Ratio

The pathway

Placement first. Then six levels, mastered in order.

A short placement quiz finds the level where ratio 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

   Informal proportional thinking: comparing quantities and using 'for every' language ahead of formal ratio work.

   • —Compare quantities using multiplicative language such as 'twice as many' and 'for every'
   • —Use doubling and halving to scale simple quantities

3. Level 2

   Year 6 standard

   Proportional reasoning through fractions of quantities and simple scaling, preparing for formal ratio in Stage 4.

   • —Find a fraction of a quantity and scale quantities up and down
   • —Solve simple 'for every' comparison problems

4. Level 3

   Year 7 standard

   Formal ratio and rate: writing, simplifying and dividing quantities, plus unit rates and speed.

   • —Write and simplify ratios
   • —Divide quantities in a given ratio
   • —Calculate speed and unit rates in real-life applications
   • —Operate with ratios alongside fractions, decimals and percentages (NESA MA4-RAT-01)

5. Level 4

   Year 8 standard

   Multi-step proportional reasoning with ratios and rates across measurement and financial contexts.

   • —Simplify ratios to lowest terms and divide quantities in given ratios
   • —Solve rate problems involving distance, time and speed
   • —Apply proportional reasoning across contexts and justify strategies

6. Level 5

   Year 9 standard

   Rates within formulas: distance–speed–time work with substitution and rearrangement.

   • —Apply the distance, speed and time relationship
   • —Rearrange formulas to solve rate problems
   • —Interpret gradient as a rate of change in context

7. Level 6

   Year 10 standard

   Rates and proportion embedded in modelling: formula manipulation and interpretation of real-world relationships.

   • —Manipulate formulas involving compound rates such as speed
   • —Solve multi-step real-world problems involving proportional relationships
   • —Interpret rates of change within graphs and models

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.