Geometry

The pathway

Placement first. Then six levels, mastered in order.

A short placement quiz finds the level where geometry genuinely starts for your child. From there, each level ends in a mastery quiz, passed before the next level opens.

1. Placement quiz

   Finds the starting level. No assumptions from age or school year.

2. Level 1

   Year 5 standard

   Classifying 2D shapes, measuring angles, and first formulas for area and volume.

   • —Classify triangles and quadrilaterals by their properties (NESA MA3-2DS-01)
   • —Identify and measure acute, obtuse, right and straight angles with a protractor
   • —Calculate the area of rectangles and composite shapes using decomposition
   • —Find the volume of rectangular prisms using unit cubes and the formula
   • —Identify nets, faces, edges and vertices of 3D objects

3. Level 2

   Year 6 standard

   Angle relationships, metric conversions, and area and volume formulas applied with confidence.

   • —Understand angle relationships and calculate unknown angles
   • —Calculate the perimeter and area of rectangles and triangles (NESA MA3-2DS-02)
   • —Calculate the volume of rectangular prisms
   • —Construct and interpret nets and cross-sections of 3D objects (NESA MA3-3DS-01)
   • —Convert between metric units of length, mass and capacity

4. Level 3

   Year 7 standard

   Angle reasoning: angles on a line, around a point, and the angle sum properties of triangles and quadrilaterals.

   • —Identify adjacent and vertically opposite angles and calculate angles on a line and around a point (NESA MA4-ANG-01)
   • —Apply angle sum properties of triangles and quadrilaterals
   • —Calculate perimeter and area of rectangles, triangles and composite shapes (NESA MA4-ARE-01)
   • —Solve problems using geometric properties and justify solutions

5. Level 4

   Year 8 standard

   Parallel lines, formal angle relationships and a first meeting with Pythagoras' theorem.

   • —Identify corresponding and alternate angles formed by parallel lines and transversals
   • —Apply properties of parallelograms, rectangles and rhombi to solve problems
   • —Apply Pythagoras' theorem to right-angled triangles (NESA MA4-PYT-01)
   • —Calculate the area of triangles and parallelograms and the volume of prisms (NESA MA4-VOL-01)

6. Level 5

   Year 9 standard

   Congruence, formal reasoning, Pythagoras in context, and the introduction of trigonometric ratios.

   • —Prove triangle relationships using congruency and angle properties
   • —Solve for unknown sides using Pythagoras' theorem in context
   • —Apply sine, cosine and tangent ratios to right-angled triangles (NESA MA5-TRG-01)
   • —Solve problems involving angles of elevation and depression
   • —Calculate the surface area and volume of prisms and cylinders

7. Level 6

   Year 10 standard

   Geometric proof and extended trigonometry: congruency tests, formal reasoning and multi-step applications.

   • —Apply congruency tests and construct geometric proofs for triangles and quadrilaterals
   • —Apply Pythagoras' theorem and trigonometric ratios in multi-step word problems
   • —Apply trigonometry to problems involving angles of elevation and depression (NESA MA5-TRG-02)
   • —Calculate volume and surface area of prisms and cylinders with algebraic expressions in formulas

All topics and levels are aligned to the NSW Mathematics K–10 Syllabus (NESA). Level 1 corresponds to the Year 5 standard and Level 6 to the Year 10 standard, spanning Stages 3 to 5 of the NSW curriculum.