Year 3 standard elaborations — Australian Curriculum: Mathematics
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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 3 Australian Curriculum
achievement standard represents a C standard — a sound level of knowledge and understanding of the content, and application of skills.
Year 3 Australian Curriculum: Mathematics achievement standard
By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They
model and represent unit fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps
with given information. Students recognise angles in real situations. They interpret and compare data displays.
Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students
correctly count out change from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length,
mass and capacity. They tell time to the nearest minute. Students make models of three-dimensional objects. Students conduct chance experiments
and list possible outcomes. They carry out simple data investigations for categorical variables.
Source: Australian Curriculum, Assessment and Reporting Authority (ACARA), Australian Curriculum v6.0 Mathematics for Foundation–10, www.australiancurriculum.edu.au/mathematics/Curriculum/F-10
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:
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 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 3 Mathematics standard elaborations
A
B
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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 3 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014
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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 models
and representations in a
range of situations,
including some that are
complex unfamiliar
Development of models
and representations in
complex familiar or
simple unfamiliar
situations
Development of models
and representations in
simple familiar
situations
Statements about
simple models and
representations
Isolated statements
about given 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 3 standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Queensland Curriculum & Assessment Authority
July 2014
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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 3 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014
The following terms and key words are used in the Year 3 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 3 include:
Number and algebra
• connecting number representations with number sequences
• identifying even numbers using skip counting by twos or by grouping
even collections of objects in twos
• reproducing numbers in words using their numerical representations
and vice versa
• recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens
and 10 000 ones
• demonstrating the connection between addition and subtraction using
partitioning or by writing equivalent number sentences
• identifying and describing the rules a number pattern and then creating
the pattern
Measurement and geometry
• recognising there are 60 minutes in an hour and 60 seconds in a
minute
• describing key features of three-dimensional objects
• interpreting maps and communicating positions
• identifying symmetry in the natural and built environment
Statistics and probability
• identifying and describing outcomes of chance experiments
• identifying the variations between trials of chance experiments.
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 3 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 3 include:
Number and algebra
• odd and even numbers, numbers to 10 000, addition, subtraction,
multiplication, division, double, multiple, shared between, divided by,
halve, remainder, equals, is the same as
• greater than, less than, ascending and descending
• horizontal, vertical
• fraction, halves, thirds, quarters, fifths, representing unit fractions
correctly, number line
• dollars, cents, change
Measurement and geometry
• centimetres, metres, grams, kilograms, millilitres and litres
• estimate, measure
• using appropriate language to communicate times
• three-dimensional, symmetry, top view, front view, side view, depth,
height, width
• position, location, map, plan, legend, key, scale, directions, compass,
north, east, south, west
Statistics and probability
• chance, experiment, trial, variation, outcome, data, random, tally
• more likely, less likely, equally likely
• category, list, table, title, survey, recording sheet, symbol, column
graph, picture graph.
Modelling
Depicting a situation that expresses relationships, usually using concrete
materials.
Examples in Year 3 include:
• partitioning areas, lengths and collections to create halves, thirds,
quarters and fifths, such as folding the same sized sheets of paper to
illustrate different unit fractions and comparing the number of parts with
their sizes
• using concrete materials to model the addition and subtraction of two or
more numbers
• modelling even and odd numbers of up to two digits using arrays with
two rows
• making models of three-dimensional objects, e.g. exploring the creation
of three-dimensional objects using origami, including prisms and
pyramids
• formulating and modelling authentic situations involving data collection
and representation.
Obvious
Evident; apparent
Partial
Incomplete, half-done, unfinished
Year 3 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014
Problem-solving
approaches
Use of problem-solving approaches to investigate situations.
Examples in Year 3 include:
• planning methods of data collection and representation
• using number properties to continue number patterns
• conducting repeated trials of chance experiments such as tossing a
coin or drawing a ball from a bag
• refining questions for investigations that involve collecting data,
e.g. narrowing the focus of a question such as ‘which is the most
popular breakfast cereal?’ to ‘which is the most popular breakfast
cereal among Year 3 students in our class?’
• collecting data to investigate features in the natural environment.
Procedural fluency
Recall and use of facts, definitions, technologies and procedures to find
solutions
Examples in Year 3 include:
Number and algebra
• partitioning and combining numbers flexibly
• combining knowledge of addition and subtraction facts and partitioning
to aid computation, e.g. 57 + 19 = 57 + 20 – 1
• recalling multiplication facts of two, three, five and ten and related
division facts
• using a calculator to check the solution and reasonableness of the
answer
• locating unit fractions on a number line
Measurement and geometry
• using familiar metric units to order objects
• telling time to the nearest minute
• matching a position on a map with given information
Statistics and probability
• listing outcomes from simple chance experiments
• collecting data for categorical variables.
Range
Covers the scope of relevant situations or elements
Reasons; Reasoned
Logical and sound; presented with justification
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 3 include:
• generalising from number properties and results of calculations
• justifying choices about partitioning and regrouping numbers in terms of
their usefulness for particular calculations
• interpreting variations in the results of data collections and data
displays
• comparing various student-generated data representations and
describing their similarities and differences.
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
Year 3 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014
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 3 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014