Numbers

The pathway

Placement first. Then six levels, mastered in order.

A short placement quiz finds the level where numbers 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

   Place value to millions and confident written and mental computation with all four operations.

   • —Read, write, compare and order large numbers using place value (NESA MA3-RN-01)
   • —Round numbers to the nearest 10, 100, 1 000 and 10 000 and use estimation to check answers
   • —Select and apply mental and written strategies for addition and subtraction (NESA MA3-AR-01)
   • —Multiply and divide by one- and two-digit numbers, interpreting remainders (NESA MA3-MR-01)
   • —Solve multi-step word problems using bar models and number lines

3. Level 2

   Year 6 standard

   Numbers to billions, efficient algorithms and the order of operations, ready for secondary school.

   • —Read, write and order whole numbers to billions
   • —Use efficient written strategies for 2–3 digit multiplication and long division
   • —Apply the order of operations (BODMAS) with brackets
   • —Round to any place value and estimate answers for reasonableness
   • —Justify and explain computation strategies in multi-step investigations

4. Level 3

   Year 7 standard

   Integers, primes, factors and index notation: the number system widens to include negatives and powers.

   • —Identify prime and composite numbers, factors and multiples
   • —Compare, order and calculate with integers (NESA MA4-INT-01)
   • —Apply sign rules when multiplying and dividing integers
   • —Calculate squares and cubes and use index notation
   • —Apply integers in real-life contexts such as temperature and money

5. Level 4

   Year 8 standard

   Fluent integer arithmetic and formal index laws applied to numerical and algebraic expressions.

   • —Perform all four operations with integers in multi-step problems
   • —Operate with positive integer and zero indices of numerical bases (NESA MA4-IND-01)
   • —Apply index rules to simplify expressions
   • —Evaluate complex numerical expressions with nested brackets

6. Level 5

   Year 9 standard

   Index laws extended to powers of powers, with a first introduction to surds and irrational numbers.

   • —Multiply and divide powers and apply powers of powers
   • —Simplify square roots and basic surds
   • —Apply index laws to simplify algebraic expressions
   • —Solve multi-step numerical problems combining integers, fractions and percentages

7. Level 6

   Year 10 standard

   Negative indices and full surd arithmetic, including rationalising denominators, in preparation for Stage 6 algebra.

   • —Apply index laws fluently, including negative indices
   • —Simplify surds and perform operations with them
   • —Rationalise denominators
   • —Apply index and surd skills within algebraic manipulation

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.