Mathematics Curriculum Model: New Zealand (Years 3–13)

Years 3–10 (Primary to Lower Secondary)

Year 3 (Age 7–8) - Level 2

Key Concepts & Topics: Place value to 1,000, addition & subtraction, simple multiplication, skip counting, time (to quarter hours), basic fractions (halves, quarters), measurement, 2D/3D shapes, data display (bar graphs).

Core Skills Developed: Number sense, estimating, grouping, pattern recognition, basic geometry.

Year 4 (Age 8–9) - Level 2–3

Key Concepts & Topics: Multiplication & division facts (×2, ×5, ×10), perimeter & area (rectangles), angles (right angle), simple fractions (⅓, ⅕), reading scales, interpreting simple graphs.

Core Skills Developed: Problem solving with all four operations, spatial reasoning, unit conversion (cm–m).

Year 5 (Age 9–10) - Level 3

Key Concepts & Topics: Place value to 10,000, fractions & decimals, order of operations (intro), perimeter/area/volume, angles (acute/obtuse), symmetry, chance & probability, basic algebraic patterns.

Core Skills Developed: Applying strategies for multiplication/division, understanding decimals, and interpreting data.

Year 6 (Age 10–11) - Level 3–4

Key Concepts & Topics: Operations with decimals, improper fractions & mixed numbers, percentages, coordinate grids, transformations (translation/reflection/rotation), more complex word problems.

Core Skills Developed: Using ratios, converting units, understanding probability, drawing & measuring angles.

Year 7 (Age 11–12) - Level 4

Key Concepts & Topics: Multiples, factors, primes, algebraic expressions, negative numbers, volume, surface area, intro to statistics (mean/median/mode), sample space, intro to graphs.

Core Skills Developed: Algebraic thinking, representing problems symbolically, using statistical data.

Year 8 (Age 12–13) - Level 4–5

Key Concepts & Topics: Equations (1-step & 2-step), Pythagoras (intro), expanding & factorising, percentages increase/decrease, compound shapes, Cartesian plane, real-life statistics.

Core Skills Developed: Algebra fluency, solving multistep problems, understanding distributions.

Year 9 (Age 13–14) - Level 5

Key Concepts & Topics: Linear equations, geometry (parallel lines, angle rules), powers & roots, more advanced statistics (box plots, dot plots), probability trees, scale & maps.

Core Skills Developed: Constructing equations, visualising data trends, analysing statistical results.

Year 10 (Age 14–15) - Level 5–6

Key Concepts & Topics: Quadratic expressions (intro), trigonometry basics, linear graphs, algebraic fractions, scientific notation, simultaneous equations (substitution), probability experiments.

Core Skills Developed: Applying abstract reasoning, solving systems of equations, statistical reliability.

Years 11–13 (NCEA Levels 1–3)

Year 11 (Age 15–16) - NCEA Level 1

Topics: Number & algebra, linear & quadratic equations, coordinate geometry, trigonometry, chance & data, measurement & geometry.

Focus Areas: External: Algebra & Graphs; Internal: Statistical investigation, Number, Measurement.

Year 12 (Age 16–17) - NCEA Level 2

Topics: Sequences & series, non-linear graphs, networks, probability distributions, calculus (intro), matrices, trigonometry (unit circle).

Focus Areas: External: Algebra & Calculus; Internal: Probability, Statistics, Geometry.

Year 13 (Age 17–18) - NCEA Level 3

Topics: Differentiation & integration, complex numbers, statistical inference, linear programming, conic sections, advanced probability & statistical models.

Focus Areas: Options: Calculus, Statistics, Mathematics with Calculus, Mathematics with Statistics. University preparation.