Syllabus links

Stage 4 Mathematics Number and Algebra: Linear Relationships

The Board of Studies NSW Syllabus for the Australian Curriculum in Mathematics K-10 prescribes the study of the effects of transformations on coordinates of points in Stage 4 Number and Algebra, substrand Linear Relationships.

Outcomes

A student:

• communicates and connects mathematical ideas using appropriate terminology, diagrams and symbols MA4-1WM
• recognises and explains mathematical relationships using reasoning MA4-3WM
• creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane MA4-11NA

Content

Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates (ACMMG181).

This series addresses the following dot points. The dot points addressed in this Syllabus BITE are shown in bold.

• use the notation P' to name the 'image' resulting from a transformation of a point P on the Cartesian plane
• plot and determine the coordinates for P' resulting from translating P one or more times
• plot and determine the coordinates for P' resulting from reflecting P in either the x- or y-axis
  • investigate and describe the relationship between the coordinates of P and P' following a reflection in the x- or y-axis, e.g. if P is reflected in the x-axis, P' has the same x-coordinate, and its y-coordinate has the same magnitude but opposite sign
  • recognise that a translation can produce the same result as a single reflection and vice versa
• plot and determine the coordinates for P' resulting from rotating P by a multiple of 90° about the origin
  • investigate and describe the relationship between the coordinates of P and P' following a rotation of 180° about the origin, e.g. if P is rotated 180° about the origin, the x- and y coordinates of P' have the same magnitude but are opposite in sign
  • recognise that a combination of translations and/or reflections can produce the same result as a single rotation and that a combination of rotations can produce the same result as a single translation and/or reflection

Working mathematically

This series addresses all five components of Working Mathematically. In the earlier parts of the series the emphasis is on fluency and understanding. Later parts emphasise reasoning, communicating and problem-solving.

The diversity of learners

Each resource includes an initial activity, supporting students who require revision of key concepts. Each resource also includes a bonus activity containing material that can extend suitable students beyond the curriculum content.

Australian curriculum content descriptions

(ACMMG181) Describe translations, reflections in an axis and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries

More information

Resource type: Interactive Resource

ScOT topics: Transformation (Geometry), Cartesian Planes

File type: text/html

Language/s: English

Author: NSW Department of Education

Publisher: NSW Department of Education

Date created: Wednesday, 7 November 2018