A student:

• selects appropriate notations and conventions to communicate mathematical ideas and solutions MA5.2-1WM³

• interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems MA5.2-2WM⁴

• recognises direct and indirect proportion, and solves problems involving direct proportion MA5.2-5NA⁵

Students:

• solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208²)

This series addresses the following dot points. The dots point(s) addressed in this Syllabus bite are shown in bold.

• convert between units for rates, eg kilometres per hour to metres per second

• identify and describe everyday examples of direct proportion, eg as the number of hours worked increases, earnings also increase

• identify and describe everyday examples of inverse (indirect) proportion, eg as speed increases, the time taken to travel a particular distance decreases

• recognise direct and inverse proportion from graphs

  • distinguish between positive and negative gradients when using a graph (Reasoning)

• interpret and use conversion graphs to convert from one unit to another, eg conversions between different currencies or metric and imperial measures

• use the equation y=kx to model direct linear proportion where k is the constant of proportionality

  • given the constant of proportionality, establish an equation and use it to find an unknown quantity (Communicating, Problem Solving)

  • calculate the constant of proportionality, given appropriate information, and use this to find unknown quantities (Problem Solving)

• use graphing software or a table of values to graph equations representing linear direct proportion

This series addresses all five Working Mathematically components.

• Fluency: Students practice simplifying ratios, finding equivalent ratios, calculating constants of proportionality and drawing graphs to represent relationships.

• Understanding: Students explore examples of direct proportionality and inverse proportionality to enhance their understanding of these types of relationships.

• Reasoning: Students deduce the equations of direct and inverse proportionality and the relationship between the gradient and the constant of proportionality.

• Problem Solving: Students explore and compare a variety of methods of solution, including visual methods.

• Communicating: Students use diagrams and mathematical language to explain methods of solution.

Each resource includes an initial activity, supporting students who require revision of key concepts. Each resource also includes a bonus activity containing material that can extend suitable students.