Graphs

The pathway

Placement first. Then six levels, mastered in order.

A short placement quiz finds the level where graphs 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

   Reading graphs and locating positions: grids, column graphs and line graphs.

   • —Locate and describe position on grids using grid references (NESA MA3-GM-01)
   • —Interpret column graphs and line graphs to identify trends
   • —Draw conclusions and make comparisons using graphs

3. Level 2

   Year 6 standard

   The full coordinate plane: plotting and interpreting points in all four quadrants.

   • —Plot points in all four quadrants of the coordinate plane
   • —Interpret coordinates accurately
   • —Solve simple coordinate geometry problems

4. Level 3

   Year 7 standard

   Patterns towards graphs: plotting points from number patterns and reading real-world graphs.

   • —Plot points on the coordinate plane from tables and patterns
   • —Identify and extend numerical patterns that lead to linear relationships
   • —Read and interpret simple real-world graphs such as travel graphs

5. Level 4

   Year 8 standard

   Linear relationships: tables of values, straight-line graphs and gradient as a rate of change.

   • —Create tables of values and graph straight lines from equations
   • —Create and interpret tables and graphs of linear relationships (NESA MA4-LIN-01)
   • —Calculate gradient as a rate of change and interpret its real-life meaning
   • —Identify trends and relationships in real-world graphs

6. Level 5

   Year 9 standard

   y = mx + b: gradient, y-intercept and graphing linear equations, with a first look at non-linear graphs.

   • —Calculate gradient as rise over run from a graph
   • —Interpret the gradient and y-intercept of y = mx + b and graph linear equations
   • —Recognise simple quadratic patterns and non-linear graphs in real-world examples

7. Level 6

   Year 10 standard

   Linear and quadratic graphs: key features, interpretation and connection to equations.

   • —Graph lines from y = mx + b and interpret gradient and y-intercept
   • —Identify the shape and key features of quadratic graphs, including vertex and intercepts
   • —Interpret the meaning of graph features in modelling contexts

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.