Introducing the Australian
Curriculum: Mathematics
Consultation Version 1, ACARA, March 2010
Australian Curriculum Timeline
Phase One – K-10 English, Mathematics, Science, History
Shape May 2009; Consultation to May 2010; Online Nov 2010
11-12 Consultation to June 2010; Online Nov 2010
Phase Two – Geography, Languages, Arts
Shape June 2010; Consultation to Online 2011
Phase Three - ICT; Design & Technology; Health & PE,
Economics; Business, Civics and Citizenship
Timeline to be advised.
ACARA Curriculum Development
Process for Mathematics
 National Mathematics Curriculum Framing Paper
(NCB, November, 2008)
 Shape of the Australian Curriculum: Mathematics
(ACARA, May, 2009)
Curriculum Development Process
Mid-2009 ACARA Writing Panel formed  Preliminary Draft Australian Curriculum: Maths K-10
(ACARA, September, 2009)
 Draft Consultation Version 1.0 K-10
(ACARA, March, 2010)
 Year 11-12 Curriculum tracking about 3 months behind K-10
Mid-2010 Analysis of Feedback by K-10 Consultation and
refinement of document in preparation for online publication
by late 2010.
Considerations for Writers
 nature of the learner and learning, including
consideration of developmental changes in young
 whole curriculum and how learning areas relate
 structural matters (K/T/P; Year 7; Senior Years)
 inclusivity
 general capabilities
 cross-curriculum dimensions
Teaching & Learning Considerations
Australian Curriculum will detail what teachers are
expected to teach and students are expected to
learn for each year of schooling.
While written on a year-by-year basis, the
curriculum acknowledges that, in any one year
group, there will be a significant range of
Teaching & Learning Considerations
Teachers will be required to understand the
developmental diversity in the students they teach
and are responsible for organising learning
opportunities to meet individual learning needs.
Curriculum documents will be written in a way that
assists teachers to identify and respond to this
range of achievement.
Teaching & Learning Considerations
The curriculum should not predetermine the
instructional approach to be taken by teachers.
The curriculum should provide some flexibility for
teachers to accommodate different levels of student
development and achievement and approaches to
General Capabilities
The National Declaration on Educational Goals for
Young Australians (Melbourne Declaration, November,
2008) identified important general capabilities that
schools should help students develop, in addition to
content of particular learning areas.
It was required that these be incorporated into the
Australian Curriculum.
General Capabilities (maths focus)
 Literacy – writing, interpreting mathematical texts
 Numeracy – application of mathematics
 ICT – calculators, spreadsheets, dynamic geometry
 Thinking Skills – reasoning and problem-solving; critical
thinking and justification; identifying questions to
General Capabilities
 Creativity – approaching problems in different ways
 Self-management
 Teamwork
 Intercultural understanding (Indigenous
 Ethical behaviour
 Social competence
General Capabilities
The Australian Curriculum will ensure that young
Australians will be provided with the opportunity to
learn about, acknowledge and value:
 the cultures of Indigenous peoples
 sustainable patterns of living
 Australia’s engagement with Asia.
Phases of Learning
 Years K – 2 (5 – 8 years of age)
 Years 3 - 6 (8 – 12 years of age)
 Years 7 - 10 (12-15 years of age)
 Years 11 - 12 (15+ years of age)
Phases of Learning
Australian Curriculum will:
 take Kindergarten (Preparation, Reception,
Transition) as the first year of schooling and design
curriculum for students who are between 5 and 6
years old in this first year
 be designed for Year 7 as part of a K–10 sequence
of learning for each of the learning areas. It will be
written to be taught in either a primary or secondary
school setting.
Australian Curriculum and NTCF Maths
The renewed NTCF – Mathematics Learning Area was
based on the National Mathematics Curriculum
Framing Paper (NCB, November, 2008).
Rationale and Aims of both the Australian and
NTCF documents are consistent.
Australian Curriculum and NTCF
 Essential mathematics knowledge and skills
 Appreciate power and elegance of mathematical
reasoning, importance of developing problem-solving
 Links between components of mathematics and
relationships with other learning areas
 Recognition of digital technologies
Australian Curriculum and NTCF
 Active and confident learners and users of
 Numeracy Capability –
Numeracy is the capacity, confidence and disposition to
use mathematics to meet the demands of learning,
school, home, work, community and civic life.
p.5 Shape of Australian Curriculum: Mathematics
p.1 NTCF Introduction to Mathematics Learning Area
ACARA Literacy & Numeracy Continua
 Literacy and Numeracy Continua are being developed for
Years 2, 4, 6, 8 and 10.
 The continua will provide advice about appropriate
attention to literacy and numeracy content to be included
in the curriculum.
 They will also serve to inform the NAPLAN.
Position on Numeracy
Numeracy is fundamentally the responsibility of
mathematics and is applied in other learning areas. It is
crucial that the mathematics curriculum provides the
opportunity to apply mathematical understanding and skills
in context, both in other learning areas and in real world
Position on Numeracy
 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 world in the 21st century is information driven
and statistics and probability provide opportunities
for students to interpret data and make informed
judgements about events involving chance.
Australian Curriculum and NTCF
Renewed NTCF and Australian Curriculum are
‘standards-based’ documents.
Content organisation is different:
NTCF - organised by developmental
Key Growth Points and Bands, with related Achievement and
Reporting Standards.
ACARA – organised by year-levels with expected
achievement standards that will be reported A-E.
ACARA Achievement Standards
The achievement standard will:
• describe the quality of expected learning
• be exemplified by annotated work samples that illustrates
the quality of learning
• be accompanied by A-E descriptors to assist reports to
Year One Achievement Standard
By the end of Year 1,
Students are able to quantify collections to 20 and can count
forwards and backwards to 100. They understand and are fluent
with partitioning numbers to 10. They can read, write, order and
model two-digit numbers and understand that these numbers are
comprised of units of tens and ones. They are beginning to
understand the relationship between addition and subtraction
and use this knowledge to model and solve simple additive
Students collect data about themselves and their
peers and represent these data in lists, tables and pictographs.
They use everyday language to describe simple geometry and
Measurement ideas and use uniform informal units to measure and
compare length and capacity and use hours and half-hours to describe
ACARA Achievement Standards
 Each K–10 achievement standard will be aligned
with a ‘C level’ .
 A ‘D level’ describes a quality of learning that is
adequate for progression but may indicate the
student will need additional support or assistance in
progressing within the next level.
ACARA Achievement Standards
 Additional work samples, which illustrate
achievement well above and well below the
achievement standard, will be provided to teachers
to assist them to make on-balance judgements of A,
B, D and E standards of achievement.
Content and Proficiency Strands
Australian Curriculum
Three content strands (nouns): Declarative Knowledge
• Number and Algebra
• Measurement and Geometry
• Statistics and Probability
Number, Algebra
Measurement, Space
Chance and Data
Australian Curriculum
Expectations for proficiency (verbs) Procedural Knowledge
• Understanding
• Fluency
• Problem solving
• Reasoning
Proficiency strands include and extend upon the
NTCF’s Key Overarching Mathematical Outcomes:
working mathematically procedural knowledge.
Understanding – building robust, adaptable, transferable
mathematical concepts, the making of connections between
related concepts, the confidence to use the familiar to
develop new ideas, and the ‘why’ as well as the ‘how’ of
Fluency – skill in choosing appropriate procedures, carry
out procedures flexibly, accurately, efficiently, and
appropriately, and, in also, recalling factual knowledge
and concepts readily.
Problem-solving – the ability to make choices,
interpret, formulate, model and investigate problem
situations, and communicate solutions effectively.
Reasoning – the capacity for logical thought and
actions such as analysing, proving, evaluating, explaining,
inferring, justifying and generalising.
Key Overarching Mathematical Outcomes
 Appropriate and efficient application of skills, concepts and
techniques in a range of contexts
(Understanding, Fluency)
 Effective and meaningful communication of Mathematical
(Problem-solving, Understanding, Fluency)
 Appropriate and varied ways of working through Mathematical
(Understanding, Reasoning)
 Effective and appropriate use of technologies and other
 Generalisation
(Understanding, Reasoning)
Teaching and Learning
Proficiency strands describe ‘how’ content strands are
ie thinking and doing mathematics, and have been
incorporated into the content elaborations.
Teaching and Learning
 Challenging problems can be posed using basic
 Content acceleration may not be the best way to
extend students.
 Choosing engaging experiences as contexts for a
variety of tasks assists in making mathematics
* Enabling and Extending prompts
* Open-ended questions / activities
Content Descriptions
Content descriptions are available for each strand at
each year level and represent a scope and sequence
of what teachers are expected to teach.
Year One - Number and Algebra
1. Counting
Say, understand and reason with number sequences to and from 100
by ones from many starting point, and say number sequences of
twos, fives and tens starting from zero.
 The Australian Curriculum is attempting to reduce the
‘overcrowded curriculum’:
 Recognises interrelationships between strands;
number / algebra
space / measurement (geometry)
 Emphasises key mathematical ideas at a year level
 Generally speaking, there is good alignment between the
Content Descriptions (ACARA) and the key learnings of the
NTCF in Mathematics.
Content Elaborations
Provide additional illustrations and examples of
Assist to develop a common understanding of what is
to be taught.
Integrate content strands to the proficiency strands.
Content Elaborations
Year One - Number and Algebra
1. Counting
 saying number sequences emphasising 10 as a countable unit assists to
develop an understanding of place value
 developing fluency with forwards and backwards counting in meaningful
contexts such as circle games (eg ‘I’m going to start at 24 and when I get to
13, everyone will be sitting in a circle’)
 using a calculator to increase understanding of counting patterns (eg count
by adding 2 each time, beginning with 0 and press +2 = = repeatedly)
 understanding that skip counting (eg counting 5-cent coins) will also tell you
how much money is in a collection and can assist with counting in a faster
Hyperlinks in the content descriptions will link to
teaching resources and professional learning
Time Allocations
For Mathematics, ACARA have adopted the
recommendation of the
National Numeracy Review Report (COAG, May, 2008):
That all jurisdictions should work towards a minimum of
5 hours per week of mathematics for students in all the
primary Years K to 6/7 and a minimum of 4 hours per week
in all the lower secondary Years 7/8 to 10. This time should
include cross curricular learning.
p. 18
Learning Design Model
ACARA has provided for the Australian Curriculum:
 a rationale and aims
 content structure
 pedagogy and assessment considerations,
but has not recommended a learning design model.
Use NTCF Learning Design Approach
Eight Learning Management Questions, Smith &Lynch, 2006
concept maps
written reports
oral presentations
practical demonstrations
multimedia presentations
spreadsheets or graphs
tables or charts
models or constructions
diagrams or pictures
Strategies in
learning portfolios
diagnostic tasks
learning journal
open ended questions
work samples
directed investigations
self assessment
open investigations
reflections (oral or written)
problem solving
pen and paper tests
Newman's error analysis
Feedback to ACARA
Feedback from today’s session:
 Maths PLC (Top End / Central Australia).
Carousel Brainstorm
Topic Sheets
1. Achievement Standards / Content Descriptions
2. Elaborations (to Content Descriptions)
3. General Capabilities / Cross-Curriculum links
4. User-friendliness / Other Suggestions
Facilitator Role ; focus; record; summarise
Groups rotate through topic sheets and provide
feedback. 10-15 minutes

Mtant Presentation A cara Maths