Mathematics

Mathematical ideas have evolved and continue to develop across cultures and have been practised in Australia by Aboriginal and Torres Strait Islander Peoples for thousands of years. Through the study of mathematics, students apply their knowledge and skills to deepen their understanding of the world.

Mathematics is a reasoning and creative activity, integral to scientific and technological advances across many fields of endeavour. The symbolic nature of mathematics provides a powerful and precise means of communication.

Making connections across mathematical concepts and other subject areas enhances students’ ability to understand the purpose of learning mathematics and to develop a deeper conceptual understanding. This helps students to recognise the role of mathematics in solving problems in the world around them, applying their understanding to familiar and unfamiliar situations.

By studying mathematics, students develop essential numeracy skills and fluency, while nurturing the ability to think logically, critically and creatively. They learn about patterns and reason about relationships, creating opportunities to generalise their solutions and to solve non-routine problems.

When students enjoy learning mathematics, they develop a positive self-concept and become self-motivated learners through active participation in appropriately challenging tasks. This can enhance their resilience in solving mathematical problems relevant to further education and their everyday lives.

The aim of Mathematics K–10 is to enable students to become confident users of mathematics, learning and applying the language of mathematics to communicate efficiently and effectively. They develop an increasingly sophisticated understanding of mathematical concepts and a fluency with mathematical processes that helps them to interpret and solve problems. Students make connections within mathematics and connect mathematical concepts with the world around them. They learn to understand and appreciate how mathematics is a relevant part of their lives.

At Moorebank High School, by studying mathematics, students learn to work mathematically to develop fluency, understanding, problem-solving, reasoning and communication and numeracy skills.

Stage 4 and 5

Years 7 – 10

Years 7 – 10 CORE and PATHS

The Core–Paths structure is designed to encourage aspiration in students and provide the flexibility needed to enable teachers to create pathways for students working towards Stage 6. The structure is intended to extend students as far along the continuum of learning as possible and provide solid foundations for the highest levels of student achievement. The structure allows for a diverse range of endpoints up to the end of Stage 5.

The Core outcomes provide students with the foundation for Mathematics Standard 2 in Stage 6. Students who require ongoing support in completing all Stage 5 Core outcomes may consider either Mathematics Standard 1 in Stage 6. For these students, teachers are encouraged to continue to extend students towards demonstrating achievement in as many Stage 5 Core outcomes as possible. This is to enable as many students as possible to have the knowledge and skills necessary to engage in the highest level of mathematics possible.

The aim for most students is to demonstrate achievement of the Core and as many Path outcomes as possible by the end of Stage 5 and this should guide teacher planning. Allowing time for students to demonstrate understanding of the Core outcomes must be a key consideration.

Stage 6

Years 11 and 12

Mathematics Standard 11 – 12

Mathematics Standard 11–12 focuses on enabling students to use mathematics to make informed decisions in their daily lives. Students develop understanding and competence through real-world applications of mathematics.

Mathematics Standard 1 provides opportunities for students to build confidence and make mathematics meaningful. Students develop their mathematical knowledge and understanding through applying and modelling to prepare for post-school employment or further training.

Mathematics Standard 2 provides a pathway for students to extend their mathematical thinking by examining more complex content, and through applications and modelling.

What students learn

Through the study of Mathematics Standard 1, students:

develop their knowledge, understanding and skills in Working mathematically and in communicating concisely and systematically
consider various applications of mathematics in a broad range of contemporary contexts through mathematical modelling and use these models to solve problems related to their present and future needs
gain an appropriate mathematical background for post-school employment or further training.

Through the study of Mathematics Standard 2, students:

develop their knowledge, understanding and skills in Working mathematically and in communicating concisely and systematically
consider various applications of mathematics in a broad range of contemporary contexts through mathematical modelling and use these models to solve problems related to their present and future needs
develop an understanding of, and skills in, further aspects of mathematics for concurrent HSC studies
gain an appropriate mathematical background for a wide range of educational and employment aspirations.

Course requirements

The Year 11 course is undertaken by all students intending to study either the Year 12 Mathematics Standard 1 course or the Year 12 Mathematics Standard 2 course.

Syllabus overview

Mathematics Standard 11–12 outcomes and their related content are organised into 5 areas of study:

Algebra
Financial mathematics
Measurement
Networks
Statistics

In Year 12, students can decide whether to undertake the Mathematics Standard 1 or Mathematics Standard 2 course.

Mathematics Advanced

Mathematics Advanced 11–12 focuses on mathematical ways of viewing the world to investigate concepts, such as order, relation, pattern, uncertainty and generality. The course provides students with the opportunity to explore mathematical problems through observation, reflection and reasoning.

What students learn

Through the study of Mathematics Advanced 11–12, students:

develop knowledge, understanding and skills in Working mathematically and communicating concisely and precisely
consider various applications of mathematics in a broad range of contemporary contexts through mathematical modelling
gain an appropriate mathematical background for future pathways which involve mathematics and its applications at the tertiary level.

Course requirements

Mathematics Advanced consists of the courses Mathematics Advanced Year 11 and Mathematics Advanced Year 12. Students must study both Mathematics Advanced Year 11 and Mathematics Extension 1 Year 11 courses before they can study Year 12 Mathematics Extension courses.

Alternatively, students can study both Mathematics Advanced Year 11 and Mathematics Advanced Year 12 before they begin either Mathematics Extension 1 Year 11 and Mathematics Extension 1 Year 12, or Mathematics Extension 1 Year 12 and Mathematics Extension 2 Year 12.

The organisation of outcomes and content for Mathematics Advanced 11–12 highlights the important role Working mathematically plays across all areas of mathematics and reflects the strengthened connections between concepts. Working mathematically has been embedded in the outcomes and content of the syllabus.

Syllabus overview

Mathematics Advanced outcomes and their related content are organised into 7 areas of study:

Functions
Trigonometric functions
Sequences and series
Calculus
Exponential and logarithmic functions
Statistical analysis
Financial mathematics

Mathematics Extension 1 (Year 11 and 12)

What students learn

Through the study of Mathematics Extension 1, students:

develop thorough knowledge, understanding and skills in Working mathematically and in communicating concisely and precisely
develop rigorous mathematical arguments and proofs, and use mathematical models extensively
develop awareness of the interconnected nature of mathematics, its beauty and its functionality
gain an appropriate mathematical background for future pathways that may involve mathematics and its applications.

Course Requirements

Mathematics Extension 1 consists of the courses Mathematics Extension 1 Year 11 and Mathematics Extension 1 Year 12.

Students studying one or both Extension 1 and 2 courses must study both Mathematics Advanced Year 11 and Mathematics Extension 1 Year 11 courses before undertaking the study of Mathematics Extension 1 Year 12, or both Mathematics Extension 1 Year 12 and Mathematics Extension 2 Year 12.

An alternative approach is for students to study both Mathematics Advanced Year 11 and Mathematics Advanced Year 12 before undertaking the study of Mathematics Extension 1 Year 11 and Mathematics Extension 1 Year 12, or both Mathematics Extension 1 Year 12 and Mathematics Extension 2 Year 12.

Syllabus Overview

The organisation of outcomes and content for Mathematics Extension 1 11–12 highlights the important role Working mathematically plays across all areas of mathematics and reflects the strengthened connections between concepts. Working mathematically has been embedded in the outcomes and content of the syllabus.

Mathematics Extension 1 outcomes and their related content are organised into 7 areas of study:

Functions
Proof
Vectors
Trigonometric functions
Combinatorics
Calculus
Statistical analysis

Mathematics Extension 2 (Year 12 only)

What students learn

Through the study of Mathematics Extension 2, students:

develop strong knowledge, understanding and skills in Working mathematically and in communicating concisely and precisely
acquire knowledge, understanding and skills in relation to mathematical concepts that have applications in an increasing number of contexts
gain an appropriate mathematical background for future pathways which are founded in mathematics and its applications.

Course requirements

Mathematics Extension 2 is a Year 12-only course. Students studying the Mathematics Extension 2 Year 12 course must:

have studied the Mathematics Advanced and the Mathematics Extension 1 Year 11 courses
study the Mathematics Advanced Year 12 and Mathematics Extension 1 Year 12 courses concurrently with Mathematics Extension 2 Year 12.

An alternative approach is for students to study Mathematics Advanced Year 11 and Mathematics Advanced Year 12 before studying Mathematics Extension 1 Years 11–12 and Mathematics Extension 2 Year 12.

Syllabus Overview

The organisation of outcomes and content for Mathematics Extension 2 Year 12 highlights the important role Working mathematically plays across all areas of mathematics and reflects the strengthened connections between concepts. Working mathematically has been embedded in the outcomes and content of the syllabus.

Mathematics Extension 2 Year 12 outcomes and their related content are organised into 5 areas of study: