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Understanding the syllabus

The Years 1 to 10 Mathematics Syllabus. is based on current research into mathematics educationreflects current national and international best practicereplaces and builds on the 1987 Years 1 to 10 Mathematics syllabus.. The syllabus has links to. Early Years Curriculum GuidelinesYear 2 Diagnost

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Understanding the syllabus

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    1. Understanding the syllabus

    2. The Years 1 to 10 Mathematics Syllabus is based on current research into mathematics education reflects current national and international best practice replaces and builds on the 1987 Years 1 to 10 Mathematics syllabus. The Years 1 to 10 Mathematics Syllabus (2004) has been printed and distributed to schools. A copy may be downloaded from the Queensland Studies Authority Website, www.qsa.qld.edu.au The Years 1 to 10 Mathematics Syllabus has the same structure as other key learning area syllabuses with an outcomes approach. The syllabus was written and developed in consultation with teachers, school communities and leaders in the field of mathematics education. (Refer to the annotated bibliography on the QSA website for relevant research articles and information about best practice in mathematics teaching.)The Years 1 to 10 Mathematics Syllabus (2004) has been printed and distributed to schools. A copy may be downloaded from the Queensland Studies Authority Website, www.qsa.qld.edu.au The Years 1 to 10 Mathematics Syllabus has the same structure as other key learning area syllabuses with an outcomes approach. The syllabus was written and developed in consultation with teachers, school communities and leaders in the field of mathematics education. (Refer to the annotated bibliography on the QSA website for relevant research articles and information about best practice in mathematics teaching.)

    3. The syllabus has links to Early Years Curriculum Guidelines Year 2 Diagnostic Net Queensland Years 3, 5 and 7 testing programs national numeracy benchmarks Years 3, 5 and 7 senior secondary syllabuses. The Early Years Curriculum Guidelines have links with Level 1 core learning outcomes of the key learning area syllabuses. The Early Years learning area, Investigating and understanding environments, develops early mathematical understandings that link strongly to Level 1 of the Mathematics key learning area. Data gathered from the Queensland Years 3, 5 and 7 testing programs has informed the writing of this syllabus. This syllabus will inform future Years 3, 5 and 7 numeracy tests. Teachers use the syllabus to develop the understandings students require to engage with the Years 3, 5 and 7 numeracy tests. Year 2 Diagnostic Net key indicators have been reflected in the core learning outcomes, core content, level statements and elaborations. While the Year 2 Diagnostic Net focuses only on Number, with some inclusion of patterns and working mathematically, the Years 1 to 10 Mathematics Syllabus is organised into five strands Number, Patterns and Algebra, Measurement, Chance and Data, and Space. National numeracy benchmarks for Years 3, 5 and 7 are embedded within the syllabus. Senior secondary syllabuses: The Years 1 to 10 Mathematics Syllabus Level 6 is linked to the Years 11 and 12 Mathematics A Syllabus. The discretionary Beyond Level 6 learning outcomes are linked to Mathematics B and C. A document describing these connections in more detail is available on the QSA website. Click on the Yrs 1 & 10 tab, then click on the Mathematics tab. Click on Support Materials then Articulation.The Early Years Curriculum Guidelines have links with Level 1 core learning outcomes of the key learning area syllabuses. The Early Years learning area, Investigating and understanding environments, develops early mathematical understandings that link strongly to Level 1 of the Mathematics key learning area. Data gathered from the Queensland Years 3, 5 and 7 testing programs has informed the writing of this syllabus. This syllabus will inform future Years 3, 5 and 7 numeracy tests. Teachers use the syllabus to develop the understandings students require to engage with the Years 3, 5 and 7 numeracy tests. Year 2 Diagnostic Net key indicators have been reflected in the core learning outcomes, core content, level statements and elaborations. While the Year 2 Diagnostic Net focuses only on Number, with some inclusion of patterns and working mathematically, the Years 1 to 10 Mathematics Syllabus is organised into five strands Number, Patterns and Algebra, Measurement, Chance and Data, and Space. National numeracy benchmarks for Years 3, 5 and 7 are embedded within the syllabus. Senior secondary syllabuses: The Years 1 to 10 Mathematics Syllabus Level 6 is linked to the Years 11 and 12 Mathematics A Syllabus. The discretionary Beyond Level 6 learning outcomes are linked to Mathematics B and C. A document describing these connections in more detail is available on the QSA website. Click on the Yrs 1 & 10 tab, then click on the Mathematics tab. Click on Support Materials then Articulation.

    4. Structure The syllabus is organised into sections: rationale outcomes assessment reporting. rationale see page 1, Years 1 to 10 Mathematics Syllabus outcomes see page 13, Years 1 to 10 Mathematics Syllabus assessment see page 67, Years 1 to 10 Mathematics Syllabus reporting see page 75, Years 1 to 10 Mathematics Syllabus.rationale see page 1, Years 1 to 10 Mathematics Syllabus outcomes see page 13, Years 1 to 10 Mathematics Syllabus assessment see page 67, Years 1 to 10 Mathematics Syllabus reporting see page 75, Years 1 to 10 Mathematics Syllabus.

    5. Rationale emphasises the importance of providing opportunities for students to think, reason and work mathematically highlights how mathematics helps individuals make meaning of their world describes how the language of mathematics enables communication. Mathematics helps individuals make meaning of their world by providing a framework for explaining many physical and social phenomena. A deep understanding of mathematical knowledge, procedures and strategies empowers individuals to be effective participants in an interdependent world. The verbal and symbolic language of mathematics enables communication of shared mathematical understandings within and among communities. Mathematics helps individuals make meaning of their world by providing a framework for explaining many physical and social phenomena. A deep understanding of mathematical knowledge, procedures and strategies empowers individuals to be effective participants in an interdependent world. The verbal and symbolic language of mathematics enables communication of shared mathematical understandings within and among communities.

    6. Thinking, reasoning and working mathematically is the underlying premise on which the Years 1 to 10 Mathematics Syllabus has been developed is promoted through engagement in mathematical investigations. Teachers may develop students understandings about thinking, reasoning and working mathematically when using a hands-on, investigative approach. Investigations available as Years 1 to 10 Mathematics support materials on the QSA website provide examples of how to do this. Teachers may develop students understandings about thinking, reasoning and working mathematically when using a hands-on, investigative approach. Investigations available as Years 1 to 10 Mathematics support materials on the QSA website provide examples of how to do this.

    7. Positive dispositions towards mathematics learning are integral to thinking, reasoning and working mathematically. Positive dispositions can be developed through student engagement in mathematical investigations relevant to a range and balance of situations from life-related to purely mathematical. Positive dispositions are developed from the early phase of learning and encouraged through real-life and life-like contexts. Teachers can develop students positive dispositions through a student-centred approach, and by listening to and valuing students ideas. Positive dispositions can be developed through student engagement in mathematical investigations relevant to a range and balance of situations from life-related to purely mathematical. Positive dispositions are developed from the early phase of learning and encouraged through real-life and life-like contexts. Teachers can develop students positive dispositions through a student-centred approach, and by listening to and valuing students ideas.

    8. Students think, reason and work mathematically when they see the mathematics in situations encountered. Students see the mathematics when they consider a context, situation, problem or issue and look for the mathematics that relates to it. Students understand that particular mathematical knowledge, processes or strategies may be applied to and helpful in solving the problem.Students see the mathematics when they consider a context, situation, problem or issue and look for the mathematics that relates to it. Students understand that particular mathematical knowledge, processes or strategies may be applied to and helpful in solving the problem.

    9. Students think, reason and work mathematically when they plan, investigate, conjecture, justify, think critically, generalise, communicate and reflect on mathematical understandings and procedures. For example: Students plan how they will attack a problemfor example, they ask themselves what needs to be done first. Students investigate by finding out new information, testing new ideas and experimenting with new procedures and strategies. Students conjecture by suggesting possible solutions to a situation, problem, question or issue. Students justify choices and decisions about how to approach or solve a problem, question, significant task or issue. Students think critically when challenging their own and others ideas. Students generalise about mathematical problems. Students communicate and reflect on mathematical understandings and procedures and share their work and ideas with others. For example: Students plan how they will attack a problemfor example, they ask themselves what needs to be done first. Students investigate by finding out new information, testing new ideas and experimenting with new procedures and strategies. Students conjecture by suggesting possible solutions to a situation, problem, question or issue. Students justify choices and decisions about how to approach or solve a problem, question, significant task or issue. Students think critically when challenging their own and others ideas. Students generalise about mathematical problems. Students communicate and reflect on mathematical understandings and procedures and share their work and ideas with others.

    10. Students think, reason and work mathematically when they select and use relevant mathematical knowledge, procedures, strategies and technologies to analyse and interpret information. For example: When investigating the design of a cross-country course, students need to identify the mathematics involved. For example, they may identify that they will need measurement, and the ability to read and create maps and plans using scale (they can see the mathematics). They would need to plan how to go about the task, and research and practise strategies associated with measuring and constructing plans and maps for others to follow (they are planning mathematically). Students may then select how to communicate their findings to others to assist them to prepare and conduct a successful cross-country event. Throughout this process, students build on previous mathematical knowledge. (Refer to page 1, Years 1 to 10 Mathematics Syllabus for information on thinking, reasoning and working mathematically.) For example: When investigating the design of a cross-country course, students need to identify the mathematics involved. For example, they may identify that they will need measurement, and the ability to read and create maps and plans using scale (they can see the mathematics). They would need to plan how to go about the task, and research and practise strategies associated with measuring and constructing plans and maps for others to follow (they are planning mathematically). Students may then select how to communicate their findings to others to assist them to prepare and conduct a successful cross-country event. Throughout this process, students build on previous mathematical knowledge. (Refer to page 1, Years 1 to 10 Mathematics Syllabus for information on thinking, reasoning and working mathematically.)

    11. Mathematical knowledge includes knowing about mathematics knowing how to do mathematics and knowing when and where to use mathematics. Knowing about mathematics involves: knowing that mathematics is an invented, sophisticated and abstract symbol system developing an appreciation of mathematics as diverse and complex with interwoven and interconnected concepts. For example: understanding addition and subtraction facts understanding that an addition problem may be represented in a range of ways, or knowing ways to represent three-dimensional shapes so that they will be universally recognised. Knowing how to do mathematics involves: applying relevant mathematical knowledge, procedures and strategies in a range and balance of situations from life-related to purely mathematical. For example: knowing how to accurately use addition, multiplication and division to work out a budget for a class party or event, and to purchase what is needed. Knowing when and where to use mathematics involves: being familiar with the mathematics inherent in many life contexts knowing why particular mathematical concepts, procedures and strategies are applicable in different situations. For example: knowing that an understanding of international time zones is needed to plan and make bookings for a world trip knowing how to choose best value products in a supermarket by calculating and comparing sizes and prices. (Refer to page 2, Years 1 to 10 Mathematics Syllabus for information about mathematical knowledge.) Knowing about mathematics involves: knowing that mathematics is an invented, sophisticated and abstract symbol system developing an appreciation of mathematics as diverse and complex with interwoven and interconnected concepts. For example: understanding addition and subtraction facts understanding that an addition problem may be represented in a range of ways, or knowing ways to represent three-dimensional shapes so that they will be universally recognised. Knowing how to do mathematics involves: applying relevant mathematical knowledge, procedures and strategies in a range and balance of situations from life-related to purely mathematical. For example: knowing how to accurately use addition, multiplication and division to work out a budget for a class party or event, and to purchase what is needed. Knowing when and where to use mathematics involves: being familiar with the mathematics inherent in many life contexts knowing why particular mathematical concepts, procedures and strategies are applicable in different situations. For example: knowing that an understanding of international time zones is needed to plan and make bookings for a world trip knowing how to choose best value products in a supermarket by calculating and comparing sizes and prices. (Refer to page 2, Years 1 to 10 Mathematics Syllabus for information about mathematical knowledge.)

    12. An outcomes approach The Years 1 to 10 Mathematics Syllabus is based on an outcomes approach.

    13. Principles underpinning an outcomes approach a clear focus on learning outcomes high expectations for all students a focus on development planning curriculum with learners and outcomes in mind expanded opportunities to learn. A clear focus on learning outcomes Attention is directed towards: what the outcomes explicitly ask students to know and to be able to do with what they know the outcomes that are appropriate for the developmental levels of particular groups of students how outcomes can be used in planning for learning and assessment. High expectations for all students learning outcomes are designed to extend students expectations of what they will come to know and do with what they know. Continua of learning outcomes provide students with signposts or learning pathways showing where they are heading. Note: Adequate time and support need to be provided so that students may demonstrate what they know and can do with what they know. A focus on development learning outcomes are presented in sequences of conceptual and cognitive development. Planning curriculum with learners and outcomes in mind learning outcomes provide a framework for planning for learning and assessing simultaneously. Strategies for assessment are viewed as integral to the planning process. Planning for learning and teaching should focus on a learner-centred approach. Barriers to learning need to be identified and overcome. Expanded opportunities to learn All students have different learning needs and students will not necessarily be ready to demonstrate their learning in the same way or at the same time. Teachers provide a range of contexts and multiple opportunities for students to develop the necessary knowledge, practices and dispositions to demonstrate their learning. (For more information, see Summary of principles of an outcomes approach to education, available from the QSA website. Click on Yrs 1 to 10. Click on Outcomes and KLA information.)A clear focus on learning outcomes Attention is directed towards: what the outcomes explicitly ask students to know and to be able to do with what they know the outcomes that are appropriate for the developmental levels of particular groups of students how outcomes can be used in planning for learning and assessment. High expectations for all students learning outcomes are designed to extend students expectations of what they will come to know and do with what they know. Continua of learning outcomes provide students with signposts or learning pathways showing where they are heading. Note: Adequate time and support need to be provided so that students may demonstrate what they know and can do with what they know. A focus on development learning outcomes are presented in sequences of conceptual and cognitive development. Planning curriculum with learners and outcomes in mind learning outcomes provide a framework for planning for learning and assessing simultaneously. Strategies for assessment are viewed as integral to the planning process. Planning for learning and teaching should focus on a learner-centred approach. Barriers to learning need to be identified and overcome. Expanded opportunities to learn All students have different learning needs and students will not necessarily be ready to demonstrate their learning in the same way or at the same time. Teachers provide a range of contexts and multiple opportunities for students to develop the necessary knowledge, practices and dispositions to demonstrate their learning. (For more information, see Summary of principles of an outcomes approach to education, available from the QSA website. Click on Yrs 1 to 10. Click on Outcomes and KLA information.)

    14. Outcomes There is a hierarchy of outcomes in the syllabus: overall learning outcomes key learning area outcomes core, discretionary and Foundation Level learning outcomes. Outcomes are descriptions of what learners should know and be able to do with what they know as a result of learning experiences. Outcomes are descriptions of what learners should know and be able to do with what they know as a result of learning experiences.

    15. Overall learning outcomes are common to all key learning areas assist students to become lifelong learners, achieve their potential and play active roles in their family and work lives are the outcomes expected both during, and as a result of, learning experiences throughout the 10 years of the common curriculum. Underpinning the Queensland Years 1 to 10 curriculum are 27 overall learning outcomes that are grouped under headings that collectively describe the seven valued attributes of a lifelong learner. These headings are listed as bullet points on the next slide.Underpinning the Queensland Years 1 to 10 curriculum are 27 overall learning outcomes that are grouped under headings that collectively describe the seven valued attributes of a lifelong learner. These headings are listed as bullet points on the next slide.

    16. A lifelong learner is a knowledgeable person with deep understanding a complex thinker a responsive creator an active investigator an effective communicator a participant in an interdependent world a reflective and self-directed learner. The contribution of the Mathematics key learning area to the development of each of these attributes is described in the Years 1 to 10 Mathematics Syllabus on pages 2 to 4. As students engage in a range and balance of investigations from real-life to purely mathematical they will continue to develop these attributes.The contribution of the Mathematics key learning area to the development of each of these attributes is described in the Years 1 to 10 Mathematics Syllabus on pages 2 to 4. As students engage in a range and balance of investigations from real-life to purely mathematical they will continue to develop these attributes.

    17. Key learning area outcomes are the intended results of extended engagement with the Years 1 to 10 Mathematics key learning area are the big picture outcomes for Mathematics across Years 1 to 10. The eight key learning area outcomes are listed on page 13 of the Years 1 to 10 Mathematics Syllabus. They highlight the uniqueness of the Mathematics key learning area and reflect the attributes of a lifelong learner.The eight key learning area outcomes are listed on page 13 of the Years 1 to 10 Mathematics Syllabus. They highlight the uniqueness of the Mathematics key learning area and reflect the attributes of a lifelong learner.

    18. Level statements are included for each level of each strand of the syllabus summarise learning outcomes at each level and provide the conceptual framework for developing the learning outcomes. Level statements also include information related to core content and contexts that contribute to the interpretation and intent of the learning outcomes. The level statements at Foundation Level have been developed for students with disabilities demonstrating a level of understanding before that of Level 1.Level statements also include information related to core content and contexts that contribute to the interpretation and intent of the learning outcomes. The level statements at Foundation Level have been developed for students with disabilities demonstrating a level of understanding before that of Level 1.

    19. Core learning outcomes describe learnings considered essential for all students describe what students should know and be able to do with what they know are sequenced across Levels 1 to 6 are presented in levels of increasing complexity and sophistication provide the focus for planning for learning and teaching. The core learning outcomes are presented in tables on pages 18 to 37 of the Years 1 to 10 Mathematics Syllabus. Teachers may prefer to use the core learning outcomes table for the Years 1 to 10 Mathematics Syllabus by accessing it from the QSA website. (This table is also available as a Microsoft Word file.) The core learning outcomes are presented in tables on pages 18 to 37 of the Years 1 to 10 Mathematics Syllabus. Teachers may prefer to use the core learning outcomes table for the Years 1 to 10 Mathematics Syllabus by accessing it from the QSA website. (This table is also available as a Microsoft Word file.)

    20. The sequencing of the learning outcomes based on each topic is such that each level is nested within the following level. This diagram illustrates the development of conceptual understandings in outcomes. The successive levels of learning outcomes indicate a progression of increasing sophistication and complexity in what students are expected to know and be able to do with what they know. For example, the knowledge, procedures and strategies required by the Level 1 outcome in Number concepts, are reflected in the outcomes for other levels. (For more information, see information on page 15, Years 1 to 10 Mathematics Syllabus.) In addition to these six levels, there are two other levels Foundation Level and Beyond Level 6. These levels are described in the following slides.This diagram illustrates the development of conceptual understandings in outcomes. The successive levels of learning outcomes indicate a progression of increasing sophistication and complexity in what students are expected to know and be able to do with what they know. For example, the knowledge, procedures and strategies required by the Level 1 outcome in Number concepts, are reflected in the outcomes for other levels. (For more information, see information on page 15, Years 1 to 10 Mathematics Syllabus.) In addition to these six levels, there are two other levels Foundation Level and Beyond Level 6. These levels are described in the following slides.

    21. Foundation Level learning outcomes are examples of outcomes for students with disabilities. Foundation Level outcomes could also be developed by teachers to meet the needs and interests of individual students or groups of students. Some examples are offered for each topic in the Years 1 to 10 Mathematics Syllabus. They are listed under the Foundation Level heading as Example learning outcomes. The level statements provide a framework for schools to develop learning outcomes that meet the individual needs of students with disabilities. Some examples are offered for each topic in the Years 1 to 10 Mathematics Syllabus. They are listed under the Foundation Level heading as Example learning outcomes. The level statements provide a framework for schools to develop learning outcomes that meet the individual needs of students with disabilities.

    22. Discretionary learning outcomes describe learnings beyond what are considered essential are included in the Years 1 to 10 Mathematics Syllabus at Beyond Level 6 are linked with learnings identified in senior syllabus documents. Suggested break: To deliver this presentation in two parts, break at the completion of this slide. In the Years 1 to 10 Mathematics Syllabus, discretionary learning outcomes are included for Beyond Level 6 only. They are included for students who have demonstrated all outcomes, including those at Level 6. There is no core content linked to Beyond Level 6. The discretionary learning outcomes are appropriate for students who intend to study Mathematics B and C. They are intended to broaden students understandings and provide opportunities for students to pursue interests and challenges beyond the requirements of the core learning outcomes. Some discretionary learning outcomes at Beyond Level 6 are considered as preparation for further specialised study in mathematics in the multiple pathways available to students. Teachers could use the level statements to develop additional discretionary learning outcomes that are specific to their school community/context. Suggested break: To deliver this presentation in two parts, break at the completion of this slide. In the Years 1 to 10 Mathematics Syllabus, discretionary learning outcomes are included for Beyond Level 6 only. They are included for students who have demonstrated all outcomes, including those at Level 6. There is no core content linked to Beyond Level 6. The discretionary learning outcomes are appropriate for students who intend to study Mathematics B and C. They are intended to broaden students understandings and provide opportunities for students to pursue interests and challenges beyond the requirements of the core learning outcomes. Some discretionary learning outcomes at Beyond Level 6 are considered as preparation for further specialised study in mathematics in the multiple pathways available to students. Teachers could use the level statements to develop additional discretionary learning outcomes that are specific to their school community/context.

    23. Mathematics key learning area Five strands are used to organise the Mathematics key learning area: Number (N) Patterns and Algebra (PA) Measurement (M) Chance and Data (CD) Space (S) Suggested break: Begin part 2 of the presentation here. The five strands are used for organisational convenience. Typically, the concepts within the strands are used all at once or in different combinations, depending on the mathematics of the situation encountered. For example: when working out how much flooring will be needed for a housing design, a builder or architect will use understandings about number, space and measurement when designing a product, an entrepreneur might analyse data from the marketplace and use understandings about number to inform decisions related to its manufacture. When teaching mathematics, teachers should help students to see connections and relationships between and within the strands.Suggested break: Begin part 2 of the presentation here. The five strands are used for organisational convenience. Typically, the concepts within the strands are used all at once or in different combinations, depending on the mathematics of the situation encountered. For example: when working out how much flooring will be needed for a housing design, a builder or architect will use understandings about number, space and measurement when designing a product, an entrepreneur might analyse data from the marketplace and use understandings about number to inform decisions related to its manufacture. When teaching mathematics, teachers should help students to see connections and relationships between and within the strands.

    24. Topics identify the key aspects of mathematics within each strand are interconnected within the strands are coded to aid identification. For example, CD 3.2 identifies Chance and Data strand, core learning outcome Level 3, topic 2 Data. Coding The level is inserted after the alphabetic code and before the dot point. The number after the dot point refers to the topic as it is sequenced throughout the syllabus. Teachers may also refer to the core learning outcomes table to assist interpretation. There are 11 topics: three in the Number strand and two in each of the other strands. In the coding system, an additional D is used to indicate that the learning outcome is discretionary. These discretionary outcomes are only found in Beyond Level 6 in the Years 1 to 10 Mathematics Syllabus. (For information about coding, see page 17, Years 1 to 10 Mathematics Syllabus.)Coding The level is inserted after the alphabetic code and before the dot point. The number after the dot point refers to the topic as it is sequenced throughout the syllabus. Teachers may also refer to the core learning outcomes table to assist interpretation. There are 11 topics: three in the Number strand and two in each of the other strands. In the coding system, an additional D is used to indicate that the learning outcome is discretionary. These discretionary outcomes are only found in Beyond Level 6 in the Years 1 to 10 Mathematics Syllabus. (For information about coding, see page 17, Years 1 to 10 Mathematics Syllabus.)

    25. Number strand Topics: Number concepts N_.1 Addition and subtraction N_.2 Multiplication and division N_.3 Number Number concepts this topic develops numeration and number sense, including the subsets of numbers within the set of rational numbers, the base ten system and the uses and purposes of money in our society. Addition and subtraction this topic promotes the connections between these concepts, understandings of number that support mental computation strategies and other computation methods. Multiplication and division this topic promotes the connections between these concepts, understandings of number that support mental computation strategies, fractional and proportional thinking, and other computation methods.Number Number concepts this topic develops numeration and number sense, including the subsets of numbers within the set of rational numbers, the base ten system and the uses and purposes of money in our society. Addition and subtraction this topic promotes the connections between these concepts, understandings of number that support mental computation strategies and other computation methods. Multiplication and division this topic promotes the connections between these concepts, understandings of number that support mental computation strategies, fractional and proportional thinking, and other computation methods.

    26. Key emphases of Number strand are the language and conventions associated with number different representations of numbers links between the four operations based on the knowledge of each operation mental strategies for calculations of exact and approximate answers money conventions, financial literacy and factors influencing decisions. The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. There is an emphasis on creating different representations of numbers, that is, with concrete materials, models, words, symbols, etc. In everyday life, the four operations are used together often. For example, when making decisions about best value buys in the supermarket, determining whether a multi-pack or single item is the best value. There is an emphasis on developing strategies for mental computation as most computations in everyday life are performed mentally. Financial literacy gives students the ability to make informed judgments and to make effective decisions regarding the use and management of money. (For more information, see Financial literacy in schools discussion paper (2003), available from the Australian Securities and Investment Commission Newsletter website www.fido.asic.gov.au. Enter Financial Literacy in Schools discussion paper as a search. Click on Download a copy of the discussion paper. (See pages 43 to 49, Years 1 to 10 Mathematics Syllabus for Number core content.)The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. There is an emphasis on creating different representations of numbers, that is, with concrete materials, models, words, symbols, etc. In everyday life, the four operations are used together often. For example, when making decisions about best value buys in the supermarket, determining whether a multi-pack or single item is the best value. There is an emphasis on developing strategies for mental computation as most computations in everyday life are performed mentally. Financial literacy gives students the ability to make informed judgments and to make effective decisions regarding the use and management of money. (For more information, see Financial literacy in schools discussion paper (2003), available from the Australian Securities and Investment Commission Newsletter website www.fido.asic.gov.au. Enter Financial Literacy in Schools discussion paper as a search. Click on Download a copy of the discussion paper. (See pages 43 to 49, Years 1 to 10 Mathematics Syllabus for Number core content.)

    27. Patterns and Algebra strand Topics: Patterns and functions PA_.1 Equivalence and equations PA_.2 The introduction of Algebra at Level 1 may be new for some teachers. Some teachers, however, have been engaging students in algebraic thinking although not labelling it as algebra. The Years 1 to 10 Mathematics Syllabus shows how early learning experiences with patterns, functions, equivalence and equations provide the foundation for algebraic thinking. It ensures consistency of language and concepts across Years 1 to 10. Patterns and Algebra Patterns and functions this topic develops understandings of consistent change and relationships. Equivalence and equations this topic develops understandings of balance and the methods associated with solving equations.The introduction of Algebra at Level 1 may be new for some teachers. Some teachers, however, have been engaging students in algebraic thinking although not labelling it as algebra. The Years 1 to 10 Mathematics Syllabus shows how early learning experiences with patterns, functions, equivalence and equations provide the foundation for algebraic thinking. It ensures consistency of language and concepts across Years 1 to 10. Patterns and Algebra Patterns and functions this topic develops understandings of consistent change and relationships. Equivalence and equations this topic develops understandings of balance and the methods associated with solving equations.

    28. Key emphases of Patterns and Algebra strand are the language and conventions associated with patterns and algebra backtracking, equivalence and balance interpretation of relationships through different representations of functions strategies and methods for solving equations links between, and use of, the four operations when solving equations. The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. The emphasis on backtracking, equivalence and balance is supported by research and encourages students to see equations as more than one-way, answer-driven representations. An understanding of backtracking, equivalence and balance at early levels contributes to complex understandings needed in later levels. In the early phase, students are encouraged to use concrete materials for example, function machines and balance scales to explore relationships and to develop algebraic thinking by moving from concrete representations to abstract representations. Knowledge and use of strategies and methods for solving equations and links between the four operations also supports the intent of the Number strand. Students are encouraged to see connections between operations when posing solving problems. (See pages 50 to 53, Years 1 to 10 Mathematics Syllabus for Patterns and Algebra core content.)The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. The emphasis on backtracking, equivalence and balance is supported by research and encourages students to see equations as more than one-way, answer-driven representations. An understanding of backtracking, equivalence and balance at early levels contributes to complex understandings needed in later levels. In the early phase, students are encouraged to use concrete materials for example, function machines and balance scales to explore relationships and to develop algebraic thinking by moving from concrete representations to abstract representations. Knowledge and use of strategies and methods for solving equations and links between the four operations also supports the intent of the Number strand. Students are encouraged to see connections between operations when posing solving problems. (See pages 50 to 53, Years 1 to 10 Mathematics Syllabus for Patterns and Algebra core content.)

    29. Measurement strand Topics: Length, mass, area and volume M_.1 Time M_.2 Measurement Length, mass, area and volume this topic promotes understandings of estimation and measurement of these attributes, units of measure and the relationships between them. Time this topic develops understandings of units and conventions associated with measuring and recording the passage and duration of time. Length, mass area and volume have been grouped together as the same number system is used to measure these. Students learn the different units used to measure the various attributes. (As Time uses different number systems for measurement, it is a separate topic.) Measurement Length, mass, area and volume this topic promotes understandings of estimation and measurement of these attributes, units of measure and the relationships between them. Time this topic develops understandings of units and conventions associated with measuring and recording the passage and duration of time. Length, mass area and volume have been grouped together as the same number system is used to measure these. Students learn the different units used to measure the various attributes. (As Time uses different number systems for measurement, it is a separate topic.)

    30. Key emphases of Measurement strand are the language and conventions of measurement strategies for comparing different measurements skills for measuring relationships between units of measure and between the dimensions for formulae conversion of measurements into manageable forms when calculating time-management skills. The use of the same language and conventions from Levels 1 to 6 to ensures continuity and consistency across Years 1 to 10. In the measurement strand, there is an emphasis on developing estimation skills and personal referents for use in situations where ready access to measuring instruments is limited. There is also a focus on the development of the skills of direct comparison and indirect comparison. For example, using chopsticks laid end to end to measure how long a desk is, or estimating how many chopsticks long a desk is. Students are required to use the instruments appropriate for a particular attribute and to measure as accurately as possible. This physical component of mathematics also develops fine and gross motor skills, coordination and spatial awareness. There is a focus on understandings of the number systems used. For example, multiples of 10 or 100 are used for measurement of length, mass, area and volume. Time is measured using a number of different systems a base 60 system for hours (minutes and seconds) and other systems for weeks, months, years, etc. Knowledge, strategies and procedures for making sensible adjustments of numbers to make them more manageable are emphasised. Students also develop strategies for making exact and approximate calculations. The measurement strand emphasises learning to efficiently manage time, taking into consideration factors that impact on the use of time. (See pages 54 to 57, Years 1 to 10 Mathematics Syllabus for Measurement core content.)The use of the same language and conventions from Levels 1 to 6 to ensures continuity and consistency across Years 1 to 10. In the measurement strand, there is an emphasis on developing estimation skills and personal referents for use in situations where ready access to measuring instruments is limited. There is also a focus on the development of the skills of direct comparison and indirect comparison. For example, using chopsticks laid end to end to measure how long a desk is, or estimating how many chopsticks long a desk is. Students are required to use the instruments appropriate for a particular attribute and to measure as accurately as possible. This physical component of mathematics also develops fine and gross motor skills, coordination and spatial awareness. There is a focus on understandings of the number systems used. For example, multiples of 10 or 100 are used for measurement of length, mass, area and volume. Time is measured using a number of different systems a base 60 system for hours (minutes and seconds) and other systems for weeks, months, years, etc. Knowledge, strategies and procedures for making sensible adjustments of numbers to make them more manageable are emphasised. Students also develop strategies for making exact and approximate calculations. The measurement strand emphasises learning to efficiently manage time, taking into consideration factors that impact on the use of time. (See pages 54 to 57, Years 1 to 10 Mathematics Syllabus for Measurement core content.)

    31. Chance and Data strand Topics: Chance CD_.1 Data CD_.2 Both Chance and Data are now included from Year 1. Chance and Data Chance this topic develops understandings of likelihood and the use of experimental and theoretical approaches to estimate or determine numerical probability to make judgments and decisions. Data this topic develops understandings related to collecting and handling data, exploring and displaying data, and identifying and interpreting variation.Both Chance and Data are now included from Year 1. Chance and Data Chance this topic develops understandings of likelihood and the use of experimental and theoretical approaches to estimate or determine numerical probability to make judgments and decisions. Data this topic develops understandings related to collecting and handling data, exploring and displaying data, and identifying and interpreting variation.

    32. Key emphases of Chance and Data strand are the language and conventions of chance and data data collection methods and displays appropriate for a range of purposes selection of strategies for situations involving probability and statistics application of strategies to calculate probability and analyse data interpretations of probabilities and statistics to inform judgments and decisions. The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. There is a focus on students developing their own methods for gathering relevant data to investigate personal or topical issues. There is an emphasis on students creating and interpreting a range of data displays. The core content provides a range of strategies that students can select from and apply when calculating probability and analysing and interpreting data. (See pages 58 to 61, Years 1 to 10 Mathematics Syllabus for Chance and Data core content.) The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. There is a focus on students developing their own methods for gathering relevant data to investigate personal or topical issues. There is an emphasis on students creating and interpreting a range of data displays. The core content provides a range of strategies that students can select from and apply when calculating probability and analysing and interpreting data. (See pages 58 to 61, Years 1 to 10 Mathematics Syllabus for Chance and Data core content.)

    33. Space strand Topics: Shape and line S_.1 Location, direction and movement S_.2 Space Shape and line this topic promotes understandings of the geometric terms and properties used to identify 3D shapes and objects and 2D shapes, and to visualise and create representations. Location, direction and movement this topic promotes understandings of the construction and interpretation of maps, plans and grids, and the identification and description of locations, directions and movements through familiar environments.Space Shape and line this topic promotes understandings of the geometric terms and properties used to identify 3D shapes and objects and 2D shapes, and to visualise and create representations. Location, direction and movement this topic promotes understandings of the construction and interpretation of maps, plans and grids, and the identification and description of locations, directions and movements through familiar environments.

    34. Key emphases of Space strand are the language of, and conventions associated with, space geometric properties connections within and between families of shapes methods to represent orientation and movement, and to construct shapes visualisation strategies for dynamic spatial reasoning. The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. There is a focus on the understanding of geometric terms and properties to enable students to classify families and subgroups of shapes. Students develop understandings of the similarities and differences within and between families of shapes. Students develop understandings to identify and describe locations, directions and movements in and through real and represented environments. There is a focus on the development of skills to visualise and represent shapes, and to visualise movements of shapes and objects within particular environments. (See pages 62 to 66, Years 1 to 10 Mathematics syllabus for Space core content.)The use of the same language and conventions from Levels 1 to 6 ensures continuity and consistency across Years 1 to 10. There is a focus on the understanding of geometric terms and properties to enable students to classify families and subgroups of shapes. Students develop understandings of the similarities and differences within and between families of shapes. Students develop understandings to identify and describe locations, directions and movements in and through real and represented environments. There is a focus on the development of skills to visualise and represent shapes, and to visualise movements of shapes and objects within particular environments. (See pages 62 to 66, Years 1 to 10 Mathematics syllabus for Space core content.)

    35. Core content is strand and level specific is organised using subsets of the topics is used with the core learning outcomes to plan for learning and teaching should be in a range of contexts. Mathematics is different from some other key learning areas because the core content is strand and level specific. In Health and Physical Education, for example, the core content is not level-specific and may be used at any level. The level-specific core content is related to the developmental sequence of learning. This core content is organised using subsets of the topics. Subset headings appear in a lighter shade where there is no specific core content for that level. Refer to page 47 of the Years 1 to 10 Mathematics Syllabus for an example of text in a lighter shade. Although the core content is organised in strands at each level, there will be some natural overlap as opportunities for learning are planned. The organisation of content within a level should not be considered hierarchical. Core content should be placed in a range of contexts. Note: There is no core content for Foundation Level. Additionally, there is no core content for Beyond Level 6. These levels are not part of the core. Mathematics is different from some other key learning areas because the core content is strand and level specific. In Health and Physical Education, for example, the core content is not level-specific and may be used at any level. The level-specific core content is related to the developmental sequence of learning. This core content is organised using subsets of the topics. Subset headings appear in a lighter shade where there is no specific core content for that level. Refer to page 47 of the Years 1 to 10 Mathematics Syllabus for an example of text in a lighter shade. Although the core content is organised in strands at each level, there will be some natural overlap as opportunities for learning are planned. The organisation of content within a level should not be considered hierarchical. Core content should be placed in a range of contexts. Note: There is no core content for Foundation Level. Additionally, there is no core content for Beyond Level 6. These levels are not part of the core.

    36. Assessment Use assessment information to: provide ongoing feedback about learning to students inform decision making related to student learning.

    37. focus on students demonstration of learning be comprehensive be valid and reliable take account of individual learners provide opportunities for students to take responsibility for their own learning and for monitoring their own progress reflect equity principles. To collect comprehensive evidence, teachers need to provide multiple opportunities in a variety of contexts for students to demonstrate their learning. Because students have different learning styles, evidence should be gathered from various sources using a variety of techniques. It is essential that assessment opportunities assess what they are intended to assess and that judgments about students demonstrations of learning are based on a broad range of evidence gathered and recorded over time. When planning assessment, teachers need to take account of the fact that each student will progress at an individual rate. Factors that influence students learning, in particular, their prior knowledge, experiences and unique circumstances, should also be considered. As teachers plan learning experiences, they should also plan how they will assess students learning and monitor their progress. Students should be given the opportunity to set their own learning goals and to monitor their own progress. To collect comprehensive evidence, teachers need to provide multiple opportunities in a variety of contexts for students to demonstrate their learning. Because students have different learning styles, evidence should be gathered from various sources using a variety of techniques. It is essential that assessment opportunities assess what they are intended to assess and that judgments about students demonstrations of learning are based on a broad range of evidence gathered and recorded over time. When planning assessment, teachers need to take account of the fact that each student will progress at an individual rate. Factors that influence students learning, in particular, their prior knowledge, experiences and unique circumstances, should also be considered. As teachers plan learning experiences, they should also plan how they will assess students learning and monitor their progress. Students should be given the opportunity to set their own learning goals and to monitor their own progress.

    38. Assessment involves providing students with opportunities to demonstrate what they know and can do with what they know gathering and recording evidence of students learning using evidence to make overall judgments about students learning. Teachers can use learning activities as assessment opportunities or design specific tasks that give students opportunities to demonstrate their learning. Sources of evidence can include learning activities as well as specifically designed assessment tasks. Assessment techniques include observation, consultation and focused analysis. (See table on page 71, Years 1 to 10 Mathematics Syllabus.) Record keeping must support planning and should be manageable and easily maintained. It must provide a way of documenting evidence drawn from a range of contexts about student learning. A student folio is a useful way of collating and storing evidence about a students learning. (To find out more about assessment, refer to pages 67 to 74, Years 1 to 10 Mathematics Syllabus.) Teachers can use learning activities as assessment opportunities or design specific tasks that give students opportunities to demonstrate their learning. Sources of evidence can include learning activities as well as specifically designed assessment tasks. Assessment techniques include observation, consultation and focused analysis. (See table on page 71, Years 1 to 10 Mathematics Syllabus.) Record keeping must support planning and should be manageable and easily maintained. It must provide a way of documenting evidence drawn from a range of contexts about student learning. A student folio is a useful way of collating and storing evidence about a students learning. (To find out more about assessment, refer to pages 67 to 74, Years 1 to 10 Mathematics Syllabus.)

    39. Reporting is the process of communicating information and judgments about students learning should provide students and parents/carers with timely and accurate information that they can understand, interpret and use to support student learning. The information provided should be constructive and enable students to reflect on their progress and negotiate future learning and assessment. This kind of reporting is an important and ongoing part of the learning and teaching process, and can occur incidentally as well as in planned ways.The information provided should be constructive and enable students to reflect on their progress and negotiate future learning and assessment. This kind of reporting is an important and ongoing part of the learning and teaching process, and can occur incidentally as well as in planned ways.

    40. Information and judgments about student learning are communicated to students parents/carers other professionals. Information reported to students and parents/carers as part of the ongoing learning and teaching process could include: explanations of particular assessment opportunities evidence about demonstrations of learning judgments about demonstrations of learning identification of future assessment opportunities. The language, formats and modes used for reporting should be meaningful and relevant to the proposed audience. Possible modes for reporting include: written reports (print or electronic) studentteacher conferences teacherparent interviews student-led three-way conferences (student, teacher and parents/carers) culminating presentations student folios (print or electronic). (To find out more about reporting, refer to pages 75 to 76, Years 1 to 10 Mathematics Syllabus.)Information reported to students and parents/carers as part of the ongoing learning and teaching process could include: explanations of particular assessment opportunities evidence about demonstrations of learning judgments about demonstrations of learning identification of future assessment opportunities. The language, formats and modes used for reporting should be meaningful and relevant to the proposed audience. Possible modes for reporting include: written reports (print or electronic) studentteacher conferences teacherparent interviews student-led three-way conferences (student, teacher and parents/carers) culminating presentations student folios (print or electronic). (To find out more about reporting, refer to pages 75 to 76, Years 1 to 10 Mathematics Syllabus.)

    41. Support materials are intended to help teachers develop understandings about the Mathematics key learning area and the syllabus. The support materials focus on: the nature of the key learning area understanding of the core learning outcomes important topics in mathematics.The support materials focus on: the nature of the key learning area understanding of the core learning outcomes important topics in mathematics.

    42. Materials to support the syllabus Understanding the syllabus core learning outcomes table elaborations Planning sample investigations ideas for investigations planning advice P12 links connections with - senior syllabus documents - Early Years Curriculum - Years 3, 5 and 7 testing program Additional information annotated bibliography A variety of materials are available to support the Years 1 to 10 Mathematics Syllabus. Teachers can explore the QSA website for support materials specific to the Mathematics key learning area or for information about other key learning areas. A variety of materials are available to support the Years 1 to 10 Mathematics Syllabus. Teachers can explore the QSA website for support materials specific to the Mathematics key learning area or for information about other key learning areas.

    43. Contact us Queensland Studies Authority PO Box 307 Spring Hill Queensland 4004 Australia Phone: +61 7 3864 0299 Fax: +61 7 3221 2553 Visit the QSA website at www.qsa.qld.edu.au

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