Year 4 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 4 Australian Curriculum
achievement standard represents a C standard — a sound level of knowledge and understanding of the content, and application of skills.
Year 4 Australian Curriculum: Mathematics achievement standard
By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in
familiar contexts and make connections between fraction and decimal notations up to two decimal places. Students solve simple purchasing problems.
They identify unknown quantities in number sentences. They describe number patterns resulting from multiplication. Students compare areas of regular and
irregular shapes using informal units. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent and
independent events. They describe different methods for data collection and representation, and evaluate their effectiveness.
Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts. Students locate familiar fractions on a
number line. They continue number sequences involving multiples of single digit numbers. Students use scaled instruments to measure temperatures, lengths,
shapes and objects. They convert between units of time. Students create symmetrical shapes and patterns. They classify angles in relation to a right angle.
Students list the probabilities of everyday events. They construct data displays from given or collected data.
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 4 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 4 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 4 standard elaborations — Australian Curriculum: Mathematics
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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 4 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 4 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 4 include:
Number and algebra
• making connections between representations of numbers, such as
reproducing five-digit numbers in words using their numerical
representations, and vice versa
• extending place value to decimals
• recognising and demonstrating that the place-value pattern is built on
the operations of multiplication or division of tens
• comparing large numbers with each other
• recognising that number sequences can be extended indefinitely, and
determining any patterns in the sequences
• converting mixed numbers to improper fractions and vice versa
• using knowledge of fractions to establish equivalences between
fractions and decimal notation
• identifying examples of number patterns in everyday life
Measurement and geometry
• comparing time durations
• describing properties of symmetrical shapes
• interpreting information found in maps
Statistics and probability
• identifying events where the chance of one will not be affected by the
occurrence of the other, such as explaining that the probability of
tossing a coin and getting a head does not depend on the previous
result
• describing different methods of collecting data.
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
Efficiency; Efficient
Well-organised and productive with minimal expenditure of effort
Year 4 standard elaborations — Australian Curriculum: Mathematics
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Explanation; Explanatory;
Explain*
Provide additional information that demonstrates understanding of
reasoning and/or application
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 4 include:
Number and algebra
• odd and even numbers, numbers up to tens of thousands,
multiplication, division, addition and subtraction
• place value, round to, digit, decimal, remainder, estimate
• zero, ones, tens, hundreds, thousands, tens of thousands
• double, half, halve, halves, quarters, eighths, thirds, sixths, tenths,
hundredths, denominator, numerator
• number line
• greater than, less than, largest, smallest, ascending, descending
• dollars, cents and other currencies, change
Measurement and geometry
• reading graduated scales using correct terminology, e.g. degrees
Celsius for temperature and grams of kilograms for mass
• volume, capacity, area, perimeter, height, width, temperature, mass
• square metres (m2) and square centimetres (cm2) (not meters squared
and centimetres squared)
• am, pm, seconds, minutes, hours, days, months, years, timetable,
midday, noon, midnight
• object, two-dimensional shape (2D shape), three-dimensional object
(3D object), cone, cube, cylinder, prism, pyramid, sphere, surface, flat
surface, curved surface, face, edge, vertex (vertices), net, pentagon,
hexagon, octagon, regular shape, irregular shape
• line (axis) of symmetry, reflect (flip), translate (slide), rotate (turn),
clockwise, anti-clockwise, half-turn, quarter-turn, three-quarter
• equal to, greater than or less than a right angle, right angle
• horizontal, vertical, opposite, angle, perpendicular
• compass. legend, key, scale, north, east, south, west, north-east,
south-east, south-west, north-west
Year 4 standard elaborations — Australian Curriculum: Mathematics
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Statistics and probability
• probability, chance, least likely, most likely, equally likely, dependent,
independent
• chance, event, expected results, actual results
• data, count, tally, collect, survey, recording sheet, rating scale,
category, display, symbol, tally mark, table, column graph
• picture graph, vertical columns, horizontal bars, scale
• column graph, picture graph, vertical columns, horizontal bars, title,
key, vertical axis, horizontal axis, axes
• communicating information using graphical displays.
Modelling
Depicting a situation that expresses relationships, usually using concrete
materials.
Examples in Year 4 include:
• modelling authentic situations involving operations
• using properties of numbers to continue patterns
• exploring the relationship between families of fractions (halves,
quarters and eighths or thirds and sixths) by folding a series of paper
strips to construct a fraction wall
• creating patterns with shapes and their transformations
• identifying common two-dimensional shapes that are part of a
composite shape by re-creating it from these shapes
• creating a two-dimensional shapes from verbal or written instructions
• constructing suitable data displays, with and without the use of digital
technologies, from given or collected data, such as column graphs and
picture graphs where one picture can represent many data values.
Obvious
Evident; apparent
Partial
Incomplete, half-done, unfinished
Problem-solving
approaches
Use of problem-solving approaches to investigate situations.
Examples in Year 4 include:
• investigating the properties of odd and even numbers by using the four
operations with pairs of odd or even numbers or one odd and one even
number, then using the relationships established to check the accuracy
of calculations
• comparing areas using grid paper and volume using centicubes
• comparing areas using metric units, such as counting the number of
square centimetres required to cover two areas by overlaying the areas
with a grid of centimetre squares
• solving problems involving direction, location and distance using
compass points, legends and directions with a map
• exploring ways of presenting data and showing the results of
investigations.
Year 4 standard elaborations — Australian Curriculum: Mathematics
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Queensland Curriculum & Assessment Authority
July 2014
Procedural fluency
Recall and use of facts, definitions, technologies and procedures to find
solutions
Examples in Year 4 include:
Number and algebra
• partitioning and combining numbers flexibly
• recalling multiplication tables
• using known multiplication facts to calculate related division facts
• using mental and written strategies and appropriate digital technologies
for multiplication and for division where there is no remainder
• sequencing simple fractions
• carrying out calculations in another currency as well as in dollars and
cents, and identifying both as decimal systems
• using partitioning to find unknown quantities in number sentences
Measurement and geometry
• using instruments to measure accurately
• reading the graduated scales on a range of measuring instruments to
the nearest graduation
• identifying and using the correct operation for converting units of time
• using am and pm notation and solve simple time problems, such as
determining the arrival time given the departure time and the number of
hours travelled
• using directions to find features on a map
Statistics and probability
• listing probabilities of everyday events
• collecting and accurately recording data.
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 4 include:
• generalising from number properties and results of calculations
• deriving strategies for unfamiliar multiplication and division tasks
• using lists of events familiar to students and ordering them from ‘least
likely’ to ‘most likely’ to occur
• suggesting questions that can be answered by a given data display and
using the display to answer questions
• evaluating the appropriateness of different displays.
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
Year 4 standard elaborations — Australian Curriculum: Mathematics
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Unfamiliar
Situations or materials that have not been the focus of prior learning
experiences
Use of
To operate or put into effect
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