Credit points


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  • Term Mode
  • Semester 1Online Scheduled
  • Semester 2Online Scheduled



Unit rationale, description and aim

This unit supports the development of mathematical understanding for students planning to work in education, and particularly for students seeking admission to teacher education programs, where a confident approach and strong foundation in numeracy and mathematics knowledge and skills, and their real-world application, are required.

In this unit, students will develop conceptual understanding, procedural fluency and mathematical reasoning skills in the areas of simple functions, elementary algebra, proportional reasoning, measurement, statistics and probability needed for teaching and participation in everyday life Topics are introduced using an inquiry approach with an emphasis on application, mathematical modelling and investigation. Graphical, numerical, and algebraic representations are emphasised particularly through the appropriate use of digital technologies.

The aim of this unit is to equip students with the ability to problem solve, describe and explain mathematical understanding. The learning outcomes and unit learning activities are specifically designed to demonstrate the achievement of Australian Qualifications Framework Level 5 for Mathematics.

Learning outcomes

To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.

Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.

Explore the graduate capabilities.

Learning Outcome NumberLearning Outcome DescriptionRelevant Graduate Capabilities
LO1Describe the application of linear, quadratic, and simple exponential functions, and apply these functions to a range of contextsGC1, GC2, GC3, GC7, GC8, GC11, GC12
LO2Explain the relationships between variables in geometric, numeric and measurement related contexts, and apply algebraic methods to solve problems in those contextsGC1, GC2, GC3, GC4, GC8, GC9, GC11, GC12
LO3Solve problems with proportions as a specific type of linear relationship, particularly in contexts with rates and ratios, using numeric methods (equivalent fractions, percentages, decimals, ratios) and graphical methods (gradient as rate of change)GC1, GC2, GC3, GC4, GC7, GC8, GC9, GC11
LO4Solve statistical investigations and probability experiments to answer questions and solve problems, using category data, discrete and continuous numeric data, and time series data, display the data with appropriate graphs and tables to detect patterns and relationships in the data and report findingsGC1, GC2, GC3, GC4, GC7, GC8, GC9, GC11, GC12
LO5Solve problems and model situations in the areas of simple functions, elementary algebra, proportional reasoning, measurement, statistics and probabilityGC1, GC2, GC3, GC4, GC7, GC8, GC9, GC11, GC12


Topics will include:

  • Connecting functions, their equations, and graphs (linear, simple quadratic and exponential);
  • Creating linear, quadratic and simple exponential equations to express relationships between and among variables in contexts that are spatial, numeric or measurement related;
  • Solving problems modelled by linear, quadratic, and simple exponential equations, using a variety of techniques including changing the subject, factorisation, simultaneous equations, and graphical methods;
  • Connecting equivalent fractions, decimals and percentages as different representations of the same number, recognising the difference between part-whole and part to part relationships.
  • Solving problems with rates and ratios, using a variety of techniques including ratio tables, double number lines, percentages, and equations as appropriate
  • Gathering multi-variate categorical, numerical and time series data to answer investigatory questions, with an appreciation of sampling techniques;
  • Display data using a range of appropriate graphical representations; column (bar) and pie for categorical data, stem and leaf, dot plot, histogram, scatterplots, box and whisker for numeric data, and line graphs for time series or other continuous data;
  • Report findings from data-driven investigation appropriately with an appreciation of uncertainty;
  • Relate experimental results to theoretical models to estimate probabilities with an understanding of randomness and long-run frequency, including the use of tree diagrams, two-way tables, frequency tables, and the normal distribution;
  • Connect the commonly used standard units for length, area, volume and capacity, mass, time, temperature, speed, pressure, and density (including population), and convert between common measurement systems; confidently use the International System of Units and other measurement systems and conventions;
  • Solve a variety of problems in context.

Learning and teaching strategy and rationale

This is a 10-credit point unit and has been designed to ensure that the time needed to complete the required volume of learning to the requisite standard is approximately 150 hours in total across the semester. This includes direct teaching, reading and preparation of assessments.

This unit applies a social constructivist approach to develop pre-service teachers’ understanding of to explore mathematical concepts and develop their mathematical reasoning and problem-solving abilities. They will have the opportunity to build on their understanding of mathematics through and inquiry-centred approach which includes critical reading, lecturer modelling, active engagement, rehearsing and discussion. It is expected that students will build their mathematical proficiency including conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition across the mathematics concepts explored.

To support this strategy teaching and learning approaches may include, but are not limited to:

  • Weekly face-to-face lectures and/or online lectures (synchronous and asynchronous)
  • Hands-on tutorials and discussions that promote peer learning;
  • Self-directed reading and research
  • Collaborative learning opportunities.

The unit is hosted on a Learning Management System (LMS) site with resources and online links, announcements, and a discussion board to post questions and reflections that promote the connection between content and educational experiences.

Mode of delivery: This unit may be offered in different modes to cater to the learning needs and preferences of a range of participants.


Learning activities are delivered through a planned mix of online and in-person classes, which may include full-day sessions and/or placements, to enable interaction. Activities that require attendance will appear in a student’s timetable.

Online scheduled

All learning activities are held online, at scheduled times, and will require some attendance to enable online interaction. Activities will appear in a student’s timetable.

This unit includes 3 contact hours per week over 12 weeks, comprising 1 hour of lecture, and 2 hours of tutorials.

Students are required to actively participate in all lectures, tutorials and assigned learning activities to achieve the learning outcomes.

Assessment strategy and rationale

A range of assessment procedures are designed to allow pre-service teachers to progressively demonstrate achievement of the unit learning outcomes and to develop graduate attributes consistent with University assessment requirements.

The assessment tasks for this unit have been designed for students to apply mathematical understandings in the areas of functions, geometric, numeric and measurement related contexts to solve mathematics related problems. The assessment tasks and their weightings have been developed to meet the learning outcomes and develop graduate attributes required at the University. The assessment tasks provide opportunities for students to explain mathematical relationships, solve mathematical problems and use mathematical approaches to describe and display responses.

The assessment tasks are sequenced to allow feedback and progressive development. Through completing Task 1 students have the opportunity to work collaboratively to demonstrate capability with foundational mathematics concepts, procedures and reasoning skills. In Task 2 pre-service apply methods mathematical modelling and conduct mathematical investigations. Task 3 is an examination of the competence with the mathematical skills in a broad range of topics.

Minimum Achievement Standards

The assessment tasks and their weighting for this unit are designed to demonstrate achievement of each learning outcome. In order to pass this unit, students are required to submit all assessment tasks, meet the learning outcomes of the unit and achieve a minimum overall passing grade of 50%.

Overview of assessments

Brief Description of Kind and Purpose of Assessment TasksWeightingLearning Outcomes

Assessment Task 1

Demonstrate the mathematical concepts, procedures and reasoning skills required to solve problems using linear, quadratic and exponential functions and applying algebraic methods in geometric, numeric and measurement-related contexts.


LO1, LO2

Assessment Task 2

Solve mathematical investigations using modelling, numeric and graphical methods, statistics, and measurement methods, and report on your investigations in a written form as well as using multiple digital representations.


LO3, LO4, LO5

Assessment Task 3

Examination to assess the mathematical topics and skills taught in the unit (simple functions, elementary algebra, proportional reasoning, measurement, statistics and probability), and evaluate problem-solving, creative thinking and modelling in response to mathematical problems.


LO1, LO2, LO3, LO4, LO5

Representative texts and references

Africk, H. (2021). Elementary college geometry (2021 ed.). CUNY Academic Works. 

Booker, G. (2021). Building numeracy: From assessment to conceptual understanding and fluency. Oxford University Press. 

Demana, F., Waits, B. K., Foley, G. D., & Kennedy, D. (2022). Precalculus: Graphical, numerical, algebraic (10th ed.). Pearson. 

Eccles, P. (1997). An introduction to mathematical reasoning: Numbers, sets and functions. Cambridge University Press.

Lamon, S. J. (2020). Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers (4th ed.). Taylor and Francis. 

Matthews, C. (2019). Maths as storytelling: Maths is beautiful (chapter 7). In K. Price & J. Rogers (Eds.), Aboriginal and Torres Strait Islander education: An introduction for the teaching profession (pp. 138–160). Cambridge University Press. 

Shryock-Boyke, K (2011). Introduction to Plane Geometry: Explorations and explanations. Pearson.

Siklos, S. (2019). Advanced problems in mathematics: preparing for university (New revised edition.). Open Book Publishers. 

Stillman, G. A., Kaiser, G., & Lampen, C. E. (Eds.) (2020). Mathematical modelling education and sense-making. Springer International Publishing. 

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