Variation and rates of change A (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-RAT-P-01 identifies and solves problems involving direct and inverse variation and their graphical representations (Path: Stn, Adv)Content dot points
Each dot point has its own page with resources matched to it.
Identify and describe problems involving direct and inverse variation
- Describe typical examples of direct variation / proportion 3 resources · 1 interactive/game
- 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∝x (y is proportional to x) or y = kx, where k is the constant of variation 1 resource
- Describe typical examples of inverse (indirect) variation 3 resources · 1 interactive/game
- 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∝1/x (y is inversely proportional to x) or y = k/x,where kis 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 = kx is a straight line passing through the origin, with its gradient k being the constant of variation 2 resources
- Recognise and describe inverse variation from graphs, noting that the graph of y = k/x is a curve 2 resources
Solve problems involving direct and inverse variation and examine the relationship between graphs and equations corresponding to proportionality
- Solve problems involving direct or inverse variation using an equation 6 resources · 1 interactive/game
- Use linear conversion graphs to convert from one unit to another 2 resources
- Graph equations representing direct variation, with or without digital tools 1 resource · 1 interactive/game
Focus area resources
- Unit/PlanningStage 5 Unit 6 – constant rates of change (sample unit of learning)
- Unit/PlanningStage 5 Year 10 – maths in science elective (sample unit of learning)
Stage 5 planning resources
Stage- or course-wide documents (scope and sequences, guides) that cover this focus area alongside others.
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 03)
- Unit/PlanningSample scope and sequence: Stages 4–5 core and selected paths (NESA no. 04)
- Unit/PlanningSample scope and sequence: Stage 5 core and all paths (NESA no. 05)
- Unit/PlanningSample scope and sequence: Stage 5 core (NESA no. 02)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 06)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 01)
- Unit/PlanningSample scope and sequence: Stages 4–5 stage based (NESA no. 08)
- Unit/PlanningStage 5 – sample scope and sequence
- Unit/PlanningStage 5 – stage based – sample scope and sequence