Maths - Curriculum Information
Year 7
This unit provides a transition from primary school to secondary school mathematics study. Number concepts and skills studied previously are reviewed and consolidated, and new areas of study are introduced. In particular, the Patterns and Rules unit provides an introduction to the study of Algebra. In this unit particular emphasis is given to the development of algebraic notation and pronumerals in the Rules, Symbols and Graphs, and the Equations topics, providing the foundations for the students study of Algebra throughout secondary school. Emphasis is placed on modelling, observing and representing patterns. Fraction skills studied at primary school are reviewed, consolidated and extended and the students are introduced to the concept of chance using simulation with a variety of tools. A practical approach is taken to measurement using a variety of equipment. Students are exposed to a variety of problem solving activities in Maths 300 and the Project Day "Measurement in Sport'.
Students are encouraged and taught to use their scientific calculators wherever appropriate, and are introduced to the computer software packages 'Geometer's Sketchpad' and 'Excel spreadsheets'. Students are given the opportunity to apply mathematics to situations they personally find interesting, using various problem solving strategies. Students gain an appreciation of the dynamic nature and development of mathematics through the activity based program World of Mathematics.
Year 8
In Year 8 students are introduced to directed numbers and learn to perform the four operations with negative numbers. Students learn to handle large and small numbers through the introduction of standard form and the use of exponents. A more formal approach to the concept of chance is developed with students undertaking a variety of investigations that lead them to the determination of equally likely outcomes and the numerical representation of probabilities. Work in the algebra strand is further extended and formalised, with increased use of formal algebraic notation and the introduction of linear equations and the complete number plane. Students have the opportunity to conduct practical investigations and solve problems in both mathematical and everyday situations by participating in the 'Pentathlon' project day activity program. This activity session complements their work in the Problem Solving Task Centre where they are developing further problem solving strategies, including the appropriate use of technology and report writing skills.
Particular emphasis is given to the use of technology and mathematical tools to support the course objectives. Maths 300 and Geometers' Sketchpad software is used to investigate angles, parallel lines and polygons as well as applications of area and perimeter measurement. Scientific calculators are used in the measurement topic as well as an input/output machine in the linear modelling topic. Graphics calculators are used to demonstrate the graphical representation of linear models. Geometry and drawing tools are used in the angle and polygons topic and the scale drawing topic. Excel spreadsheets are used in the Statistics and Graphs topic.
Middle School - Core
Year 9
The unit focuses on the following areas of study:- an exploration of number and development of skills using index and scientific notation; recognise, demonstrate and calculate using the rule of Pythagoras; construct and measure shapes in two dimensions and describe and draw transformations of solids in three dimensions; express generality and manipulate expressions using the basics of both linear and quadratic algebra; measure, calculate and apply skills to lengths, areas and volumes associated with polygons, circles, prisms, pyramids and a variety of related shapes and solids; an examination of how probabilities are determined either theoretically or by experimental measurement and of how probability experiments can be analysed and designed; the development of skills associated with percentages and interest calculations including an extensive investigation into financial applications; consolidation of algebra to constructing and solving linear equations, to odeling and apply linear rules to real situations and to sketch and interpret a variety of forms of linear graphs; use of the concepts of similarity and of scale ratio to establish the basic trigonometry rules and apply these to simpler cases involving right angled triangles; application of the ideas of ratios and rates to situations where one quantity varies in terms of another such as time, distance and speed; use of concepts and strategies in topology and networks.
A range of learning activities and assessment tasks are employed to achieve the learning outcomes for the unit. Technology (Maths300, Graphmatica, Geometers' Sketchpad and Excel, scientific and graphing calculators) continues to be an integral element of mathematics teaching and learning. During Core Week a range of activities exploring Geometry in Melbourne are presented.
Advanced Mathematics 9 commences in semester two and allows students to select an advanced course of study. This will involve practical activities, problem solving, investigations and skills exercises designed to build on and extend the students' sound understanding of concepts in the areas of study. Students will complete Extension work and be assessed separately from Core Mathematics.
Year 10
Year 10 Mathematics focuses on a number of areas of study. Students investigate probability using a more theoretical basis than they met in years 8 and 9 with conditional and independent events examined. In addition to linear algebra development, quadratic algebra and graphs are introduced and extended using transformations and the technology of graphic calculators and computer software. The Space strand consolidates earlier work on angles and polygons and moves into relationships between angles in circles and a range of transformations in two and three dimensions are created using computer software. Number and measurement skills are consolidated and extended through the study of variation and ratios, operations with numbers in standard form, index laws with fractional and negative indices. The major topics are: probability, strategies for problem solving, logic and geometry, circle geometry, variation, rates and ratio, linear algebra and coordinate geometry, indices and standard form, Money and time, Data handling, Circles, with angles and polygons, Trigonometry, Applications of quadratics, Transformations, Rates of change, Periodic functions and Problem solving.
Advanced Mathematics 10 continues throughout Year 10 and allows students to select an advanced course of study. This will involve separate work on more complex aspects of the Year 10 course designed to build on and extend the students' sound understanding of concepts in the areas of study. Students will complete Extension work and be assessed separately from Core Mathematics.
Middle School Elective
Semester long units that can be elected by Year 9 or 10 students
Maths Is Making Sense
This unit is designed for motivated Year 9 students who have serious gaps and difficulties in key mathematical knowledge and skills. These gaps and difficulties would need to be significant and students would require the commitment and the ability, with assistance and encouragement, to overcome these problems. Initially some diagnosis of students' difficulties will be required, based on the learning outcomes of the Curriculum and Standards Framework. Then the focus throughout this semester unit will be on the individual's learning needs within the group, enabling each student as far as possible to better cope with her mainstream mathematics classes.
Maths Magnified
This unit is designed to extend highly motivated students of mathematics who are already quite competent in the key knowledge and skills of their mainstream mathematics classes. The learning outcomes and the areas of study selected will be based on the numerous level 6 extension sections of the Curriculum and Standards Framework for Mathematics. The particular content area chosen will also reflect the interests, abilities and potential futures of the students selecting the unit. Students selecting this unit can expect to do mathematics that is different, that is challenging and that will require considerable ability and hard work
VCE
The study of VCE Mathematics is designed to enable students to:
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develop mathematical knowledge and skills;
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apply mathematical knowledge to investigate, analyse and solve problems in situations ranging from the familiar and well-defined to unknown and open-ended cases;
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use technology as an effective support and tool for mathematical activity.
Structure of VCE Mathematics
The following units are available:
General Mathematics (Further) Units 1 and 2
The units are designed for any student progressing from Year 10 and are a preparation for Further Mathematics. Areas of study Statistics (Univariate and bivariate data); Functions and graphs (linear graphs and odeling, linear programming); Algebra (linear and non-linear relations and equations); Arithmetic (applications, sequences and series); Geometry (shape and measurement); Trigonometric ratios.
Mathematical Methods CAS Units 1 and 2
The Methods units are rigorous and theoretical in approach and students beginning Units 1 and 2 will require sound knowledge and skills from Mathematics in Year 10. They have a closely sequenced development of mathematical material and are intended particularly as preparation for Mathematical Methods Units 3 and 4 and as assumed material for Specialist Mathematics. Areas of study: Functions and Graphs; Algebra; Probability; Calculus
General Mathematics (Specialist) Units 1 and 2
The unit is specifically designed as a complementary course to units 1 and 2 of Mathematical Methods CAS. Students are required to be concurrently doing Mathematical Methods CAS. The emphasis in this course is to provide opportunities for access to a rigorous exploration of aspects of mathematical structure and proof. Areas of study Arithmetic (Number systems, Variation, Sequences and Series, Polar Coordinates and Complex Numbers); Functions and Graphs (Sketching and interpreting graphs, Kinematics); Algebra (Proof and Number); Geometry (Shape and Measurement Circle theorems, Vectors and Dynamics); Trigonometry (Circular Functions and Identities).
Further Mathematics Units 3 and 4
Are intended to be widely accessible. They provide general preparation for employment or further study. The assumed knowledge for Further Mathematics Units 3 and 4 is drawn from the courses offered in General Mathematics (Further) Units 1 and 2; students who have only done Mathematical Methods Units 1 and 2 will also have had access to this assumed knowledge. Areas of study Data analysis, Number Applications, Graphs & Relations, Geometry & Trigonometry
Mathematical Methods CAS Units 3 and 4
May be taken alone or in conjunction with either Specialist Mathematics or Further Mathematics, and is intended to provide an appropriate background for further study in science, economics or medicine. Areas of study Coordinate Geometry, Trigonometry, Calculus, Algebra and Probability
Specialist Mathematics Units 3 and 4
Must be taken in conjunction with Mathematical Methods CAS Units 3 and 4, and the areas of study extend and develop material from Mathematical Methods CAS Units 3 and 4. Specialist Mathematics is intended for those with strong interests in mathematics and those who wish to subsequently undertake further study in mathematics and related disciplines. Areas of study Coordinate Geometry, Trigonometry, Calculus, Algebra, Vectors, Kinematics and Dynamics.
Some of the Possible Combinations of Units:
| At year 11 ( Units 1 and 2 ) | At year 12 (Units 3 and 4) | |
|---|---|---|
| General Mathematics (Further) | leads to | Further Mathematics |
| Mathematical Methods CAS | leads to | Mathematical Methods CAS |
| Mathematical Methods CAS and General Mathematics (Specialist) | leads to | Mathematical Methods CAS and Specialist Mathematics |
Use of Technology
Mathematics in the real world increasingly employs technology in most applications. Hence students will be expected to appropriately select and use technology to support their learning in VCE Mathematics. This will involve the use of scientific and graphic calculators and extensive use of computer programs such as spreadsheet, database, statistical, geometry and graphing packages. Mathematical Methods CAS utilises graphing calculators that perform Algebra. At Academy students in Year 10 and VCE use the Casio Classpad 300.