Units 1 & 2 (General Linear Modelling and Relations)
Introduce linear equations and their applications in modelling contexts. Emphasis is placed on interpreting and constructing relationships between two variables, solving equations and inequalities, and graphing linear functions. Develop foundational skills in algebraic manipulation, table/graph interpretation, and function-based modelling.

Unit 1: Foundations of Linear Relationships and Modelling

1.1 Understanding Linear Equations

• Structure of Linear Equations: form y = mx + c, meaning of m (gradient) and c (y-intercept)

• Constructing Equations: from context or tables of values

• Identifying Linear Patterns: from graphs, tables, or verbal descriptions

1.2 Solving Linear Equations and Inequalities

• Equation Solving Techniques: balancing method, inverse operations

• Applications: contextual problems involving distance, speed, cost, etc.

• Inequalities: representing solutions graphically and symbolically

1.3 Graphing Linear Functions

• Plotting Using Tables: from x-values to y-values

• Interpreting Slope and Intercept: visual and contextual meaning

• Graphing from Equation: using intercepts, slope, and technology

• Parallel and Perpendicular Lines: identifying and constructing

1.4 Linear Modelling in Context

• Real-world Data: cost models, growth/decline scenarios

• Modelling Process: define variables, build equations, interpret results

• Interpolation and Extrapolation: using graphs for prediction

Unit 2: Exploring Relations and Introduction to Systems

2.1 Relations and Functions

• Definition of a Function: input-output rule, function notation

• Domain and Range: identifying allowable inputs and outputs

• Mapping Diagrams and Tables: understanding relationships visually

2.2 Introduction to Systems of Linear Equations

• Graphical Solutions: point of intersection as solution

• Substitution and Elimination Methods: solving systems algebraically

• Applications: simultaneous modelling (e.g. budgeting, constraints)

2.3 Representing and Analysing Data

• Data Collection and Tables: organizing variable pairs

• Scatter Plots: identifying trends and patterns

• Line of Best Fit: using technology to model linear associations

• Correlation and Causation: recognising limitations of linear models

2.4 Technology Integration and Communication

• Using CAS/Graphing Software: graphing, solving, modelling

• Interpreting Output: understanding graphs and solver screens

• Communicating Reasoning: clearly explaining steps and justifications in context