Mathematics K–10 - Stage 5 - Variation and rates of change A (Path) | NSW Curriculum

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Variation and rates of change A (Path)

MAO-WM-01
develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly
MA5-RAT-P-01
identifies and solves problems involving direct and inverse variation and their graphical representations (Path: Stn, Adv)

Variation and rates of change A (Path)

Stn (Standard), Adv (Advanced) and Ext (Extension) have been used to suggest paths for related Stage 6 courses.

Identify and describe problems involving direct and inverse variation

Describe typical examples of Loading /Loading
Apply the language of direct variation to everyday contexts: $y$ is directly proportional to $x, y$ is proportional to $x, y$ varies directly as $x$
Identify and represent direct variation/proportion as $y \propto x$ ( $y$ is proportional to $x$ ) or $y = k x,$ where $k$ is the constant of variation
Describe typical examples of Loading
Apply the language of inverse variation to everyday contexts: $y$ is inversely proportional to $x$ , $y$ is proportional to the reciprocal of $x$ , $y$ varies inversely as $x$
Identify and represent inverse variation/proportion as $y \propto \frac{1}{x}$ ( $y$ is inversely proportional to $x$ ) or $y = \frac{k}{x},$ where $k$ is the constant of variation

Identify and describe graphs involving direct and inverse variation

Recognise and describe direct variation from graphs, noting that the graph of $y = k x$ is a straight line passing through the origin, with its gradient $k$ being the constant of variation
Recognise and describe inverse variation from graphs, noting that the graph of $y = \frac{k}{x}$ is a curve

Solve problems involving direct and inverse variation and examine the relationship between graphs and equations corresponding to proportionality

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Life Skills

K–10Mathematics K–10 Syllabus (2022)