Mathematics
I............................................................................................. Error! Bookmark not defined.
ntroduction ..................................................................................................................... 4
Foundation Statement ..................................................................................................... 5
Rationale ......................................................................................................................... 5
John Calvin Schools
Definition .................................................................................................................... 6
Purpose ....................................................................................................................... 6
MATHEMATICS
Australian CurriculumPre-primary
Requirements ................................................................................
to Year 6 Documentation 8
Aims ............................................................................................................................ 7
Australian Curriculum – Mathematics ................................. Error! Bookmark not defined.
AC ENGLISH: Content Statements – Foundation to Year 6 ....... Error! Bookmark not
defined.
AC ENGLISH: Achievement Standards – ................................................................................... 12
AC ENGLISH: General Capabilities in English .......................................................................... 13
1. Literacy .............................................................................................................................................. 14
2. Numeracy ............................................................................. Error! Bookmark not defined.
3. ..................................................................................................... Error! Bookmark not defined.
4. ..................................................................................................... Error! Bookmark not defined.
AC ENGLISH: Cross-Curriculum Priorities in English ......................................................... 16
2014
NOTES ON TEACHING AND LEARNING............................................................................. 17
Essential Literacy Practices ................................................. Error! Bookmark not defined.
Essential Literacy Pedagogies ............................................. Error! Bookmark not defined.
How precious to me
are your thoughts, O God!
How vast is the sum of them!
Were I to count them,
they would outnumber
the grains of sand.
Psalm 139: 18,19
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 1
Copyright 2014, John Calvin Schools Support Office, for the use of the John Calvin Primary Schools.
A digital version of this document and its attachments is available at
http://www.frsa.asn.au/PrimarySchools/PrimaryCurriculum/tabid/205/language/enUS/Default.aspx.
Teachers and other staff at the John Calvin Schools may freely download, print, cut and paste or
make any other use of this material, whether in print or digitally, with no further
acknowledgement required.
For other people and organizations, incidental use is permitted, provided proper
acknowledgement is made.
People or organizations wishing to use substantial portions of this material should contact the
John Calvin Schools Support Office for permission prior to use, at this address:
[email protected]
This document will be reviewed from time to time. Feedback is solicited and will be appreciated.
Please forward such feedback to the John Calvin Schools Support Office at [email protected] .
Aart Plug, Curriculum Officer
John Calvin Schools Support Office, Armadale WA
December 2014
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
Page 1
John Calvin Schools
MATHEMATICS
Pre-Primary to Year 6 Documentation
2014
PLEASE NOTE: In the Australian Curriculum, the term FOUNDATION YEAR (or Level) is used to indicate
the year of schooling before Year 1. This reflects the fact that the various State and Territory education
systems in Australia use different names for this year level. Entry ages may also vary.
In Western Australia, the Foundation Year is referred to as PRE-PRIMARY.
In this document and the attached overviews, these terms are used interchangeably and in practice
mean the same thing.
As a rule, the term Foundation Year or Foundation Level is used when referring directly to the
Australian Curriculum documents, and Pre-Primary will refer to the actual year levels within the John
Calvin Schools Curriculum.
As a rule, the term Foundation Year or Foundation Level is used when referring directly to the
Australian Curriculum documents, Pre-Primary will refer to the actual year levels within the
John Calvin Schools.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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TABLE OF CONTENTS:
1.
FOUNDATION STATEMENT ........................................................................................ 5
2.
RATIONALE ............................................................................................................... 6
Definition .................................................................................................................................... 6
Purpose....................................................................................................................................... 6
Aims ............................................................................................................................................ 7
3.
JCS MATHEMATICS LEARNING AREA OUTCOMES : .................................................. 8
Outcome 1.
Outcome 2.
Outcome 3.
Outcome 4.
Outcome 5.
Appreciating and Valuing Mathematics ................................................................ 8
Thinking and Working Mathematically ................................................................. 8
Number and Algebra ............................................................................................. 8
Measurement and Geometry ............................................................................... 9
Statistics and Probability....................................................................................... 9
4. AUSTRALIAN CURRICULUM REQUIREMENTS .............................................................. 10
4.1 AC MATHEMATICS: Content and Proficiency Strands – Foundation to Year 6: .................. 10
4.1.1 Content Strands .............................................................................................................. 10
4.1.2 Proficiency Strands .......................................................................................................... 11
4.2 AC MATHEMATICS: Achievement Standards – Foundation to Year 6 ................................ 12
4.3 AC MATHEMATICS: Scope and Sequence – Foundation to Year 6 ..................................... 13
4.4 AC MATHEMATICS: General Capabilities in Mathematics .................................................. 14
1. Literacy .................................................................................................................................. 14
2. Numeracy .............................................................................................................................. 14
3. ICT Capability ......................................................................................................................... 15
4. Critical and Creative Thinking ................................................................................................ 15
5. Personal and Social Capability ............................................................................................... 15
6. Ethical Behaviour ................................................................................................................... 15
7. Intercultural Understanding .................................................................................................. 15
4.5 AC MATHEMATICS: Cross-Curriculum Priorities in Mathematics ....................................... 16
1. Indigenous Histories and Culture .......................................................................................... 16
2. Asia and Australia’s Engagement with Asia .......................................................................... 16
3. Sustainability ......................................................................................................................... 16
5. TEACHING AND LEARNING IN MATHEMATICS............................................................. 17
1.
2.
3.
4.
5.
Order and Complexity ........................................................................................................... 17
Proficiency in Mathematics .................................................................................................. 17
The Learning Environment .................................................................................................... 18
The Language of Mathematics .............................................................................................. 18
Student Reflection on Learning ............................................................................................ 18
6. ASSESSMENT OF STUDENT LEARNING ...................................................................... 19
7. SCHOOL-BASED REQUIREMENTS ................................................................................ 20
Time Allotments................................................................................................................................. 20
Minimum Standards .......................................................................................................................... 20
Tracking of Student Learning ............................................................................................................. 20
8. RESOURCES ............................................................................................................... 20
9. AUDIT AND REVIEW................................................................................................... 21
APPENDICES: ................................................................................................................. 22
APPENDIX 1:
APPENDIX 2:
APPENDIX 3:
APPENDIX 4:
AC MATHEMATICS: Overview Of Content Strands – Pre-primary To Year 6 ............... 23
AC MATHEMATICS: Overview Of Proficiency Strands – Pre-Primary To Year 6 .......... 27
AC MATHEMATICS: Overview Of Achievement Standards – Pre-primary To Year 6 ... 29
AC MATHEMATICS: Scope And Sequence – Pre-primary to Year 6 Overviews ........... 33
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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John Calvin Schools:
Mathematics Learning Area
At the John Calvin Schools, students understand
that mathematical concepts and skills
are powerful tools given by God,
leading them to acknowledge His sovereignty,
enabling them to come to grips
with the greatness of His work
in the created order and in human society,
and equipping them to serve Him and our neighbour within
them,
in accordance with the instruction of Holy Scripture.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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1. FOUNDATION STATEMENT
Mathematics is a human cognitive activity that finds its origin in the power and wisdom of God.
Numerical and spatial concepts and skills are powerful tools given by God to understand the
created order and human society, and to serve Him within them. Mathematical understanding
helps us to acknowledge the sovereignty of God, and enables us to understand more fully the
greatness of His work (Romans 1:20). It also equips and enables us to exercise the dominion over
creation that God has entrusted to us. Mathematical thinking and activity is governed by God’s
revelation in His Word, and is limited by our humanity and fallen condition.
Students must grow in an increasing awareness that mathematical skills and concepts are to be
used within a framework of stewardship, use of talents, service of God and the neighbour, and the
“cultural mandate” (Gen 1:28). They must also learn to understand that mathematically correct
solutions can be put to uses which are contrary to the will of God. They should therefore be
taught to discern between right and wrong use, and strive to work accurately, efficiently and
effectively. In this way, learning in mathematics is linked to the development of Biblical values
about learning and life.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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2. RATIONALE
DEFINITION
Mathematics as an area of study is composed of multiple interrelated and interdependent
numerical and spatial concepts, and the language that is associated with them. While
‘mathematics’ as such is an abstract concept that largely deals with abstract ideas, it is
grounded in the concrete observable reality of the creation order, and provides powerful tools
for living and working within creation.
‘Mathematics’ as it is taught and learned at the John Calvin Schools involves growth and
development in knowledge and understanding of the numerical and spatial concepts
themselves, and of the order and patterns that can be discerned in and through them. It also
includes the development of skills and proficiencies in using mathematical processes,
development of the language of mathematics, and growth in the ability to use mathematical
reasoning to solve concrete and abstract problems within and outside of the mathematics
classroom. Finally, it is marked by a growth in the disposition to use these understandings and
skills in a manner that is pleasing to God.
PURPOSE
The uses of Mathematics:
1. The order and complexity of mathematics are sources of wonder, pleasure and praise
of God.
2. The study of mathematics enables us to develop and communicate concrete and
abstract ideas through the use of numerical and spatial concepts, and to apply
reasoning and logic in coming to grips with these ideas and concepts.
3. The application of mathematical skills and understandings enables us to calculate and
manipulate aspects of reality in a host of practical ways, and to participate in almost
every dimension of everyday life: worship, family life, work and economic activity, and
recreation.
4. For many students, the study of Mathematics at Primary and Secondary school levels
provides the fundamentals on which mathematical specialties and professional
applications of mathematics are built.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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AIMS
In keeping with the Biblical foundation and the requirements of the Australian Curriculum, the
John Calvin Schools Mathematics curriculum aims to ensure that students:
1. Develop Numeracy through:
 an understanding of mathematical concepts,
 increasing proficiency, fluency and flexibility in using mathematical processes,
 growing ability to pose and solve problems through mathematical reasoning
in the three strands of Number and Algebra, Measurement and Geometry, and
Statistics and Probability.
2. Recognize the connections between mathematics and other disciplines, and appreciate
mathematics as an enjoyable and rewarding discipline to study.
3. Are confident, creative users and communicators of mathematics, able to investigate,
represent and interpret situations in their personal and work lives, honouring God and
serving their neighbour and the community in which God has placed them.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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3. JCS MATHEMATICS LEARNING AREA OUTCOMES :
Teaching and learning in the History Learning Area at the John Calvin Schools is subject to the
requirements of the Australian Curriculum – Mathematics. The following outcomes are seen as
essential to ensure that these requirements are met in a manner that is consistent with the distinctively
Reformed character and identity of the John Calvin Schools
Outcome 1. Appreciating and Valuing Mathematics
Students acknowledge that mathematics is a God-given tool to understand the
created order and to work within it, and that it is to obediently used to honour Him
and serve the neighbour.
Students show a growing understanding of the nature, power and scope of mathematical activity, and
acknowledge that the creativity, intuition and reasoning associated with it are God-given talents.
Students understand how mathematics is used in regulating their lives. They understand that the use of
mathematics is governed by the will of God, and distinguish between right and wrong use. They
therefore value clarity, accuracy, fluency and persistence in mathematical thinking and the use of
mathematical skills.
Outcome 2. Thinking and Working Mathematically
Students develop increasing proficiency in the use of mathematical thinking
processes and skills in all kinds of situations.
Students call on a repertoire of problem solving techniques and appropriate technology, and work
individually and collaboratively on mathematical tasks and problems.
Students choose mathematical ideas and tools suitable for dealing with the problem at hand. They
interpret and make sense of the results within the context of the situation, and evaluate the results
obtained for accuracy and appropriateness.
Students investigate, generalize and reason about patterns in number, space and data. They observe
and describe regularities and differences, using the language of mathematics with precision and clarity.
Outcome 3. Number and Algebra
Students use numbers and operations and the relationships between them efficiently
and flexibly, fluently and accurately.
Students read, write and understand the meaning, order and relative magnitude of numbers (whole
numbers, place value, fractions, decimals, percentages and negative numbers), and can move flexibly
between equivalent forms.
They understand the meaning, use and relationships between operations (addition, subtraction,
multiplication and division), and understand and can move flexibly between equivalent processes.
Students are able to carry out the calculations associated with number operations accurately and
fluently, using mental processes, pencil and paper or calculators as appropriate. They become
increasingly proficient and fluent in the recall and use of basic number facts.
While choosing from and using a range of calculation strategies in carrying out number operations,
students know and are able to use standard algorithms as useful and efficient tools for computation.
They judge the appropriate level of accuracy or precision, and are able to check whether the results of
their computations are accurate and make sense.
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Students use algebraic symbols, diagrams and graphs to describe and reason mathematically.
They recognize and describe variation and associated relationships in mathematical situations,
representing such variation verbally, or in symbols, tables and graphs. They read, write and understand
the meaning of symbolic expressions, moving flexibly between equivalent expressions. They write
equations and inequalities to describe mathematical constraints, and choose, use and interpret
appropriate solution strategies and results.
Outcome 4. Measurement and Geometry
Students describe and measure the spatial features of objects, environments and
movements.
Students decide what needs to be measured and carry out various measurements directly, using both
arbitrary and standard units of measurement, to needed levels of accuracy.
They choose and use a range of indirect measurement strategies, using prediction, averaging, sampling
or formulae as appropriate.
Students visualize, draw and model 2D and 3D shapes, locations and arrangements, and show the effects
of transformations on them. They reason about shapes, paths, transformations and arrangements, to
solve problems, and describe and justify their solutions.
Outcome 5. Statistics and Probability
Students use their knowledge of chance and data handling processes in dealing with
situations in which uncertainty is involved.
Students recognize that while nothing happens by chance, since all things are governed by the
providence of God, many situations are to us unpredictable. They understand and use the everyday
language of probability, and make predictions about the likelihood of events occurring. They realize that
individual outcomes may display long-term patterns, and that ‘probability’ is a numerical tool to describe
such patterns. They make observations and conduct experiments and simulations to investigate and
interpret such patterns of outcomes.
Students plan and undertake data collection, and organize, summarize, represent, interpret and
communicate data so collected.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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4. AUSTRALIAN CURRICULUM REQUIREMENTS
Teaching and learning in the Mathematics Learning Area at the John Calvin Schools is subject to
the requirements of the Western Australian Curriculum Assessment and Outline (SCSA) located
at: www.scsa.wa.edu.au/internet/Years_K10. SCSA incorporates and refers to the Australian
Curriculum: Mathematics.
4.1 AC MATHEMATICS: Content and Proficiency Strands – Foundation
to Year 6:
The Australian Curriculum: Mathematics is organised around the interaction of three content
strands and four proficiency strands.
At the John Calvin Schools, these strands are seen as essential to ensure that the requirements
of the Australian Curriculum are met. Teaching, learning, and assessment programs should
balance and integrate the Content and Proficiency strands in order to support the development
of knowledge, understanding and skills. In the following section, each strand will be defined
and significant features will be identified.
While it is our aim to meet these requirements in a manner that is consistent with our
distinctively Christian character and identity, the content of the Mathematics Learning Area as
such will provide limited opportunities to reflect this identity explicitly.
However, it should at all times be reflected in the general learning environment of the
classroom and the school, including in this learning area.
4.1.1
Content Strands
The content strands are Number and Algebra, Measurement and Geometry, and Statistics
and Probability. Each of these is grouped into a number of sub-strands. They describe what is
to be taught and learnt.
Number and Algebra
Measurement and Geometry
Statistics and Probability
Number and place value (F-8)
Using units of measurement
(F-10)
Chance (1-10)
Fractions and decimals (1-6)
Shape (F-7)
Data representation and
interpretation (F-10)
Money and financial
mathematics (1-10)
Geometric reasoning (3-10)
Location and transformation
(F-7)
An Overview of the Mathematics F-6 Content Strands is provided in Appendix 1, below.
For each year level F-6, the Content Strands overview for that year is also included in the Yearby-year Scope and Sequence Overviews, provided in Appendix 4, below
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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4.1.2 Proficiency Strands
The proficiency strands are Understanding, Fluency, Problem Solving, and Reasoning. They
describe how content is explored or developed, that is, the thinking and doing of mathematics.
They provide the language to build in the developmental aspects of the learning of
mathematics and have been incorporated into the content descriptions of the three content
strands described above. This approach has been adopted to ensure students’ proficiency in
mathematical skills develops throughout the curriculum and becomes increasingly
sophisticated over the years of schooling.
Further elaboration on the proficiency strands is provided in the section on Teaching and
Learning in Mathematics, below.
An Overview of the Mathematics F-6 Proficiency Strands is provided in Appendix 2, below.
For each year level F-6, the Proficiency Strands overview for that year is also included in the
Year-by-year Scope and Sequence Overviews, provided in Appendix 4, below.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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4.2 AC MATHEMATICS: Achievement Standards – Foundation to Year 6
The Australian Curriculum: Mathematics sets standards for the quality of learning that students
are expected to demonstrate by the end of each year of schooling. These Achievement
Standards are expressed in written statements, and are accompanied by annotated student
work samples illustrating achievement at various levels.
The Achievement Standards describe student progress within the Mathematics learning area,
and give teachers a framework to assess, evaluate and report on the quality of learning that
each student has achieved.
While the Australian Curriculum: Mathematics document sets out the Achievement Standards
in a global statement for each year level, this document unpacks these global statements in a
dot-pointed format. This will support teachers in planning and carrying out more detailed
assessments of student learning.
Reporting of Student Achievement is to be carried out against the Achievement Standards for
that year, using an A-B-C-D-E scale as follows:
A. Excellent – Student consistently demonstrates learning achievement well above the
Achievement Standard for the year
B. High – Student usually demonstrates learning achievement above the Achievement
Standard for the year
C. Satisfactory – Student demonstrates learning achievement that meets the
Achievement Standard for the year
D. Limited – Student demonstrates learning achievement that may approach but does not
usually meet the Achievement Standard for the year
E. Very Low – Student demonstrates learning achievement that is well below the
Achievement Standard for the year
An Overview of the F-6 Mathematics Achievement Standards is provided in Appendix 3,
below
For each year level F-6, the Achievement Standards for that year are also included in the Yearby-year Scope and Sequence Overviews, provided in Appendix 4, below.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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4.3 AC MATHEMATICS: Scope and Sequence – Foundation to Year 6
At the John Calvin Schools, teaching and learning in Mathematics will be organized by means of
a specified Scope and Sequence, ensuring that all of the content requirements of the Australian
Curriculum: Mathematics are satisfied in a coherent, comprehensive and developmentally
appropriate manner.
Year-by-year Scope and Sequence Overviews for all years up to Year 6 are provided in
Appendix 4, below.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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4.4 AC MATHEMATICS: General Capabilities in Mathematics
The Australian Curriculum lists seven General Capabilities that encompass the knowledge,
skills, behaviours and dispositions that are considered to be overarching outcomes of teaching
and learning. As with all other elements of the curriculum, these are to be addressed in a
manner which is embedded in and consistent with the distinctively Reformed identity of the
John Calvin Schools.
These General Capabilities are identified where they are applied or developed in the Content
Descriptions of the Australian Curriculum: Mathematics , and also where they offer additional
opportunities for student learning in the Content Elaborations.
The seven General Capabilities are:
 Literacy
 Numeracy
 Information and communication technology (ICT) capability
 Critical and creative thinking
 Personal and social capability
 Ethical understanding
 Intercultural understanding.
Each of these has generic applications across the curriculum, which are further elaborated
elsewhere. Their distinctive applications within the Mathematics Learning Area include the
following:
1. Literacy
Students develop literacy in mathematics as they learn the vocabulary associated with number,
space, measurement and mathematical concepts and processes. This vocabulary includes
synonyms (minus, subtract), technical terminology (digits, lowest common denominator),
passive voice (If 7 is taken from 10) and common words with specific meanings in a
mathematical context (angle, area). They develop the ability to create and interpret a range of
texts typical of Mathematics ranging from calendars and maps to complex data displays.
Students use literacy to understand and interpret word problems and instructions that contain
the particular language features of mathematics. They use literacy to pose and answer
questions, engage in mathematical problem solving, and to discuss, produce and explain
solutions.
2. Numeracy
More than any other, Mathematics has a central, foregrounded and explicit role in the
development of numeracy.
The Mathematics curriculum provides the opportunity to apply mathematical understanding
and skills in context, both in other learning areas and in real world contexts.
Financial mathematics is a particularly important context for the application of Number and
Algebra is financial mathematics.
In Measurement and Geometry, there is an opportunity to apply understanding to design.
The twenty-first century world is information driven, and through Statistics and Probability
students can interpret data and make informed judgments about events involving uncertainty
or probability.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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3. ICT Capability
Students develop ICT capability when they investigate, create and communicate mathematical
ideas and concepts using fast, automated, interactive and multimodal technologies. They
employ their ICT capability to perform calculations, draw graphs, collect, manage, analyse and
interpret data; share and exchange information and ideas and investigate and model concepts
and relationships.
Digital technologies, such as spreadsheets, dynamic geometry software and computer algebra
software, can engage students and promote understanding of key concepts.
4. Critical and Creative Thinking
Students develop critical and creative thinking as they learn to generate and evaluate
knowledge, ideas and possibilities, and use them when seeking solutions in mathematical
contexts.
Engaging students in reasoning and thinking about solutions to problems and the strategies
needed to find these solutions are core parts of the Mathematics curriculum.
Students are encouraged to be critical thinkers when justifying their choice of a calculation
strategy or identifying relevant questions during a statistical investigation. They are
encouraged to look for alternative ways to approach mathematical problems, for example,
identifying when a problem is similar to a previous one, drawing diagrams or simplifying a
problem to control some variables.
5. Personal and Social Capability
Students develop and use personal and social capability as they apply mathematical skills in a
range of personal and social contexts. This may be through activities that relate learning to
their own lives and communities, such as time management, budgeting and financial
management, and understanding statistics in everyday contexts.
The Mathematics curriculum enhances the development of students’ personal and social
capabilities by providing opportunities for initiative taking, decision making, communicating
their processes and findings, and working independently and collaboratively in the
Mathematics classroom.
6. Ethical Behaviour
There are opportunities in the Mathematics curriculum to explore, develop and apply ethical
understanding in a range of contexts. Examples include analysing data and statistics; finding
inappropriate comparisons and misleading scales when exploring the importance of fair
comparison; and interrogating statistical and financial claims and sources; developing a
responsible personal budget which reflects obligations towards work in God’s Kingdom, the
needs of the neighbour, and short- and long-term personal goals.
7. Intercultural Understanding
While Intercultural understanding is largely peripheral to learning and teaching in
Mathematics, it can be enhanced when students discover the way in which mathematical
knowledge is expressed in other traditions, and when they discover how mathematical
concepts and skills can be tools to assist them in learning about other cultures.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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4.5 AC MATHEMATICS: Cross-Curriculum Priorities in Mathematics
The Australian Curriculum lists three significant contemporary issues that are relevant to the
lives of the students, now and into the future. Schools are expected to attend to these issues
across the curriculum, to the extent and in ways that are relevant to the specific content and
skill requirements of the various learning areas. These Cross-Curriculum priorities are:

Indigenous Histories and Culture

Asia and Australia’s Engagement with Asia

Sustainability
As with all other elements of the curriculum, these are to be addressed in a manner which is
embedded in and consistent with the distinctively Reformed identity of the John Calvin
Schools.
These Cross-Curriculum Priorities are identified where they are applied or developed in the
Content Descriptions of the Australian Curriculum: Mathematics , and also where they offer
additional opportunities for student learning in the Content Elaborations.
Each of these has generic applications across the curriculum, which are further elaborated
elsewhere. Their distinctive applications within the Mathematics Learning Area include the
following:
1. Indigenous Histories and Culture
Indigenous Histories and Cultures are largely peripheral to the teaching and learning of
Mathematics at the John Calvin Schools. However, there may be opportunities for students to
appreciate the distinctive applications of mathematical concepts in indigenous cultures. They
may, for example, explore the way number and pattern are represented, or investigate time,
place, relationships and measurement concepts in indigenous contexts. They may also apply
and evaluate statistical data to deepen their understanding of the lives of indigenous
Australians.
2. Asia and Australia’s Engagement with Asia
Asia and Australia’s engagement with Asia are largely peripheral to the teaching and learning of
Mathematics at the John Calvin Schools. However, they do provide contexts for developing
and applying students’ mathematical knowledge, skills and understanding. They may draw on
knowledge of and examples from the Asia region in fields such as number, patterns,
measurement, symmetry and statistics, including in the areas of money, art, architecture,
design and travel. Their application of skills in data collection, representation and analysis can
be used to examine issues pertinent to the Asia region.
3. Sustainability
In the teaching and learning of Mathematics, the priority of sustainability provides rich,
engaging and authentic contexts for learning and applying mathematical concepts and skills. It
provides opportunities for students to develop the proficiencies of problem solving and
reasoning essential for the exploration of sustainability issues and their solutions, in
measurement, estimation, calculation, comparison, spatial reasoning, and statistical analysis.
Application of mathematical understandings and skills will enable them to make predictions,
and inform decision making and actions that support faithful stewardship and best and fairest
use of natural and human resources within the created order.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
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5. TEACHING AND LEARNING IN MATHEMATICS
The purpose of this section is to spell out and elaborate on the principles of teaching and learning that
will guide the implementation of the Australian Curriculum: Mathematics in actual classroom practice.
While they are intended to be descriptive rather than prescriptive, it should be clear that for learning
and instruction in mathematics to be effective, classroom organization and curriculum implementation
ought clearly to reflect these principles:
1. Order and Complexity
The study of mathematics is to a very significant degree the study of patterns; mathematical
learning should therefore be aimed at uncovering the patterns of order and complexity that exist in
creation. It should also aim to develop the innate capacity of students to discern and create
patterns as a tool for making sense of the created order. The development of a sense of pattern
requires frequent and consistent use of hands-on and visual aids as a starting point.
In themselves, the discovery, exploration and applications of patterns in mathematics and in
creation can awaken feelings of appreciation, pleasure, wonder, and ultimately praise of the
Creator. These affective outcomes should be encouraged and modelled.
At the same time, mathematical patterns have instrumental value: they enable students to develop
and use valuable tools for making sense of observed reality, and for working with it in predictable
and effective ways.
Good teaching will challenge and help students clarify or refine their understanding of patterns,
discard or modify those understandings which are inaccurate or unhelpful, and develop more
sophisticated and/or helpful understandings.
2. Proficiency in Mathematics
The Australian Curriculum: Mathematics highlights four proficiency strands, describing the breadth
of mathematical actions that should be emphasised when students learn and use mathematical
understandings and skills:
Understanding:
Students build a robust knowledge of adaptable and transferable mathematical concepts. They
make connections between related concepts and progressively apply the familiar to develop
new ideas. They develop an understanding of the relationship between the ‘why’ and the ‘how’
of mathematics.
Fluency:
Students are fluent when they calculate answers efficiently, when they recognise robust ways
of answering questions, when they choose appropriate methods and approximations, when
they readily recall and use definitions, facts and standard procedures, and when they can
manipulate expressions and equations to find solutions.
Problem Solving:
Students develop the ability to formulate and solve problems when they use mathematics to
represent unfamiliar or meaningful situations, when they design investigations and plan their
approaches, when they apply their existing strategies to seek solutions, and when they verify
that their answers are reasonable.
Reasoning Mathematically:
Students are reasoning mathematically when they explain their thinking, when they deduce
and justify strategies used and conclusions reached, when they adapt the known to the
unknown, when they transfer learning from one context to another, when they prove that
something is true or false and when they compare and contrast related ideas and explain their
choices.
A year-by-year Overview of Proficiency Strands for the primary years (Foundation to Year 6) is
provided in Appendix 2, below.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
Page 17
3. The Learning Environment
Success in learning mathematics is strongly associated with student beliefs about mathematics, and
about their own ability to “do mathematics”. Students should be encouraged to understand:

that mathematics makes sense,

that they can make sense of mathematics

that mathematics helps them make sense of the world
Good teaching requires that students are given the time and opportunity to explore, to think, and to
express themselves. They should be given opportunity to make the links between mathematical
learning and real-life situations.
Success in learning builds confidence in students. However, teachers sometimes explain too much,
and intervene too quickly to reduce the risk of error. Where problem solving is seen as integral to
mathematical learning, students will begin to understand that making mistakes is a positive and
productive part of the learning process. This is likely to reduce anxiety about “getting it wrong”, or of
“not being able to do it”, and to promote a willingness to take the risks that are needed for higherorder learning.
Teachers should be alert to the secular and consumer-oriented attitudes and lifestyles reflected in
numerous mathematics resources. They should arm themselves and their students to deal with that,
and if necessary find or design alternative learning strategies or activities.
4. The Language of Mathematics
All teachers, including maths teachers, are teachers of language, and all learning, including
learning of mathematics, is language learning.
Mathematical activity needs to be firmly embedded in language to enable:
 Exploration of and reflection on mathematical ideas
 Interaction between learners and teacher, between learners and text, and between
learners collaboratively.
 Clear and precise communication of ideas, findings and conclusions.
Students should be taught to understand and use the technical terms and specialist language
associated with mathematics.
They should also be given frequent opportunities for, and encouraged to use, language interaction
as an integral part of their mathematics learning. Development of the effective use of language in
mathematics will require sound modelling and scaffolding procedures by the teacher.
5. Student Reflection on Learning
At every possible opportunity, students should be asked to reflect on their own learning. This
reflection is most effective when goals for learning are clearly presented to them, and when they
are asked to think about the links between their own learning and these learning goals. Selfreflection can be oral or written, can be brief or extended, and should focus as much as possible on
the mathematical thinking and the problem-solving strategies used.
This ought to be done at every level, from K-12, and can range in complexity from:
 “This is what I was thinking…”
 “This is how I found the answer to the problem..”
through
 “I think I could also do the problem this way…”
 “I don’t think this makes sense, because…”
 “This is hard for me, because I don’t understand…..”
to:
 “This strategy will be most useful when…”
 “What I have learned in this unit will help me to…”
 “I need to find out more about…”
Students will need to be taught (through modelling and scaffolding) how to perform this kind of
reflection, and how it will help them to strengthen and deepen their own learning.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014
Page 18
6. ASSESSMENT OF STUDENT LEARNING
Assessment of student learning will be referenced to the Achievement Standards of the Australian
Curriculum: Mathematics. It will involve a range of assessment practices and activities, grouped
around focused observation, products and conversations.
The core Mathematics resource chosen for use at individual schools (see 8. below) will incorporate a
range of targeted assessment activities that provide a strong starting point for the assessment of
teaching and learning. Teaching staff will be expected to use (but not necessarily limit themselves) to
these activities.
The Western Australian Curriculum and Standards Authority Curriculum and Assessment Outline
provides a number of online resources to assist teachers in developing and using appropriate
assessment activities. They include:
 Judging Standards: This is an especially valuable tool for teachers. For each year level from
Preprimary to Year 6 it includes:
 Assessment pointers in a rubric format to provide a point of reference when assigning
grades to student activities. They are also useful for giving assessment feedback and for
setting the pitch of assessment tasks.
 For each year level, a number of Annotated Work Samples are provided. These are aligned
with the five-point reporting scales set out in the Assessment Pointers. These are examples
of student work that illustrate achievement at ‘A’ to ‘D’-grade for each year level.

Assessment Principles and Practices: This section provides an overview of the criteria that apply to
effective assessment activities across all learning areas.

Sample Assessment Activities: These show a range of approaches to assessment. Each activity
includes the planning process, showing how teachers developed assessment tasks linked to the
Achievement Standards, and teacher reflections summarizing the effectiveness of the assessment
activities.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
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7. SCHOOL-BASED REQUIREMENTS
Time Allocations
It is expected that teachers will focus on explicitly and systematically teaching numeracy in daily
mathematics sessions as well as integrating it with other learning areas.
The Australian Curriculum: Mathematics has given indicative time allocations as follows:
 Preprimary to Year 4: 200 hours per year (4 hours 30 minutes per week)
 Years 5 – 6:
160 hours per year (4 hours per week)
Actual allocations will vary, depending on whether the Mathematics curriculum is to be combined or
with other learning areas or presented as integrated learning topics.
Some schools or teachers may decide to alternate a term program in History with one, for example, in
Geography.
Individual schools will discuss and decide specific time allotments at a school based level, with a view
to ensuring that the yearly requirements of the Mathematics Learning Area are met.
Minimum Standards
Each school may discuss and incorporate a set of minimum standards, learning benchmarks or wholeschool agreements for each year level. These will state what students are expected to learn and by
when, so that student progress may be charted and suitable intervention or support for students may
be arranged if needed.
Tracking of Student Learning
The goal of student tracking is to assist teachers to establish directions for future numeracy teaching
and plan for responsive, differentiated numeracy instruction to meet students’ learning needs.
Student data can be collected through:
 Shared assessment tasks
 Timely assessments and tests
 Observations
The frequency and type of data that will be collected and the manner in which it will be monitored
and tracked will be discussed and decided at an individual school based level.
8. RESOURCES
Resources to support the teaching and learning of Mathematics are available in each school.
Decisions as to what resources are to be obtained and used will be made at an individual school level.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 20
9. AUDIT AND REVIEW
This document was prepared in 2014, for use in the John Calvin Primary Schools operated by the
FRSA. It has been agreed to by the Primary School Principals, and was endorsed by the FRSA Board
on ________________. It is to be in force from the 2015 school year onward.
This document is to be audited and reviewed by the schools during Term 3 of 2016, with a view to
ensuring continued compliance with the requirements set out by the School Curriculum and
Standards Authority of Western Australia, in a manner consistent with the guiding principles of the
schools.
Any changes proposed will be considered by the Primary Principals, in consultation with the teaching
staff of the schools, and decided upon at a joint meeting of principals. If agreed to, these changes will
be will be incorporated in a revision of this document, to take effect at the beginning of the following
school year.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 21
APPENDICES:
APPENDIX 1: AC MATHEMATICS: OVERVIEW OF CONTENT STRANDS –
Foundation to Year 6
APPENDIX 2: AC MATHEMATICS: OVERVIEW OF PROFICIENCY STRANDS –
Foundation to Year 6
APPENDIX 3: AC MATHEMATICS: OVERVIEW OF ACHIEVEMENT STANDARDS –
Foundation to Year 6
APPENDIX 4: AC MATHEMATICS SCOPE AND SEQUENCE – Year-by-Year Overviews:
Foundation to Year 6
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 22
APPENDICES
APPENDIX 1: AC MATHEMATICS:
Pre-primary to Year 6
Number and Algebra Strand
Pre-primary
OVERVIEW OF CONTENT STRANDS –
Year 1
Year 2
Year 3
 Develop confidence with number
sequences to and from 100 by ones
from any starting point. Skip count by
twos, fives and tens starting from
zero (ACMNA012)
 Recognise, model, read, write and
order numbers to at least 100.
Locate these numbers on a number
line (ACMNA013)
 Count collections to 100 by
partitioning numbers using place
value (ACMNA014)
 Represent and solve simple addition
and subtraction problems using a
range of strategies including
counting on, partitioning and
rearranging parts (ACMNA015)
 Investigate number sequences,
initially those increasing and
decreasing by twos, threes, fives and
ten from any starting point, then
moving to other sequences.
(ACMNA026)
 Recognise, model, represent and
order numbers to at least 1000
(ACMNA027)
 Group, partition and rearrange
collections up to 1000 in hundreds,
tens and ones to facilitate more
efficient counting (ACMNA028)
 Explore the connection between
addition and subtraction
(ACMNA029)
 Solve simple addition and
subtraction problems using a range
of efficient mental and written
strategies (ACMNA030)
 Recognise and represent
multiplication as repeated addition,
groups and arrays (ACMNA031)
 Recognise and represent division as
grouping into equal sets and solve
simple problems using these
representations (ACMNA032)
 Investigate the conditions required
for a number to be odd or even and
identify odd and even numbers
(ACMNA051)
 Recognise, model, represent and
order numbers to at least 10 000
(ACMNA052)
 Apply place value to partition,
rearrange and regroup numbers to at
least 10 000 to assist calculations
and solve problems (ACMNA053)
 Recognise and explain the
connection between addition and
subtraction (ACMNA054)
 Recall addition facts for single-digit
numbers and related subtraction
facts to develop increasingly efficient
mental strategies for computation
(ACMNA055)
 Recall multiplication facts of two,
three, five and ten and related
division facts (ACMNA056)
 Represent and solve problems
involving multiplication using efficient
mental and written strategies and
appropriate digital technologies
(ACMNA057)
 Recognise and describe one-half as
one of two equal parts of a whole.
(ACMNA016)
 Recognise and interpret common
uses of halves, quarters and eighths
of shapes and collections
(ACMNA033)
 Model and represent unit fractions
including 1/2, 1/4, 1/3, 1/5 and their
multiples to a complete whole
(ACMNA058)
 Recognise, describe and order
Australian coins according to their
value (ACMNA017)
 Count and order small collections of
Australian coins and notes according
to their value (ACMNA034)
 Represent money values in multiple
ways and count the change required
for simple transactions to the nearest
five cents (ACMNA059)
 Investigate and describe number
patterns formed by skip counting and
patterns with objects (ACMNA018)
 Describe patterns with numbers and
identify missing elements
(ACMNA035)
 Solve problems by using number
sentences for addition or subtraction
(ACMNA036)
 Describe, continue, and create
number patterns resulting from
performing addition or subtraction
(ACMNA060)
Number and Place Value
 Establish understanding of the
language and processes of counting
by naming numbers in sequences,
initially to and from 20, moving
from any starting point (ACMNA001)
 Connect number names, numerals
and quantities, including zero, initially
up to 10 and then beyond
(ACMNA002)
 Subitise small collections of objects
(ACMNA003)
 Compare, order and make
correspondences between
collections, initially to 20, and explain
reasoning (ACMNA289)
 Represent practical situations to
model addition and sharing
(ACMNA004)
Fractions and Decimals
Money and Financial Mathematics
Patterns and Algebra
 Sort and classify familiar objects and
explain the basis for these
classifications. Copy, continue and
create patterns with objects and
drawings (ACMNA005)
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 23
Number and Algebra Strand
Year 4
Year 5
Year 6
Number and Place Value
 Investigate and use the properties of odd and even
numbers (ACMNA071)
 Recognise, represent and order numbers to at
least tens of thousands (ACMNA072)
 Apply place value to partition, rearrange and
regroup numbers to at least tens of thousands to
assist calculations and solve problems
(ACMNA073)
 Investigate number sequences involving multiples
of 3, 4, 6, 7, 8, and 9 (ACMNA074)
 Recall multiplication facts up to 10 × 10 and related
division facts (ACMNA075)
 Develop efficient mental and written strategies and
use appropriate digital technologies for
multiplication and for division where there is no
remainder (ACMNA076)
 Identify and describe factors and multiples of whole
numbers and use them to solve problems
(ACMNA098)
 Use estimation and rounding to check the
reasonableness of answers to calculations
(ACMNA099)
 Solve problems involving multiplication of large
numbers by one- or two-digit numbers using
efficient mental, written strategies and appropriate
digital technologies (ACMNA100)
 Solve problems involving division by a one digit
number, including those that result in a remainder
(ACMNA101)
 Use efficient mental and written strategies and
apply appropriate digital technologies to solve
problems (ACMNA291)
 Identify and describe properties of prime,
composite, square and triangular numbers
(ACMNA122)
 Select and apply efficient mental and written
strategies and appropriate digital technologies to
solve problems involving all four operations with
whole numbers (ACMNA123)
 Investigate everyday situations that use integers.
Locate and represent these numbers on a number
line (ACMNA124)
 Compare and order common unit fractions and
locate and represent them on a number line
(ACMNA102)
 Investigate strategies to solve problems involving
addition and subtraction of fractions with the same
denominator (ACMNA103)
 Recognise that the place value system can be
extended beyond hundredths (ACMNA104)
 Compare, order and represent decimals
(ACMNA105)
 Compare fractions with related denominators and
locate and represent them on a number line
(ACMNA125)
 Solve problems involving addition and subtraction
of fractions with the same or related denominators
(ACMNA126)
 Find a simple fraction of a quantity where the result
is a whole number, with and without digital
technologies (ACMNA127)
 Add and subtract decimals, with and without digital
technologies, and use estimation and rounding to
check the reasonableness of answers
(ACMNA128)
 Multiply decimals by whole numbers and perform
divisions by non-zero whole numbers where the
results are terminating decimals, with and without
digital technologies (ACMNA129)
 Multiply and divide decimals by powers of 10
(ACMNA130)
 Make connections between equivalent fractions,
decimals and percentages (ACMNA131)
 Create simple financial plans (ACMNA106)
 Investigate and calculate percentage discounts of
10%, 25% and 50% on sale items, with and without
digital technologies (ACMNA132)
 Describe, continue and create patterns with
fractions, decimals and whole numbers resulting
from addition and subtraction (ACMNA107)
 Use equivalent number sentences involving
multiplication and division to find unknown
quantities (ACMNA121)
 Continue and create sequences involving whole
numbers, fractions and decimals. Describe the rule
used to create the sequence (ACMNA133)
 Explore the use of brackets and order of operations
to write number sentences (ACMNA134)
Fractions and Decimals
 Investigate equivalent fractions used in contexts
(ACMNA077)
 Count by quarters halves and thirds, including with
mixed numerals. Locate and represent these
fractions on a number line (ACMNA078)
 Recognise that the place value system can be
extended to tenths and hundredths. Make
connections between fractions and decimal
notation (ACMNA079)
Money and Financial Mathematics
 Solve problems involving purchases and the
calculation of change to the nearest five cents with
and without digital technologies (ACMNA080)
Patterns and Algebra
 Explore and describe number patterns resulting
from performing multiplication (ACMNA081)
 Solve word problems by using number sentences
involving multiplication or division where there is no
remainder (ACMNA082)
 Use equivalent number sentences involving
addition and subtraction to find unknown quantities
(ACMNA083)
Continued…
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
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AC MATHEMATICS: OVERVIEW
Pre-primary to Year 6
Measurement and Geometry Strand
Pre-primary
Year 1
OF CONTENT STRANDS –
(continued):
Year 2
Year 3
 Measure and compare the lengths
and capacities of pairs of objects
using uniform informal units
(ACMMG019)
 Tell time to the half-hour
(ACMMG020)
 Describe duration using months,
weeks, days and hours
(ACMMG021)
 Compare and order several shapes
and objects based on length, area,
volume and capacity using
appropriate uniform informal units
(ACMMG037)
 Compare masses of objects using
balance scales (ACMMG038)
 Tell time to the quarter-hour, using
the language of 'past' and 'to'
(ACMMG039)
 Name and order months and
seasons (ACMMG040)
 Use a calendar to identify the date
and determine the number of days in
each month (ACMMG041)
 Measure, order and compare objects
using familiar metric units of length,
mass and capacity (ACMMG061)
 Tell time to the minute and
investigate the relationship between
units of time (ACMMG062)
 Recognise and classify familiar twodimensional shapes and threedimensional objects using obvious
features (ACMMG022)
 Describe and draw two-dimensional
shapes, with and without digital
technologies (ACMMG042)
 Describe the features of threedimensional objects (ACMMG043)
 Make models of three-dimensional
objects and describe key features
(ACMMG063)
 Interpret simple maps of familiar
locations and identify the relative
positions of key features
(ACMMG044)
 Investigate the effect of one-step
slides and flips with and without
digital technologies (ACMMG045)
 Identify and describe half and quarter
turns (ACMMG046)
 Create and interpret simple grid
maps to show position and pathways
(ACMMG065)
 Identify symmetry in the environment
(ACMMG066)
Using Units of Measurement
 Use direct and indirect comparisons
to decide which is longer, heavier or
holds more, and explain reasoning in
everyday language(ACMMG006)
 Compare and order the duration of
events using the everyday language
of time(ACMMG007)
 Connect days of the week to familiar
events and actions(ACMMG008)
Shape
 Sort, describe and name familiar
two-dimensional shapes and threedimensional objects in the
environment (ACMMG009)
Location and Transformation
 Describe position and
movement(ACMMG010)
 Give and follow directions to familiar
locations(ACMMG023)
Geometric Reasoning
 Identify angles as measures of turn
and compare angle sizes in everyday
situations (ACMMG064)
Statistics and Probability Strand
Pre-primary
Year 1
Year 2
Year 3
Chance
 Identify outcomes of familiar events
involving chance and describe them
using everyday language such as
‘will happen’, ‘won’t happen’ or ‘might
happen’ (ACMSP024)
 Identify practical activities and
everyday events that involve
chance. Describe outcomes as
‘likely’ or ‘unlikely’ and identify
some events as ‘certain’ or
‘impossible’ (ACMSP047)
 Conduct chance experiments,
identify and describe possible
outcomes and recognise variation
in results (ACMSP067)
Data Representation and Interpretation
 Answer yes/no questions to
collect information(ACMSP011)
 Choose simple questions and gather
responses (ACMSP262)
 Represent data with objects and
drawings where one object or
drawing represents one data value.
Describe the displays (ACMSP263)
 Identify a question of interest based
on one categorical variable. Gather
data relevant to the
question(ACMSP048)
 Collect, check and classify data
(ACMSP049)
 Create displays of data using lists,
table and picture graphs and
interpret them (ACMSP050)
 Identify questions or issues for
categorical variables. Identify data
sources and plan methods of data
collection and recording
(ACMSP068)
 Collect data, organise into categories
and create displays using lists,
tables, picture graphs and simple
column graphs, with and without the
use of digital technologies
(ACMSP069)
 Interpret and compare data displays
(ACMSP070)
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 25
Measurement and Geometry Strand
Year 4
Year 5
Year 6
Using Units of Measurement
 Use scaled instruments to measure and compare
lengths, masses, capacities and temperatures
(ACMMG084)
 Compare objects using familiar metric units of area
and volume (ACMMG290)
 Convert between units of time (ACMMG085)
 Use am and pm notation and solve simple time
problems (ACMMG086)
 Choose appropriate units of measurement for
length, area, volume, capacity and mass
(ACMMG108)
 Calculate the perimeter and area of rectangles
using familiar metric units (ACMMG109)
 Compare 12- and 24-hour time systems and
convert between them (ACMMG110)
 Connect decimal representations to the metric
system (ACMMG135)
 Convert between common metric units of length,
mass and capacity (ACMMG136)
 Solve problems involving the comparison of
lengths and areas using appropriate units
(ACMMG137)
 Connect volume and capacity and their units of
measurement (ACMMG138)
 Interpret and use timetables (ACMMG139)
 Connect three-dimensional objects with their nets
and other two-dimensional representations
(ACMMG111)
 Construct simple prisms and pyramids
(ACMMG140)
 Use a grid reference system to describe locations.
Describe routes using landmarks and directional
language (ACMMG113)
 Describe translations, reflections and rotations of
two-dimensional shapes. Identify line and rotational
symmetries (ACMMG114)
 Apply the enlargement transformation to familiar
two dimensional shapes and explore the properties
of the resulting image compared with the original
(ACMMG115)
 Investigate combinations of translations, reflections
and rotations, with and without the use of digital
technologies (ACMMG142)
 Introduce the Cartesian coordinate system using all
four quadrants (ACMMG143)
 Estimate, measure and compare angles using
degrees. Construct angles using a protractor
(ACMMG112)
 Investigate, with and without digital technologies,
angles on a straight line, angles at a point and
vertically opposite angles. Use results to find
unknown angles (ACMMG141)
Shape
 Compare the areas of regular and irregular shapes
by informal means (ACMMG087)
 Compare and describe two dimensional shapes
that result from combining and splitting common
shapes, with and without the use of digital
technologies (ACMMG088)
Location and Transformation
 Use simple scales, legends and directions to
interpret information contained in basic maps
(ACMMG090)
 Create symmetrical patterns, pictures and shapes
with and without digital technologies (ACMMG091)
Geometric Reasoning
 Compare angles and classify them as equal to,
greater than or less than a right angle
(ACMMG089)
Statistics and Probability Strand
Year 4
Year 5
Year 6
Chance
 Describe possible everyday events and order their
chances of occurring (ACMSP092)
 Identify everyday events where one cannot happen
if the other happens (ACMSP093)
 Identify events where the chance of one will not be
affected by the occurrence of the other
(ACMSP094)
 List outcomes of chance experiments involving
equally likely outcomes and represent probabilities
of those outcomes using fractions (ACMSP116)
 Recognise that probabilities range from 0 to 1
(ACMSP117)
 Describe probabilities using fractions, decimals and
percentages (ACMSP144)
 Conduct chance experiments with both small and
large numbers of trials using appropriate digital
technologies (ACMSP145)
 Compare observed frequencies across
experiments with expected frequencies
(ACMSP146)
Data Representation and Interpretation
 Select and trial methods for data collection,
including survey questions and recording sheets
(ACMSP095)
 Construct suitable data displays, with and without
the use of digital technologies, from given or
collected data. Include tables, column graphs and
picture graphs where one picture can represent
many data values (ACMSP096)
 Evaluate the effectiveness of different displays in
illustrating data features including variability
(ACMSP097)
 Pose questions and collect categorical or
numerical data by observation or survey
(ACMSP118)
 Construct displays, including column graphs, dot
plots and tables, appropriate for data type, with and
without the use of digital technologies
(ACMSP119)
 Describe and interpret different data sets in context
(ACMSP120)
 Interpret and compare a range of data displays,
including side-by-side column graphs for two
categorical variables (ACMSP147)
 Interpret secondary data presented in digital media
and elsewhere (ACMSP148)
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 26
APPENDIX 2: AC MATHEMATICS:
OVERVIEW OF PROFICIENCY STRANDS – Pre-primary to Year 6
Year
P
Understanding
Fluency
 connecting names, numerals and quantities
 counting numbers in sequences readily
 continuing patterns
 comparing the lengths of objects directly
1
 connecting names, numerals and quantities
 partitioning numbers in various ways
 counting number in sequences readily forward
and backwards
 locating numbers on a line
 naming the days of the week
2
 connecting number calculations with counting
sequences
 partitioning and combining numbers flexibly
 identifying and describing the relationship
between addition and subtraction
 identifying and describing relationship
between multiplication and division
 counting numbers in sequences readily,
 using units iteratively to compare
measurements,
 listing possible outcomes of chance events
 describing and comparing time durations
3
 connecting number representations with
number sequences
 partitioning and combining numbers flexibly
 representing unit fractions
 using appropriate language to communicate
times
 identifying environmental symmetry
 making connections between representations
of numbers
 partitioning and combining numbers flexibly
 extending place value to decimals
 using appropriate language to communicate
times
 using informal units for comparing, and
describing properties of symmetrical shapes
 recalling multiplication facts
 using familiar metric units to order and
compare objects
 identifying and describing outcomes of
chance experiments
 interpreting maps and communicating
positions
 recalling multiplication tables
 communicating sequences of simple fractions
 using instruments to measure accurately
 creating patterns with shapes and their
transformations
 collecting and recording data
 making connections between representations
of numbers,
 using fractions to represent probabilities,
comparing and ordering fractions and
decimals
 representing fractions and decimals in various
ways
 describing properties of different sets of
numbers,
 using fractions and decimals to describe
probabilities,
 representing fractions and decimals in various
ways
 describing connections between fractions and
decimals
 making reasonable estimations
 choosing appropriate units of measurement
for calculation of perimeter and area
 using estimation to check the reasonableness
of answers to calculations
 using instruments to measure angles
4
5
6
 representing negative numbers on a number
line
 calculating simple percentages
 using brackets appropriately
 converting between fractions and decimals
 using operations with fractions, decimals and
percentages
 measuring using metric units
 interpreting timetables
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 27
Year
P
1
2
Problem Solving
 using materials to model authentic problems
 sorting objects
 using familiar counting sequences to solve
unfamiliar problems
 discussing the reasonableness of answers
 using materials to model authentic problems
 giving and receiving directions to unfamiliar
places
 using familiar counting sequences to solve
unfamiliar problems
 discussing the reasonableness of answers
 formulating problems from authentic situations
 making models and using number sentences
that represent problem situations
 planning routes on maps
 matching transformations with their original
shape
3
 formulating and modelling authentic situations
involving planning methods of data collection
and representation
 making models of three-dimensional objects
 using number properties to continue number
patterns
4
 formulating, modelling and recording authentic
situations involving operations, comparing
large numbers and time
 durations, and using properties of numbers to
continue patterns
5
 formulating and solving authentic problems
using numbers and measurements
 creating transformations
 identifying line and rotational symmetries
6
 formulating and solving authentic problems
using numbers and measurements
 creating similar shapes through enlargements
 representing secondary data
 calculating angles
Mathematical Reasoning
 explaining comparisons of quantities
 creating patterns
 explaining processes for indirect comparison
of length
 explaining direct and indirect comparisons of
length using uniform informal units
 justifying representations of data
 explaining patterns that have been created
 using known facts to derive strategies for
unfamiliar calculations
 comparing and contrasting related models of
operations
 describing connections between 2-D and 3-D
representations
 creating and interpreting simple
representations of data
 using generalising from number properties
and results of calculations
 comparing angles
 creating and interpreting variations in the
results of data collections and data displays
 using generalising from number properties
and results of calculations
 deriving strategies for unfamiliar multiplication
and division tasks
 comparing angles
 communicating information using graphical
displays
 evaluating the appropriateness of different
displays
 investigating strategies to perform
calculations efficiently creating financial plans
 interpreting results of chance experiments
 interpreting data sets
 explaining mental strategies for performing
calculations
 describing results for continuing number
sequences
 investigating new situations using known
properties of angles
 explaining the transformation of one shape
into another
 inferring from the results of experiments
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 28
APPENDIX 3: AC MATHEMATICS:
OVERVIEW OF ACHIEVEMENT STANDARDS – Pre-primary to Year 6
Number and Algebra Strand
Pre-primary
Year 1
Year 2
Year 3
 count to and from 100
 locate numbers up to 100 on a
number line.
 partition numbers up to 100 using
place value.
 solve simple addition and
subtraction problems using
counting strategies
 count to and from 1000 by
grouping, partitioning and
rearranging using place value.
 solve simple addition and
subtraction problems using a
small range of mental and written
strategies
 represent multiplication and
division by grouping into sets.
 count to and from 10 000 using a
range of strategies.
 recall number facts for single digit
numbers.
 identify odd and even numbers
 recognise the connection
between multiplication and
division.
 solve simple addition and
subtraction problems using a
range of mental and written
strategies with increasing fluency
 count to and from 100
 locate numbers up to 100 on a
number line.
 partition numbers up to 100 using
place value.
 solve simple addition and
subtraction problems using
counting strategies
 count to and from 1000 by
grouping, partitioning and
rearranging using place value.
 solve simple addition and
subtraction problems using a
small range of mental and written
strategies
 represent multiplication and
division by grouping into sets.
 count to and from 10 000 using a
range of strategies.
 recall number facts for single digit
numbers.
 identify odd and even numbers
 recognise the connection
between multiplication and
division.
 solve simple addition and
subtraction problems using a
range of mental and written
strategies with increasing fluency
 recognise Australian coins.
 associate collections of
Australian coins with their
value.
 represent money values in
various ways.
 correctly count out change
from financial transactions.
 continue simple patterns.
 describe number sequences
resulting from skip counting by
2’s, 5’s and 10’s
 recognise increasing and
decreasing number sequences
involving 2’, 3’s and 5’s
 identify the missing element in
a number sequence.
 describe number patterns
involving addition and
subtraction
Number and Place Value
 count to and from 20
 make connections between
number names, numerals and
quantities up to 20.
Fractions and Decimals
 count to and from 20
 make connections between
number names, numerals and
quantities up to 20.
Money and Financial Mathematics
Patterns and Algebra
 order and describe collections
 group objects based on a
common characteristics
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 29
Number and Algebra Strand
Year 4
Year 5
Year 6
 identify and describe factors and multiples
 solve simple problems involving the four
operations using a range of mental and written
strategies, including standard algorithms
 check the reasonableness of answers using
estimation and rounding.
 locate and represent positive and negative
numbers and zero on a number line.
 describe the use of positive and negative
whole numbers and zero in everyday contexts.
 recognise the properties of special numbers
 solve problems involving all four operations
with whole numbers
 compare, order and represent decimals and
unit fractions
 perform addition and subtraction of fractions
with the same denominator.
 locate and represent fractions and zero on a
number line.
 calculate a simple fraction of a quantity.
 solve problems involving the addition and
subtraction of related fractions
 add, subtract and multiply decimals
 divide decimals where the result is rational.
 connect fractions, decimals and
percentages as different representations of
the same number.
 make connections between the powers of
10 and the multiplication and division of
decimals.
 plan simple budgets.
 calculate common percentage discounts on
sale items.
 continue patterns by adding and subtracting
fractions and decimals.
 find unknown quantities in equivalent number
sentences.
 describe rules used in sequences involving
whole numbers, fractions and decimals.
 write correct number sentences using brackets
and order of operations.
 describe the four quadrants on the
Cartesian plane.
Number and Place Value
 recall multiplication facts to 10X10 and related
division facts.
 use written and mental strategies, including
standard algorithms, to solve addition and
subtraction problems
 use appropriate strategies for calculations
involving multiplication and division.
 solve simple problems using the properties of
odd and even numbers.
Fractions and Decimals
 locate familiar fractions on a number line.
 recognise common equivalent fractions in
familiar contexts
 make connections between fraction and
decimal notations up to two decimal places.
Money and Financial Mathematics
 solve simple purchasing problems.
Patterns and Algebra
 continue number sequences involving
multiples of single digit numbers.
 describe number patterns resulting from
multiplication.
 use relevant number sentences to solve
problems.
Continued…
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 30
AC MATHEMATICS:
OVERVIEW OF ACHIEVEMENT STANDARDS – Pre-primary to Year 6
Measurement and Geometry Strand
Foundation
Year 1
(cont):
Year 2
Year 3
 compare lengths and capacities
using informal units
 tell time to the half hour.
 describe time duration using
hours, days, weeks and months
 compare and order shapes and
objects using informal units.
 tell the time to the quarter hour.
 use metric units for length mass
and capacity.
 tell the time to the nearest
minute.
 classify and describe twodimensional shapes and threedimensional objects.
 draw and describe shapes
 identify the features of threedimensional objects.
 describe the features of threedimensional objects
 use the language of direction to
move from place to place.
 interpret simple maps of
familiar locations.
 explain the effects of one-step
transformations.
 match positions on maps given
relevant information.
 identify symmetrical shapes in
real situations.
Using Units of Measurement
 compare objects directly and
indirectly using mass, length
and capacity.
 explain the order and duration
of events
 connect events and the days of
the week.
Shape
 compare and sort shapes and
objects.
Location and Transformation
Geometric Reasoning
 Identify angles in real
situations.
Statistics and Probability Strand
Foundation
Year 1
Year 2
Year 3
Chance
 identify outcomes of simple
familiar events
 list outcomes for everyday
events.
 conduct chance experiments
and describe possible
outcomes
 collect data from questions
 create lists, tables and picture
graphs.
 make sense of collected
information
 carry out simple data
experiments for categorical
variables.
 interpret and compare data
displays
Data Representation and Interpretation
 answer simple questions to
collect information
 collect data by asking
questions.
 draw and describe simple data
displays.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 31
Measurement and Geometry Strand
Year 4
Year 5
Year 6
 use appropriate units of measurement for
length, area, volume, capacity and mass
 calculate perimeter and area of rectangles.
 convert between 12 and 24 hour time.
 connect decimal representations to the
metric system
 choose appropriate units of measurement to
solve problems.
 interpret and use timetables.
 connect three-dimensional objects with twodimensional representations
 construct simple prisms and pyramids
 use a grid reference system to describe
locations.
 describe transformations of two-dimensional
shapes
 identify line and rotational symmetry.
 describe combinations of translations.
 measure and construct different angles.
 use the properties of angles to solve
problems.
Using Units of Measurement
 use scaled instruments to measure and
compare lengths, shapes and objects.
 convert between units of time.
 solve problems involving time duration.
Shape
 compare areas of regular and irregular
shapes using informal units.
Location and Transformation
 interpret information contained in maps.
 create symmetrical shapes and patterns.
Geometric Reasoning
 compare and classify angles in relation
to a right-angle.
Statistics and Probability Strand
Year 4
Year 5
Year 6
 describe probabilities of everyday events.
 recognise that probabilities range between 0
and 1
 list outcomes of chance experiments.
 predict and communicate probabilities using
simple fractions, decimals and percentages.
 compare observed and expected
frequencies
Chance
 describe probabilities of everyday events
 identify dependent and independent events.
Data Representation and Interpretation
 describe different methods for data
collection,
 construct data displays
 evaluate effectiveness of data displays
 pose questions to gather data
 construct, describe and interpret different
data sets.
 interpret and compare a variety of data
 interpret and compare data displays for two
categorical variables.
 evaluate secondary data displayed in the
media
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 32
APPENDIX 4: AC MATHEMATICS
SCOPE AND SEQUENCE – Foundation to Year 6 Overviews
Year Overview: Pre-primary Year
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
including but not necessarily limited to:

connecting names, numerals and quantities










counting numbers in sequences readily
continuing patterns
comparing the lengths of objects directly
using materials to model authentic problems
sorting objects
using familiar counting sequences to solve unfamiliar problems
discussing the reasonableness of answers
explaining comparisons of quantities
creating patterns
explaining processes for indirect comparison of length
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
Number and
place value
 Establish understanding of the language and
processes of counting by naming numbers in
sequences, initially to and from 20, moving from any
starting point (ACMNA001)
 Connect number names, numerals and quantities,
including zero, initially up to 10 and then beyond
(ACMNA002)
 Subitise small collections of objects (ACMNA003)
 Compare, order and make correspondences
between collections, initially to 20, and explain
reasoning (ACMNA289)
 Represent practical situations to model addition and
sharing (ACMNA004)
 count to and from 20
 make connections between number names, numerals
and quantities up to 20.
 Sort and classify familiar objects and explain the
basis for these classifications. Copy, continue and
create patterns with objects and drawings
(ACMNA005)
 order and describe collections
 group objects based on a common characteristics
Fractions and
decimals
Money and
financial
mathematics
Patterns and
algebra
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 33
Year Overview: Pre-primary Year (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement
Shape
 Use direct and indirect comparisons to decide
which is longer, heavier or holds more, and
explain reasoning in everyday language
(ACMMG006)
 Compare and order the duration of events using
the everyday language of time (ACMMG007)
Connect days of the week to familiar events and
actions (ACMMG008)
 Sort, describe and name familiar twodimensional shapes and three-dimensional
objects in the environment (ACMMG009)
 compare objects directly and indirectly using
mass, length and capacity.
 explain the order and duration of events
 connect events and the days of the week.
 Describe position and movement (ACMMG010)
 Use appropriate language to describe position
and movement.
 compare and sort shapes and objects.
Geometric
reasoning
Location and
transformation
STATISTICS AND PROBABILITY Strand:
Chance
Data
representation
and interpretation
 Answer yes/no questions to collect information
(ACMSP011)
 answer simple questions to collect information
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 34
AC MATHEMATICS
SCOPE AND SEQUENCE –
Year Overview: Year 1
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
Pre-primary to Year 6 Overviews
including but not necessarily limited to:












connecting names, numerals and quantities
partitioning numbers in various ways
counting number in sequences readily forward and backwards
locating numbers on a line
naming the days of the week
using materials to model authentic problems
giving and receiving directions to unfamiliar places
using familiar counting sequences to solve unfamiliar problems
discussing the reasonableness of answers
explaining direct and indirect comparisons of length using uniform informal units
justifying representations of data
explaining patterns that have been created
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
 Develop confidence with number sequences to and
from 100 by ones from any starting point. Skip count
by twos, fives and tens starting from zero
(ACMNA012)
 Recognise, model, read, write and order numbers to
at least 100. Locate these numbers on a number
line (ACMNA013)
 Count collections to 100 by partitioning numbers
using place value (ACMNA014)
 Represent and solve simple addition and subtraction
problems using a range of strategies including
counting on, partitioning and rearranging parts
(ACMNA015)
 Recognise and describe one-half as one of two
equal parts of a whole. (ACMNA016)




Money and
financial
mathematics
 Recognise, describe and order Australian coins
according to their value (ACMNA017)
 recognise Australian coins.
Patterns and
algebra
 Investigate and describe number patterns formed by
skip counting and patterns with objects
(ACMNA018)
 continue simple patterns.
 describe number sequences resulting from skip
counting by 2’s, 5’s and 10’s
Number and
place value
Fractions and
decimals
count to and from 100
locate numbers up to 100 on a number line.
partition numbers up to 100 using place value.
solve simple addition and subtraction problems using
counting strategies
 identify representations of one half.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 35
Year Overview: Year 1 (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement
Shape
 Measure and compare the lengths and
capacities of pairs of objects using uniform
informal units (ACMMG019)
 Tell time to the half-hour (ACMMG020)
 Describe duration using months, weeks, days
and hours (ACMMG021)
 Recognise and classify familiar two-dimensional
shapes and three-dimensional objects using
obvious features (ACMMG022)
 compare lengths and capacities using informal
units
 tell time to the half hour.
 describe time duration using hours, days, weeks
and months
 Give and follow directions to familiar locations
(ACMMG023)
 use the language of direction to move from place
to place.
 classify and describe two-dimensional shapes
and three-dimensional objects.
Geometric
reasoning
Location and
transformation
STATISTICS AND PROBABILITY Strand:
Chance
 Identify outcomes of familiar events involving
chance and describe them using everyday
language such as ‘will happen’, ‘won’t happen’ or
‘might happen’ (ACMSP024)
 identify outcomes of simple familiar events
Data
representation
and interpretation
 Choose simple questions and gather responses
(ACMSP262)
 Represent data with objects and drawings where
one object or drawing represents one data value.
Describe the display (ACMSP263)
 answer simple questions to collect information
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 36
AC MATHEMATICS
SCOPE AND SEQUENCE –
Year Overview: Year 2
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
Pre-primary to Year 6 Overviews
including but not necessarily limited to:
















connecting number calculations with counting sequences
partitioning and combining numbers flexibly
identifying and describing the relationship between addition and subtraction
identifying and describing relationship between multiplication and division
counting numbers in sequences readily,
using units iteratively to compare measurements,
listing possible outcomes of chance events
describing and comparing time durations
formulating problems from authentic situations
making models and using number sentences that represent problem situations
planning routes on maps
matching transformations with their original shape
using known facts to derive strategies for unfamiliar calculations
comparing and contrasting related models of operations
describing connections between 2-D and 3-D representations
creating and interpreting simple representations of data
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
Number and
place value
Fractions and
decimals
Money and
financial
mathematics
Patterns and
algebra
 Investigate number sequences, initially those
increasing and decreasing by twos, threes, fives and
ten from any starting point, then moving to other
sequences (ACMNA026)
 Recognise, model, represent and order numbers to
at least 1000 (ACMNA027)
 Group, partition and rearrange collections up to
1000 in hundreds, tens and ones to facilitate more
efficient counting (ACMNA028)
 Explore the connection between addition and
subtraction (ACMNA029)
 Solve simple addition and subtraction problems
using a range of efficient mental and written
strategies (ACMNA030)
 Recognise and represent multiplication as repeated
addition, groups and arrays (ACMNA031)
 Recognise and represent division as grouping into
equal sets and solve simple problems using these
representations (ACMNA032)
 Recognise and interpret common uses of halves,
quarters and eighths of shapes and collections
(ACMNA033)
 Count and order small collections of Australian coins
and notes according to their value (ACMNA034)
 count to and from 1000 by grouping, partitioning and
rearranging using place value.
 solve simple addition and subtraction problems using a
small range of mental and written strategies
 represent multiplication and division by grouping into
sets.
 Describe patterns with numbers and identify missing
elements (ACMNA035)
 Solve problems by using number sentences for
addition or subtraction (ACMNA036)
 recognise increasing and decreasing number
sequences involving 2’, 3’s and 5’s
 identify the missing element in a number sequence.
 divide collections and shapes into halves quarters
and eighths.
 associate collections of Australian coins with their
value.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 37
Year Overview: Year 2 (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement





Shape


Compare and order several shapes and objects
based on length, area, volume and capacity
using appropriate uniform informal units
(ACMMG037)
Compare masses of objects using balance
scales (ACMMG038)
Tell time to the quarter-hour, using the
language of 'past' and 'to' (ACMMG039)
Name and order months and seasons
(ACMMG040)
Use a calendar to identify the date and
determine the number of days in each month
(ACMMG041)
Describe and draw two-dimensional shapes,
with and without digital technologies
(ACMMG042)
Describe the features of three-dimensional
objects (ACMMG043)



draw and describe shapes
identify the features of three-dimensional
objects.
Interpret simple maps of familiar locations and
identify the relative positions of key features
(ACMMG044)
Investigate the effect of one-step slides and
flips with and without digital technologies
(ACMMG045)
Identify and describe half and quarter turns
(ACMMG046)


interpret simple maps of familiar locations.
explain the effects of one-step transformations.

compare and order shapes and objects using
informal units.
tell the time to the quarter hour.
Geometric
reasoning
Location and
transformation



STATISTICS AND PROBABILITY Strand:
Chance
Data
representation
and interpretation
 Identify practical activities and everyday events
that involve chance. Describe outcomes as
‘likely’ or ‘unlikely’ and identify some events as
‘certain’ or ‘impossible’ (ACMSP047)
 Identify a question of interest based on one
categorical variable. Gather data relevant to the
question (ACMSP048)
 Collect, check and classify data (ACMSP049)
 Create displays of data using lists, table and
picture graphs and interpret them (ACMSP050)
 list outcomes for everyday events.
 collect data from questions
 create lists, tables and picture graphs.
 make sense of collected information
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 38
AC MATHEMATICS
SCOPE AND SEQUENCE –
Year Overview: Year 3
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
Pre-primary to Year 6 Overviews
including but not necessarily limited to:















connecting number representations with number sequences
partitioning and combining numbers flexibly
representing unit fractions
using appropriate language to communicate times
identifying environmental symmetry
recalling multiplication facts
using familiar metric units to order and compare objects
identifying and describing outcomes of chance experiments
interpreting maps and communicating positions
formulating and modelling authentic situations involving planning methods of data collection and representation
making models of three-dimensional objects
using number properties to continue number patterns
using generalising from number properties and results of calculations
comparing angles
creating and interpreting variations in the results of data collections and data displays
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
Number and
place value
Fractions and
decimals
Money and
financial
mathematics
Patterns and
algebra
 Investigate number sequences, initially those
increasing and decreasing by twos, threes, fives and
ten from any starting point, then moving to other
sequences (ACMNA026)
 Recognise, model, represent and order numbers to
at least 1000 (ACMNA027)
 Group, partition and rearrange collections up to
1000 in hundreds, tens and ones to facilitate more
efficient counting (ACMNA028)
 Explore the connection between addition and
subtraction (ACMNA029)
 Solve simple addition and subtraction problems
using a range of efficient mental and written
strategies (ACMNA030)
 Recognise and represent multiplication as repeated
addition, groups and arrays (ACMNA031)
 Recognise and represent division as grouping into
equal sets and solve simple problems using these
representations (ACMNA032)
 Recognise and interpret common uses of halves,
quarters and eighths of shapes and collections
(ACMNA033)
 Count and order small collections of Australian coins
and notes according to their value (ACMNA034)
 count to and from 1000 by grouping, partitioning and
rearranging using place value.
 solve simple addition and subtraction problems using a
small range of mental and written strategies
 represent multiplication and division by grouping into
sets.
 Describe patterns with numbers and identify missing
elements (ACMNA035)
 Solve problems by using number sentences for
addition or subtraction (ACMNA036)
 recognise increasing and decreasing number
sequences involving 2’, 3’s and 5’s
 identify the missing element in a number sequence.
 divide collections and shapes into halves quarters
and eighths.
 associate collections of Australian coins with their
value.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 39
Year Overview: Year 3 (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement





Shape


Compare and order several shapes and objects
based on length, area, volume and capacity
using appropriate uniform informal units
(ACMMG037)
Compare masses of objects using balance
scales (ACMMG038)
Tell time to the quarter-hour, using the
language of 'past' and 'to' (ACMMG039)
Name and order months and seasons
(ACMMG040)
Use a calendar to identify the date and
determine the number of days in each month
(ACMMG041)
Describe and draw two-dimensional shapes,
with and without digital technologies
(ACMMG042)
Describe the features of three-dimensional
objects (ACMMG043)



draw and describe shapes
identify the features of three-dimensional
objects.
Interpret simple maps of familiar locations and
identify the relative positions of key features
(ACMMG044)
Investigate the effect of one-step slides and
flips with and without digital technologies
(ACMMG045)
Identify and describe half and quarter turns
(ACMMG046)


interpret simple maps of familiar locations.
explain the effects of one-step transformations.

list outcomes for everyday events.



collect data from questions
create lists, tables and picture graphs.
make sense of collected information

compare and order shapes and objects using
informal units.
tell the time to the quarter hour.
Geometric
reasoning
Location and
transformation



STATISTICS AND PROBABILITY Strand:
Chance
Data
representation
and interpretation




Identify practical activities and everyday events
that involve chance. Describe outcomes as
‘likely’ or ‘unlikely’ and identify some events as
‘certain’ or ‘impossible’ (ACMSP047)
Identify a question of interest based on one
categorical variable. Gather data relevant to the
question (ACMSP048)
Collect, check and classify data (ACMSP049)
Create displays of data using lists, table and
picture graphs and interpret them (ACMSP050)
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 40
AC MATHEMATICS
SCOPE AND SEQUENCE –
Year Overview: Year 4
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
Pre-primary to Year 6 Overviews
including but not necessarily limited to:

















making connections between representations of numbers
partitioning and combining numbers flexibly
extending place value to decimals
using appropriate language to communicate times
using informal units for comparing, and describing properties of symmetrical shapes
recalling multiplication tables
communicating sequences of simple fractions
using instruments to measure accurately
creating patterns with shapes and their transformations
collecting and recording data
formulating, modelling and recording authentic situations involving operations, comparing large numbers and
time
durations, and using properties of numbers to continue patterns
using generalising from number properties and results of calculations
deriving strategies for unfamiliar multiplication and division tasks
comparing angles
communicating information using graphical displays
evaluating the appropriateness of different displays
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
Number and
place value
Fractions and
decimals
Money and
financial
mathematics
Patterns and
algebra
 Investigate and use the properties of odd and even numbers
(ACMNA071)
 Recognise, represent and order numbers to at least tens of
thousands (ACMNA072)
 Apply place value to partition, rearrange and regroup
numbers to at least tens of thousands to assist calculations
and solve problems (ACMNA073)
 Investigate number sequences involving multiples of 3, 4, 6,
7, 8, and 9 (ACMNA074)
 Recall multiplication facts up to 10 × 10 and related division
facts (ACMNA075)
 Develop efficient mental and written strategies and use
appropriate digital technologies for multiplication and for
division where there is no remainder (ACMNA076)
 Investigate equivalent fractions used in contexts
(ACMNA077)
 Count by quarters halves and thirds, including with mixed
numerals. Locate and represent these fractions on a
number line (ACMNA078)
 Recognise that the place value system can be extended to
tenths and hundredths. Make connections between fractions
and decimal notation (ACMNA079)
 Solve problems involving purchases and the calculation of
change to the nearest five cents with and without digital
technologies (ACMNA080)
 recall multiplication facts to 10X10 and related
division facts.
 use written and mental strategies, including
standard algorithms, to solve addition and
subtraction problems
 use appropriate strategies for calculations
involving multiplication and division.
 solve simple problems using the properties of
odd and even numbers.
 Explore and describe number patterns resulting from
performing multiplication (ACMNA081)
 Solve word problems by using number sentences involving
multiplication or division where there is no remainder
(ACMNA082)
 Use equivalent number sentences involving addition and
subtraction to find unknown quantities (ACMNA083)
 continue number sequences involving
multiples of single digit numbers.
 describe number patterns resulting from
multiplication.
 use relevant number sentences to solve
problems.
 locate familiar fractions on a number line.
 recognise common equivalent fractions in
familiar contexts
 make connections between fraction and
decimal notations up to two decimal places.
 solve simple purchasing problems.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 41
Year Overview: Year 4 (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement
Shape
Geometric
reasoning
Location and
transformation
 Use scaled instruments to measure and
compare lengths, masses, capacities and
temperatures (ACMMG084)
 Compare objects using familiar metric units of
area and volume (ACMMG290)
 Convert between units of time (ACMMG085)
 Use am and pm notation and solve simple time
problem (ACMMG086)
 Compare the areas of regular and irregular
shapes by informal means (ACMMG087)
 Compare and describe two dimensional shapes
that result from combining and splitting common
shapes, with and without the use of digital
technologies (ACMMG088)
 Compare angles and classify them as equal to,
greater than or less than a right angle
(ACMMG089)
 Use simple scales, legends and directions to
interpret information contained in basic maps
(ACMMG090)
 Create symmetrical patterns, pictures and
shapes with and without digital technologies
(ACMMG091)
STATISTICS AND PROBABILITY Strand:
Chance  Describe possible everyday events and order
their chances of occurring (ACMSP092)
 Identify everyday events where one cannot
happen if the other happens (ACMSP093)
 Identify events where the chance of one will not
be affected by the occurrence of the other
(ACMSP094)
Data  Select and trial methods for data collection,
including survey questions and recording sheets
representation
(ACMSP095)
and interpretation  Construct suitable data displays, with and
without the use of digital technologies, from
given or collected data. Include tables, column
graphs and picture graphs where one picture
can represent many data values (ACMSP096)
 Evaluate the effectiveness of different displays in
illustrating data features including variability
(ACMSP097)
 use scaled instruments to measure and compare
lengths, shapes and objects.
 convert between units of time.
 solve problems involving time duration.
 compare areas of regular and irregular shapes
using informal units.
 compare and classify angles in relation to a
right-angle.
 interpret information contained in maps.
 create symmetrical shapes and patterns.
 describe probabilities of everyday events
 identify dependent and independent events.
 describe different methods for data collection,
 construct data displays
 evaluate effectiveness of data displays
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 42
AC MATHEMATICS
SCOPE AND SEQUENCE –
Year Overview: Year 5
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
Pre-primary to Year 6 Overviews
including but not necessarily limited to:












making connections between representations of numbers,
using fractions to represent probabilities, comparing and ordering fractions and decimals
representing fractions and decimals in various ways
choosing appropriate units of measurement for calculation of perimeter and area
using estimation to check the reasonableness of answers to calculations
using instruments to measure angles
formulating and solving authentic problems using numbers and measurements
creating transformations
identifying line and rotational symmetries
investigating strategies to perform calculations efficiently creating financial plans
interpreting results of chance experiments
interpreting data sets
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
Number and
place value
Fractions and
decimals
Money and
financial
mathematics
Patterns and
algebra
 Identify and describe factors and multiples of whole
numbers and use them to solve problems
(ACMNA098)
 Use estimation and rounding to check the
reasonableness of answers to calculations
(ACMNA099)
 Solve problems involving multiplication of large
numbers by one- or two-digit numbers using efficient
mental, written strategies and appropriate digital
technologies (ACMNA100)
 Solve problems involving division by a one digit
number, including those that result in a remainder
(ACMNA101)
 Use efficient mental and written strategies and apply
appropriate digital technologies to solve problems
(ACMNA291)
 Compare and order common unit fractions and
locate and represent them on a number line
(ACMNA291)
 Investigate strategies to solve problems involving
addition and subtraction of fractions with the same
denominator (ACMNA103)
 Recognise that the system can be extended beyond
hundredths (ACMNA104)
 Compare, order and represent decimals
(ACMNA105)
 Create simple financial plans (ACMNA106)
 identify and describe factors and multiples
 solve simple problems involving the four operations
using a range of mental and written strategies, including
standard algorithms
 check the reasonableness of answers using estimation
and rounding.
 Describe, continue and create patterns with
fractions, decimals and whole numbers resulting
from addition and subtraction (ACMNA107)
 Use equivalent number sentences involving
multiplication and division to find unknown quantities
(ACMNA121)
 continue patterns by adding and subtracting
fractions and decimals.
 find unknown quantities in equivalent number
sentences.
 compare, order and represent decimals and unit
fractions
 perform addition and subtraction of fractions with the
same denominator
 plan simple budgets.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 43
Year Overview: Year 5 (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement



Shape
Geometric
reasoning
Location and
transformation





Choose appropriate units of measurement for
length, area, volume, capacity and mass
(ACMMG108)
Calculate the perimeter and area of rectangles
using familiar metric units (ACMMG109)
Compare 12- and 24-hour time systems and
convert between them (ACMMG110)
Connect three-dimensional objects with their
nets and other two-dimensional representations
(ACMMG111)
Estimate, measure and compare angles using
degrees. Construct angles using a protractor
(ACMMG112)
Use a grid reference system to describe
locations. Describe routes using landmarks and
directional language (ACMMG113)
Describe translations, reflections and rotations
of two-dimensional shapes. Identify line and
rotational symmetries (ACMMG114)
Apply the enlargement transformation to familiar
two dimensional shapes and explore the
properties of the resulting image compared with
the original (ACMMG115)
STATISTICS AND PROBABILITY Strand:
Chance  List outcomes of chance experiments involving
equally likely outcomes and represent
probabilities of those outcomes using fractions
(ACMSP116)
 Recognise that probabilities range from 0 to 1
(ACMSP117)
Data  Pose questions and collect categorical or
numerical data by observation or survey
representation
(ACMSP118)
and interpretation  Construct displays, including column graphs,
dot plots and tables, appropriate for data type,
with and without the use of digital technologies
(ACMSP119)
 Describe and interpret different data sets in
context (ACMSP120)



use appropriate units of measurement for
length, area, volume, capacity and mass
calculate perimeter and area of rectangles.
convert between 12 and 24 hour time.

connect three-dimensional objects with twodimensional representations

measure and construct different angles.

use a grid reference system to describe
locations.
describe transformations of two-dimensional
shapes
identify line and rotational symmetry.







describe probabilities of everyday events.
recognise that probabilities range between 0
and 1
list outcomes of chance experiments.
pose questions to gather data
construct, describe and interpret different data
sets.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 44
AC MATHEMATICS
SCOPE AND SEQUENCE –
Year Overview: Year 6
Proficiencies
Understanding
Fluency
Problem Solving
Mathematical
Reasoning
Sub-strands
Pre-primary to Year 6 Overviews
including but not necessarily limited to:





















describing properties of different sets of numbers,
using fractions and decimals to describe probabilities,
representing fractions and decimals in various ways
describing connections between fractions and decimals
making reasonable estimations
representing negative numbers on a number line
calculating simple percentages
using brackets appropriately
converting between fractions and decimals
using operations with fractions, decimals and percentages
measuring using metric units
interpreting timetables
formulating and solving authentic problems using numbers and measurements
creating similar shapes through enlargements
representing secondary data
calculating angles
explaining mental strategies for performing calculations
describing results for continuing number sequences
investigating new situations using known properties of angles
explaining the transformation of one shape into another
inferring from the results of experiments
Content Descriptions
Achievement Standards
NUMBER AND ALGEBRA Strand
Number and
place value
Fractions and
decimals
Money and
financial
mathematics
Patterns and
algebra
 Identify and describe factors and multiples of whole
numbers and use them to solve problems (ACMNA098)
 Use estimation and rounding to check the reasonableness
of answers to calculations (ACMNA099)
 Solve problems involving multiplication of large numbers by
one- or two-digit numbers using efficient mental, written
strategies and appropriate digital technologies (ACMNA100)
 Solve problems involving division by a one digit number,
including those that result in a remainder (ACMNA101)
 Use efficient mental and written strategies and apply
appropriate digital technologies to solve problems
(ACMNA291)
 Compare and order common unit fractions and locate and
represent them on a number line (ACMNA291)
 Investigate strategies to solve problems involving addition
and subtraction of fractions with the same denominator
(ACMNA103)
 Recognise that the system can be extended beyond
hundredths (ACMNA104)
 Compare, order and represent decimals (ACMNA105)
 Create simple financial plans (ACMNA106)
 identify and describe factors and multiples
 solve simple problems involving the four
operations using a range of mental and written
strategies, including standard algorithms
 check the reasonableness of answers using
estimation and rounding.
 Describe, continue and create patterns with fractions,
decimals and whole numbers resulting from addition and
subtraction (ACMNA107)
 Use equivalent number sentences involving multiplication
and division to find unknown quantities (ACMNA121)
 continue patterns by adding and subtracting
fractions and decimals.
 find unknown quantities in equivalent number
sentences.
 compare, order and represent decimals and
unit fractions
 perform addition and subtraction of fractions
with the same denominator
 plan simple budgets.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 45
Year Overview: Year 6 (continued):
Sub-strands
Content Descriptions
Achievement Standards
MEASUREMENT AND GEOMETRY Strand:
Using units of
measurement
Shape
Geometric
reasoning
Location and
transformation
 Choose appropriate units of measurement for
length, area, volume, capacity and mass
(ACMMG108)
 Calculate the perimeter and area of rectangles
using familiar metric units (ACMMG109)
 Compare 12- and 24-hour time systems and
convert between them (ACMMG110)
 Connect three-dimensional objects with their
nets and other two-dimensional representations
(ACMMG111)
 Estimate, measure and compare angles using
degrees. Construct angles using a protractor
(ACMMG112)
 Use a grid reference system to describe
locations. Describe routes using landmarks and
directional language (ACMMG113)
 Describe translations, reflections and rotations of
two-dimensional shapes. Identify line and
rotational symmetries (ACMMG114)
 Apply the enlargement transformation to familiar
two dimensional shapes and explore the
properties of the resulting image compared with
the original (ACMMG115)
STATISTICS AND PROBABILITY Strand:
Chance  List outcomes of chance experiments involving
equally likely outcomes and represent
probabilities of those outcomes using fractions
(ACMSP116)
 Recognise that probabilities range from 0 to 1
(ACMSP117)

Pose questions and collect categorical or
Data
numerical data by observation or survey
representation
(ACMSP118)
and interpretation  Construct displays, including column graphs, dot
plots and tables, appropriate for data type, with
and without the use of digital technologies
(ACMSP119)
 Describe and interpret different data sets in
context (ACMSP120)
 use appropriate units of measurement for length,
area, volume, capacity and mass
 calculate perimeter and area of rectangles.
 convert between 12 and 24 hour time.
 connect three-dimensional objects with twodimensional representations
 measure and construct different angles.
 use a grid reference system to describe
locations.
 describe transformations of two-dimensional
shapes
 identify line and rotational symmetry.
 describe probabilities of everyday events.
 recognise that probabilities range between 0 and
1
 list outcomes of chance experiments.
 pose questions to gather data
 construct, describe and interpret different data
sets.
John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 –
2014
Page 46
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