Teacher notes and syllabus links

Syllabus bites: Cartesian coordinate system - Syllabus links

Stage 3 Mathematics - Number and Algebra: Patterns and Algebra

The NSW syllabus for the Australian curriculum — Mathematics K-10¹ introduces the Cartesian plane in Stage 3 Number and Algebra, substrand 'Patterns and Algebra '.

The notion of locating position and plotting coordinates is established in the Stage 2 Measurement and Geometry substrand, ‘Position’. It is further developed in Stage 3 to include negative numbers and the use of the four-quadrant number plane. Refer also to Stage 3 Number and Algebra, Whole Numbers 2.

The Cartesian plane is used in algebra in Stages 4 to 6 to describe patterns and relationships between numbers, i.e. relationships between x-values and y-values.

Outcomes

A student:

• describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA3-1WM.
• selects and applies appropriate problem-solving strategies, including the use of digital technologies, in undertaking investigations MA3-2WM.
• gives a valid reason for supporting one possible solution over another MA3-3WM.
• analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane MA3-8NA.

Content

Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

• recognise that the number plane (Cartesian plane) is a visual way of describing location on a grid.
• recognise that the number plane consists of a horizontal axis (x-axis) and a vertical axis (y-axis), creating four quadrants [Literacy] .
  • recognise that the horizontal axis and the vertical axis meet at right angles (Reasoning).
• identify the point of intersection of the two axes as the origin, having coordinates (0, 0) [Literacy].
• plot and label points, given coordinates, in all four quadrants of the number plane [Literacy].
  • plot a sequence of coordinates to create a picture (Communicating) [Literacy].
• identify and record the coordinates of given points in all four quadrants of the number plane.
  • recognise that the order of coordinates is important when locating points on the number plane, eg the point (2, 3) is a location different from (3, 2) (Communicating).

Background

The Cartesian plane (commonly referred to as ‘the number plane’) is named after the French philosopher and mathematician René Descartes (1596–1650), who was one of the first to develop analytical geometry on the number plane. On a number plane, the 'coordinates of a point' refers to an ordered pair (x, y) describing the horizontal position x first, followed by the vertical position y.

The Cartesian plane is applied in real-world contexts, eg when determining the incline (slope) of a road between two points.

The Cartesian plane is used in algebra in Stages 4 to 6 to describe patterns and relationships between numbers.

Language

Students should be able to communicate using the following language:

• axis, axes
• coordinates
• horizontal axis (x-axis)
• intersect
• number plane (Cartesian plane)
• origin
• plot
• point
• point of intersection
• quadrant
• right angles
• vertical axis (y-axis)

Material reproduced from the NSW Education Standards Authority Mathematics K–10 Syllabus.