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Proposed inclusions into aTemplate

    Mathematics Years 710 Syllabus: Advice on Programming and Assessment

    3 Practical programming and assessment

3.1 Sample program overviews

    The sample program overviews contained in this section demonstrate the flexibility available to teachers in implementing this syllabus. Consideration will need to be given to the knowledge, skills and understanding of students as they enter secondary school in order to plan units of work that meet their needs. While decisions may be made early in Year 7 about possible overviews, they will need to be reviewed and revised as students’ needs change, particularly for those students who experience considerable growth in

    understanding during the early years of secondary school.

    Teachers in schools will manage this in ways appropriate for their students. They will need to consider how to most effectively meet the needs of different groups of students over the four years from Year 7 to Year 10. Some students who enter Year 7 may not have demonstrated the mathematics outcomes for Stage 3, or perhaps even for Stage 2. Other students may have commenced work on Stage 4 topics while still in primary school.

    For those students who require more time to learn mathematical concepts, it is possible to include the mathematical content outlined in Stage 3, Stage 4 and Stage 5.1 in programs covering the first four years of secondary school. It may be that the three years from Year 7 to Year 9 are needed to achieve the outcomes up to and including those in Stage 4, with students commencing work on Stage 5.1 outcomes from the beginning of, or during, Year 10.

    For those students who require less time to learn mathematical concepts, it may be possible to achieve Stage 4 outcomes during Year 8 or earlier, and then to complete work in Stages 5.1 and 5.2 during Years 9 and 10. Other students may be able to complete all of Stages 5.1, 5.2 and 5.3 by the end of Year 10.

    Teachers can program for related topics from different Stages to be taught sequentially or concurrently in a particular year. For example, students who are able to work with abstractions and generalisations could cover the work on Properties of Geometrical Figures in Stages 4 and 5.2 concurrently as a lead-in to Deductive Geometry in Stage 5.3. Topics from different strands may be integrated, for example, teachers may extend work on positive integral indices (Stage 4) to cover negative indices (Stage 5.1) and fractional indices (Stage 5.3) within both the Number and Patterns and Algebra strands.

    Sample program overviews, or ‘scope and sequences’, for different groups of students are outlined below. The overviews have been designed for:

    ; students who have not completed Stage 3 by the end of Year 6 and who may achieve Stage 5.1

    outcomes by the end of Year 10

    ; students who have not completed Stage 3 by the end of Year 6 but who can be expected to achieve

    Stage 5.2 outcomes by the end of Year 10

    ; students who have completed Stage 3 in Year 6 and who will aim to achieve Stage 5.2

    ; students who complete Stage 4 in Year 8 and who wish to study the Stage 6 Mathematics course

    (Stage 5.2 outcomes plus additional outcomes from Stage 5.3)

    ; students who commence Stage 4 in Year 7 and who will achieve all Stage 5.3 outcomes including

    the optional outcomes

    ; students who have commenced Stage 4 in Year 6 and who will achieve all 5.3 outcomes including

    the optional outcomes.

    Each of these overviews contains a list of the outcome codes and topic headings that could be treated in each Year from 7 to 10. Note that the topics are listed in the sequence in which they appear in the syllabus rather than in any recommended teaching sequence.

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    Mathematics Years 710 Syllabus: Advice on Programming and Assessment

    Program overview for students who have not completed Stage 3 by the end of Year 6 and who may

    achieve Stage 5.1 outcomes by the end of Year 10

    Year 7 Year 8 Year 9 Year 10

    NS3.1 Whole Numbers NS3.5 Chance NS4.4 Probability NS5.1.1 Rational

    Numbers NS3.2 Addition and NS4.1 Operations with PAS4.3, PAS4.4

    Subtraction Whole Numbers Algebraic Techniques NS5.1.2 Consumer

    Arithmetic NS3.3 Multiplication and NS4.2 Integers DS4.2 Data Analysis and Division Evaluation NS5.1.3 Probability NS4.3 Fractions,

    NS3.4 Fractions and Decimals and MS3.3 Volume and PAS4.5 Linear Decimals Percentages Capacity Relationships

    PAS3.1a, PAS3.1b PAS4.1 Algebraic MS4.2 Surface Area and PAS5.1.1 Algebraic Patterns and Algebra Techniques Volume Techniques

    DS3.1 Data PAS4.2 Number Patterns SGS4.1 Properties of PAS5.1.2 Coordinate

    Solids Geometry MS3.1 Length DS4.1 Data

    Representation SGS4.4 Properties of DS5.1.1 Data MS3.2 Area

    Geometrical Figures Representation and MS4.1 Perimeter and MS3.4 Mass Analysis Area MS3.5, MS4.3 Time MS5.1.1 Perimeter and SGS4.2 Angles SGS3.1 3D Space Area SGS4.3 Properties of SGS3.2a, SGS3.2b 2D MS5.1.2 Trigonometry Geometrical Figures Space

    SGS3.3 Position

Program overview for students who have not completed Stage 3 by the end of Year 6 but who can be

    expected to achieve Stage 5.2 outcomes by the end of Year 10

    Year 7 Year 8 Year 9 Year 10

    NS3.1 Whole Numbers NS4.3 Fractions, NS5.1.1 Rational NS5.2.2 Consumer

    Decimals and Numbers Arithmetic NS3.2 Addition and

    Percentages Subtraction NS5.2.1 Rational PAS5.2.1, PAS5.2.2

    NS4.4 Probability Numbers Algebraic Techniques NS3.3 Multiplication and

    (part in Year 9 and part Division PAS4.3, PAS4.4 NS5.1.2 Consumer

    in Year 10) Algebraic Techniques Arithmetic NS3.4 Fractions and

    PAS5.2.3, PAS5.2.4 Decimals PAS4.5 Linear NS5.1.3 Probability

    Coordinate Geometry Relationships NS3.5 Chance PAS5.1.1 Algebraic

    PAS5.2.5 Graphs of DS4.1 Data Techniques NS4.1 Operations with Physical Phenomena Representation Whole Numbers PAS5.1.2 Coordinate

    DS5.2.1 Data Analysis DS4.2 Data Analysis and Geometry NS4.2 Integers and Evaluation Evaluation PAS5.2.1, PAS5.2.2 PAS3.1a, PAS3.1b MS5.2.2 Surface Area MS3.3 Volume and Algebraic Techniques Patterns and Algebra and Volume Capacity (part in Year 9 and part PAS4.1 Algebraic in Year 10) MS5.2.3 Trigonometry MS4.1 Perimeter and Techniques

    Area DS5.1.1 Data SGS5.2.2 Properties of PAS4.2 Number Patterns Representation and Geometrical Figures MS4.2 Surface Area and DS3.1 Data Analysis Volume MS3.1 Length MS5.1.1 Perimeter and SGS4.3, SGS4.4 MS3.2 Area Area Properties of Geometrical MS3.4 Mass Figures MS5.2.1 Perimeter and MS3.5, MS4.3 Time Area

    SGS3.1 3D Space MS5.1.2 Trigonometry

    SGS3.2a, SGS3.2b 2D SGS5.2.1 Properties of Space Geometrical Figures

    SGS3.3 Position

    SGS4.1 Properties of

    Solids

    SGS4.2 Angles

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Mathematics Years 710 Syllabus: Advice on Programming and Assessment

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    Mathematics Years 710 Syllabus: Advice on Programming and Assessment

    Program overview for students who have completed Stage 3 in Year 6 and who will aim to achieve

    Stage 5.2

    Year 7 Year 8 Year 9 Year 10

    Review and NS5.1.1 Rational NS5.2.1 Rational NS5.2.2 Consumer Consolidation of Stage 3 Numbers Numbers Arithmetic

    NS4.1 Operations with PAS4.4 Algebraic NS5.1.2 Consumer PAS5.2.1, PAS5.2.2 Whole Numbers Techniques Arithmetic Algebraic Techniques

    (part in Year 9 and part NS4.2 Integers PAS4.5 Linear NS5.1.3 Probability

    in Year 10) Relationships NS4.3 Fractions, PAS5.1.1 Algebraic

    PAS5.2.3, PAS5.2.4 Decimals and DS4.1 Data Techniques

    Coordinate Geometry Percentages Representation PAS5.1.2 Coordinate

    PAS5.2.5 Graphs of NS4.4 Probability DS4.2 Data Analysis and Geometry

    Physical Phenomena Evaluation PAS4.1 Algebraic PAS5.2.1, PAS5.2.2

    DS5.2.1 Data Analysis Techniques MS4.2 Surface Area and Algebraic Techniques

    and Evaluation Volume (part in Year 9 and part PAS4.2 Number Patterns

    in Year 10) MS5.2.2 Surface Area SGS4.3, SGS4.4 PAS4.3 Algebraic and Volume Properties of Geometrical DS5.1.1 Data Techniques

    Figures Representation and MS5.2.3 Trigonometry MS4.1 Perimeter and Analysis SGS5.2.2 Properties of Area

    MS5.1.1 Perimeter and Geometrical Figures MS4.3 Time Area SGS4.1 Properties of MS5.2.1 Perimeter and Solids Area SGS4.2 Angles MS5.1.2 Trigonometry

    SGS5.2.1 Properties of

    Geometrical Figures

Program overview for students who complete Stage 4 in Year 8 and who wish to study the Stage 6

    Mathematics course (Stage 5.2 outcomes plus additional outcomes from Stage 5.3)

    Year 7 Year 8 Year 9 Year 10

    Review and NS5.1.1 Rational NS5.1.3 Probability NS5.3.1 Real Numbers Consolidation of Stage 3 Numbers NS5.2.2 Consumer PAS5.2.4 Coordinate NS4.1 Operations with NS5.2.1 Rational Arithmetic Geometry

    Whole Numbers Numbers PAS5.1.1 Algebraic PAS5.3.1, PAS5.3.2 NS4.2 Integers NS5.1.2 Consumer Techniques Algebraic Techniques

    Arithmetic NS4.3 Fractions, PAS5.2.1, PAS5.2.2 PAS5.3.3, PAS5.3.4 Decimals and PAS4.4 Algebraic Algebraic Techniques Coordinate Geometry Percentages Techniques PAS5.1.2 Coordinate PAS5.2.5 Graphs of NS4.4 Probability PAS4.5 Linear Geometry Physical Phenomena

    Relationships PAS4.1 Algebraic PAS5.2.3 Coordinate MS5.3.2 Trigonometry Techniques DS4.1 Data Geometry SGS5.3.1 Deductive

    Representation PAS4.2 Number Patterns DS5.1.1 Data Geometry

    DS4.2 Data Analysis and Representation and PAS4.3 Algebraic SGS5.3.2 Deductive

    Evaluation Analysis Techniques Geometry

    MS4.2 Surface Area and DS5.2.1 Data Analysis MS4.1 Perimeter and SGS5.3.3 Deductive

    Volume and Evaluation Area Geometry

    SGS4.3, SGS4.4 MS5.1.1, MS5.2.1 MS4.3 Time

    Properties of Geometrical Perimeter and Area SGS4.1 Properties of Figures MS5.2.2 Surface Area Solids

    and Volume SGS4.2 Angles

    MS5.1.2, MS5.2.3

    Trigonometry

    SGS5.2.1, SGS 5.2.2

    Properties of Geometrical

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Mathematics Years 710 Syllabus: Advice on Programming and Assessment

Figures

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    Mathematics Years 710 Syllabus: Advice on Programming and Assessment

    Program overview for students who commence Stage 4 in Year 7 and who will achieve all Stage 5.3

    outcomes including the optional outcomes

    Year 7 Year 8 Year 9 Year 10

    NS4.1 Operations with NS5.1.1 Rational NS5.2.2 Consumer NS5.3.2 Probability Whole Numbers Numbers Arithmetic PAS5.3.1, PAS5.3.2 NS4.2 Integers NS5.2.1 Rational NS5.3.1 Real Numbers Algebraic Techniques

    Numbers NS4.3 Fractions, PAS5.2.1, PAS5.2.2 PAS5.3.3, PAS5.3.4 Decimals and Percentages NS5.1.2 Consumer Algebraic Techniques Coordinate Geometry

    Arithmetic NS4.4 Probability PAS5.2.3, PAS5.2.4 PAS5.2.5, PAS5.3.5

    NS5.1.3 Probability Coordinate Geometry Graphs of Physical PAS4.1 Algebraic

    Phenomena Techniques PAS4.5 Linear DS5.2.1 Data Analysis

    Relationships and Evaluation #PAS5.3.6, #PAS5.3.7 PAS4.2 Number Patterns

    Curve Sketching and PAS5.1.1 Algebraic MS5.2.2 Surface Area and PAS4.3, PAS4.4 Polynomials Techniques Volume Algebraic Techniques

    #PAS5.3.8 Functions and PAS5.1.2 Coordinate MS5.3.1 Surface Area and DS4.1 Data Logarithms Geometry Volume Representation

    MS5.3.2 Trigonometry DS4.2 Data Analysis and MS5.1.2 Trigonometry MS4.1 Perimeter and

    Evaluation #SGS5.3.4 Circle Area MS5.2.3 Trigonometry

    Geometry DS5.1.1 Data MS4.2 Surface Area and SGS5.3.1 Deductive

    Representation and Volume Geometry

    Analysis MS4.3 Time SGS5.3.2 Deductive

    MS5.1.1, MS5.2.1 Geometry SGS4.1 Properties of Perimeter and Area Solids SGS5.3.3 Deductive

    SGS4.4. SGS5.2.1, Geometry SGS4.2 Angles SGS5.2.2 Properties of SGS4.3 Properties of Geometrical Figures Geometrical Figures

Program overview for students who have commenced Stage 4 in Year 6 and who will achieve all

    Stage 5.3 outcomes including the optional outcomes

    Year 6 Year 7 Year 8 Year 9 Year 10

    Stage 3 content as NS4.2 Integers NS5.1.1 Rational NS5.2.2 Consumer PAS5.3.1, well as some Stage Numbers Arithmetic PAS5.3.2 Algebraic NS4.3 Fractions,

    4 topics that might Techniques Decimals and NS5.2.1 Rational NS5.3.1 Real

    include: Percentages Numbers Numbers PAS5.3.3,

     PAS5.3.4 NS4.4 Probability NS5.1.2 Consumer NS5.3.2 Probability

    Coordinate NS4.1 Operations Arithmetic PAS4.1 Algebraic PAS5.2.1, Geometry with Whole Techniques NS5.1.3 Probability PAS5.2.2 Algebraic Numbers PAS5.2.5, Techniques PAS4.2 Number PAS4.5 Linear PAS5.3.5 Graphs of DS4.1 Data Patterns Relationships PAS5.2.3, Physical Representation PAS5.2.4 PAS4.3, PAS4.4 PAS5.1.1 Algebraic Phenomena MS4.3 Time Coordinate Algebraic Techniques #PAS5.3.6, Geometry Techniques PAS5.1.2 #PAS5.3.7 Curve DS5.2.1 Data MS4.1 Perimeter Coordinate Sketching and Analysis and and Area Geometry Polynomials Evaluation MS5.1.1, MS5.2.1 DS4.2 Data #PAS5.3.8 MS5.2.2 Surface Perimeter and Area Analysis and Functions and Area and Volume Evaluation MS4.2 Surface Logarithms MS5.3.1 Surface Area and Volume DS5.1.1 Data MS5.3.2 Area and Volume Representation and SGS4.1 Properties Trigonometry Analysis MS5.1.2 of Solids #SGS5.3.4 Circle Trigonometry SGS4.4. SGS5.2.1, SGS4.2 Angles Geometry SGS5.2.2 Properties MS5.2.3 SGS4.3 Properties of Geometrical Trigonometry of Geometrical Figures SGS5.3.2 Deductive Figures

    SGS5.3.1 Deductive Geometry

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    Mathematics Years 710 Syllabus: Advice on Programming and Assessment

    Geometry SGS5.3.3 Deductive

    Geometry

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    Mathematics Years 710 Syllabus: Advice on Programming and Assessment

    3.2 Programmed units of work

    These sample units of work are designed to assist teachers as they plan for the implementation of the Mathematics Years 710 Syllabus. The units provide initial programming ideas for selected syllabus content. Each unit of work relates to a particular topic from the syllabus.

The sample units of work include:

    ; a Stage 3 unit of work on Two-dimensional Space to support Year 7 students who have not

    demonstrated achievement of Stage 3 outcomes in this area

    ; a Stage 4 unit of work on Fractions to assist in the teaching of this topic area to a Year 7 class

    ; a Stage 5.1 unit of work on Trigonometry to demonstrate an introduction to a traditional topic of

    10 syllabus Mathematics that was not taught at this level in the previous Years 9

    ; a Stage 5.2 unit of work on Graphs of Physical Phenomena that demonstrates teaching and

    learning in a newer area

    ; a Stage 5.3 unit of work on Graphs of Physical Phenomena that builds on the Stage 5.2 unit.

    Each of these units includes the specific content outcome(s) that provide the main focus of the unit as well as the key ideas, knowledge and skills statements, and Working Mathematically statements from the syllabus. The page reference to the relevant content page in the syllabus is also provided.

    Working Mathematically ;

    The Working Mathematically outcomes are listed so that teachers consider the

    development and assessment of these outcomes as well as the content outcomes.

    Assessment activities that provide opportunities for students to demonstrate one or

    more of the five Working Mathematically processes (Questioning, Applying

    Strategies, Communicating, Reasoning, Reflecting) have been labelled with;;

    Advice regarding the appropriate use of technology, links to other substrands and strands, suitable resources, and language and literacy considerations are also provided. The resources include suggested references to support some of the Learning Experiences. A reference list for the units of work included can be found at the end of this section (p 48).

    The Learning Experiences provide suggestions to support teaching and learning for this topic. Teachers are encouraged to choose experiences appropriate for their students, and to develop additional learning experiences when necessary. The assessment activities also provide suggestions for teachers to choose where appropriate. Each unit will need to be adapted to meet the needs of particular students.

    The assessment activity and annotated work sample included at the end of each unit demonstrate how teachers can monitor student performance and provide feedback to support further learning.

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