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Mathematics STEM Advanced Pathway – Stage 5

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Mathematics STEM Advanced Pathway for Stage 5

This is one of two additional Pathways available for students studying Stage 5 Mathematics. These Pathways are supported by teaching and learning resources including suggested Scope and Sequences and many-resourced programs. The other pathway is Mathematics STEM Pathway.

Choosing the Mathematics STEM Advanced Pathway for Stage 5

Candidates have shown during Stage 4 that the 5.3 Pathway may be suitable for them in Year 9, but there are indications that consolidation of key concepts is required in preparation for Mathematics Advanced in Stage 6.

The Mathematics STEM Advanced Pathway is written to elevate these students to achieve the 5.3 Outcomes recommended as minimum preparation for Stage 6 Mathematics Advanced (from 2018).

This diagram below represents three types of engagement with the Mathematics STEM Advanced Pathway.

  • a 5.3 class might take the STEM Pathway instead of a 'regular' 5.3 Pathway because the Teaching and Learning Programs fit the school’s objectives for that class
  • a 5.3 class, student or group of students might commence a 'regular' 5.3 Pathway and move to the STEM Pathway if progress indicates need for consolidation and an alternative presentation of Content
  • a 5.3 class, student or group of students might commence a 'regular' 5.3 Pathway and supplement this with resources from the STEM Pathway.

Maths STEM Advanced Pathway for Stage 5

A range of delivery methods could include:

  • Traditional: delivered to classes as a whole within the planned Scope and Sequence for Mathematics
  • Boot camp: delivered as an 'immersion' – full day incursion or excursion for targeted students within large groups or as a class
  • Workshop: individual or small groups withdrawn from classes (including non-maths classes) to address an identified issue
  • Student-directed: packaged materials provided to students to work on in their own time with teacher support.

Teaching and Learning Programs compared to Concentrated Studies

The Teaching and Learning Programs integrate Outcomes across Strands and Stages. Content is compacted and combined to demonstrate to students the connections between different topics in Mathematics and the role of Mathematics in STEM applications.

The Concentrated Studies focus on skills from within Strands and often from within a single Outcome. Content is selected for its complexity and/or rigour.

Suggested scope and sequence

Download the full version of the Sample scope and sequence Mathematics Stage 5 – STEM Advanced pathway (PDF, 7 pages, 134KB)  (Word, 7 pages, 42KB).

Sample units of work


Present formulae as efficient tools for reliable and simplified work and identify STEM careers that require fluency with formulae use. Strengthen student vocabulary, formula selection and substitute and solve skills.

Rearranging formulae in order to solve for different variables strengthens algebraic skills and develops student understanding of the relationships between variables. Recognition of commonalities between formulae helps students become more efficient learners, ie – is it necessary to memorise every formula and its variations?

Apply formulae to problem-solving in STEM applications.

Teaching and learning resource: Formulae sample unit (PDF, 20 pages, 553KB)  (Word, 20 pages, 68KB)

Outcomes addressed: MA5.2-4NA, MA5.2-11MG, MA5.2-12MG, MA5.3-15MG

Duration: 5 weeks

Substitute and Solve

Feedback from HSC Mathematics marking consistently refers to common errors in questions that require substitution to solve. Basic arithmetic errors are also common. This short sequence draws 'tables of values' from linear and non-linear relationship outcomes to allow a high-intensity practice of substitution to solve – includes substitution of negative numbers. Emphasis on calculator use and looking for patterns in the independent variable row in order to identify symmetry and possible errors.

Teaching and learning resource: Substitute and Solve sample concentrated study unit of work (PDF, 5 pages, 289KB)  (Word, 5 pages, 38KB)

Outcomes addressed: MA5.1-6NA, MA5.1-7NA, MA5.3-9NA

Duration: 2 weeks

Equations and Inequations

Develop students' ability to approach solving equations and inequations in a logical and sequential way. Increase students' ability to interpret inequations by presenting 'real-world' STEM examples.

Teaching and learning resource: Equations and Inequations sample concentrated study unit of work (PDF, 7 pages, 436KB)  (Word, 7 pages, 82KB)

Outcomes addressed: MA5.2-8NA

Duration: 5 weeks

Simultaneous Equations

Demystify the algebraic process. Allow simultaneous equations to be seen as fun puzzles. Provide genuine applications and a concrete STEM activity.

Teaching and learning resource: Simultaneous Equations sample concentrated study unit of work (PDF, 9 pages, 692KB)  (Word, 9 pages, 537KB)

Outcomes addressed: MA5.2-8NA

Duration: 4 weeks


Increase student understanding of the purpose of indices by examining scientific notation and the efficiency of index notation when describing immense or minute things. Engage students with examples such as 'going viral' in social networks and examples of STEM projects.

Teaching and learning resource: Indices sample unit (PDF, 10 pages, 469KB)  (Word, 10 pages, 60KB)

Outcomes addressed: MA5.1-5NA, MA5.1-9MG, MA5.2-7NA

Duration: 4 weeks

Diagrams, Scale and Ratio

Develop students' ability to interpret information presented in diagrams and graphs with an emphasis on interpreting axis labels, scale and comparing similar diagrams in different orientations.

Teaching and learning resource: Diagrams, Scale and Ratio sample unit (PDF, 15 pages, 503KB)  (Word, 15 pages, 100KB)

Outcomes addressed: MA5.1-11MG, MA5.3-4NA

Duration: 5 weeks

Flight 5.3

Equip students to select relevant information from a diagram or written description and appropriate degrees of accuracy for practical examples. The science, technology and engineering feats that allow modern flight provide context for the mathematics of location, gradient and coordinate geometry.

Teaching and learning resource: Flight 5.3 sample unit (PDF, 18 pages, 764KB)  (Word, 18 pages, 261KB)

Outcomes addressed: MA5.1-10MG, MA5.2-9NA, MA5.2-13MG, MA5.3-8NA, MA5.3-15MG

Duration: 5 weeks

Probability and Data

Empower students to select, interpret and use appropriate diagrams and vocabulary to describe chance and data. Prepare students for rate-of-change graphs by presenting 'real-world' examples of time series graphs in Bivariate Data.

Teaching and learning resource: Probability and Data sample unit (PDF, 18 pages, 724KB)  (Word, 18 pages, 565KB)

Outcomes addressed: MA5.1-12SP, MA5.2-15SP, MA5.2-16SP, MA5.2-17SP

Duration: 5 weeks


Equip students to answer in exact form, retaining surds, fractions and pi in their answers. Increase student understanding of precision and the importance of accuracy in STEM applications.

Teaching and learning resource: Precision programming template with direction (PDF, 5 pages, 429KB)  (Word, 5 pages, 34KB)

Outcomes addressed: MA5.3-6NA

Duration: 5 weeks

Quick Sketch

Equip students to recognise shapes by their equations and recognise transformations in graphs and their equations. Allow students to realise that the key features of a graph allow quick sketches – but at this stage only extract key features that can be found in equations without any algebraic manipulation.  Allow students to see the consistency of the way transformations 'work' across the different types of curves.

Teaching and learning resource: Quick Sketch sample unit (PDF, 16 pages, 528KB)  (Word, 16 pages, 55KB)

Outcomes addressed: MA5.1-6NA, MA5.1-7NA, MA5.2-10NA, MA5.3-9NA

Duration: 5 weeks

Factorise and Expand

Establish student certainty that factorised and expanded forms are equivalent. Separate the notion of 'solve for x' from factorising and expanding. Establish that several equally valid methods exist.

Teaching and learning resource: Factorise and Expand sample concentrated study unit of work (PDF, 9 pages, 501KB)  (Word, 9 pages, 53KB)

Outcomes addressed: MA5.2-6NA, MA5.3-5NA

Duration: 5 weeks

Detailed Sketch

To be studied some time after 'Quick Sketch' in order to review transformations and develop additional skills to improve the quality of sketches. Application of algebraic skills, expansion and factorisation to move between forms of the equation. This unit should refer back to 'Quick Sketch' for STEM applications and further develop them rather than introduce new ones.

Teaching and learning resource: Detailed Sketch programming template with direction  (PDF, 7 pages, 325KB)  (Word, 7 pages, 33KB)

Outcomes addressed: MA5.1-6NA, MA5.2-9NA, MA5.2-10NA, MA5.3-7NA, MA5.3-9NA

Duration: 6 weeks

Algebraic Fractions

Draw all fractions Content from the algebraic outcomes and allow students to focus on this form of expression and equation. Engage students with meaningful 'real-world' examples of algebraic fractions essential to STEM research.

Teaching and learning resource: Algebraic Fractions sample concentrated study unit of work (PDF, 9 pages, 454KB)  (Word, 9 pages, 43KB)

Outcomes addressed: MA5.2-6NA, MA5.2-8NA, MA5.3-5NA, MA5.3-7NA

Duration: 4 weeks

The Unit Circle

Prepare students for Stage 6 Trigonometry by investigating the Unit Circle, Trigonometric graphs and solution of trigonometric equations. Explore 'real-world' STEM examples of trigonometric graphs.

Teaching and learning resource: The Unit Circle sample concentrated study unit of work (PDF, 6 pages, 483KB)  (Word, 6 pages, 38KB)

Outcomes addressed: Elements of MA5.3-15MG

Duration: 5 weeks

Rearrange and Solve

Review all algebraic and graphing skills by finding the points of intersection of linear and non-linear graphs. Rearrange literal equations and hence review skills from 'Formulae'.

Teaching and learning resource: Rearrange and Solve programming template with direction (PDF, 4 pages, 361KB)  (Word, 4 pages, 34KB)

Outcomes addressed: Elements of MA5.3-7NA

Duration: 5 weeks

More information

Essential skills and understandings are incorporated as compacted Content in related 5.2 Outcomes:

  • MA5.1.4NA Financial Mathematics
  • MA5.1-8MG Area and Surface Area
  • MA5.3-18SP Single Variable Data Analysis
  • MA5.2-14MG Properties of Geometrical Figures
  • MA5.1-13SP Probability.

Essential understandings are addressed in the 'real-world' examples included in the graphing programs:

  • MA5.2-5NA Ratios and Rates
  • MA5.3-16MG Properties of Geometrical Figures (similarity ratio Content only).

Not included:

  • MA5.3-19SP Bivariate Data Analysis
  • MA5.3-16MG Properties of Geometrical Figures (establishment of properties and conventions for proofs)
  • 5.3 Outcomes identified as 'recommended' for Extension 1.

Outcomes and Content

The outcomes and content document showcases the specific Stage 5 material accessed by this Pathway.

Download the Mathematics Stage 5 – STEM Advanced Pathway – Outcomes and Content (PDF, 25 pages, 14.5MB).

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