Syllabus links
Stage 5 Mathematics Number and Algebra: Ratios and Rates
The Board of Studies NSW Syllabus for the Australian Curriculum in Mathematics K10 prescribes the study of relationships involving direct and indirect proportion in Stage 5 Number and Algebra, substrand Ratios and Rates.
A student:

selects appropriate notations and conventions to communicate mathematical ideas and solutions MA5.21WM

interprets mathematical or reallife situations, systematically applying appropriate strategies to solve problems MA5.22WM

recognises direct and indirect proportion, and solves problems involving direct proportion MA5.25NA
Students:

solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
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.