Prep Year 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 Prep Year Australian Curriculum
achievement standard represents a child who is Working with (WW) the curriculum — demonstrating understanding of the required knowledge and
applying skills in situations familiar to them.
Prep1 Year Australian Curriculum: Mathematics achievement standard
By the end of the Foundation year, students make connections between number names, numerals and quantities up to 10. They compare objects using mass,
length and capacity. Students connect events and the days of the week. They explain the order and duration of events. They use appropriate language
to describe location.
Students count to and from 20 and order small collections. They group objects based on common characteristics and sort shapes and objects. Students answer
simple questions to collect information.
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:
Applying (AP)
Making connections (MC)
Working with (WW)
Exploring (EX)
Becoming aware (BA)
Familiar and unfamiliar
Simple familiar and some
simple unfamiliar
Familiar
Some simple familiar; guided
Partial, isolated and directed
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.
Prep in Queensland is the Foundation Year of the Australian Curriculum and refers to the year before Year 1. Children beginning Prep in January are required to be five years
of age by 30 June.
14197
1
Prep Year Mathematics standard elaborations
Applying
(AP)
Making connections
(MC)
Working with
(WW)
REVISED DRAFT
Exploring
(EX)
Becoming aware
(BA)
Conceptual
understanding
Procedural
fluency
Mathematical
language and
symbols
Understanding & Fluency
Understanding and skills dimensions
The folio of a child’s work has the following characteristics:
Connection and
description of
mathematical concepts
in familiar and unfamiliar
situations
Connection and
description of
mathematical concepts
in familiar and some
simple, unfamiliar
situations
Recognition and
identification of
mathematical concepts
in familiar situations
Identification of
mathematical concepts,
with guidance
Identification of simple
mathematical concepts,
with direction
Recall and use of facts,
definitions and
procedures to find
solutions in familiar and
unfamiliar situations
Recall and use of facts,
definitions and
procedures to find
solutions in familiar and
some simple, unfamiliar
situations
Recall and use of facts,
definitions and
procedures to find
solutions in familiar
situations
Some recall of facts and
definitions, and use of
procedures, with
guidance
Partial recall of simple
facts and definitions, or
use of simple
procedures, with
direction
Clear use of appropriate
mathematical language,
actions, materials, and
recordings
Consistent use of
everyday and some
appropriate
mathematical language,
actions, materials, and
recordings
Use of everyday and
some appropriate
mathematical language,
actions, materials, and
recordings
Use of everyday and
some aspects of
mathematical language,
actions, materials, and
recordings
Use of everyday
language
Prep Year standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Queensland Curriculum & Assessment Authority
July 2014
Page 2 of 7
Applying
(AP)
Making connections
(MC)
Working with
(WW)
Exploring
(EX)
Becoming aware
(BA)
Use of relevant
problem-solving
approaches to investigate
familiar and some simple,
unfamiliar situations
Use of problem-solving
approaches to
investigate familiar
situations
Use of problem-solving
approaches, with
guidance
Use of simple
problem-solving
approaches with
direction
Mathematical
modelling
Modelling and
representation of familiar
and unfamiliar situations
Modelling and
representation of familiar
and some simple,
unfamiliar situations
Modelling and
representation of
familiar situations
Modelling and
representation, with
guidance
Simple modelling and
representation with
direction
Clear explanation of
mathematical thinking,
including explanation
and demonstration of
how answers were
obtained
Explanation of
mathematical thinking,
including explanation and
demonstration of how
answers were obtained
Description of
mathematical thinking,
including description
and demonstration of
how answers were
obtained
Partial description of
mathematical thinking,
including statements
about answers
Isolated statements
about mathematical
thinking
Problem-solving
approaches
Use of relevant
problem-solving
approaches to
investigate familiar and
unfamiliar situations
Reasoning
and
justification
Problem solving & Reasoning
Understanding and skills dimensions
The folio of a child’s work has the following characteristics:
Note: Colour highlights have been used in the table to emphasise the qualities that discriminate between the standards.
Key
AP
The child applies the curriculum content and demonstrates a thorough understanding
of the required knowledge. The child demonstrates a high level of skill that can be
transferred to new situations.
EX
The child is exploring the curriculum content and demonstrates understanding of
aspects of the required knowledge. The child uses a varying level of skills in
situations familiar to them.
MC
The child makes connections using the curriculum content and demonstrates a clear
understanding of the required knowledge. The child applies a high level of skill in
situations familiar to them, and is beginning to transfer skills to new situations.
BA
The child is becoming aware of the curriculum content and demonstrates a basic
understanding of aspects of required knowledge. The child is beginning to use skills
in situations familiar to them.
WW
The child can work with the curriculum content and demonstrates understanding of
the required knowledge. The child applies skills in situations familiar to them.
Prep Year standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Queensland Curriculum & Assessment Authority
July 2014
Page 3 of 7
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.
Prep Year standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Page 4 of 7
Queensland Curriculum & Assessment Authority
July 2014
The following terms and key words are used in the Prep Year 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
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
Conceptual
understanding
Connection, description, recognition and identification of mathematical
concepts
Examples in Prep include:
Number and algebra
• connecting names, numerals and quantities
• creating patterns
• understanding that numbers are said in a particular order and there are
patterns in the way we say them
Measurement and geometry
• knowing and identifying the days of the week and linking specific days
to familiar events
• choosing events and actions that make connections with students’
everyday family routines
• sorting and describing squares, circles, triangles, rectangles, spheres
and cubes
• describing and connecting position and movement using the everyday
language of location and direction, such as ‘between’, ‘near’, ‘next to’,
‘forwards’, ‘towards’
Statistics and probability
• using data displays to answer simple questions such as ‘how many
students answered “yes” to having brown hair?’
Connection; Connect
Establish a link
Consistent
Regular in occurrence; in agreement and not self-contradictory
Demonstration;
Demonstrate
To point out, indicate; to clearly and deliberately show
Description; Descriptive;
Describe*
Give an account of characteristics or features
Direction; Directed
Following the instructions of the facilitator
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
Guided
Visual and/or verbal prompts to facilitate or support independent action
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
Prep Year standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Page 5 of 7
Queensland Curriculum & Assessment Authority
July 2014
Justification; Justify*
Show how an argument or conclusion is right or reasonable
Mathematical language
and symbols
Use of everyday and appropriate mathematical language, materials,
diagrams and symbols.
Examples in Prep include:
Number and algebra
• naming numbers to and from 20
• count forwards, count backwards, number before, number after, more
than, less than, zero, is the same as
• more, less, same as, not the same as (when comparing characteristics
of objects)
• first, second, third
• coins, notes, cents, dollars
• pattern, group,
• whole, part, half, equal
Measurement and geometry
• between, near, next to, forwards, towards, closer, close, further, far,
left, right
• tall, taller, short, shorter, length, longer, heavy, tall, taller, bigger, big
smaller, small, same
• shape, area, surface, object, curve, round, flat
• circle, triangle, square, rectangle
Statistics and probability
• information, collect, yes, no, true, false, group.
Modelling
Depicting a situation that expresses relationships, usually using concrete
materials.
Examples in Prep include:
• using materials to model authentic problems
• creating and describing patterns using materials, sounds, movements
or drawings
• representing responses to questions using simple displays, including
grouping students according to their answers.
Partial
Incomplete, half-done, unfinished
Problem-solving
approaches
Use of problem-solving approaches to investigate situations.
Examples in Prep include:
• using materials and objects to explore mathematical problems
• sorting objects
• using a range of practical strategies for adding small groups of
numbers, such as visual displays or concrete materials
• using familiar counting sequences to solve unfamiliar problems
• posing questions about themselves and familiar objects and events
• guessing and checking
• trial and error
• manipulating materials.
Prep Year standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Page 6 of 7
Queensland Curriculum & Assessment Authority
July 2014
Procedural fluency
Recall and use of facts, definitions, technologies and procedures to find
solutions.
Examples in Prep include:
Number and algebra
• readily counting numbers in sequences
• continuing patterns
Measurement and geometry
• comparing the lengths of objects
• sequencing familiar events in time order
• following and giving simple directions to guide a friend around an
obstacle path and vice versa
Statistics and probability
• answering yes/no questions to collect information.
Reasoning and
justification
Description, explanation and demonstration of mathematical thinking.
Examples in Prep include:
• explaining comparisons of quantities
• explaining processes for indirect comparison of length
• using concrete materials and pictorial representations to support
conclusions
• discussing the reasonableness of the answer.
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
Simple
Involving few elements, components or steps; obvious data or outcomes
Statement; State
A sentence or assertion
Unfamiliar
Situations or materials that have not been the focus of prior learning
experiences
Use of
To operate or put into effect
Prep Year standard elaborations — Australian Curriculum: Mathematics
REVISED DRAFT
Page 7 of 7
Queensland Curriculum & Assessment Authority
July 2014