Material taken directly from Australian Curriculum: Mathematics (v4.1) developed by the Australian Curriculum, Assessment and Reporting Authority (ACARA), is highlighted in blue.
The Australian Curriculum sets out what all young people should be taught through the specification of curriculum content and achievement standards.
The Australian Curriculum content and achievement standards are the mandatory aspects of the Australian Curriculum.
2.1 Australian Curriculum content
The Australian Curriculum content has three components: content descriptions (section 2.1.1), general capabilities (section 2.1.2) and crosscurriculum priorities (section 2.1.3).
Schools design their programs to give students opportunities to develop their knowledge, understanding and skills in each of the three components.
Figure 2: Three components of the Australian Curriculum: Mathematics
Content descriptions: Disciplinary learning (section 2.1.1)
The Australian Curriculum: Mathematics is organised around the interaction of three content strands and four proficiency strands:
 content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. They describe what is to be taught and learnt
 substrands: a sequence of development of concepts through and across year levels within the content strands
 proficiency strands: Understanding, Fluency, Problem Solving, and Reasoning. They describe how content is explored or developed, that is, the thinking and doing of Mathematics.
Content elaborations: illustrate and exemplify content. These elaborations are not a requirement for the teaching of the Australian Curriculum.
Crosscurriculum priorities: Contemporary issues (section 2.1.3)
The three crosscurriculum priorities provide contexts for learning:
 Aboriginal and Torres Strait Islander histories and cultures — to gain a deeper understanding of, and appreciation for, Aboriginal and Torres Strait Islander histories and cultures and the impact they have had, and continue to have, on our world
 Asia and Australia's engagement with Asia — to develop a better understanding and appreciation of Australia's economic, political and cultural interconnections to Asia
 Sustainability — to develop an appreciation for more sustainable patterns of living, and to build capacities for thinking, valuing and acting that are necessary to create a more sustainable future.
General capabilities: Essential 21stcentury skills (section 2.1.2)
These seven capabilities can be divided into two groups:
 capabilities that support children to be successful learners — Literacy, Numeracy, Information and communication technology (ICT) capability, and Critical and creative thinking
 capabilities that develop ways of being, behaving and learning to live with others — Personal and social capability, Ethical understanding and Intercultural understanding.
2.1.1 Australian Curriculum: Mathematics Year 7 content descriptions
The content descriptions at each year level set out the knowledge, understanding, skills and processes that teachers are expected to teach and students are expected to learn. They do not prescribe approaches to teaching.
In Mathematics, the content descriptions are organised using three strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability.
Content descriptions are grouped into substrands to illustrate the clarity and sequence of development of concepts through and across the year levels. They support the ability to see the connections across strands and the sequential development of concepts from Prep to Year 10.Table 1: Strands and substrands
Number and Algebra 
Measurement and Geometry 
Statistics and Probability 

Number and place value (F–8) 
Using units of measurement 
Chance (1–10) 
Fractions and decimals 
Shape (F–7) 
Data representation and interpretation (F–10) 
Real numbers (7–10) 
Geometric reasoning (3–10) 

Money and financial mathematics (1–10) 
Location and transformation (F–7) 

Patterns and algebra 
Pythagoras and trigonometry (9–10) 

Linear and nonlinear relationships (8–10) 


Australian Curriculum: Mathematics Year 7 strands, substrands and content descriptions
Number and Algebra

Number and place value
 Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149)
 Investigate and use square roots of perfect square numbers (ACMNA150)
 Apply the associative, commutative and distributive laws to aid mental and written computation (ACMNA151)
 Compare, order, add and subtract integers (ACMNA280)

Real numbers
 Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (ACMNA152)
 Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)
 Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)
 Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)
 Round decimals to a specified number of decimal places (ACMNA156)
 Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)
 Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies (ACMNA158)
 Recognise and solve problems involving simple ratios (ACMNA173)

Money and financial mathematics
 Investigate and calculate 'best buys', with and without digital technologies (ACMNA174)

Patterns and algebra
 Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)
 Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176)
 Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

Linear and nonlinear relationships
 Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)
 Solve simple linear equations (ACMNA179)
 Investigate, interpret and analyse graphs from authentic data (ACMNA180)^{1}
Measurement and Geometry

Using units of measurement
 Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (ACMMG159)
 Calculate volumes of rectangular prisms (ACMMG160)

Shape
 Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)

Location and transformation
 Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries (ACMMG181)

Geometric reasoning
 Identify corresponding, alternate and cointerior angles when two straight lines are crossed by a transversal (ACMMG163)
 Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)
 Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)
 Classify triangles according to their side and angle properties and describe quadrilaterals (ACMMG165)
Statistics and Probability

Chance
 Construct sample spaces for singlestep experiments with equally likely outcomes (ACMSP167)
 Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)

Data representation and interpretation
 Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169)
 Construct and compare a range of data displays including stemandleaf plots and dot plots (ACMSP170)
 Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171)
 Describe and interpret data displays using median, mean and range (ACMSP172)
^{1}Codes included with the Australian Curriculum content descriptions relate to hyperlinks into the Australian Curriculum website. Each unique identifier provides the user with the content description, content elaboration, and links to general capabilities, crosscurriculum priorities and modes.
Content elaborations
Content elaborations illustrate and exemplify content and assist teachers in developing a common understanding of the content descriptions. The elaborations are not a requirement for the teaching of the Australian Curriculum. They are not individualised teaching points intended to be taught to all students.
2.1.2 General capabilities
The general capabilities are embedded in the content descriptions. The seven capabilities can be divided into two broad groups. These broad groups include capabilities that:
 support students to be successful learners: Literacy, Numeracy, Information and communication technology (ICT) capability, and Critical and creative thinking
 develop ways of being, behaving and learning to live with others: Personal and social capability, Ethical understanding and Intercultural understanding.
Australian Curriculum Numeracy learning continuum
The Numeracy learning continuum is organised into six interrelated elements:
 Estimating and calculating with whole numbers
 Recognising and using patterns and relationships
 Using fractions, decimals, percentages, ratios and rates
 Using spatial reasoning
 Interpreting statistical information
 Using measurement
These elements are drawn from the strands of the Australian Curriculum: Mathematics as shown in the table below:
Numeracy continuum 
Australian Curriculum: Mathematics 

Estimating and calculating with whole numbers 
Number and Algebra 
Recognising and using patterns and relationships 
Number and Algebra 
Using fractions, decimals, percentages, ratios and rates 
Number and Algebra 
Using spatial reasoning 
Measurement and Geometry 
Interpreting statistical information 
Statistics and Probability 
Using measurement 
Measurement and Geometry 
The diagram below sets out these elements.
See also: ACARA Numeracy.
P–10 Numeracy Indicators
The QCAA P–10 Numeracy Indicators are aligned to the Australian Curriculum (v4.1) and informed by data from Queensland performance on national assessment. The Indicators are organised as Year level descriptions and provide specific detail to support planning for, and monitoring of, children’s numeracy knowledge, understanding and skills across the learning areas. For further information, see: P–10 Literacy and Numeracy Indicators.
Table 2: General capabilities that support students to be successful learners are embedded in the Mathematics content descriptions where appropriate.

Definition 
In Mathematics 
Links 

Literacy 
Students become literate as they develop the knowledge, skills and dispositions to interpret and use language confidently for learning and communicating in and out of school and for participating effectively in society. Literacy involves students in listening to, reading, viewing, speaking, writing and creating oral, print, visual and digital texts, and using and modifying language for different purposes in a range of contexts. 
Literacy is an important aspect of mathematics. Students develop literacy in mathematics as they learn the vocabulary associated with number, space, measurement and mathematical concepts and processes. This vocabulary includes synonyms (minus, subtract), technical terminology (digits, lowest common denominator), passive voice (If 7 is taken from 10) and common words with specific meanings in a mathematical context (angle, area). They develop the ability to create and interpret a range of texts typical of Mathematics ranging from calendars and maps to complex data displays. Students use literacy to understand and interpret word problems and instructions that contain the particular language features of mathematics. They use literacy to pose and answer questions, engage in mathematical problem solving, and to discuss, produce and explain solutions. 

Numeracy 
Students become numerate as they develop the knowledge and skills to use mathematics confidently across all learning areas at school and in their lives more broadly. Numeracy involves students in recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully. 
Mathematics has a central role in the development of numeracy in a manner that is more explicit and foregrounded than is the case in other learning areas. It is important that the Mathematics curriculum provides the opportunity to apply mathematical understanding and skills in context, both in other learning areas and in real world contexts. 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 twentyfirst century world is information driven, and through Statistics and Probability students can interpret data and make informed judgments about events involving chance. 

ICT capability 
Students develop ICT capability as they learn to use ICT effectively and appropriately to access, create and communicate information and ideas, solve problems and work collaboratively in all learning areas at school, and in their lives beyond school. ICT capability involves students in learning to make the most of the technologies available to them, adapting to new ways of doing things as technologies evolve and limiting the risks to themselves and others in a digital environment. 
Students develop ICT capability when they investigate, create and communicate mathematical ideas and concepts using fast, automated, interactive and multimodal technologies. They employ their ICT capability to perform calculations, draw graphs, collect, manage, analyse and interpret data; share and exchange information and ideas and investigate and model concepts and relationships. Digital technologies, such as spreadsheets, dynamic geometry software and computer algebra software, can engage students and promote understanding of key concepts. 

Critical and creative thinking 
Students develop capability in critical and creative thinking as they learn to generate and evaluate knowledge, clarify concepts and ideas, seek possibilities, consider alternatives and solve problems. Critical and creative thinking are integral to activities that require students to think broadly and deeply using skills, behaviours and dispositions such as reason, logic, resourcefulness, imagination and innovation in all learning areas at school and in their lives beyond school. 
Students develop critical and creative thinking as they learn to generate and evaluate knowledge, ideas and possibilities, and use them when seeking solutions. Engaging students in reasoning and thinking about solutions to problems and the strategies needed to find these solutions are core parts of the Mathematics curriculum. Students are encouraged to be critical thinkers when justifying their choice of a calculation strategy or identifying relevant questions during a statistical investigation. They are encouraged to look for alternative ways to approach mathematical problems, for example, identifying when a problem is similar to a previous one, drawing diagrams or simplifying a problem to control some variables. 
Table 3: General capabilities that develop ways of being, behaving and learning to live with others are embedded in the Mathematics content descriptions where appropriate.

Definition 
In Mathematics 
Links 

Personal and social capability 
Students develop personal and social capability as they learn to understand themselves and others, and manage their relationships, lives, work and learning more effectively. The personal and social capability involves students in a range of practices including recognising and regulating emotions, developing empathy for and understanding of others, establishing positive relationships, making responsible decisions, working effectively in teams and handling challenging situations constructively. 
Students develop and use personal and social capability as they apply mathematical skills in a range of personal and social contexts. This may be through activities that relate learning to their own lives and communities, such as time management, budgeting and financial management, and understanding statistics in everyday contexts. The Mathematics curriculum enhances the development of students' personal and social capabilities by providing opportunities for initiative taking, decision making, communicating their processes and findings, and working independently and collaboratively in the Mathematics classroom. 

Ethical understanding 
Students develop the capability to behave ethically as they identify and investigate the nature of ethical concepts, values, character traits and principles, and understand how reasoning can assist ethical judgment. Ethical understanding involves students in building a strong personal and socially oriented ethical outlook that helps them to manage context, conflict and uncertainty, and to develop an awareness of the influence that their values and behaviour have on others. 
There are opportunities in the Mathematics curriculum to explore, develop and apply ethical understanding in a range of contexts, for example through analysing data and statistics; seeking intentional and accidental distortions; finding inappropriate comparisons and misleading scales when exploring the importance of fair comparison; and interrogating financial claims and sources. 

Intercultural understanding 
Students develop intercultural understanding as they learn to value their own cultures, languages and beliefs, and those of others. They come to understand how personal, group and national identities are shaped, and the variable and changing nature of culture. The capability involves students in learning about and engaging with diverse cultures in ways that recognise commonalities and differences, create connections with others and cultivate mutual respect. 
Intercultural understanding can be enhanced in Mathematics when students are exposed to a range of cultural traditions. Students learn to understand that mathematical expressions use universal symbols, while mathematical knowledge has its origin in many cultures. Students realise that proficiencies such as understanding, fluency, reasoning and problem solving are not culture or language specific, but that mathematical reasoning and understanding can find different expression in different cultures and languages. New technologies and digital learning environments provide interactive contexts for exploring mathematical problems from a range of cultural perspectives and within diverse cultural contexts. Students can apply mathematical thinking to identify and resolve issues related to living with diversity. 
2.1.3 Crosscurriculum priorities
The Australian Curriculum gives special attention to three crosscurriculum priorities about which young Australians should learn in all learning areas. The priorities provide contexts for learning. The three priorities are Aboriginal and Torres Strait Islander histories and cultures, Asia and Australia’s engagement with Asia, and Sustainability.
Aboriginal and Torres Strait Islander histories and cultures  Asia and Australia's engagement with Asia  Sustainability 

The Aboriginal and Torres Strait Islander priority provides opportunities for all learners to deepen their knowledge of Australia by engaging with the world’s oldest continuous living cultures. This knowledge and understanding will enrich their ability to participate positively in the ongoing development of Australia. The Australian Curriculum: Mathematics values Aboriginal and Torres Strait Islander histories and cultures. It provides opportunities for students to appreciate that Aboriginal and Torres Strait Islander societies have sophisticated applications of mathematical concepts. Students will explore connections between representations of number and pattern and how they relate to aspects of Aboriginal and Torres Strait Islander cultures. They will investigate time, place, relationships and measurement concepts in Aboriginal and Torres Strait Islander contexts. Students will deepen their understanding of the lives of Aboriginal and Torres Strait Islander Peoples through the application and evaluation of statistical data. 
In the Australian Curriculum: Mathematics, the priority of Asia and Australia’s engagement with Asia provides rich and engaging contexts for developing students’ mathematical knowledge, skills and understanding. The Australian Curriculum: Mathematics provides opportunities for students to learn about the understandings and applications of Mathematics in Asia. Mathematicians from Asia continue to contribute to the ongoing development of Mathematics. In this learning area, students develop mathematical understanding in fields such as number, patterns, measurement, symmetry and statistics by drawing on knowledge of and examples from the Asia region. These could include calculation, money, art, architecture, design and travel. Investigations involving data collection, representation and analysis can be used to examine issues pertinent to the Asia region. 
In the Australian Curriculum: Mathematics, the priority of sustainability provides rich, engaging and authentic contexts for developing students’ abilities in number and algebra, measurement and geometry, and statistics and probability. The Australian Curriculum: Mathematics provides opportunities for students to develop the proficiencies of problem solving and reasoning essential for the exploration of sustainability issues and their solutions. Mathematical understandings and skills are necessary to measure, monitor and quantify change in social, economic and ecological systems over time. Statistical analysis enables prediction of probable futures based on findings and helps inform decision making and actions that will lead to preferred futures. In this learning area, students can observe, record and organise data collected from primary sources over time and analyse data relating to issues of sustainability from secondary sources. They can apply spatial reasoning, measurement, estimation, calculation and comparison to gauge local ecosystem health and can cost proposed actions for sustainability. 
For further information and resources to support planning to include the crosscurriculum priority Aboriginal and Torres Strait Islander histories and cultures, see: Aboriginal and Torres Strait Islander histories and cultures resources: Mathematics. 
For further information and resources to support planning to include the crosscurriculum priority Asia and Australia’s engagement with Asia, see: Asia Education Foundation website. 
For further information and resources to support planning to include the crosscurriculum priority Sustainability, see: Crosscurriculum priorities. 
2.2 Achievement standards
The Australian Curriculum is standardsbased.
The Australian Curriculum achievement standards are a mandatory aspect of the Australian Curriculum for schools to implement.
The Australian Curriculum achievement standards are organised as Understanding and Skills and describe a broad sequence of expected learning, across P–10. The achievement standard emphasises the depth of conceptual understanding, the sophistication of skills and the ability to apply essential knowledge children typically demonstrate at the end of each teaching and learning year. The achievement standard should be read in conjunction with the content descriptions.
Figure 3: By the end of Year 7, students are expected to typically know and be able to do the following:
Understanding dimension  
By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the connections between whole numbers and index notation and the relationship between perfect squares and square roots. They solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to algebra. They interpret simple linear representations and model authentic information. Students describe different views of threedimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving angles formed by a transversal crossing two parallel lines. Students identify issues involving the collection of continuous data. They describe the relationship between the median and mean in data displays. 
The Understanding dimension relates to concepts underpinning and connecting knowledge in a learning area and to the ability to appropriately select and apply knowledge to solve problems in that learning area.  
Skills dimension  
Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution. They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets. They construct stemandleaf plots and dotplots. 
The Skills dimension relates to the specific techniques, strategies and processes in a learning area. 
2.2.1 Year 7 standard elaborations
Year 7 standard elaborations (Table 4) provides a basis for judging how well students have demonstrated what they know, understand and can do using the Australian Curriculum achievement standard. It is a resource to assist teachers to make consistent and comparable evidencebased A to E judgments. The standard elaborations should be used in conjunction with the Australian Curriculum achievement standard and content descriptions for the relevant year level.
Teachers can use the standard elaborations to:
 match the evidence of learning in a folio or collection of student work gathered over the reporting period to determine how well a student has achieved against the achievement standard on a fivepoint scale (see section 4)
 inform the development of an assessment program and individual assessments (see section 3.3)
 inform the development of taskspecific standards (see section 3.4 and section 3.5)
The structure of the Mathematics standard elaborations
The standards elaborations for Mathematics have been developed using the Australian Curriculum content descriptions and the achievement standard. They promote:
 alignment of curriculum, assessment and reporting, connecting curriculum and evidence in assessment, so that what is assessed relates directly to what children have had the opportunity to learn
 continuity of skill development from one year of schooling to another.
2.3 Planning in the Mathematics learning area
Schools plan their curriculum and assessment using the Australian Curriculum content descriptions and achievement standards.
Curriculum and assessment planning within schools occurs at three levels:
Whole school plan
Year level plan / Multiple year level plan
Unit overview / Unit overview planning for multiple year levelsFor planning templates and Year 7 Mathematics exemplar year and unit plans, see the resources section.
2.3.1 Time allocation
Indicative time allocations support schools in planning teaching and learning experiences using the Australian Curriculum: Mathematics. Schools may decide to timetable more hours for a learning area.
The indicative time allocations are presented as two sets of minimum hours per year that provide reasonable flexibility. In Year 7, the minimum number of hours for teaching, learning and assessment per year for the Australian Curriculum: Mathematics is:
 at least 111 hours per year where there are 37 teaching weeks available in the year
 at least 120 hours per year where there are 40 teaching weeks available in the year.
2.3.2 Principles for effective planning
The principles that underpin effective curriculum and assessment planning include:
 High expectations for all students — High student expectations are built on differentiation of teaching and learning for all students in single and multiple yearlevel contexts.
 Alignment of teaching and learning, and assessment and reporting — Curriculum and assessment planning is thoughtful and ensures that all parts are connected. Plans are reviewed regularly to inform future planning, teaching, learning and assessment.
 Standards and schoolbased assessment for learning — Teachers use standards to build a shared understanding of the qualities found in student work, and to communicate student achievement to students, parents/carers and the system.
 Balance of informed prescription and teacher professional judgment — Teachers exercise their professional judgment and make decisions about teaching and learning in their school within the context of the Australian Curriculum and system and sector priorities.
2.3.3 Elements of effective planning for alignment
Curriculum and assessment planning is guided by five interdependent elements of professional practice. These five elements can be used in any sequence but all should be considered:
 Identify curriculum
 Develop assessment
 Sequence teaching and learning
 Make judgments
 Use feedback
Figure 4: The five elements for effective curriculum and assessment planning
Identify curriculum (section 2.3.4)
The Australian Curriculum content and achievement standards are the basis for planning teaching, learning and assessment.
Develop assessment (section 3)
Assessment is an integral part of teaching and learning. The assessment provides the evidence of student learning on which judgments can be made against the achievement standard.
Sequence teaching and learning (section 2.3.6)
The selection and sequence of learning experiences and teaching strategies support student learning of the curriculum content and work towards providing evidence of achievement through assessment.
Make judgments (section 2.2, section 3.5 and section 4.2)
Judgment about evidence of student learning is made against the Australian Curriculum achievement standard. The standard elaborations assist teachers in making judgments on a fivepoint scale and in identifying the taskspecific standards.
Use feedback (section 3.6 and section 4)
Students receive regular feedback through monitoring, which provides ongoing feedback as part of the teaching and learning process. Formal feedback is provided to students and their parents/carers at the time of reporting. Teachers use feedback to inform their planning for teaching and learning.
Planning that considers these five elements strengthens alignment and ensures that:
 what is taught informs how it is taught, how students are assessed and how the learning is reported
 what is assessed relates directly to what students have had an opportunity to learn
 specific feedback, based on what has been learnt and assessed, provides a basis for decisions about continuous improvement in teaching and learning
 what is reported to students, parents/carers and other teachers aligns with what has been learnt.
2.3.4 Identifying curriculum
Year 7 Mathematics teaching and learning programs are developed from the:
 Year 7 Australian Curriculum: Mathematics content descriptions to:
 determine the scope of learning and ensure all required learning is included
 identify relevant general capabilities
 determine appropriate contexts for teaching and learning, including the crosscurriculum priorities
 Year 7 Australian Curriculum: Mathematics achievement standard to identify the expected and valued qualities of student work.
When planning a teaching and learning program, consider:
 What am I required to teach?
 What should students have the opportunity to learn?
 What are the expected and valued qualities of student work?
See the Mathematics scope and sequence (ACARA PDF) developed by the Australian Curriculum, Assessment and Reporting Authority.
2.3.5 Developing assessment
Assessment provides the evidence of learning. An assessment program is planned at the same time as the teaching and learning program and is developed using the content descriptions and achievement standard.
When developing assessment, consider:
 What evidence of student learning do I need to collect?
 How and when will I collect the evidence of student learning?
See section 3 for advice about developing an assessment program.
2.3.6 Sequencing teaching and learning
Learning experiences and teaching strategies are selected and sequenced to support active engagement in learning and to provide opportunities for students to engage with all aspects of the curriculum content to develop their understanding and skills.
When sequencing teaching and learning, consider:
 How will I sequence teaching strategies and learning experiences to cover the curriculum content, ensure depth of learning and support student success in the assessment?
 How do I include opportunities for all my students to learn?
Build on concepts, skills and processes; challenge and engage children
The content descriptions are organised in strands and substrands in order to ensure that learning is appropriately ordered and that unnecessary repetition is avoided. However, a concept or skill introduced at one year level may be revisited, strengthened and extended at later year levels as needed. This organisation illustrates the clarity and sequence of development of concepts through and across the year levels and supports the ability to see the connections across strands and the sequential development of concepts from Prep to Year 10.
In Mathematics, challenging problems can be posed using basic ageappropriate content. Acceleration by using content beyond a student's year level may not be the best way to extend proficient mathematicians. Choosing engaging experiences as contexts for a variety of tasks assists in making Mathematics inclusive, and these tasks can be effectively differentiated both for students experiencing difficulty and those who complete tasks easily. The proficiency strands apply expectations of the range and nature of how mathematical content is enacted, and can help focus teaching.
See the Mathematics scope and sequence (ACARA PDF) developed by the Australian Curriculum, Assessment and Reporting Authority.
Proficiency strands
The proficiency strands describe the actions in which students can engage when learning and using the content. While not all proficiency strands apply to every content description, they indicate the breadth of mathematical actions that teachers can emphasise.
UnderstandingStudents 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.
FluencyStudents 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 SolvingStudents 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.
ReasoningStudents 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.
The relationship between the content and proficiency strands
The content strands describe the 'what' that is to be taught and learnt while the proficiency strands describe the 'how' of the way content is explored or developed i.e. the thinking and doing of mathematics. Each of the 'content descriptions' in the mathematics includes terms related to understanding, fluency, problem solving or reasoning. In this way, proficiency strands describe how students interact with the content i.e. they describe how the mathematical content strands are enacted via mathematical behaviours. They provide the language to build in the developmental aspects of the learning of mathematics.
Include the general capabilities
The general capabilities are relevant to teaching and learning in Mathematics, and explicit teaching of the capabilities should be incorporated in teaching and learning activities where appropriate. Section 2.1.2 outlines how the general capabilities are an integral part of a Mathematics program.
Embed meaningful contexts
Schools develop learning contexts to suit the content to be taught and their students’ interests and learning needs. It is important to actively engage students in learning that is relevant and of interest to them. The focus or context for learning should connect with issues of personal or social relevance to students. The crosscurriculum priorities provide rich and engaging contexts for developing students’ abilities in listening, speaking/signing, reading, viewing, writing and creating. . (See section 2.1.3 for information about the priorities).
Year 7 should include opportunities to:
 describe patterns in uses of indices with whole numbers, recognise equivalences between fractions, decimals, percentages and ratios, plot points on the Cartesian plane, identify angles formed by a transversal crossing a pair of lines, and connect the laws and properties of numbers to algebraic terms and expressions
 calculate accurately with integers, represent fractions and decimals in various ways, investigate best buys, find measures of central tendency and calculate areas of shapes and volumes of prisms
 formulate and solve authentic problems using numbers and measurements, work with transformations and identify symmetry, calculate angles and interpret sets of data collected through chance experiments
 apply the number laws to calculations, apply known geometric facts to draw conclusions about shapes, apply an understanding of ratio and interpret data displays.
2.3.7 Educational equity
Equity means fair treatment of all. In developing teaching, learning and assessment programs, teachers provide opportunities for all students to demonstrate what they know and what they can do.
See the QCAA Equity statement:
 QCAA Equity statement (PDF, 35 kB)
The QCAA undertakes all its functions based on the equity principles included within this statement.
Catering for diversity
Schools and school sectors determine which students require special provisions, applying principles of participation and equity. Consideration should be given to:
 adjustments and supports for students who have been identified as having specific educational requirements to make participation possible in all or part of the teaching and learning experiences and assessments
 interpreter or educational devices (e.g. pictures, electronic whiteboards, interactive devices) to assist students for whom English is not their first language and who are assessed as not achieving a reading level appropriate to complete the assessment.
In exceptional circumstances, the school, in consultation with staff and parents/carers, may make decisions about the level of student engagement with a particular assessment, according to school sector policy.
Inclusive strategies
Adjustments to teaching, learning and assessment can be grouped into five broad areas: timing, scheduling, setting, presentation and response.
Teachers consider the inclusive strategies to make adjustments to teaching and learning experiences and assessments to enable all students to demonstrate their knowledge, skills or competencies.
The inclusive strategies should be considered in combination when planning, developing and documenting the adjustment of learning experiences and assessment. For example, when planning an assessment, the teacher may need to consider adjusting the timing, setting, presentation and response to ensure the student is given the opportunities to demonstrate their learning.
Evaluating the use and effectiveness of any adjustment is necessary to ensure meaningful student participation and achievement.
For further information and resources about inclusive strategies, see Catering for diversity.
English as an Additional Language or Dialect
For further information and resources about English as an Additional Language or Dialect, see:
Last reviewed: 26 November 2014