Home > Year 4 Mathematics — Australian Curriculum in Queensland

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Australian Curriculum in Queensland

March 2013 (amended April 2015)

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Resources referred to in this document may have been updated or replaced. Please always check the QCAA website for the most current resources to support the implementation of the Australian Curriculum: Mathematics:

www.qcaa.qld.edu.au/13656.html.

· Section 2.2.1 Year 4 standards elaborations Table 4: The Year 4 standards elaborations removed; replaced with link to updated standards elaborations on the QCAA website; subsequent tables renumbered. · Appendix 1: Mathematics standards elaborations terms table removed. Updated term definitions are available as part of the standards elaborations web documents. · Table of contents updated. Year 4 Mathematics — Australian Curriculum in Queensland © The State of Queensland (Queensland Studies Authority) 2015 Selected materials in this publication are drawn from the Australian Curriculum and are used under a Creative Commons attribution non-commercial share-alike licence. This material is presented in blue text. Queensland Studies Authority Level 7, 154 Melbourne Street, South Brisbane PO Box 307 Spring Hill QLD 4004 Australia Phone: (07) 3864 0299 Fax: (07) 3221 2553 Email: office@qsa.qld.edu.au Website:www.qsa.qld.edu.au

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Amendments notice: April 2015 .............................................................................................. ii

1.1 Rationale ............................................................................................................. 1 1.2 Aims .................................................................................................................... 2 1.3 Mathematics in Queensland K–12 ....................................................................... 2

2.1 Australian Curriculum content .............................................................................. 4

2.1.1 Australian Curriculum: Mathematics Year 4 content descriptions .................... 5 2.1.2 General capabilities ........................................................................................... 8 2.1.3 Cross-curriculum priorities .............................................................................. 14

2.2 Achievement standards ..................................................................................... 15

2.2.1 Year 4 standard elaborations .......................................................................... 16

2.3 Planning in the Mathematics learning area ........................................................ 17

2.3.1 Time allocation ................................................................................................ 17 2.3.2 Principles for effective planning ...................................................................... 17 2.3.3 Elements of effective planning for alignment .................................................. 18 2.3.4 Identifying curriculum ...................................................................................... 19 2.3.5 Developing assessment .................................................................................. 19 2.3.6 Sequencing teaching and learning .................................................................. 20 2.3.7 Educational equity ........................................................................................... 22

3.1 Standards-based assessment............................................................................ 23 3.2 School-based assessment ................................................................................. 23 3.3 Developing an assessment program .................................................................. 24 3.4 Year 4 Mathematics assessment folio ................................................................ 25

3.4.1 Assessment techniques, formats and categories ........................................... 26 3.4.2 Assessment conditions.................................................................................... 28 3.4.3 Developing assessments ................................................................................ 29

3.5 Making judgments .............................................................................................. 31 3.6 Using feedback .................................................................................................. 32

4.1 Reporting standards .......................................................................................... 33 4.2 Making an on-balance judgment on a folio ......................................................... 35

4.2.1 Making an on-balance judgment for mid-year reporting ................................. 36 4.2.2 Applying the Australian Curriculum achievement standards .......................... 37

4.3 Moderation......................................................................................................... 38

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Rationale

Planning teaching and learning

Aims

Standards elaborations, A to E

Australian Curriculum content

Assessment advice and guidelines

Achievement standards

Reporting advice and guidelines

Requirements are taken directly from the Australian Curriculum: Mathematics (v4.1) developed by the Australian Curriculum, Assessment and Reporting Authority (ACARA). This material is presented in blue text. Links to Australian Curriculum support materials are also provided where appropriate. Advice, guidelines and resources are based on the Australian Curriculum Year level descriptions and organisation sections. They have been developed by the Queensland Studies Authority (QSA) to assist teachers in their planning and assessment and include links to Queensland-developed supporting resources, exemplars and templates.

Learning mathematics creates opportunities for and enriches the lives of all Australians. The Australian Curriculum: Mathematics provides students with essential mathematical skills and knowledge in Number and Algebra, Measurement and Geometry, and Statistics and Probability. It develops the numeracy capabilities that all students need in their personal, work and civic life, and provides the fundamentals on which mathematical specialties and professional applications of mathematics are built. Mathematics has its own value and beauty and the Australian Curriculum: Mathematics aims to instil in students an appreciation of the elegance and power of mathematical reasoning. Mathematical ideas have evolved across all cultures over thousands of years, and are constantly developing. Digital technologies are facilitating this expansion of ideas and providing access to new tools for continuing mathematical exploration and invention. The curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently. The Australian Curriculum: Mathematics ensures that the links between the various components of mathematics, as well as the relationship between mathematics and other disciplines, are made clear. Mathematics is composed of multiple but interrelated and interdependent concepts and systems which students apply beyond the mathematics classroom. In science, for example, understanding sources of error and their impact on the confidence of conclusions is vital, as is the use of mathematical models in other disciplines.

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In geography, interpretation of data underpins the study of human populations and their physical environments; in history, students need to be able to imagine timelines and time frames to reconcile related events; and in English, deriving quantitative and spatial information is an important aspect of making meaning of texts. The curriculum anticipates that schools will ensure all students benefit from access to the power of mathematical reasoning and learn to apply their mathematical understanding creatively and efficiently. The mathematics curriculum provides students with carefully paced, in-depth study of critical skills and concepts. It encourages teachers to help students become self-motivated, confident learners through inquiry and active participation in challenging and engaging experiences.

The Australian Curriculum: Mathematics aims to ensure that students:

· are confident, creative users and communicators of mathematics, able to investigate,

represent and interpret situations in their personal and work lives and as active citizens

· develop an increasingly sophisticated understanding of mathematical concepts and

fluency with processes, and are able to pose and solve problems and reason in Number and Algebra, Measurement and Geometry, and Statistics and Probability

· recognise connections between the areas of mathematics and other disciplines and

appreciate mathematics as an accessible and enjoyable discipline to study.

The K–12 curriculum in Queensland is aligned to the goals for Australian schooling, as expressed in the

* Ministerial Council on Education, Employment, Training and Youth Affairs 2008, Melbourne Declaration on Educational Goals for Young Australians, viewed October 2012, <www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Young_

Australians.pdf>.

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Figure 1 below shows the progression of the Mathematics learning area K–12 in

Queensland, and includes the

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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: •

•

Fluency, Problem Solving, and Reasoning. They describe how content is explored or developed, that is, the thinking and doing of Mathematics.

General capabilities: Essential 21st-century skills (section 2.1.2)

These seven capabilities can be divided into two groups: •

Cross-curriculum priorities: Contemporary issues (section 2.1.3)

The three cross-curriculum priorities provide contexts for learning: •

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 has three components: content descriptions (section 2.1.1), general capabilities (section 2.1.2) and cross-curriculum 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.

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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:

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(ACMMG084)

Describe possible everyday events and order their chances of occurring

(ACMSP092)

Recognise, represent and order numbers to at least tens of thousands

(ACMNA072)

Compare objects using familiar metric units of area and volume (ACMMG290) Identify everyday events where one cannot happen if the other happens

(ACMSP093)

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Convert between units of time (ACMMG085) Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094) Use am and pm notation and solve simple time problems

(ACMMG086)

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

(ACMMG087)

Select and trial methods for

data collection, including

survey questions and recording sheets

(ACMSP095)

Recall multiplication facts up to 10 �� 10 and related division facts (ACMNA075) Develop efficient mental and written strategies and use appropriate digital technologies for

multiplication and for

division where there is no

remainder (ACMNA076)

Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

(ACMMG088)

Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and

picture graphs where one

picture can represent many

data values (ACMSP096)

fractions used in contexts (ACMNA077)

Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090) Evaluate the effectiveness of different displays in illustrating data features including variability

(ACMSP097)

Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Create symmetrical patterns, pictures and shapes with and without digital technologies

(ACMMG091)

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value system can be

extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

angle (ACMMG089)

(ACMNA080)

number patterns resulting

from performing multiplication (ACMNA081) Solve word problems by using number sentences involving multiplication or division where there is no

remainder (ACMNA082)

Use equivalent number sentences involving addition and subtraction to find unknown quantities

(ACMNA083)†

Content elaborations illustrate and exemplify content and assist teachers in developing a common understanding of the content descriptions. The elaborations are

† Codes included with the Australian Curriculum content descriptions relate to hyperlinks into the Australian

Curriculum website <www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10>. Each unique identifier provides the user with the content description, content elaboration, and links to general capabilities, cross-curriculum priorities and modes.

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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. Each of the general capabilities can be relevant to teaching and learning in Mathematics and explicit teaching of the capabilities should be incorporated in teaching and learning activities where appropriate. See also: www.australiancurriculum.edu.au/GeneralCapabilities/Overview/General-

capabilities-in-the-Australian-Curriculum

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:

Estimating and calculating with whole numbers Number and Algebra Measurement and Geometry Recognising and using patterns and relationships Number and Algebra Statistics and Probability Using fractions, decimals, percentages, ratios and rates Number and Algebra Measurement and Geometry Using spatial reasoning Measurement and Geometry Interpreting statistical information Statistics and Probability Using measurement Measurement and Geometry

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The diagram below sets out these elements.

From: www.australiancurriculum.edu.au/GeneralCapabilities/Numeracy/Organising-

elements/Organising-elements

See also:

www.australiancurriculum.edu.au/GeneralCapabilities/Numeracy/Introduction/Introduction

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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.

ACARA Literacy capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Literacy/Introduction/Intr oduction

QSA Literacy Indicators

www.qsa.qld.edu.au/1792 9.html

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

ACARA Numeracy capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Numeracy/Introduction/I ntroduction

QSA Numeracy Indicators

www.qsa.qld.edu.au/1792 9.html

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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.

ACARA ICT capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Information-and- Communication- Technology- capability/Introduction/Intr oduction

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.

ACARA Critical and creative thinking capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Critical-and-creative- thinking/Introduction/Intro duction

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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.

ACARA Personal and social capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Personal-and-social- capability/Introduction/Intr oduction

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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.

ACARA Ethical understanding capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Ethical- understanding/Introductio n/Introduction

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.

ACARA Intercultural understanding capability continua

www.australiancurriculum. edu.au/GeneralCapabilitie s/Intercultural- understanding/Introductio n/Introduction

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The Australian Curriculum gives special attention to three cross-curriculum 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.

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 cross-curriculum priority Aboriginal and Torres Strait Islander histories and cultures, see:

www.qsa.qld.edu.au/downloads/ aust_curric/ac_ccp_atsi_cultures _maths.pdf

For further information and resources to support planning to include the cross-curriculum priority Asia and Australia��s engagement with Asia, see:

www.asiaeducation.edu.au/aust_ curr_strategy_landing_page.html

For further information and resources to support planning to include the cross-curriculum priority Sustainability, see:

www.australiancurriculum.edu.a u/CrossCurriculumPriorities

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The Australian Curriculum is standards-based.

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.

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.

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.

The Skills dimension relates to the specific techniques, strategies and processes in a learning area.

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The Year 4 standard elaborations provide a basis for judging

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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

www.qsa.qld.edu.au/downloads/p_10/ac_plan_implementing.pdf

· Year level plan / Multiple year level plan

www.qsa.qld.edu.au/downloads/p_10/ac_p10_year_level_planning.pdf www.qsa.qld.edu.au/downloads/p_10/ac_p10_multi_year_level_plan.pdf

· Unit overview / Unit overview planning for multiple year levels

www.qsa.qld.edu.au/downloads/p_10/ac_p10_unit_overview_planning.pdf www.qsa.qld.edu.au/downloads/p_10/ac_p10_multi_unit_overview_plan.pdf

For planning templates and Year 4 Mathematics exemplar year and unit plans, see:

www.qsa.qld.edu.au/yr4-maths-resources.html

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 4, the minimum number of hours for teaching, learning and assessment per year for the Australian Curriculum: Mathematics is: · at least 166 hours per year where there are 37 teaching weeks available in the year · at least 180 hours per year where there are 40 teaching weeks available in the year. See www.qsa.qld.edu.au/downloads/early_middle/ac_time_alloc_entitlement_advice.pdf

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 year-level 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 school-based 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.

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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.

Use feedback (sections 3.6 and 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.

Make judgments (sections 2.2, 3.5 and

4.2)

Judgment about evidence of student learning is made against the Australian Curriculum content and achievement standard. The standard elaborations assist teachers in making judgments A to E and in identifying the task-specific standards.

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.

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

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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.

Year 4 Mathematics teaching and learning programs are developed from the: · Year 4 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 cross-curriculum priorities · Year 4 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?

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.

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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?

The content descriptions are organised in strands and sub-strands 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 age-appropriate content. Acceleration by using content beyond students�� 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.

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.

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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.

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.

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 cross-curriculum priorities provide rich and engaging contexts and should be incorporated where appropriate. (See section

2.1.3 for information about the priorities).

Year 4 should include opportunities to:

· make connections between representations of numbers, partition and combine numbers flexibly, extend place values, use appropriate language to communicate times, and describe properties of symmetrical shapes · recall multiplication tables, communicate sequences of simple fractions, use instruments to measure accurately, create patterns with shapes and their transformations, and collect and record data · formulate, model and record authentic situations involving operations, compare large numbers with each other, compare time durations, and use properties of numbers to continue patterns · generalise from number properties and results of calculations, derive strategies for unfamiliar multiplication and division task, compare angles, communicate information using graphical displays and evaluate the appropriateness of different displays.

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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 QSA

www.qsa.qld.edu.au/downloads/approach/qsa_equity_statement.pdf

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.

www.qsa.qld.edu.au/18307.html

www.acara.edu.au/verve/_resources/English_as_an_Additional_Language_or_Dialect_ Teacher_Resource_05_06_12.pdf

· Annotated content descriptions: English Foundation to Year 10

www.acara.edu.au/verve/_resources/EALD_Learning_Area_Annotations_English_Revis ed_06_05_12.pdf

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Assessment is an integral part of teaching and learning. It is the purposeful collection of evidence about students�� achievements. An awareness of what learning is assessed and how it is assessed helps both students and parents/carers develop an understanding of what is valued and where to focus attention. Assessment is used for a variety of purposes, but its most important use is in supporting student learning. Sufficient and suitable evidence is collected to enable fair judgments to be made about student learning. Once the evidence is collected and analysed, it is summarised and presented in ways that are meaningful and useful to: · help students achieve the highest standards they can · promote, assist and improve teaching and learning · build a shared understanding of the qualities of student work and communicate meaningful information about students�� progress and achievements to students, teachers, parents/carers and the system. See Appendix 2: Principles of assessment.

The Australian Curriculum is standards-based (see section 2.2). Teacher judgment is guided by achievement standards that are fixed reference points used to describe what is valued as important for young people to know, understand and do. The standards describe the expected qualities of student work and give a common frame of reference and a shared language to describe student achievement. Standards-based assessment is an integral part of the teaching and learning process that is planned and ongoing.

School-based assessment involves individual teachers or groups of teachers making informed decisions about what evidence of learning will be collected at suitable intervals as part of the teaching and learning program. School-based assessment puts teachers�� professional knowledge and practice at the centre of aligning what is taught, how it is taught, how student learning is assessed and how learning is reported.

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An assessment program is planned at the same time as the teaching and learning program and is developed using the achievement standard and the content descriptions. A planned assessment program will: · guide and support targeted teaching and learning · ensure students have opportunities to demonstrate the depth and breadth of their learning in all aspects of the achievement standard · provide regular feedback to students about how they can improve their learning · clarify future teaching and learning needs · ensure teachers have sufficient evidence of learning to make defensible on-balance judgments about the quality of students�� work against the standard.

The assessment program includes: · a range and balance of assessment categories, techniques and conditions appropriate for the learning area, the year level, the school context and the student cohort · opportunities for students to become familiar with the assessment techniques and for teachers to monitor student achievement and provide feedback to students. For fact sheets about assessment for learning, see: · Assessment for learning — A new perspective

www.qsa.qld.edu.au/downloads/p_10/as_afl_new_perspective.doc

· Assessment for learning — Improving assessment pedagogy

www.qsa.qld.edu.au/downloads/p_10/as_afl_improv_pedagogy.doc

· Assessment for learning — School improvement

www.qsa.qld.edu.au/downloads/p_10/as_afl_school_improve.doc

· Assessment for learning — Student achievement

www.qsa.qld.edu.au/downloads/p_10/as_afl_student_achieve.doc

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· Assessment for learning — Inclusive practice

www.qsa.qld.edu.au/downloads/p_10/as_afl_inclusive_practice.doc

· Assessment for learning — Developing student understanding

www.qsa.qld.edu.au/downloads/p_10/as_afl_dev_stud_understand.doc

The planned assessment program specifies the evidence of learning that is summative assessment or assessment

Range is informed by:

· content descriptions

· all aspects of the curriculum content

across the three strands — Number and Algebra, Measurement and Geometry, and Statistics and Probability · assessment categories: - written - spoken/signed - multimodal · all aspects of the Australian Curriculum achievement standard: Understanding and Skills · assessment techniques (section 3.4.1): - modelling and problem-solving task - mathematical investigation - supervised assessment - collection of work - observation record · a variety of assessment categories, techniques and conditions. · assessment conditions (section 3.4.2): - supervised - open.

An example of an assessment program for Year 4 Mathematics is in the Year 4 exemplar year plan: www.qsa.qld.edu.au/downloads/p_10/ac_maths_yr4_plan.doc. The Year 4 standard elaborations (section 0) identify the valued features in the content descriptions and the achievement standard for Australian Curriculum: Mathematics. Teachers can use the standard elaborations to ensure their assessment program includes opportunities for students to demonstrate their achievement in

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The following table provides information and examples about assessment techniques, formats and categories for developing a range and balance within an assessment program.

· communicate ideas.

A mathematical investigation should be conducted over an extended time frame. Challenges, contexts or situations could include: · mathematical experiments · field activities · case studies · proposals to organisations. Supervised assessment items will be in response to questions or statements. Stimulus materials may also be used. They may be seen or unseen. Examples of presentation formats for a collection of work include: · worked solutions to mathematical problems · labelled diagrams · written explanations · graphs and tables · journal entries · short reports on short practical activities · oral, electronic or multimodal presentations.

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Observation records can be used as an independent assessment technique or across all assessment techniques. They are used to record evidence of the learner��s ability to use mathematical skills and communicate mathematical understanding in a task. An observation record is a collection of evidence gathered by teachers in digital and/or written formats about learning in a range of contexts. Examples include: annotated work samples, anecdotes, observations, questioning and interviewing, checklists.

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The following table provides information and examples about assessment conditions including suggested lengths for developing a range and balance within an assessment program.

A modelling and problem-solving task or mathematical investigation can be: · undertaken individually and/or in groups · prepared in class time and/or in students�� own time.

When using open conditions, teachers should ensure that students�� work is their own, particularly where students have access to electronic resources or when they are preparing collaborative assessments. Methods teachers can use to monitor that students�� work is their own include requesting that students: · submit plans and drafts of their work · produce and maintain documentation that charts the development of responses · acknowledge resources used.

· written responses 30–200 words* · spoken/signed or multimodal responses 1–2 minutes* Supervised assessment items will typically: · be undertaken individually · be held under test/exam conditions · allow perusal time, if required · allow time to check for student understanding of instructions · use stimulus materials that are succinct enough to allow students to engage with them in the time provided. (If stimulus materials are lengthy, they may need to be given to students prior to the implementation of the supervised assessment) · be completed in one uninterrupted supervised session or a number of supervised sessions.

· 10–35 mins · < 150 words* *The length of student responses should be considered in the context of the assessment. Longer responses do not necessarily provide better quality evidence of achievement.

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When developing assessment, teachers construct assessments that show the alignment between what has been taught (curriculum), how it is taught (pedagogy), how students are assessed and how the learning is reported. Figure 5 below shows the process of alignment.

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The following checklist assists and supports schools with reviewing and evaluating their assessments.

The extent to which an assessment appears to assess (on face value) what it intends to assess. · Identify the specific content descriptions and aspects of the achievement standard being assessed to determine what is being assessed. · Consider whether student responses to the assessment will provide evidence of learning for the intended curriculum.

The extent to which the assessment measures what it claims to measure (either the subject-matter content or behaviour). · Review the assessment to determine what is valued in the assessment. · Check that it is clear what students are expected to know and be able to do to complete this assessment. · Ensure students will be able to demonstrate the full range of standards A to E in their responses to the assessment. For example, does the assessment require sufficient depth and breadth of the targeted knowledge, understanding and skills; does it encourage students to demonstrate a range of thinking skills? · Use the standard elaborations to confirm that the assessment provides opportunities for students to demonstrate their achievement in particular targeted aspects of the curriculum content and achievement standard.

The extent to which students will find the assessment engaging. · Use an appropriate and meaningful context to engage students. · Ensure the assessment is pitched appropriately for the year level.

The extent to which the assessment clearly communicates to students what is needed for producing their best performance. · Identify specific terms students are required to know and consider whether students are likely to understand the terms or not. · Check the level of language required to interpret the assessment and consider how well students will be able to understand what the assessment requires them to do. · Consider the clarity of the instructions, cues, format, diagrams, illustrations and graphics and how well they assist students to understand what they are required to do.

The extent to which the assessment provides opportunities for all students to demonstrate what they know and can do. · Check for any cultural, gender or social references and stereotypes. · List aspects of the task that might need adjusting for verified students. (See section 2.3.7.) Note that adjustments to the task should not impact on judgments made about student achievement.

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Note: When students undertake assessment in a group or team, the assessment must be designed so that teachers can validly assess the work of individual students and not apply a judgment of the group processes and outcome to all individuals. See the following: · Designing good assessment (video)

www.qsa.qld.edu.au/19788.html

· Assessment instrument — multiple-choice responses

www.qsa.qld.edu.au/downloads/p_10/as_ai_multiple_choice.doc

· Scaffolding — supporting student performance

www.qsa.qld.edu.au/downloads/p_10/as_scaffolding.doc

· Thinking like an assessor vs activity designer

www.qsa.qld.edu.au/downloads/p_10/as_assessor_vs_designer.doc

· Sample assessments:

www.qsa.qld.edu.au/yr4-maths-resources.html

When making judgments about the evidence in student work, teachers are advised to use task-specific standards. Task-specific standards give teachers: · a tool for directly matching the evidence of learning in the student response to the standards · a focal point for discussing student responses · a tool to help provide feedback to students. Task-specific standards are not a checklist; rather they are a guide that: · highlights the valued features that are being targeted in the assessment and the qualities that will inform the overall judgment · specifies particular

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Task-specific standards can be prepared as a matrix or continua. See templates with features shown for: · Continua

www.qsa.qld.edu.au/downloads/p_10/ac_maths_tss_continua.dot

· Matrix

www.qsa.qld.edu.au/downloads/p_10/ac_maths_tss_matrix.dot

Feedback is defined as the process of seeking and interpreting evidence for use by students and their teachers to decide where the students are in their learning, where they need to go and how best to get there. Feedback gathered throughout the teaching and learning cycle informs future teaching learning and assessment. Its purpose is to recognise, encourage and improve student learning. Assessment feedback is most helpful if the specific elements of the content (knowledge, understanding and skills) are identified and specific suggestions are provided. The standard elaborations provide a resource for developing specific feedback to students about the valued features in the content and achievement standards. Assessment alone will not contribute to improved learning. It is what teachers and students do with assessment and other available information that makes a difference. See: · Seeking and providing feedback

www.qsa.qld.edu.au/downloads/p_10/as_feedback_about.doc

· About feedback

www.qsa.qld.edu.au/downloads/p_10/as_feedback_provide.doc

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Schools are required to provide parents/carers with plain-language reports twice a year. In most schools, this takes place at the end of each semester. The report must: · be readily understandable and give an accurate and objective assessment of the student��s progress and achievement · include a judgment of the student��s achievement reported as A, B, C, D or E (or equivalent five-point scale), clearly defined against the Australian Curriculum achievement standards.

The reporting standards are summary statements that succinctly describe typical performance at each of the five levels (A–E) for the two dimensions of the Australian Curriculum achievement standards — understanding (including knowledge) and application of skills for the purpose of reporting twice-yearly.

Evidence in a student��s work typically demonstrates a

The key purpose of reporting student achievement and progress is to improve student learning. The following principles underpin reporting school-based, standards-based assessment: · Alignment of teaching, learning, assessment and reporting: what is taught (curriculum) must inform how it is taught (pedagogy), how students are assessed (assessment) and how the learning is reported. (See section 2) · A collection of evidence or folio of student work: summative judgments for reporting purposes are based on a planned and targeted selection of evidence of student learning collected over the reporting period. (See section 3) · On-balance judgments: professional decisions made by teachers about the overall quality of a student��s work in a range of assessments that best matches the valued features of a learning area described in the achievement standards

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· Moderation: Making consistent judgments about students�� achievements within and between schools occurs when teachers develop shared understandings of the curriculum content and achievement standards. Moderation provides students and their parents/carers with confidence that the awarded grades are an accurate judgment of achievement and that the report is meaningful, professional and consistent. Student achievement is reported against the Australian Curriculum achievement standard for the year level they are taught. Teachers make reasonable adjustments during the cycle of teaching, learning and assessment to support the learning of students with disabilities, for example adjustments to presentation, response, timing, scheduling and location. In most instances, the required curriculum content, achievement and reporting standards will be used for these students. (See section 2.3.7 for inclusivity materials.) School sectors and schools make decisions following negotiation with parents/carers about the provision of modified or accelerated learning and assessment programs to meet the learning needs of some students. Reporting achievement for these students should clearly indicate the year level of the curriculum content and the achievement standards against which judgments about student achievement have been made. Achievement in a learning area is only one source of information on student achievement and progress. Schools may report on other important aspects of student engagement at school separate from achievement in a learning area such as: · student participation and skills in school-based extracurricular activities · student attributes such as effort, punctuality, and social and behavioural skills · student attendance · other school or system priorities.

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By the end of the year, a planned and targeted assessment program will result in an assessment folio of evidence of students�� learning (summative assessment) on which the overall standard is awarded. The range and balance of assessment in the folio ensures there is sufficient evidence of achievement in both dimensions of the Australian Curriculum achievement standard — Understanding and Skills — to make an on-balance judgment for reporting. An on-balance judgment involves a teacher, or a group of teachers, making a professional decision about how the pattern of evidence in the folio best matches the standards.

A folio of evidence of students�� learning (summative assessment) on which the achievement standard is awarded. S tandard elaboratio ns as s is t in m a k in g an on -b ala nc e jud g m ent by des c ribing the c h arac teris tic s of s tud ent w ork in a folio, A to E . Consider all the evidence of achievement in the folio with reference to the expected standard described in the Australian Curriculum achievement standard. Is the pattern of evidence at the expected standard? When looking at the pattern of evidence of achievement, consider: · How well does the evidence of student learning demonstrate understanding and skills? · What is the pattern of achievement in the valued features: – Understanding and Fluency – Problem Solving and Reasoning?

· How well does recent

evidence of student learning in understanding and skills demonstrate student progress? The pattern of evidence is at the expected standard. The pattern of evidence is below the expected standard. Are the characteristics in the evidence of learning best described as C or B or A? Are the characteristics in the evidence of learning best described as D or E? Is there an ��easy-fit�� or match to one of the A–E standards for all the valued features? In this case, the on-balance judgment will be obvious. If there is uneven performance across the valued features, weigh up the contribution of each valued feature across the range and balance of the assessments and decide whether the pattern of evidence of learning is more like an A or B or C etc.

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An on-balance judgment does not involve averaging grades across different assessments or ��ticking�� every box. Rather it is a professional judgment that considers all the evidence of achievement in the folio. The standard elaborations assist in making the on-balance decision. The elaborations describes

For mid-year reporting, the on-balance judgment is based on the pattern of evidence of student achievement and progress

Page 41 |

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The achievement standards guide teacher judgment about how well students have achieved. The most effective way to build consistent and comparable on-balance teacher judgment is through planned activities when teachers — in a partnership or team situation — engage in focused professional dialogue to discuss and analyse the quality of student work, compare their judgments about student achievement and determine the match between the evidence in student work and standards. This process is known as moderation. Professional dialogue increases teachers�� awareness about the variety of ways in which students may respond to the assessment and the types of evidence that may be available to support teacher judgments. In this way, teachers gain valuable insights about how the standards can be demonstrated in student work. They build a shared understanding about the match of evidence to standards, enhancing classroom practice and supporting the alignment of curriculum and assessment. Moderation provides students and their parents/carers with confidence that the standards awarded are defensible judgments of achievement and that the report is meaningful, professional and consistent. See the following fact sheets for more information: · Consistency of judgments — Calibration model

www.qsa.qld.edu.au/downloads/p_10/as_coj_calibration.doc

· Consistency of judgments — Conferencing model

www.qsa.qld.edu.au/downloads/p_10/as_coj_conferencing.doc

· Consistency of judgments — Expert model

www.qsa.qld.edu.au/downloads/p_10/as_coj_expert.doc

See also the suggested approaches to moderation in the Year level plan:

www.qsa.qld.edu.au/downloads/p_10/ac_maths_yr4_plan.doc

Page 43 |

For definitions of terms used by ACARA in the development of the Australian Curriculum: Mathematics, see: www.australiancurriculum.edu.au/Mathematics/Glossary.

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The standards elaborations for Mathematics have been developed from the proficiency strands

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The following principles were developed to inform the policy context of the national curriculum and provide a basis on which local decisions about specific approaches to assessment can be built. 1. The main purposes of assessment are to inform teaching, improve learning and report on the achievement of standards. 2. Assessment is underpinned by principles of equity and excellence. It takes account of the diverse needs of students and contexts of education, and the goal of promoting equity and excellence in Australian schooling. 3. Assessment is aligned with curriculum, pedagogy and reporting. Quality assessment has curricular and instructional validity — what is taught informs what is assessed, and what is assessed informs what is reported. 4. Assessment aligned with curriculum, pedagogy and reporting includes assessment of deep knowledge of core concepts within and across the disciplines, problem solving, collaboration, analysis, synthesis and critical thinking. 5. Assessment involves collecting evidence about expected learning as the basis for judgments about the achieved quality of that learning. Quality is judged with reference to published standards and is based on evidence. 6. Assessment evidence should come from a range of assessment activities. The assessment activity is selected because of its relevance to the knowledge, skills and understanding to be assessed, and the purpose of the assessment. 7. Information collected through assessment activities is sufficient and suitable to enable defensible judgments to be made. To show the depth and breadth of the student learning, evidence of student learning is compiled over time. Standards are reviewed periodically and adjusted according to evidence to facilitate continuous improvement. 8. Approaches to assessment are consistent with and responsive to local and jurisdictional policies, priorities and contexts. It is important that schools have the freedom and support to develop quality assessment practices and programs that suit their particular circumstances and those of the students they are assessing. 9. Assessment practices and reporting are transparent. It is important that there is professional and public confidence in the processes used, the information obtained and the decisions made.

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