Mathematics

General

Stage 6 Syllabus

Programming Advice

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Contents

1 Introduction 3

2 Sequencing notes 4

3 Coverage of outcomes across topics 7

4 Sample scope and sequences 10

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1  Introduction

This material is designed to assist teachers in programming appropriate sequences of learningforstudentsstudying the Stage 6 Preliminary Mathematics General course, the HSCMathematicsGeneral 2 (Board Developed) course (BDC) and the HSC Mathematics General1 (Content Endorsed) course (CEC).

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2 Sequencing notes

Learning in mathematics is sequential. Teachers need to ensure that they program in an appropriate order those topics that contain the knowledge, skills and understanding that are prerequisite to the study of other topics. For example, the content of the Preliminary Mathematics General topic ‘Relative frequency and probability’ (PB1) will need to be programmed for study priorto the content of the ‘Digital download and file storage’ (FSCo2) topic in the Mathematics and Communication Focus Study within Preliminary Mathematics General. The following sequencing tables list particular course topics that are prerequisite tothe study of other course topics.

Preliminary Mathematics General (BDC) – sequencing table

Topic / Prerequisite topics /
FM1 Earning and managing money
FM2 Investing money / AM1 Algebraic manipulation
FM3 Taxation
DS1 Statistics and society, data collection andsampling
DS2 Displaying and interpreting single datasets
DS3 Summary statistics
MM1 Units of measurement and applications
MM2 Applications of perimeter, area andvolume
MM3 Similarity of two-dimensional figures, rightangled triangles
PB1 Relative frequency and probability
AM1 Algebraic manipulation
AM2 Interpreting linear relationships
FSCo1 Mobile phone plans / DS2 Displaying and interpreting single data sets
MM1 Units of measurement and applications
AM2 Interpreting linear relationships
FSCo2 Digital download and file storage / DS2 Displaying and interpreting single data sets
DS3 Summary statistics
MM1 Units of measurement and applications
PB1 Relative frequency and probability
FSDr1 Costs of purchase and insurance / DS2 Displaying and interpreting single data sets
DS3 Summary statistics
MM1 Units of measurement and applications
AM2 Interpreting linear relationships
FSDr2 Running costs and depreciation / DS2 Displaying and interpreting single data sets
DS3 Summary statistics
AM1 Algebraic manipulation
AM2 Interpreting linear relationships
FSDr3 Safety / DS2 Displaying and interpreting single data sets
DS3 Summary statistics
AM1 Algebraic manipulation

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HSC Mathematics General 2 (BDC) – sequencing table

Topic / Prerequisite topics /
FM4 Credit and borrowing / AM3 Further algebraic skills and techniques
FM5 Annuities and loan repayments / AM3 Further algebraic skills and techniques
DS4 Interpreting sets of data
DS5 The normal distribution
DS6 Sampling and populations / PB2 Multistage events and applications ofprobability
MM4 Further applications of area and volume
MM5 Applications of trigonometry
MM6 Spherical geometry
PB2 Multistage events and applications ofprobability
AM3 Further algebraic skills and techniques
AM4 Modelling linear relationships
AM5 Modelling non-linear relationships
FSHe1 Body measurements / AM4 Modelling linear relationships
FSHe2 Medication / AM3 Further algebraic skills and techniques
FSHe3 Life expectancy / DS4 Interpreting sets of data
PB2 Multistage events and applications ofprobability
FSHe1 Body measurements
FSRe1 Water availability and usage / MM4 Further applications of area and volume
FSRe2 Dams, land and catchment areas / MM4 Further applications of area and volume
FSRe3 Energy and sustainability

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HSC Mathematics General 1 (CEC) – sequencing table

Topic / Prerequisite topics /
FM4CEC Credit cards
DS4CEC Distributions / DS5CEC Interpreting sets of data
DS5CEC Interpreting sets of data
DS6CEC Working with statistics
MM4CEC Further applications of area andvolume
PB2CEC Multistage events and applications ofprobability
AM3CEC Further algebraic skills
AM4CEC Modelling with functions
FSDe1CEC Scale drawings and house plans
FSDe2CEC Design
FSHo1CEC Accommodation costs: buying andrenting / AM4CEC Modelling with functions
FSHo2CEC Costs of running a household, maintenance and repairs / FSDe1CEC Scale drawings and house plans
FSHu1CEC Blood
FSHu2CEC Body measurements / AM4CEC Modelling with functions
FSHu3CEC Lung capacity / MM4CEC Further applications of area andvolume
(Itis suggested that FSHu3CEC is studied immediately following MM4CEC.)
FSPe1CEC Water usage and collection / DS5CEC Interpreting sets of data
MM4CEC Further applications of area andvolume
FSPe2CEC Electricity
FSPe3CEC Sustainability and energy-efficient housing / MM4CEC Further applications of area andvolume
FSDe1CEC Scale drawings and house plans

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3 Coverage of outcomes across topics

Preliminary Mathematics General (BDC) – coverage of outcomes across topics

Topic / Outcomes
MGP-1 / MGP-2 / MGP-3 / MGP-4 / MGP-5 / MGP-6 / MGP-7 / MGP-8 / MGP-9 / MGP-10
FM1 Earning and managing money / ü / ü / ü / ü
FM2 Investing money / ü / ü / ü / ü / ü / ü
FM3 Taxation / ü / ü / ü / ü
DS1 Statistics and society, data collection and sampling / ü / ü / ü / ü
DS2 Displaying and interpreting single data sets / ü / ü / ü / ü / ü
DS3 Summary statistics / ü / ü / ü / ü / ü
MM1 Units of measurement and applications / ü / ü / ü / ü
MM2 Applications of perimeter, area and volume / ü / ü / ü / ü
MM3 Similarity of two-dimensional figures, right-angled triangles / ü / ü / ü / ü
PB1 Relative frequency and probability / ü / ü / ü
AM1 Algebraic manipulation / ü / ü / ü / ü / ü
AM2 Interpreting linear relationships / ü / ü / ü / ü / ü
FSCo1 Mobile phone plans / ü / ü / ü / ü / ü / ü / ü
FSCo2 Digital download and file storage / ü / ü / ü / ü / ü / ü / ü / ü / ü
FSDr1 Costs of purchase and insurance / ü / ü / ü / ü / ü / ü / ü
FSDr2 Running costs and depreciation / ü / ü / ü / ü / ü
FSDr3 Safety / ü / ü / ü / ü / ü / ü

ü Indicates that the specified outcome is addressed in the topic.

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HSC Mathematics General 2 (BDC) – coverage of outcomes across topics

Topic / Outcomes
MG2H-1 / MG2H-2 / MG2H-3 / MG2H-4 / MG2H-5 / MG2H-6 / MG2H-7 / MG2H-8 / MG2H-9 / MG2H-10
FM4 Credit and borrowing / ü / ü / ü / ü
FM5 Annuities and loan repayments / ü / ü / ü / ü / ü
DS4 Interpreting sets of data / ü / ü / ü / ü / ü
DS5 The normal distribution / ü / ü / ü / ü / ü
DS6 Sampling and populations / ü / ü / ü / ü / ü / ü
MM4 Further applications of area and volume / ü / ü / ü
MM5 Applications of trigonometry / ü / ü / ü
MM6 Spherical geometry / ü / ü / ü
PB2 Multistage events and applications of probability / ü / ü / ü / ü / ü
AM3 Further algebraic skills and techniques / ü / ü / ü
AM4 Modelling linear relationships / ü / ü / ü
AM5 Modelling non-linear relationships / ü / ü / ü
FSHe1 Body measurements / ü / ü / ü / ü / ü
FSHe2 Medication / ü / ü
FSHe3 Life expectancy / ü / ü / ü / ü / ü / ü
FSRe1 Water availability and usage / ü / ü / ü / ü / ü / ü / ü / ü
FSRe2 Dams, land and catchment areas / ü / ü / ü / ü / ü / ü
FSRe3 Energy and sustainability / ü / ü / ü / ü / ü

ü Indicates that the specified outcome is addressed in the topic.

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HSC Mathematics General 1 (CEC) – coverage of outcomes across topics

Topic / Outcomes
MG1H-1 / MG1H-2 / MG1H-3 / MG1H-4 / MG1H-5 / MG1H-6 / MG1H-7 / MG1H-8 / MG1H-9 / MG1H-10
FM4CEC Credit cards / ü / ü / ü / ü
DS4CEC Distributions / ü / ü / ü / ü / ü / ü
DS5CEC Interpreting sets of data / ü / ü / ü / ü / ü
DS6CEC Working with statistics / ü / ü / ü / ü / ü / ü
MM4CEC Further applications of area and volume / ü / ü / ü
PB2CEC Multistage events and applications of probability / ü / ü / ü / ü
AM3CEC Further algebraic skills / ü / ü / ü
AM4CEC Modelling with functions / ü / ü / ü
FSDe1CEC Scale drawings and house plans / ü / ü / ü / ü / ü
FSDe2CEC Design / ü / ü / ü / ü / ü / ü
FSHo1CEC Accommodation costs: buying andrenting / ü / ü / ü / ü / ü / ü / ü
FSHo2CEC Costs of running a household, maintenance and repairs / ü / ü / ü / ü / ü
FSHu1CEC Blood / ü / ü / ü / ü / ü / ü / ü
FSHu2CEC Body measurements / ü / ü / ü / ü / ü / ü / ü
FSHu3CEC Lung capacity / ü / ü / ü / ü / ü / ü
FSPe1CEC Water usage and collection / ü / ü / ü / ü / ü / ü / ü / ü
FSPe2CEC Electricity / ü / ü / ü / ü
FSPe3CEC Sustainability and energy-efficient housing / ü / ü / ü

ü Indicates that the specified outcome is addressed in the topic.

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4 Sample scope and sequences

The creation of a scope and sequence is an important step in the design of effective teaching and learningprograms within a course. A scope and sequence provides an overview of the placement, sequenceand duration ofunits of work.

There is no predetermined order in which the content of the Preliminary Mathematics General course, theHSC Mathematics General 2 course and the HSC Mathematics General 1 course should be taught. Thisflexibility supports different programming arrangements to suit the requirements of different schools and classes of students. Section 2 of this document indicates particular course topics that are prerequisite to the study of other course topics.

The Strands and Focus Studies of the Preliminary Mathematics General course, the HSC Mathematics General 2 course and the HSC Mathematics General 1 course may be programmed in a variety of ways,including:

·  programming each topic in the Focus Studies to be studied over a continuous time period and following the study of the prerequisite topics in the Strands, egprogramming the ‘Safety’ (FSDr3) topic in the Mathematics and Driving Focus Study to be studied over a continuous period of oneanda half weeks after the Strand topics ‘Displaying and interpreting single datasets’ (DS2), ‘Algebraicmanipulation’ (AM1) and ‘Summary statistics’ (DS3)

·  integrating the topics in the Focus Studies into units of work based on the topics in theStrands, egbreaking up the ‘Safety’ (FSDr3) topic in the Mathematics and Driving FocusStudy for integration into other units of work based on the Strands ‘Displaying andinterpreting single data sets’ (DS2), ‘Algebraic manipulation’ (AM1) and ‘Summarystatistics’(DS3)

·  programming ‘blocks’ in which more than one of the topics in a Strand or Focus Study are studied sequentially or concurrently over a continuous time period, egprogramming the three topics in the Data and Statistics Strand, ‘Statistics and society, data collection and sampling’ (DS1), ‘Displaying andinterpreting single data sets’ (DS2) and ‘Summary statistics’ (DS3), for study over a continuous time period.

The two sets of scope and sequences, ‘Sample scope and sequences1’ and ‘Sample scope and sequences2’, presented here are SAMPLES ONLY and each comprises three parts:

·  a single common Preliminary Mathematics General scope and sequence

·  an HSC Mathematics General 2 scope and sequence that is designed to follow the common Preliminary Mathematics General scope and sequence of the set

·  an HSC Mathematics General 1 scope and sequence that is also designed to follow the common Preliminary Mathematics General scope and sequence of the set.

The sample scope and sequences indicate some of the ways in which units of work may be grouped to formteaching sequences, and different ways of ordering the units of work within a school’s teaching and learning program. The scope and sequences indicate periods for school assessment. These periods vary from school to school in terms of both location and duration, and do not imply any specific number of tasks or type of assessment task. Decisions about the number, timing and type of assessment tasks are made at the school level.

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SAMPLE scope and sequences 1 – Preliminary Mathematics General (BDC)

Term 1 / Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Unit / Earning and managing money / Statistics and society,
data collection and sampling / Displaying and interpreting
single data sets / Algebraic
manipulation / Units of measurement
and applications / Relative frequency and probability …à
Strand topic/
Focus Study topic / FM1 / DS1 / DS2 / AM1 / MM1 / PB1 …à
Outcome(s) / MGP-1, MGP-6,
MGP-9, MGP-10 / MGP-1, MGP-2,
MGP-7, MGP-10 / MGP-2, MGP-5,
MGP-7, MGP-9, MGP-10 / MGP-1, MGP-2, MGP-3,
MGP-9, MGP-10 / MGP-2, MGP-3,
MGP-4, MGP-5 / MGP-2,
MGP-8, MGP-10
Term 2 / Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Unit / ß
…Relative frequency and probability / Interpreting linearrelationships / Summary statistics / Communication:
Digital download
and file storage / Investing money / Driving: Costs of purchase
and insurance
Strand topic/
Focus Study topic / ß… PB1 / AM2 / DS3 / FSCo2 / FM2 / FSDr1
Outcome(s) / See T1 / MGP-1, MGP-2,
MGP-3, MGP-9, MGP-10 / MGP-1, MGP-2,
MGP-7, MGP-9, MGP-10 / MGP-1, MGP-2, MGP-3,
MGP-5, MGP-6, MGP-7,
MGP-8, MGP-9, MGP-10 / MGP-1, MGP-2, MGP-3,
MGP-6, MGP-9, MGP-10 / MGP-1, MGP-2, MGP-5,
MGP-6, MGP-7, MGP-8, MGP-9
Term 3 / Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10
Unit / Driving: Safety / Communication:
Mobile phone plans / Applications of perimeter,
area and volume / Driving: Running costs
and depreciation / Similarity of 2D figures,
right-angled triangles / Taxation
Strand topic/
Focus Study topic / FSDr3 / FSCo1 / MM2 / FSDr2 / MM3 / FM3
Outcome(s) / MGP-1, MGP-2, MGP-3,
MGP-7, MGP-9, MGP-10 / MGP-2, MGP-3, MGP-5,
MGP-6, MGP-7, MGP-9, MGP-10 / MGP-2, MGP-3,
MGP-4, MGP-5 / MGP-1, MGP-2,
MGP-6, MGP-7, MGP-9 / MGP-2, MGP-3,
MGP-4, MGP-5 / MGP-2, MGP-3,
MGP-6, MGP-9

The scope and sequences in this sample set demonstrate an approach where various topics within each Focus Study are studied following the study of the prerequisite topics in the Strands. Other approaches to sequencing are possible. For example, teachers may choose to integrate smaller parts of the topics intheFocus Studies into the appropriate units of work that they have programmed based on the topics in the Strands.