Maths Course

Lesson 1 • Working with Fractions

Develops skills in simplifying, comparing, and computing with fractions. Connects fraction concepts to division and ratio reasoning.

Lesson 2 • Understanding the Number System

Covers integers, rational numbers, and real numbers on the number line. Establishes the numeric vocabulary used throughout the course.

Lesson 3 • Decimals and Percentages

Converts between decimals, fractions, and percentages and applies them to real-world problems. Reinforces place-value understanding from earlier sections.

Lesson 4 • Factors, Multiples, and Primes

Explores divisibility, prime factorisation, GCF, and LCM. Supports fraction work and prepares students for algebraic factorising.

Lesson 1 • Percentage as Proportional Reasoning

Reframes percentage problems as proportions to unify solution strategies. Extends percentage skills from Chapter 1 into flexible problem-solving.

Lesson 2 • Proportions and Cross-Multiplication

Sets up and solves proportions using cross-multiplication and unit analysis. Directly extends ratio skills to equation solving.

Lesson 3 • Unit Rates and Unit Pricing

Calculates unit rates and applies them to cost, speed, and efficiency comparisons. Bridges arithmetic fluency to practical decision-making.

Lesson 4 • Introduction to Ratios

Defines ratios and part-to-part vs. part-to-whole comparisons. Grounds proportional thinking in concrete, visual examples.

Lesson 1 • Multi-Step and Literal Equations

Solves equations with variables on both sides and rearranges formulas. Prepares students for applied formula manipulation in later chapters.

Lesson 2 • Variables and Algebraic Expressions

Introduces variables, constants, and expression structure. Builds the symbolic language required for all algebraic work ahead.

Lesson 3 • Word Problems and Algebraic Modelling

Translates verbal scenarios into equations and solves them systematically. Integrates arithmetic, ratio, and equation skills in applied contexts.

Lesson 4 • Solving One-Step and Two-Step Equations

Applies inverse operations to isolate variables in linear equations. Establishes the core equation-solving routine used throughout algebra.

Lesson 1 • Slope-Intercept and Standard Forms

Writes and interprets linear equations in slope-intercept and standard form. Enables flexible equation manipulation for graphing and analysis.

Lesson 2 • The Coordinate Plane

Reviews quadrants, ordered pairs, and plotting points. Provides the graphical foundation for all function work in this chapter.

Lesson 3 • Slope and Rate of Change

Defines slope as rise over run and connects it to rate of change. Links proportional reasoning from Chapter 2 to graphical analysis.

Lesson 4 • Interpreting and Applying Linear Models

Uses linear equations to model data trends and make predictions. Connects graphical and algebraic representations to real-world scenarios.

Lesson 1 • Systems of Inequalities

Graphs systems of linear inequalities and identifies feasible regions. Extends inequality skills from Chapter 3 to two-variable contexts.

Lesson 2 • Elimination Method

Adds or subtracts equations to eliminate a variable and solve the system. Provides an efficient alternative to substitution for complex systems.

Lesson 3 • Applied Systems Problems

Models mixture, rate, and break-even scenarios with systems of equations. Integrates all solution methods in realistic, multi-step problem contexts.

Lesson 4 • Graphical Method for Systems

Solves systems by graphing two lines and identifying intersection points. Builds visual intuition for what a system solution represents.

Lesson 1 • Circles: Circumference and Area

Introduces pi and applies it to circumference and area calculations. Extends plane-figure measurement to curved shapes.

Lesson 2 • Perimeter and Area of Plane Figures

Derives and applies formulas for perimeter and area of common 2D shapes. Connects measurement to real-world design and planning tasks.

Lesson 3 • Geometric Reasoning and Proof

Introduces deductive reasoning, congruence, and similarity proofs. Develops logical argumentation skills that support advanced mathematical thinking.

Lesson 4 • Surface Area and Volume of Solids

Calculates surface area and volume for prisms, cylinders, pyramids, cones, and spheres. Builds three-dimensional spatial reasoning from 2D area skills.

Lesson 1 • Applications of Quadratic Models

Models projectile motion, area optimisation, and revenue problems with quadratics. Applies all quadratic skills to realistic, multi-step scenarios.

Lesson 2 • Introduction to Polynomials

Defines degree, leading coefficient, and standard form of polynomials. Extends algebraic expression skills from Chapter 3 to higher-degree terms.

Lesson 3 • Factorising Polynomials

Applies GCF, trinomial, and special-product factorising techniques. Provides the algebraic tools needed to solve quadratic equations by factorising.

Lesson 4 • Graphing Quadratic Functions

Identifies vertex, axis of symmetry, and intercepts of parabolas. Connects algebraic form to graphical behaviour of quadratic functions.

Lesson 1 • Data Visualisation

Constructs and interprets histograms, box plots, and scatter plots. Connects numerical summaries to visual representations for clearer communication.

Lesson 2 • Inferential Reasoning and Data Interpretation

Introduces sampling, bias, and basic inference from data. Develops critical thinking about data quality and the validity of conclusions.

Lesson 3 • Fundamentals of Probability

Defines probability, sample spaces, and basic probability rules. Establishes the theoretical framework for all probability calculations.

Lesson 4 • Compound Events and Counting

Applies multiplication rules, permutations, and combinations to count outcomes. Extends basic probability to multi-stage and combinatorial scenarios.