Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
The Australian Curriculum achievement standards are an expectation of the depth of understanding, the extent of knowledge and the sophistication of
skills that students should typically demonstrate at the end of a teaching and learning year. In Queensland, the Year 6 Australian Curriculum
achievement standard represents a C standard — a sound level of knowledge and understanding of the content, and application of skills.
Year 6 Australian Curriculum: Mathematics achievement standard
By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday
contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations
of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the
multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal
representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and
volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using
the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for
two categorical variables. They evaluate secondary data displayed in the media.
Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide
decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and
order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids.
Students list and communicate probabilities using simple fractions, decimals and percentages.
Source: Australian Curriculum, Assessment and Reporting Authority (ACARA), Australian Curriculum v6.0 Mathematics for Foundation–10, www.australiancurriculum.edu.au/mathematics/Curriculum/F-10
A
B
C
D
E
Complex unfamiliar
Complex familiar or simple
unfamiliar
Simple familiar
Some simple familiar
Partial, isolated and obvious
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The standards elaborations (SEs) should be used in conjunction with the Australian Curriculum achievement standard and content descriptions for the
relevant year level. They provide additional clarity about using the Australian Curriculum achievement standard to make judgments on a five-point
scale. In mathematics, performance is represented by the complexity and familiarity of the aspects of the standard being assessed, for example:
The SEs for Mathematics have been developed using the proficiency strands Understanding, Fluency, Problem solving and Reasoning.
They promote and support:
 aligning curriculum, assessment and reporting, connecting curriculum and evidence in assessment, so that what is assessed relates directly to what
students have had the opportunity to learn
 continuing skill development from one year of schooling to another
 making judgments on a five-point scale based on evidence of learning in a folio of student work
 planning an assessment program and individual assessments
 developing task-specific standards and grading guides.
Year 6 Mathematics standard elaborations
A
B
REVISED DRAFT
C
D
E
Conceptual
understanding
Connection and
description of
mathematical concepts
and relationships in a
range of situations,
including some that are
complex unfamiliar
Connection and
description of
mathematical concepts
and relationships in
complex familiar or
simple unfamiliar
situations
Recognition and
identification of
mathematical concepts
and relationships in
simple familiar situations
Some identification of
simple mathematical
concepts
Statements about
obvious mathematical
concepts
Procedural
fluency
Recall and use of facts,
definitions, technologies
and procedures to find
solutions in a range of
situations including some
that are complex
unfamiliar
Recall and use of facts,
definitions, technologies
and procedures to find
solutions in complex
familiar or simple
unfamiliar situations
Recall and use of facts,
definitions, technologies
and procedures to find
solutions in simple
familiar situations
Some recall and use of
facts, definitions,
technologies and simple
procedures
Partial recall of facts,
definitions and use of
simple procedures
Mathematical
language and
symbols
Understanding & Fluency
Understanding and skills dimensions
The folio of student work has the following characteristics:
Effective and clear use of
appropriate
mathematical
terminology, diagrams
and symbols
Consistent use of
appropriate
mathematical
terminology, diagrams
and symbols
Satisfactory use of
appropriate
mathematical
terminology, diagrams
and symbols
Use of aspects of
mathematical
terminology, diagrams
and symbols
Use of everyday
language
Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Queensland Curriculum & Assessment Authority
July 2014
Page 2 of 8
A
B
C
D
E
Problem-solving
approaches
Mathematical
modelling
Reasoning
and
justification
Problem solving & Reasoning
Understanding and skills dimensions
The folio of student work has the following characteristics:
Systematic application of
relevant problem-solving
approaches to
investigate a range of
situations, including
some that are complex
unfamiliar
Application of relevant
problem-solving
approaches to investigate
complex familiar or simple
unfamiliar situations
Application of
problem-solving
approaches to
investigate simple
familiar situations
Some selection and
application of
problem-solving
approaches in simple
familiar situations
Partial selection of
problem-solving
approaches
Development of
mathematical models
and representations in a
range of situations,
including some that are
complex unfamiliar
Development of
mathematical models and
representations in
complex familiar or simple
unfamiliar situations
Development of
mathematical models
and representations in
simple familiar situations
Statements about simple
mathematical models
and representations
Isolated statements
about given
mathematical models
and representations
Clear explanation of
mathematical thinking
and reasoning, including
justification of choices
made, strategies used
and conclusions reached
Explanation of
mathematical thinking and
reasoning, including
reasons for choices
made, strategies used
and conclusions reached
Description of
mathematical thinking
and reasoning, including
discussion of choices
made, strategies used
and conclusions
reached
Statements about
choices made and
strategies used
Isolated statements
about given strategies or
conclusions
Note: Colour highlights have been used in the table to emphasise the qualities that discriminate between the standards.
Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Queensland Curriculum & Assessment Authority
July 2014
Page 3 of 8
Notes
The SEs describe the qualities of achievement in the two dimensions common to all Australian
Curriculum learning area achievement standards:
 understanding
 skills.
Dimension*
Description
Understanding*
The concepts underpinning and connecting knowledge in a learning area,
related to a student’s ability to appropriately select and apply knowledge
to solve problems in that learning area
Skills*
The specific techniques, strategies and processes in a learning area
The SEs for Mathematics have been developed from the proficiency strands Understanding,
Fluency, Problem solving and Reasoning.
Proficiency
Description
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. Students build understanding when they connect
related ideas, when they represent concepts in different ways, when they
identify commonalities and differences between aspects of content, when
they describe their thinking mathematically and when they interpret
mathematical information.
Fluency
Students develop skills in choosing appropriate procedures, carrying out
procedures flexibly, accurately, efficiently and appropriately, and recalling
factual knowledge and concepts readily. 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 recall definitions and regularly use facts, and
when they can manipulate expressions and equations to find solutions.
Problem solving
Students develop the ability to make choices, interpret, formulate, model
and investigate problem situations, and communicate solutions effectively.
Students 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
Students develop an increasingly sophisticated capacity for logical
thought and actions, such as analysing, proving, evaluating, explaining,
inferring, justifying and generalising. 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.
Source: ACARA, Australian Curriculum: Content structure, www.australiancurriculum.edu.au/Mathematics/Content-structure
*
The asterisk (*) denotes dimensions and terms described by ACARA. Unmarked terms are described by QCAA.
Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
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Queensland Curriculum & Assessment Authority
July 2014
The following terms and key words are used in the Year 6 Mathematics SEs. They help to clarify
the descriptors and should be used in conjunction with the ACARA Australian Curriculum
Mathematics glossary: www.australiancurriculum.edu.au/mathematics/Glossary
Term
Description
Accuracy; Accurate
Consistent with a standard, rule, convention or known fact
Application, Apply*
Use or employ in a particular situation
Appropriate
Fitting, suitable to the context
Aspects
Particular parts or features
Clarity; Clear
Without ambiguity; explicit
Comparison; Compare*
Estimate, measure or note how things are similar or dissimilar
Complexity; Complex
Involving a number of elements, components or steps
Conceptual
understanding
Connection, description, recognition and identification of mathematical
concepts and relationships.
Examples in Year 6 include:
Number and algebra
 recognising patterns and describing relationships between fractions,
decimals and percentages
 describing properties of whole numbers
 representing positive and negative numbers, and describing of the role
of zero on a number line
 connecting fractions, decimals and percentages as different
representations of fractional amounts
Measurement and geometry
 identifying the relationship between different units of measurement,
such as recognising that 1 ml is equivalent to 1 cm3
 identifying, visualising and quantifying the attributes of shapes and
objects, such as right, acute, obtuse, straight and reflex angles
 exploring measurement concepts and geometric relationships, such as
understanding that the Cartesian plane provides a graphical or visual
way of describing location
Statistics and probability
 describing probabilities as factions and decimals
 identifying that experimental results tend to become closer to the
predicted result when conducting a larger number of trials
 translating data represented in different displays.
Connection; Connect
Establish a link
Consistent
Regular in occurrence; in agreement and not self-contradictory
Description; Descriptive;
Describe*
Give an account of characteristics or features
Discussion; Discuss*
Talk or write about a topic, taking in to account different issues or ideas
Effective
Capably meets the described requirements
Explanation; Explanatory;
Explain*
Provide additional information that demonstrates understanding of
reasoning and/or application
Year 6 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014
Familiar
Situations or materials that have been the focus of prior
learning experiences
Given
Known or provided
Identification; Identify*
Establish or indicate who or what someone or something is
Investigate*
Plan, collect and interpret data/information and draw conclusions about
Isolation; Isolated
Unconnected; set apart
Justification; Justify*
Show how an argument or conclusion is right or reasonable
Mathematical language
and symbols
Use of appropriate mathematical terminology, diagrams and symbols.
Examples in Year 6 include:
Number and algebra
 ascending and descending order, digit, place value, whole number,
positive number, negative number, integer, prime, composite, square
and triangular number
 factor, highest common factor (HCF), multiple, lowest common multiple
(LCM)
 product, multiplication, sum, operation, division, remainder, fraction,
decimal
 estimate, speed, per, operations, order of operation
 brackets, number sentence, is the same as. equal parts, half, quarter,
eighth, third, sixth, twelfth, fifth, tenth, hundredth, thousandth,
one-thousandth
 fraction, numerator, denominator, mixed numeral, proper fraction,
improper fraction, decimal, decimal point
 percentage, percentage discount
Measurement and geometry
 plane (Cartesian plane), horizontal axis (x-axis), vertical axis (y-axis),
axes, quadrant
 intersect, point of intersection, right angles, origin, coordinates, point,
plot
 length, distance, kilometre, metre, centimetre, millimetre, measure,
measuring device, ruler, tape measure, capacity, container, litre
 perimeter, dimensions, width, base (of triangle), perpendicular height,
volume, dimensions, length, width, height
 12-hour time, 24-hour time, time zone, daylight saving, local time, hour,
minute, second, am (notation), pm (notation)
 object, shape, three-dimensional object (3D object), prism, cube,
pyramid, base, face, edge, vertex (vertices), apex, top view, front view,
side view, depth, net
 right, acute, obtuse, straight and reflex angles, degrees, translation,
reflection, rotation, symmetry
Statistics and probability
 frequency, observed frequency, expected frequency, outcome,
variation, random, fair, trial, likely, unlikely, certain, impossible,
probability
 variable, categorical variable, data, secondary data.
Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
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Queensland Curriculum & Assessment Authority
July 2014
Mathematical modelling
Depicting a situation that expresses relationships using mathematical
concepts and language.
Examples in Year 6 include:
 using number lines to position and order integers around zero
 demonstrating equivalence between fractions using drawings and
models
 solving problems involving fractions by making diagrams of fractions as
parts of shapes
 investigating length and area of familiar objects using concrete
materials and digital representations
 constructing prisms and pyramids from nets, and skeletal models
 constructing data representations.
Obvious
Evident; apparent
Partial
Incomplete, half-done, unfinished
Problem-solving
approaches
Use of problem-solving approaches to investigate situations.
Examples in Year 6 include:
 interpreting the results of calculations to provide an answer appropriate
to the context
 creating plans for investigating practical situations
 formulating and modelling practical situations, such as solving additive
problems involving fractions using methods by making diagrams of
fractions as parts of shapes
 interpreting mathematical or real-life situations
 determining the evidence needed to support a conclusion
 formulating a plan
 conducting repeated trials of chance experiments
 comparing different representations of data from secondary sources to
investigate an issue
 generalising mathematical ideas to interpret and solve problems
 verifying that answers are reasonable.
Procedural fluency
Recall and use of facts, definitions, technologies and procedures to find
solutions.
Examples in Year 6 include:
Number and algebra
 using appropriate strategies for addition and subtraction of small
numbers to those involving large numbers, including strategies to solve
word problems and problems involving money
 rounding numbers to a specified place value, such as 453903 to the
nearest one hundred thousand
 calculating simple percentages
 using brackets appropriately
 solving realistic problems using a number line
 using operations with fractions, decimals and percentages
Measurement and geometry
 measuring using metric units
 using the correct operations when converting units
 defining right, acute, obtuse, straight and reflex angles
 reading timetables
Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
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Queensland Curriculum & Assessment Authority
July 2014
Statistics and probability
 collecting data using a survey
 tabulating data with and without the use of digital technologies such as
spread sheets
 listing the outcomes of chance experiments.
Range
Covers the scope of relevant situations or elements
Reasoning and
justification
Description and explanation of mathematical thinking and reasoning,
including discussion, justification and evaluation of choices made,
strategies used and conclusions reached.
Examples in Year 6 include:
 explaining mental strategies for performing calculations
 using empty number lines to record mental strategies
 explaining number patterns, such as the relationship between the way
each pattern of numbers is created and the name of the number group
 explaining the transformation of one shape into another
 explaining why the actual results of chance experiments may differ
from expected results
 discussing the efficiency of different strategies to solve realistic
problems
 discussing data representations in the media
 giving a valid reason for supporting one possible solution over another.
Reasons; Reasoned
Logical and sound; presented with justification
Recall*
Remember information, ideas or experiences
Recognition; Recognise
To be aware of, or acknowledge
Relevant
Connected to the matter in hand
Represent*
Use words, images, symbols or signs to convey meaning
Satisfactory
Meets the expectation or expected standard; sufficient and competent
Simple
Involving few elements, components or steps; obvious data or outcomes
Statement; State
A sentence or assertion
Systematic
Methodical, organised and logical
Unfamiliar
Situations or materials that have not been the focus of prior learning
experiences
Use of
To operate or put into effect
Year 6 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
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Queensland Curriculum & Assessment Authority
July 2014