Mathematics
Head of Department: Mr Andrew Arratoon
Year 10
Mathematical education today is based on the ability to use Mathematical skills and techniques in life related situations and the ability to communicate solutions in a Mathematical manner. Students further develop the ability to apply Mathematical problem solving techniques to life related situations and are given the opportunity to develop further skills with calculators, computer software and other appropriate tools.
The Year 10 Mathematics courses are designed to give students a positive approach to Mathematics and to develop the skills needed in Senior Mathematical Studies.
Mathematics
The Mathematics course continues to develop skills and techniques necessary for Senior Mathematics. Students further develop the ability to apply Mathematical problem solving techniques to life related situations and are given the opportunity to develop further skills with calculators, computer software and other appropriate tools.
Course Outline
1. Number Study
2. Ratio and Proportion
3. Trigonometry
4. Geometry
5. Coordinate Geometry
6. Money and Business
7. Function Stud
8. Chance and Data
9. Advanced Equations
10. Measurement
11. Advanced Alegbra
Assessment Criteria
• Understanding – the ability to apply concepts to solve problems and to represent information mathematically
• Skills – apply problem solving strategies, apply mathematical procedures accurately, use appropriate mathematical language, terms and conventions when communicating explanations and solutions.
Career Options
A good result in Year 10 Mathematics is desirable for students progressing to Mathematics B or Mathematics C in Years 11 and 12. Mathematics B leads to many University courses and this must be considered when choosing subjects.
Extreme Mathematics
Extreme Mathematics is modelled largely around the Year 10 Mathematics course, however it offers many additional learning opportunities in order to target students seeking a greater challenge or with a passion for Mathematics. The course is ideally suited to those who are considering doing Mathematics C in Year 11.
Some of the additional learning opportunities could include:
• Introduction to the use of Graphics calculators as a learning tool (normally occurs during Year 11)
• Participation in the Interschool Science and Engineering challenge
• Deeper exploration of many concepts
• Enhanced use of technology to support learning eg Graphmatica, Excel spreadsheets
Note that final placement into the Extreme Mathematics group will be a school decision should there be more students requesting this course than can be accommodated (usually one class).
Assessment criteria will be the same as described above in Mathematics.
Supported Class
One Mathematics class in Year 10 will provide additional support for those students who are experiencing some difficulties with Mathematics.
The teaching in these classes will focus around achieving competency at ‘C’ level objectives only with a particular emphasis on life applications of Mathematics. Student placement into these classes will be based on previous results in Mathematics, and involve parent consultation.
Year 11 and 12
As a result of the rapid changes in technology and the consequential changes in Mathematics, the face of Mathematics education is changing, from an emphasis on mechanical calculations out of context, to one of life related problem solving. Skills and techniques continue to be important, but they are now put in context.
Mathematics B and C will be offered in Year 11 and 12. These subjects are intended for students who wish to pursue tertiary studies that require competency in formal Mathematics procedures and structures. Mathematics A will also be offered to Years 11 and 12. Mathematics A is intended to raise the level of competence in Mathematics required for intelligent citizenship and to provide students wishing to pursue general tertiary studies with a competence in Mathematics.
Prevocational Mathematics is best suited to those students looking at a ‘trade’ pathway after year 12.
Mathematics A
Background
The study of Mathematics A will emphasise the development of positive attitudes towards the student’s involvement in mathematics. This development is encouraged by an approach involving problem solving and applications, working
systematically and logically, and communicating with and about mathematics. This often involves the use of computer software, calculators and other appropriate instruments.
Having completed the course of study, students of the subject should:
• be able to recognise when problems in their everyday life are suitable for mathematical analysis and solution, and be able to attempt such analysis or solution with confidence
• be aware of the uncertain nature of their world and be able to use mathematics to assist in making informed decisions in real life situations
• be able to manage their financial affairs in an informed way
• be able to visualise and represent spatial relationships in both two and three dimensions
• be aware of the diverse applications of Mathematics
• comprehend mathematical information which is presented in a variety of forms
• communicate mathematical information in a variety of forms
• be able to benefit from the availability of a wide range of mathematical instruments
Content
The core of Mathematics A focuses on three strands of Mathematics:
• Financial Mathematics
• Applied Geometry
• Statistics and Probability
Operations Research and further work on Probability and Statistics are offered through the extensions
Prerequisites
A sound level of achievement in Year 10 Mathematics is desirable.
Exit Criteria
The general objectives of this course are assessed in three categories:
• Knowledge and Procedures - The ability to recall and accurately apply familiar procedures will be tested. This also includes the selection and use of appropriate technology.
• Modelling and Problem Solving - The ability to apply knowledge to model and solve problems, ranging from familiar simple to unfamiliar complex, will be tested. This includes developing strategies in modelling, developing a solution consistent with the problem and extending and generalising from problems
• Communication and Justification - The ability involved in the presentation, communication (both mathematical and everyday language), interpretation and justification of mathematical problems will be tested. This will include communicating ideas, information and results appropriately, developing logical arguments expressed in everyday language, mathematical language or a combination of both and justifying procedures used.
Career Options
Tertiary pathways excluding Sciences (including Health Sciences), IT, Finance and Engineering.
Mathematics B
Background
The aim of Mathematics B is to encourage students to develop positive attitudes towards Mathematics by an approach involving problem solving and applications. Students will also be encouraged to work systematically and logically, and to communicate with and about Mathematics. This often involves the use of computer software, graphics calculators and other appropriate instruments. The School uses the TI 84 plus graphics calculator.
Having completed the course of study, students should:
• be able to recognise when problems are suitable for mathematical analysis and solution
• be able to use mathematics to assist in making informed decisions in life related situations
• be able to manage their financial affairs in an informed way
• be able to visualise and represent spatial relationships in both two and three dimensions
• understand mathematical information which is presented in a variety of forms
• communicate mathematical information in a variety of forms
• be able to use appropriately selected mathematical instruments
• be able to recognise functional dependencies
Content
The subject matter has been organised into the following topics:
• Applied Geometry
• Introduction to functions
• Rates of change
• Periodic Functions and Applications
• Exponential and Logarithmic Functions and Applications
• Optimisation
• Financial Mathematics
• Introduction to Integration
• Applied Statistical Analysis
Throughout the course fundamental knowledge and skills are identified and these aspects are revised. The course is arranged in a spiral structure which allows for the revisiting of topics throughout the two years.
Prerequisite
A ‘B’ level of achievement in Year 10 Mathematics or Extreme Mathematics is desirable.
Exit Criteria
The general objectives of this course are assessed in three categories:
• Knowledge and Procedures - The ability to recall and accurately apply familiar procedures will be tested. This also includes the selection and use of appropriate technology.
• Modelling and Problem Solving - The ability to apply knowledge to model and solve problems, ranging from familiar simple to unfamiliar complex, will be tested. This includes developing strategies in modelling, developing a solution consistent with the problem and extending and generalising from problems.
• Communication and Justification - The ability involved in the presentation, communication (both mathematical and everyday language), interpretation and justification of mathematical problems will be tested. This will include communicating ideas, information and results appropriately, developing logical arguments expressed in everyday language, mathematical language or a combination of both and justifying procedures used.
Career Options
Tertiary pathways including Engineering, Sciences (including Mathematics), Health Sciences, Finance, IT and Aviation.
Mathematics C
Background
The study of Mathematics C will give students the opportunity to extend their mathematical knowledge into new areas, and hence will provide an excellent preparation for the further study of mathematics in a wide variety of fields. The additional rigour and structure of the mathematics required in this subject will equip students with valuable thinking skills. Students will use the TI 84 plus graphics calculator.
Having completed the course of study students should:
• be able to recognise when problems are suitable for mathematical analysis and solution
• be able to use mathematics to assist in making informed decisions in life related situations
• be able to manage their financial affairs in an informed way
• be able to visualise and represent spatial relationships in both two and three dimensions
• understand mathematical information which is presented in a variety of forms
• communicate mathematical information in a variety of forms
• be able to use appropriately selected mathematical instruments
• be able to recognise functional dependencies
• be aware of the wide range of mathematics vocations
• have an appreciation of the power and beauty of mathematics
Content
The course contains both core and option topics. All core topics must be studied, and two options topics are to be completed.
The core topics are:
• Introduction to groups
• Real and Complex Number Systems
• Matrices and Applications
• Vectors and Applications
• Calculus
• Structures and Patterns
Prerequisite
A ‘B’ level of achievement in Year 10 Mathematics or Extreme Mathematics is desirable. Students studying Mathematics C must also study Mathematics B.
Exit Criteria
The general objectives of this course are assessed in three categories:
• Knowledge and Procedures - The ability to recall and accurately apply familiar procedures will be tested. This also includes the selection and use of appropriate technology.
• Modelling and Problem Solving - The ability to apply knowledge to model and solve problems, ranging from familiar simple to unfamiliar complex, will be tested. This includes developing strategies in modelling, developing a solution consistent with the problem and extending and generalising from problems.
• Communication and Justification - The ability involved in the presentation, communication (both mathematical and everyday language), interpretation and justification of mathematical problems will be tested. This will include communicating ideas, information and results appropriately, developing logical arguments expressed in everyday language, mathematical language or a combination of both and justifying procedures used.
Career Options
Tertiary pathways including Engineering, Aviation and Mathematics.
Prevocational Mathematics
Prevocational Mathematics is ideally suited to those students who do not wish to pursue tertiary studies after Year 12, but are likely to be looking at some sort of trade or vocational career pathway. The content addressed is chosen to align with the specific needs of the student’s career pathways, as well as focusing on developing a range of numeracy skills. Content includes but is not limited to:-
• Financial Literacy
• Measurement
• Navigation (maps, scales etc)
• Domestic Maths (budgeting, home renovations etc)
• Trade Maths – construction, plumbing, electrical, mechanical
While the subject is not one that contributes to OP scores, it does contribute to the QCE and fulfils the Numeracy requirement of the QCE.
Prerequisite
Generally suited to students who have achieved a C or less in Year 10 Mathematics.
Career Options
A range of Vocational Trades.
