Linear relationships A
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-LIN-C-01 determines the midpoint, gradient and length of an interval, and graphs linear relationships, with and without digital toolsContent dot points
Each dot point has its own page with resources matched to it.
Find the midpoint and gradient of a line segment (interval) on the Cartesian plane
- Plot and join 2 points to form an interval on the Cartesian plane and use the interval as the hypotenuse of a right-angled triangle 2 resources · 2 interactive/game
- Apply the relationship gradient m = (rise)/(run) to find the gradient/slope of the interval joining the 2 points 6 resources · 1 interactive/game
- Distinguish between intervals with positive and negative gradients from a diagram 3 resources · 3 interactive/game
- Explain why horizontal intervals have a gradient of 0 and vertical intervals have undefined gradients using the gradient relationship 2 resources · 2 interactive/game
- Determine the midpoint of horizontal and vertical intervals on the Cartesian plane
- Apply the process for calculating the mean to find the midpoint, M of the interval joining 2 points on the Cartesian plane 3 resources · 1 interactive/game
- Use graphing applications to find the midpoint and gradient/slope of an interval 2 resources · 2 interactive/game
Find the distance between 2 points located on the Cartesian plane
- Use the interval between 2 points as the hypotenuse of a right-angled triangle on the Cartesian plane and apply Pythagoras’ theorem to determine the length of the interval joining the 2 points 3 resources · 1 interactive/game
- Use graphing applications to find the distance between 2 points on the Cartesian plane 2 resources · 2 interactive/game
Recognise and graph equations
- Recognise that equations of the form y = mx + c represent linear relationships or straight lines
- Construct tables of values and use coordinates to graph a variety of linear relationships on the Cartesian plane, with and without digital tools 2 resources
- Identify the x- and y- intercepts of lines
- Determine whether a point lies on a line using substitution
Examine parallel, horizontal and vertical lines
- Explain that parallel lines have equal gradients/slopes 4 resources · 1 interactive/game
- Explain why the x-axis has the equation y = 0 and the y-axis has the equation x = 0
- Recognise y = c as a line parallel to the x-axis and x = k as a line parallel to the y-axis 3 resources
- Graph vertical and horizontal lines 5 resources · 2 interactive/game
Focus area resources
- Unit/PlanningStage 5 Unit 2 – working with triangles (sample unit of learning)
- Unit/PlanningStage 5 Unit 6 – constant rates of change (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