selects appropriate notations and conventions to communicate mathematical ideas and solutions
interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems
recognises direct and indirect proportion, and solves problems involving direct proportion
- Solve problems involving direct proportion; explore the relationship between graphs and equations corresponding to simple rate problems (ACMNA208)
- 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
When describing everyday examples involving proportion, teachers should model common words and language structures before independent work is required, eg 'As the speed increases, the time taken to travel a particular distance decreases', 'The greater the speed, the less time is taken to travel a particular distance', 'The time taken to travel a particular distance is reduced when the speed is increased'.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA5.2-5NA the sub-elements (and levels) of Number patterns and algebraic thinking (NPA7) and Comparing units (CoU3) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.
The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.