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NSW Syllabuses

Mathematics learning in Stage 5

The arrangement of content in Stage 5 acknowledges the wide range of achievement of students in Mathematics by the time they reach the end of Year 8. Three substages of Stage 5 (Stages 5.1, 5.2 and 5.3) have been identified and made explicit in the syllabus:

  • Stage 5.1 is designed to assist in meeting the needs of students who are continuing to work towards the achievement of Stage 4 outcomes when they enter Year 9
  • Stage 5.2 builds on the content of Stage 5.1 and is designed to assist in meeting the needs of students who have achieved Stage 4 outcomes, generally by the end of Year 8
  • Stage 5.3 builds on the content of Stage 5.2 and is designed to assist in meeting the needs of students who have achieved Stage 4 outcomes before the end of Year 8.

Students studying some or all of the content of Stage 5.2 also study all of the content of Stage 5.1. Similarly, students studying some or all of the content of Stage 5.3 also study all of the content of Stage 5.1 and Stage 5.2. Content written in different substages within Stage 5 may be studied continuously. For example, students may study the content of the Linear Relationships substrand in Stage 5.1, followed immediately by the content of the Linear Relationships substrand in Stage 5.2, or by the content of the Linear Relationships substrand in Stage 5.2 and the Linear Relationships substrand in Stage 5.3. 

Two alternative Pathways exist for Stage 5 Mathematics:

  • Mathematics STEM, an elevating pathway for students intending to study Mathematics Standard in Stage 6, and
  • Mathematics STEM Advanced, a consolidation pathway for students intending to study Mathematics Advanced in Stage 6.

In these Pathways, content is presented in the context of STEM applications and emphasises the interconnectedness of the different Strands.

The following diagram illustrates the relationship between the Pathways in Stage 5.

This diagram shows the relationship between Stage 5.1, 5.2 and 5.3 outcomes.

A large variety of 'endpoints' is possible in Stage 5. For example, some students may achieve all of the Stage 5.2 outcomes and a selection of the Stage 5.3 outcomes by the end of Year 10.

When planning learning experiences for students in Years 9 and 10, teachers need to consider the courses of study that their students plan to follow beyond Stage 5. The table below outlines Stage 5 content recommendations in relation to current Stage 6 Mathematics Board Developed Courses. Other students may study mathematics in Stage 6 through Board Endorsed Courses or Life Skills. The diagram contained in the section titled The place of the Mathematics K–10 Syllabus in the K–12 curriculum shows the relationship between Stage 5 Mathematics and the various courses offered in Stage 6.

Intended Stage 6
Board Developed Course

Recommended Stage 5 content (minimum)

Mathematics Standard

(substrands identified by ◊)

All substrands of Stage 5.1 and the following Stage 5.2 substrands:

  • Area and surface area
  • Financial Mathematics
  • Linear Relationships
  • Non-Linear Relationships
  • Right-Angled Triangles (Trigonometry)
  • Single Variable Data Analysis
  • Volume

and at least some of the content of the following Stage 5.2 substrands:

  • Equations
  • Probability

(The Mathematics STEM Pathway addresses this content)

Mathematics Advanced

§

(substrands identified by §)

All substrands of Stage 5.1 and Stage 5.2 and the following Stage 5.3 substrands:

  • Algebraic Techniques
  • Surds and Indices
  • Equations
  • Linear Relationships
  • Trigonometry and Pythagoras' Theorem
  • Single Variable Data Analysis

and at least some of the content of the following Stage 5.3 substrands:

  • Non-Linear Relationships
  • Properties of Geometrical Figures

(The Mathematics STEM Advanced Pathway addresses this content)

Mathematics Extension 1

#

(optional substrands identified by #)

All substrands of Stage 5.1, Stage 5.2 and Stage 5.3, including the optional Stage 5.3 substrands:

  • Polynomials
  • Logarithms
  • Functions and Other Graphs
  • Circle Geometry