1. Number Systems and Properties
- Integers and rational numbers
- Fractions, decimals, and percentages
- Absolute value and opposites
- Number lines and distance on the number line
- Prime factorization
- Factors, multiples, GCD, and LCM
- Powers and exponents
- Powers of 10 and scientific notation
- Square roots and irrational numbers at an introductory level
- Estimation, approximation, and reasonableness checks
- Order of operations and efficient calculation strategies

2. Ratio, Proportion, and Percent Applications
- Ratios: part-part and part-whole relationships
- Equivalent ratios
- Unit rate and unit price
- Proportional relationships in tables, graphs, and equations
- Scale drawings and scale factors
- Percent of a quantity
- Percent increase and decrease
- Percentage change
- Discounts, markups, tax, profit/loss, and simple interest at an introductory level
- Multi-step proportional reasoning problems
- Proportional reasoning in measurement and real-life contexts

3. Expressions, Equations, and Inequalities
- Variables and algebraic notation
- Writing expressions from words and contexts
- Evaluating expressions by substitution
- Simplifying algebraic expressions
- Distributive property and combining like terms
- Expanding and factorizing simple expressions at an introductory level
- One-step, two-step, and multi-step linear equations
- Equations with brackets or variables on both sides
- Equations from word problems
- Inequalities and solution sets
- Representing inequalities on number lines
- Simple simultaneous linear equations at an introductory level
- True/false statements and algebraic validity

4. Functions and Sequences
- Input-output rules and function tables
- Function notation at an introductory level
- Linear relationships
- Simple non-linear patterns
- Arithmetic sequences
- Geometric sequences at an introductory level
- Term-to-term rules and nth-term rules
- Tables, graphs, and rules for relationships
- Slope/rate of change at an introductory level
- Intercepts and starting values in context
- Comparing functions from tables, graphs, equations, and descriptions
- Graph interpretation: increasing, decreasing, trends, and limitations

5. Geometry and Coordinate Reasoning
- Angle relationships involving lines, triangles, quadrilaterals, and polygons
- Parallel lines cut by a transversal
- Properties of triangles and quadrilaterals
- Congruence and similarity at an introductory level
- Perimeter and area of triangles, parallelograms, trapezia, circles, and composite figures
- Volume and surface area of prisms, cylinders, and simple solids
- Nets and 3D reasoning
- Coordinate plane in all four quadrants
- Distance, midpoint, and gradient/slope at an introductory level
- Coordinate geometry in diagrams and real-life contexts
- Scale factor effects on perimeter, area, and volume

6. Transformations, Symmetry, and Spatial Reasoning
- Translations, reflections, rotations, and enlargements
- Describing transformations on grids and coordinate planes
- Line symmetry and rotational symmetry
- Congruence through transformations
- Tessellations and geometric patterns
- Orientation and movement on grids
- Combining and decomposing shapes
- Folding, nets, and 3D visualization
- Shape analogies and spatial puzzles
- Visual pattern investigations

7. Pythagoras and Introductory Trigonometric Reasoning
- Right triangles and geometric relationships
- Pythagorean theorem and its applications
- Finding missing side lengths in right triangles
- Distance in coordinate grids using right-triangle reasoning
- Real-life problems involving right triangles
- Introductory trigonometric ratios where appropriate: sine, cosine, and tangent
- Angle of elevation and angle of depression at an introductory level
- Choosing efficient methods for right-triangle problems

8. Data Analysis, Statistics, and Probability
- Data collection, sampling, and bias at an introductory level
- Tables, bar graphs, line graphs, histograms, box plots, and scatter plots at an introductory level
- Mean, median, mode, and range
- Variability and spread at an introductory level
- Comparing distributions
- Outliers
- Misleading graphs and incomplete information
- Probability language and simple probability calculations
- Experimental and theoretical probability
- Simple compound probability and independent events
- Tree diagrams and outcome tables at an introductory level
- Evaluating claims from data

9. Logical Reasoning and Problem Solving
- Multi-step logic puzzles
- Reasoning from clues and constraints
- Classification and odd-one-out problems
- Always/sometimes/never reasoning
- Counterexamples at an introductory level
- Deductive and inductive reasoning
- Error analysis and correcting flawed reasoning
- Elimination strategies
- Working backwards
- Case testing and systematic listing
- Number, algebra, geometry, and probability puzzles
- Non-routine olympiad-style problems

10. Mathematical Modelling and Real-World Applications
- Multi-step problem solving in real-life contexts
- Modelling with equations, inequalities, tables, diagrams, and graphs
- Speed, distance, time, and unit-rate contexts
- Budgeting, discounts, tax, profit/loss, and simple interest
- Maps, scale drawings, recipes, timetables, and measurement contexts
- Interpreting constraints and making decisions
- Estimation, bounds, and reasonableness checks
- Comparing options and evaluating solutions
- Designing or analyzing simple plans, games, or systems
- Real-world data and graph interpretation