Algebra

The pathway

Placement first. Then six levels, mastered in order.

A short placement quiz finds the level where algebra 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

   Algebraic thinking without symbols: number patterns and missing-number sentences.

   • —Identify, describe and extend number patterns
   • —Find missing numbers in number sentences using inverse operations

3. Level 2

   Year 6 standard

   First formal algebra: pronumerals to represent unknowns and simple expression work.

   • —Use pronumerals to represent unknown values
   • —Simplify simple algebraic expressions
   • —Find unknown values in simple equations

4. Level 3

   Year 7 standard

   Writing, simplifying and evaluating expressions: translating words into algebra.

   • —Understand variables and constants and write algebraic expressions
   • —Collect like terms to simplify expressions
   • —Evaluate expressions by substitution using the order of operations
   • —Simplify, expand and factorise simple algebraic expressions (NESA MA4-ALG-01)
   • —Translate word problems into algebra

5. Level 4

   Year 8 standard

   Fluent manipulation with multiple variables, negative values and index notation.

   • —Identify terms, coefficients and constants and write expressions from word descriptions
   • —Simplify expressions with multiple variables (NESA MA4-ALG-02)
   • —Substitute positive and negative values into expressions and formulas
   • —Translate real-world situations into algebra

6. Level 5

   Year 9 standard

   Expanding brackets, factorising common factors and working with algebraic fractions and indices.

   • —Expand brackets and factorise using common factors
   • —Simplify complex expressions, including algebraic fractions (NESA MA5-ALG-01)
   • —Apply index laws to algebraic expressions
   • —Explain and justify algebraic reasoning

7. Level 6

   Year 10 standard

   Factorisation techniques including difference of two squares and quadratic trinomials: the gateway to Stage 6.

   • —Factorise using the difference of two squares and simple quadratics
   • —Expand and factorise quadratic expressions
   • —Simplify and substitute into algebraic fractions
   • —Construct clear algebraic reasoning and proof

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.