and their representations
Mensuration
Calculating areas, volumes, and surface areas of various geometric shapes
Angles and parallel lines
Properties of angles formed by parallel lines and transversals
Polygons
Properties of polygons including angle sums and regular polygons
Congruent triangles
Understanding and applying conditions for triangle congruence
Similar triangles
Understanding similarity in triangles and applying proportional relationships
Quadrilaterals
Properties of various quadrilaterals including parallelograms, rhombuses, and trapezoids
Centres of triangles
Properties of centers of triangles including centroid, orthocenter, and circumcenter
Pythagoras' theorem
Applications of the Pythagorean theorem in right triangles and coordinate geometry
Rectangular coordinate system
Plotting points, calculating distances, and finding midpoints on coordinate planes
Trigonometry
Introduction to trigonometric ratios and their applications in right triangles
Organisation of data
Methods of data collection and organizing data for statistical analysis
Presentation of data
Creating and interpreting various statistical diagrams and charts
Measures of central tendency
Calculating and interpreting mean, median, and mode from data sets
Probability
Concepts of probability, likelihood, and calculating probabilities of events
Inquiry and investigation
Applying mathematical concepts to solve open-ended problems through investigation
Quadratic equations in one unknown
Solving quadratic equations using various methods
Functions and graphs
Understanding and graphing various functions
Exponential and logarithmic functions
Working with exponential and logarithmic functions and their applications
More about polynomials
Advanced topics in polynomial functions including factor and remainder theorems
More about equations
Solving cubic and other higher-degree equations
Variations
Understanding direct, inverse, and joint variations and their applications
Arithmetic and geometric sequences and their summations
Working with arithmetic and geometric sequences and series
Inequalities and linear programming
Solving systems of inequalities and linear programming problems
More about graphs of functions
Transformations of functions and their graphs
Equations of straight lines
Working with different forms of linear equations and their geometric interpretations
Basic properties of circles
Understanding fundamental properties of circles and related theorems
Loci
Determining and describing loci in the plane
Equations of circles
Working with standard and general forms of circle equations
More about trigonometry
Advanced trigonometric concepts, identities, and applications
Permutations and combinations
Counting techniques using permutations and combinations
More about probability
Advanced probability concepts including conditional probability
Measures of dispersion
Calculating and interpreting variance, standard deviation, and other dispersion measures
Uses and abuses of statistics
Critically evaluating statistical methods and presentations
Further applications
Applying mathematical concepts to real-world problems and scenarios
Inquiry and investigation
Open-ended exploration of mathematical concepts through investigation
Binomial expansion
Expanding binomial expressions using the binomial theorem
Exponential and logarithmic functions
Advanced applications of exponential and logarithmic functions
Derivative of a function
Introduction to differentiation and basic differentiation rules
Differentiation of a function
Techniques for differentiating various types of functions
Second derivative
Understanding and applications of second-order derivatives
Applications of differentiation
Using derivatives for optimization, related rates, and curve sketching
Indefinite integration and its applications
Basic integration techniques and their applications
Definite integration and its applications
Evaluating and applying definite integrals to area problems
Approximation of definite integrals using the trapezoidal rule
Numerical methods for approximating definite integrals
Conditional probability and Bayes' theorem
Advanced probability concepts including Bayes' theorem
Discrete random variables
Understanding and working with discrete random variables
Probability distribution, expectation and variance
Analyzing probability distributions and their properties
The binomial distribution
Understanding and applying the binomial probability distribution
The Poisson distribution
Understanding and applying the Poisson probability distribution
Applications of the binomial and the Poisson distributions
Practical applications of binomial and Poisson distributions
Basic definition and properties of normal distribution
Understanding the normal distribution and its key properties
Standardisation of a normal variable and use of the standard normal table
Working with z-scores and the standard normal distribution
Applications of the normal distribution
Practical applications of the normal distribution in various contexts
Sampling distribution and point estimates
Introduction to sampling distributions and statistical estimation
Confidence interval for a population mean
Constructing and interpreting confidence intervals
Inquiry and investigation
Open-ended exploration of M1 concepts through investigation
Odd and even functions
Understanding and working with odd and even functions
Mathematical induction
Using the principle of mathematical induction for mathematical proofs
The binomial theorem
Advanced applications of the binomial theorem
More about trigonometric functions
Advanced topics in trigonometry including addition formulas
Introduction to e
Understanding the number e and its role in mathematics
Limits
Understanding and calculating limits of functions
Differentiation
Advanced differentiation techniques and applications
Applications of differentiation
Advanced applications of derivatives in optimization and analysis
Indefinite integration and its applications
Advanced integration techniques and applications
Definite integration
Advanced techniques for evaluating definite integrals
Applications of definite integration
Using definite integrals to solve area, volume, and other applied problems
Determinants
Understanding and calculating determinants and their applications
Matrices
Matrix operations and properties for solving systems
Systems of linear equations
Solving systems of linear equations using matrix methods
Introduction to vectors
Vector operations and representations in two and three dimensions
Scalar product and vector product
Understanding and applying dot and cross products of vectors
Applications of vectors
Using vectors to solve geometric and physical problems
Inquiry and investigation
Open-ended exploration of M2 concepts through investigation