Math Outline (Years 5–12) — Headings Only

Year 5–6 Foundations
- Place value, rounding, estimation
- Integers and number properties (factors, multiples, primes)
- Fractions: equivalence, compare/order, add/subtract
- Decimals: place value, operations, rounding
- Percent basics and simple applications
- Ratios (intro) and rates (intro)
- Measurement: length, area, volume, mass, time
- Perimeter, area of rectangles/triangles (intro)
- Angles: types, measuring, simple constructions
- Coordinates (1st quadrant), simple graphing
- Data: tables, bar charts, line plots
- Probability: simple chance, experimental probability (intro)

Year 7–8 Core
Number & Operations
- Integers, rational numbers, order of operations
- Fractions/decimals/percent conversions
- Ratio, rates, unit rates, proportional reasoning
- Exponents (integer powers), roots (intro), scientific notation (intro)

Algebra
- Algebraic expressions: simplify, expand (distributive law)
- Linear equations (one-variable): solve and check
- Inequalities (one-variable): solve and graph on number line
- Coordinate plane (4 quadrants), graphing basics
- Patterns, sequences (arithmetic), rules
- Introduction to functions: input-output, function notation (informal)

Geometry & Measurement
- Angle relationships: parallel lines, triangles
- Triangles and quadrilaterals: properties and classification
- Congruence and simple constructions
- Perimeter/area of common shapes; volume of prisms (intro)
- Transformations: translation, rotation, reflection, dilation (intro)
- Pythagoras theorem (intro or Year 8)

Data & Probability
- Data displays: histograms, dot plots, box plots (intro)
- Mean/median/mode/range; outliers
- Basic probability rules; sample space

Year 9–10 Advanced Core
Algebra
- Linear functions: slope, intercept, graphing
- Systems of linear equations: solve (graphing/substitution/elimination)
- Linear inequalities: graphing solution regions (intro)
- Polynomials: operations, factoring basics
- Quadratic expressions and equations (intro to standard forms)
- Exponents and exponent laws (deeper), radicals
- Rational expressions (intro), restrictions and simplification

Functions
- Function notation, domain/range (intro)
- Quadratic functions: graphs and key features (vertex, roots)
- Exponential growth/decay (intro)
- Piecewise functions (intro)

Geometry
- Similarity and scale factor
- Pythagoras theorem (applications)
- Trigonometry basics: sine/cosine/tangent in right triangles
- Circles: circumference, area, arcs (intro)
- Coordinate geometry (intro): distance, midpoint (optional)

Statistics & Probability
- Scatterplots, correlation, line of best fit (intro)
- Two-way tables, conditional probability (intro)
- Standard deviation (intro), normal distribution idea (intro)
- Counting basics (permutations/combinations intro)

Year 11–12 Senior / Precalculus / Calculus Prep
Algebra & Functions
- Advanced quadratics and transformations
- Polynomial functions: zeros, factor theorem (intro), graphs
- Exponential and logarithmic functions (intro/standard)
- Trigonometric functions: unit circle, graphs, identities (intro)
- Sequences and series: arithmetic/geometric, sums
- Complex numbers (intro)
- Vectors (2D): magnitude, direction, dot product (intro)

Calculus (Intro)
- Limits concept (informal)
- Differentiation: derivative as rate of change, basic rules
- Applications of derivatives: tangent, optimization (intro)
- Integration: area under curve (informal), basic antiderivatives (intro)
- Applications of integrals (intro)

Advanced Statistics (Intro)
- Sampling and study design
- Confidence intervals (conceptual)
- Hypothesis testing (conceptual)
- Regression (deeper), residuals

Optional Extensions
- Discrete mathematics: logic, sets, graphs (intro)
- Financial mathematics: compound interest, annuities (intro)
- Matrices (intro)
