Equations

The pathway

Placement first. Then six levels, mastered in order.

A short placement quiz finds the level where equations 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

   Pre-equation reasoning: finding unknowns in number sentences using inverse operations.

   • —Find missing values in number sentences involving the four operations
   • —Check answers using inverse operations

3. Level 2

   Year 6 standard

   Simple unknowns: solving for a pronumeral in one-step number relationships.

   • —Find unknown values in simple equations
   • —Use pronumerals to represent unknowns in number sentences

4. Level 3

   Year 7 standard

   One-step linear equations solved formally with inverse operations and checked by substitution.

   • —Solve one-step linear equations using inverse operations
   • —Check solutions by substitution
   • —Use algebraic techniques to solve simple linear equations (NESA MA4-EQU-01)

5. Level 4

   Year 8 standard

   Equations of increasing complexity, translated from and applied back to word problems.

   • —Solve linear equations of increasing complexity (NESA MA4-EQU-02)
   • —Translate word problems into equations
   • —Solve equations involving fractions
   • —Justify solution methods in multi-step algebraic problems

6. Level 5

   Year 9 standard

   Two-step and fractional equations, with word problems translated into algebra and solved systematically.

   • —Solve one-step and two-step linear equations, including with fractions
   • —Solve linear equations, inequalities and simple quadratic equations (NESA MA5-EQU-01)
   • —Translate real-world problems into equations and justify strategies

7. Level 6

   Year 10 standard

   Multi-step linear equations with variables on both sides, plus quadratic equations via factorising.

   • —Solve multi-step equations with variables on both sides
   • —Solve simple quadratic equations using the zero-product rule
   • —Solve quadratic equations using a variety of techniques (NESA MA5-QUA-01)
   • —Check solutions and communicate reasoning clearly

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.