Space, Shape & Design (Intermediate Level)

Unit Outline (Higher Education)

Level of Unit in Course

AQF Level(s) of Course

Level of Unit in Course

Introductory

Intermediate

Effective Term:

2026/05

Institute / School :

Institute of Innovation, Science & Sustainability

Unit Title:

Space, Shape & Design (Intermediate Level)

Unit ID:

MATHS2009

Credit Points:

15.00

Prerequisite(s):

(At least 30 credit points from MATHS subject-area at any level)

Co-requisite(s):

Nil

Exclusion(s):

(MATHS1009)

ASCED:

010101

Other Change:

Brief description of the Unit

This unit is aimed at a broad audience with experience in the use of symbols and mathematical language, who are interested in studying the patterns and order evident in nature and the spatial design of art, architecture and industry. It will provide students with some experience of the thinking and techniques necessary to establish evidence of general patterns and calculations related to spatial measurement and design. This unit will also include further experience of the formal use of mathematics to solve spatial problems. This unit will be particularly valuable to prospective teachers of mathematics at both primary and secondary level and to other students interested in developing a broad understanding of 2-D and 3-D shapes.

Grade Scheme:

Graded (HD, D, C, P, MF, F, XF)

Work Experience Indicator:

No work experience

Placement Component:

Supplementary Assessment:Yes

Where supplementary assessment is available a student must have failed overall in the Unit but gained a final mark of 45 per cent or above, has completed all major assessment tasks (including all sub-components where a task has multiple parts) as specified in the Unit Description and is not eligible for any other form of supplementary assessment

Course Level:

Learning Outcomes:

Knowledge:

K1.	investigate geometric properties of various 2D and 3D shapes;

K2.	identify and analyse symmetries in geometric patterns and structures;

K3.	compare and contrast Euclidean geometry with non-Euclidean geometries, including spherical and hyperbolic;

K4.	investigate and describe planar tessellations and topological ideas;

K5.	determine features of conic sections through their equations;

Skills:

S1.	investigate packing arrangements for circles, spheres, and other shapes in 2D and 3D;

S2.	explore the basic principles of projective geometry and how it relates to perspective and infinity;

S3.	construct simple mathematical proofs;

S4.	use the proper language and symbols associated with the geometric concepts covered;

S5.	use and appreciate current technology to investigate and explore geometrical patterns and associated properties;

Application of knowledge and skills:

A1.	provide practical examples of the use of geometry in 2D and 3D constructions;

A2.	solve real world problems through geometric modelling;

A3.	illustrate the mathematical properties associated with aspects of space, shape and design;

Other outcomes:

Unit Content:

Topics in this unit may include an introduction to the concepts of Euclidean and elementary non-Euclidean geometry. Throughout the unit, the ideas will be developed using practical applications and examples from nature, art, architecture and industry. Topics to be covered in this unit will be taken from the following: 2-D and 3-D shapes, geometric properties, tessellations, scale, perspective, symmetry, topology, graph theory, fractals, kaleidoscopes, Golden Mean, and principles of trigonometry.

Graduate Attributes:

Federation University recognises that students require key transferable employability skills to prepare them for their future workplace and society. FEDTASKS (Transferable Attributes Skills and Knowledge) provide a targeted focus on five key transferable Attributes, Skills, and Knowledge that are be embedded within curriculum, developed gradually towards successful measures and interlinked with cross-discipline and Co-operative Learning opportunities. One or more FEDTASK, transferable Attributes, Skills or Knowledge must be evident in the specified learning outcomes and assessment for each FedUni Unit, and all must be directly assessed in each Course.

FED TASK and descriptor		Development and acquisition of FEDTASKS in the Unit
FED TASK and descriptor		Level
FEDTASK 1 Interpersonal	Students at this level will demonstrate an advanced ability in a range of contexts to effectively communicate, interact and work with others both individually and in groups. Students will be required to display high level skills in-person and/or online in: • Using and demonstrating a high level of verbal and non-verbal communication • Demonstrating a mastery of listening for meaning and influencing via active listening • Demonstrating and showing empathy for others • High order skills in negotiating and conflict resolution skills\\ • Demonstrating mastery of working respectfully in cross-cultural and diverse teams.	Level 2 - Student demonstrates some independence within provided guidelines
FEDTASK 2 Leadership	Students at this level will demonstrate a mastery in professional skills and behaviours in leading others. • Creating and sustaining a collegial environment • Demonstrating a high level of self -awareness and the ability to self-reflect and justify decisions • Inspiring and initiating opportunities to lead others • Making informed professional decisions • Demonstrating initiative in new professional situations.
FEDTASK 3 Critical Thinking and Creativity	Students at this level will demonstrate high level skills in working in complexity and ambiguity using the imagination to create new ideas. Students will be required to display skills in: • Reflecting critically to generate and consider complex ideas and concepts at an abstract level • Analysing complex and abstract ideas, concepts and information • Communicate alternative perspectives to justify complex ideas • Demonstrate a mastery of challenging conventional thinking to clarify complex concepts • Forming creative solutions in problem solving to new situations for further learning.	Level 2 - Student demonstrates some independence within provided guidelines
FEDTASK 4 Digital Literacy	Students at this level will demonstrate the ability to work competently across a wide range of tools, platforms and applications to achieve a range of tasks. Students will be required to display skills in: • Mastering, exploring, evaluating, managing, curating, organising and sharing digital information professionally • Collating, managing complex data, accessing and using digital data securely • Receiving and responding professionally to messages in a range of professional digital media • Contributing competently and professionally to digital teams and working groups • Participating at a high level in digital learning opportunities.	Level 1 - Students require directions and boundaries from mentor
FEDTASK 5 sustainable and Ethical Mindset	Students at this level will demonstrate a mastery of considering and assessing the consequences and impact of ideas and actions in enacting professional ethical and sustainable decisions. Students will be required to display skills in: • Demonstrate informed judgment making that considers the impact of devising complex solutions in ambiguous global economic environmental and societal contexts • Professionally committing to the promulgation of social responsibility • Demonstrate the ability to evaluate ethical, socially responsible and/or sustainable challenges and generating and articulating responses • Communicating lifelong, life-wide and life-deep learning to be open to the diverse professional others • Generating, leading and implementing required actions to foster sustainability in their professional and personal life

	Learning Outcomes Assessed	Assessment Tasks	Assessment Type	Weighting	Professional Standards
1.	K1, K2, K3, K4, K5, S1, S2, S3, S4	A range of tasks and problems are explored to support the understanding of the content and the development of skills and knowledge throughout the unit	Portfolio of completed work	10 - 30%
2.	K1, S4, S5, A1, A2, A3	Self-directed or group exploration of geometric concepts and ideas	Project/Presentation/Assignment	20 - 40%
3.	K1, S4, S5	Software based investigation and analysis of geometric concepts and ideas	Software based investigation	10 - 20%
4.	K1, K2, K3, K4, K5, S1, S2, S3, S4, S5	A test on any part of or all the material covered in the unit	Test(s) / Examination(s)	30 - 50%

Adopted Reference Style:

APA ()

Professional Standards / Competencies:

Standard / Competency