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AC ENGLISH: Cross-Curriculum Priorities in English ......................................................... 16 2014 NOTES ON TEACHING AND LEARNING............................................................................. 17 Essential Literacy Practices ................................................. Error! Bookmark not defined. Essential Literacy Pedagogies ............................................. Error! Bookmark not defined. How precious to me are your thoughts, O God! How vast is the sum of them! Were I to count them, they would outnumber the grains of sand. Psalm 139: 18,19 John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 1 Copyright 2014, John Calvin Schools Support Office, for the use of the John Calvin Primary Schools. A digital version of this document and its attachments is available at http://www.frsa.asn.au/PrimarySchools/PrimaryCurriculum/tabid/205/language/enUS/Default.aspx. Teachers and other staff at the John Calvin Schools may freely download, print, cut and paste or make any other use of this material, whether in print or digitally, with no further acknowledgement required. For other people and organizations, incidental use is permitted, provided proper acknowledgement is made. People or organizations wishing to use substantial portions of this material should contact the John Calvin Schools Support Office for permission prior to use, at this address: [email protected] This document will be reviewed from time to time. Feedback is solicited and will be appreciated. Please forward such feedback to the John Calvin Schools Support Office at [email protected] . Aart Plug, Curriculum Officer John Calvin Schools Support Office, Armadale WA December 2014 John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 1 John Calvin Schools MATHEMATICS Pre-Primary to Year 6 Documentation 2014 PLEASE NOTE: In the Australian Curriculum, the term FOUNDATION YEAR (or Level) is used to indicate the year of schooling before Year 1. This reflects the fact that the various State and Territory education systems in Australia use different names for this year level. Entry ages may also vary. In Western Australia, the Foundation Year is referred to as PRE-PRIMARY. In this document and the attached overviews, these terms are used interchangeably and in practice mean the same thing. As a rule, the term Foundation Year or Foundation Level is used when referring directly to the Australian Curriculum documents, and Pre-Primary will refer to the actual year levels within the John Calvin Schools Curriculum. As a rule, the term Foundation Year or Foundation Level is used when referring directly to the Australian Curriculum documents, Pre-Primary will refer to the actual year levels within the John Calvin Schools. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 2 TABLE OF CONTENTS: 1. FOUNDATION STATEMENT ........................................................................................ 5 2. RATIONALE ............................................................................................................... 6 Definition .................................................................................................................................... 6 Purpose....................................................................................................................................... 6 Aims ............................................................................................................................................ 7 3. JCS MATHEMATICS LEARNING AREA OUTCOMES : .................................................. 8 Outcome 1. Outcome 2. Outcome 3. Outcome 4. Outcome 5. Appreciating and Valuing Mathematics ................................................................ 8 Thinking and Working Mathematically ................................................................. 8 Number and Algebra ............................................................................................. 8 Measurement and Geometry ............................................................................... 9 Statistics and Probability....................................................................................... 9 4. AUSTRALIAN CURRICULUM REQUIREMENTS .............................................................. 10 4.1 AC MATHEMATICS: Content and Proficiency Strands – Foundation to Year 6: .................. 10 4.1.1 Content Strands .............................................................................................................. 10 4.1.2 Proficiency Strands .......................................................................................................... 11 4.2 AC MATHEMATICS: Achievement Standards – Foundation to Year 6 ................................ 12 4.3 AC MATHEMATICS: Scope and Sequence – Foundation to Year 6 ..................................... 13 4.4 AC MATHEMATICS: General Capabilities in Mathematics .................................................. 14 1. Literacy .................................................................................................................................. 14 2. Numeracy .............................................................................................................................. 14 3. ICT Capability ......................................................................................................................... 15 4. Critical and Creative Thinking ................................................................................................ 15 5. Personal and Social Capability ............................................................................................... 15 6. Ethical Behaviour ................................................................................................................... 15 7. Intercultural Understanding .................................................................................................. 15 4.5 AC MATHEMATICS: Cross-Curriculum Priorities in Mathematics ....................................... 16 1. Indigenous Histories and Culture .......................................................................................... 16 2. Asia and Australia’s Engagement with Asia .......................................................................... 16 3. Sustainability ......................................................................................................................... 16 5. TEACHING AND LEARNING IN MATHEMATICS............................................................. 17 1. 2. 3. 4. 5. Order and Complexity ........................................................................................................... 17 Proficiency in Mathematics .................................................................................................. 17 The Learning Environment .................................................................................................... 18 The Language of Mathematics .............................................................................................. 18 Student Reflection on Learning ............................................................................................ 18 6. ASSESSMENT OF STUDENT LEARNING ...................................................................... 19 7. SCHOOL-BASED REQUIREMENTS ................................................................................ 20 Time Allotments................................................................................................................................. 20 Minimum Standards .......................................................................................................................... 20 Tracking of Student Learning ............................................................................................................. 20 8. RESOURCES ............................................................................................................... 20 9. AUDIT AND REVIEW................................................................................................... 21 APPENDICES: ................................................................................................................. 22 APPENDIX 1: APPENDIX 2: APPENDIX 3: APPENDIX 4: AC MATHEMATICS: Overview Of Content Strands – Pre-primary To Year 6 ............... 23 AC MATHEMATICS: Overview Of Proficiency Strands – Pre-Primary To Year 6 .......... 27 AC MATHEMATICS: Overview Of Achievement Standards – Pre-primary To Year 6 ... 29 AC MATHEMATICS: Scope And Sequence – Pre-primary to Year 6 Overviews ........... 33 John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 3 John Calvin Schools: Mathematics Learning Area At the John Calvin Schools, students understand that mathematical concepts and skills are powerful tools given by God, leading them to acknowledge His sovereignty, enabling them to come to grips with the greatness of His work in the created order and in human society, and equipping them to serve Him and our neighbour within them, in accordance with the instruction of Holy Scripture. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 4 1. FOUNDATION STATEMENT Mathematics is a human cognitive activity that finds its origin in the power and wisdom of God. Numerical and spatial concepts and skills are powerful tools given by God to understand the created order and human society, and to serve Him within them. Mathematical understanding helps us to acknowledge the sovereignty of God, and enables us to understand more fully the greatness of His work (Romans 1:20). It also equips and enables us to exercise the dominion over creation that God has entrusted to us. Mathematical thinking and activity is governed by God’s revelation in His Word, and is limited by our humanity and fallen condition. Students must grow in an increasing awareness that mathematical skills and concepts are to be used within a framework of stewardship, use of talents, service of God and the neighbour, and the “cultural mandate” (Gen 1:28). They must also learn to understand that mathematically correct solutions can be put to uses which are contrary to the will of God. They should therefore be taught to discern between right and wrong use, and strive to work accurately, efficiently and effectively. In this way, learning in mathematics is linked to the development of Biblical values about learning and life. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 5 2. RATIONALE DEFINITION Mathematics as an area of study is composed of multiple interrelated and interdependent numerical and spatial concepts, and the language that is associated with them. While ‘mathematics’ as such is an abstract concept that largely deals with abstract ideas, it is grounded in the concrete observable reality of the creation order, and provides powerful tools for living and working within creation. ‘Mathematics’ as it is taught and learned at the John Calvin Schools involves growth and development in knowledge and understanding of the numerical and spatial concepts themselves, and of the order and patterns that can be discerned in and through them. It also includes the development of skills and proficiencies in using mathematical processes, development of the language of mathematics, and growth in the ability to use mathematical reasoning to solve concrete and abstract problems within and outside of the mathematics classroom. Finally, it is marked by a growth in the disposition to use these understandings and skills in a manner that is pleasing to God. PURPOSE The uses of Mathematics: 1. The order and complexity of mathematics are sources of wonder, pleasure and praise of God. 2. The study of mathematics enables us to develop and communicate concrete and abstract ideas through the use of numerical and spatial concepts, and to apply reasoning and logic in coming to grips with these ideas and concepts. 3. The application of mathematical skills and understandings enables us to calculate and manipulate aspects of reality in a host of practical ways, and to participate in almost every dimension of everyday life: worship, family life, work and economic activity, and recreation. 4. For many students, the study of Mathematics at Primary and Secondary school levels provides the fundamentals on which mathematical specialties and professional applications of mathematics are built. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 6 AIMS In keeping with the Biblical foundation and the requirements of the Australian Curriculum, the John Calvin Schools Mathematics curriculum aims to ensure that students: 1. Develop Numeracy through: an understanding of mathematical concepts, increasing proficiency, fluency and flexibility in using mathematical processes, growing ability to pose and solve problems through mathematical reasoning in the three strands of Number and Algebra, Measurement and Geometry, and Statistics and Probability. 2. Recognize the connections between mathematics and other disciplines, and appreciate mathematics as an enjoyable and rewarding discipline to study. 3. Are confident, creative users and communicators of mathematics, able to investigate, represent and interpret situations in their personal and work lives, honouring God and serving their neighbour and the community in which God has placed them. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 7 3. JCS MATHEMATICS LEARNING AREA OUTCOMES : Teaching and learning in the History Learning Area at the John Calvin Schools is subject to the requirements of the Australian Curriculum – Mathematics. The following outcomes are seen as essential to ensure that these requirements are met in a manner that is consistent with the distinctively Reformed character and identity of the John Calvin Schools Outcome 1. Appreciating and Valuing Mathematics Students acknowledge that mathematics is a God-given tool to understand the created order and to work within it, and that it is to obediently used to honour Him and serve the neighbour. Students show a growing understanding of the nature, power and scope of mathematical activity, and acknowledge that the creativity, intuition and reasoning associated with it are God-given talents. Students understand how mathematics is used in regulating their lives. They understand that the use of mathematics is governed by the will of God, and distinguish between right and wrong use. They therefore value clarity, accuracy, fluency and persistence in mathematical thinking and the use of mathematical skills. Outcome 2. Thinking and Working Mathematically Students develop increasing proficiency in the use of mathematical thinking processes and skills in all kinds of situations. Students call on a repertoire of problem solving techniques and appropriate technology, and work individually and collaboratively on mathematical tasks and problems. Students choose mathematical ideas and tools suitable for dealing with the problem at hand. They interpret and make sense of the results within the context of the situation, and evaluate the results obtained for accuracy and appropriateness. Students investigate, generalize and reason about patterns in number, space and data. They observe and describe regularities and differences, using the language of mathematics with precision and clarity. Outcome 3. Number and Algebra Students use numbers and operations and the relationships between them efficiently and flexibly, fluently and accurately. Students read, write and understand the meaning, order and relative magnitude of numbers (whole numbers, place value, fractions, decimals, percentages and negative numbers), and can move flexibly between equivalent forms. They understand the meaning, use and relationships between operations (addition, subtraction, multiplication and division), and understand and can move flexibly between equivalent processes. Students are able to carry out the calculations associated with number operations accurately and fluently, using mental processes, pencil and paper or calculators as appropriate. They become increasingly proficient and fluent in the recall and use of basic number facts. While choosing from and using a range of calculation strategies in carrying out number operations, students know and are able to use standard algorithms as useful and efficient tools for computation. They judge the appropriate level of accuracy or precision, and are able to check whether the results of their computations are accurate and make sense. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 8 Students use algebraic symbols, diagrams and graphs to describe and reason mathematically. They recognize and describe variation and associated relationships in mathematical situations, representing such variation verbally, or in symbols, tables and graphs. They read, write and understand the meaning of symbolic expressions, moving flexibly between equivalent expressions. They write equations and inequalities to describe mathematical constraints, and choose, use and interpret appropriate solution strategies and results. Outcome 4. Measurement and Geometry Students describe and measure the spatial features of objects, environments and movements. Students decide what needs to be measured and carry out various measurements directly, using both arbitrary and standard units of measurement, to needed levels of accuracy. They choose and use a range of indirect measurement strategies, using prediction, averaging, sampling or formulae as appropriate. Students visualize, draw and model 2D and 3D shapes, locations and arrangements, and show the effects of transformations on them. They reason about shapes, paths, transformations and arrangements, to solve problems, and describe and justify their solutions. Outcome 5. Statistics and Probability Students use their knowledge of chance and data handling processes in dealing with situations in which uncertainty is involved. Students recognize that while nothing happens by chance, since all things are governed by the providence of God, many situations are to us unpredictable. They understand and use the everyday language of probability, and make predictions about the likelihood of events occurring. They realize that individual outcomes may display long-term patterns, and that ‘probability’ is a numerical tool to describe such patterns. They make observations and conduct experiments and simulations to investigate and interpret such patterns of outcomes. Students plan and undertake data collection, and organize, summarize, represent, interpret and communicate data so collected. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 9 4. AUSTRALIAN CURRICULUM REQUIREMENTS Teaching and learning in the Mathematics Learning Area at the John Calvin Schools is subject to the requirements of the Western Australian Curriculum Assessment and Outline (SCSA) located at: www.scsa.wa.edu.au/internet/Years_K10. SCSA incorporates and refers to the Australian Curriculum: Mathematics. 4.1 AC MATHEMATICS: Content and Proficiency Strands – Foundation to Year 6: The Australian Curriculum: Mathematics is organised around the interaction of three content strands and four proficiency strands. At the John Calvin Schools, these strands are seen as essential to ensure that the requirements of the Australian Curriculum are met. Teaching, learning, and assessment programs should balance and integrate the Content and Proficiency strands in order to support the development of knowledge, understanding and skills. In the following section, each strand will be defined and significant features will be identified. While it is our aim to meet these requirements in a manner that is consistent with our distinctively Christian character and identity, the content of the Mathematics Learning Area as such will provide limited opportunities to reflect this identity explicitly. However, it should at all times be reflected in the general learning environment of the classroom and the school, including in this learning area. 4.1.1 Content Strands The content strands are Number and Algebra, Measurement and Geometry, and Statistics and Probability. Each of these is grouped into a number of sub-strands. They describe what is to be taught and learnt. Number and Algebra Measurement and Geometry Statistics and Probability Number and place value (F-8) Using units of measurement (F-10) Chance (1-10) Fractions and decimals (1-6) Shape (F-7) Data representation and interpretation (F-10) Money and financial mathematics (1-10) Geometric reasoning (3-10) Location and transformation (F-7) An Overview of the Mathematics F-6 Content Strands is provided in Appendix 1, below. For each year level F-6, the Content Strands overview for that year is also included in the Yearby-year Scope and Sequence Overviews, provided in Appendix 4, below John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 10 4.1.2 Proficiency Strands The proficiency strands are Understanding, Fluency, Problem Solving, and Reasoning. They describe how content is explored or developed, that is, the thinking and doing of mathematics. They provide the language to build in the developmental aspects of the learning of mathematics and have been incorporated into the content descriptions of the three content strands described above. This approach has been adopted to ensure students’ proficiency in mathematical skills develops throughout the curriculum and becomes increasingly sophisticated over the years of schooling. Further elaboration on the proficiency strands is provided in the section on Teaching and Learning in Mathematics, below. An Overview of the Mathematics F-6 Proficiency Strands is provided in Appendix 2, below. For each year level F-6, the Proficiency Strands overview for that year is also included in the Year-by-year Scope and Sequence Overviews, provided in Appendix 4, below. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 11 4.2 AC MATHEMATICS: Achievement Standards – Foundation to Year 6 The Australian Curriculum: Mathematics sets standards for the quality of learning that students are expected to demonstrate by the end of each year of schooling. These Achievement Standards are expressed in written statements, and are accompanied by annotated student work samples illustrating achievement at various levels. The Achievement Standards describe student progress within the Mathematics learning area, and give teachers a framework to assess, evaluate and report on the quality of learning that each student has achieved. While the Australian Curriculum: Mathematics document sets out the Achievement Standards in a global statement for each year level, this document unpacks these global statements in a dot-pointed format. This will support teachers in planning and carrying out more detailed assessments of student learning. Reporting of Student Achievement is to be carried out against the Achievement Standards for that year, using an A-B-C-D-E scale as follows: A. Excellent – Student consistently demonstrates learning achievement well above the Achievement Standard for the year B. High – Student usually demonstrates learning achievement above the Achievement Standard for the year C. Satisfactory – Student demonstrates learning achievement that meets the Achievement Standard for the year D. Limited – Student demonstrates learning achievement that may approach but does not usually meet the Achievement Standard for the year E. Very Low – Student demonstrates learning achievement that is well below the Achievement Standard for the year An Overview of the F-6 Mathematics Achievement Standards is provided in Appendix 3, below For each year level F-6, the Achievement Standards for that year are also included in the Yearby-year Scope and Sequence Overviews, provided in Appendix 4, below. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 12 4.3 AC MATHEMATICS: Scope and Sequence – Foundation to Year 6 At the John Calvin Schools, teaching and learning in Mathematics will be organized by means of a specified Scope and Sequence, ensuring that all of the content requirements of the Australian Curriculum: Mathematics are satisfied in a coherent, comprehensive and developmentally appropriate manner. Year-by-year Scope and Sequence Overviews for all years up to Year 6 are provided in Appendix 4, below. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 13 4.4 AC MATHEMATICS: General Capabilities in Mathematics The Australian Curriculum lists seven General Capabilities that encompass the knowledge, skills, behaviours and dispositions that are considered to be overarching outcomes of teaching and learning. As with all other elements of the curriculum, these are to be addressed in a manner which is embedded in and consistent with the distinctively Reformed identity of the John Calvin Schools. These General Capabilities are identified where they are applied or developed in the Content Descriptions of the Australian Curriculum: Mathematics , and also where they offer additional opportunities for student learning in the Content Elaborations. The seven General Capabilities are: Literacy Numeracy Information and communication technology (ICT) capability Critical and creative thinking Personal and social capability Ethical understanding Intercultural understanding. Each of these has generic applications across the curriculum, which are further elaborated elsewhere. Their distinctive applications within the Mathematics Learning Area include the following: 1. Literacy 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. 2. Numeracy More than any other, Mathematics has a central, foregrounded and explicit role in the development of numeracy. The Mathematics curriculum provides the opportunity to apply mathematical understanding and skills in context, both in other learning areas and in real world contexts. Financial mathematics is a particularly important context for the application of Number and Algebra is financial mathematics. In Measurement and Geometry, there is an opportunity to apply understanding to design. The twenty-first century world is information driven, and through Statistics and Probability students can interpret data and make informed judgments about events involving uncertainty or probability. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 14 3. ICT Capability 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. 4. Critical and Creative Thinking Students develop critical and creative thinking as they learn to generate and evaluate knowledge, ideas and possibilities, and use them when seeking solutions in mathematical contexts. 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. 5. Personal and Social Capability 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. 6. Ethical Behaviour There are opportunities in the Mathematics curriculum to explore, develop and apply ethical understanding in a range of contexts. Examples include analysing data and statistics; finding inappropriate comparisons and misleading scales when exploring the importance of fair comparison; and interrogating statistical and financial claims and sources; developing a responsible personal budget which reflects obligations towards work in God’s Kingdom, the needs of the neighbour, and short- and long-term personal goals. 7. Intercultural Understanding While Intercultural understanding is largely peripheral to learning and teaching in Mathematics, it can be enhanced when students discover the way in which mathematical knowledge is expressed in other traditions, and when they discover how mathematical concepts and skills can be tools to assist them in learning about other cultures. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 15 4.5 AC MATHEMATICS: Cross-Curriculum Priorities in Mathematics The Australian Curriculum lists three significant contemporary issues that are relevant to the lives of the students, now and into the future. Schools are expected to attend to these issues across the curriculum, to the extent and in ways that are relevant to the specific content and skill requirements of the various learning areas. These Cross-Curriculum priorities are: Indigenous Histories and Culture Asia and Australia’s Engagement with Asia Sustainability As with all other elements of the curriculum, these are to be addressed in a manner which is embedded in and consistent with the distinctively Reformed identity of the John Calvin Schools. These Cross-Curriculum Priorities are identified where they are applied or developed in the Content Descriptions of the Australian Curriculum: Mathematics , and also where they offer additional opportunities for student learning in the Content Elaborations. Each of these has generic applications across the curriculum, which are further elaborated elsewhere. Their distinctive applications within the Mathematics Learning Area include the following: 1. Indigenous Histories and Culture Indigenous Histories and Cultures are largely peripheral to the teaching and learning of Mathematics at the John Calvin Schools. However, there may be opportunities for students to appreciate the distinctive applications of mathematical concepts in indigenous cultures. They may, for example, explore the way number and pattern are represented, or investigate time, place, relationships and measurement concepts in indigenous contexts. They may also apply and evaluate statistical data to deepen their understanding of the lives of indigenous Australians. 2. Asia and Australia’s Engagement with Asia Asia and Australia’s engagement with Asia are largely peripheral to the teaching and learning of Mathematics at the John Calvin Schools. However, they do provide contexts for developing and applying students’ mathematical knowledge, skills and understanding. They may draw on knowledge of and examples from the Asia region in fields such as number, patterns, measurement, symmetry and statistics, including in the areas of money, art, architecture, design and travel. Their application of skills in data collection, representation and analysis can be used to examine issues pertinent to the Asia region. 3. Sustainability In the teaching and learning of Mathematics, the priority of sustainability provides rich, engaging and authentic contexts for learning and applying mathematical concepts and skills. It provides opportunities for students to develop the proficiencies of problem solving and reasoning essential for the exploration of sustainability issues and their solutions, in measurement, estimation, calculation, comparison, spatial reasoning, and statistical analysis. Application of mathematical understandings and skills will enable them to make predictions, and inform decision making and actions that support faithful stewardship and best and fairest use of natural and human resources within the created order. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 16 5. TEACHING AND LEARNING IN MATHEMATICS The purpose of this section is to spell out and elaborate on the principles of teaching and learning that will guide the implementation of the Australian Curriculum: Mathematics in actual classroom practice. While they are intended to be descriptive rather than prescriptive, it should be clear that for learning and instruction in mathematics to be effective, classroom organization and curriculum implementation ought clearly to reflect these principles: 1. Order and Complexity The study of mathematics is to a very significant degree the study of patterns; mathematical learning should therefore be aimed at uncovering the patterns of order and complexity that exist in creation. It should also aim to develop the innate capacity of students to discern and create patterns as a tool for making sense of the created order. The development of a sense of pattern requires frequent and consistent use of hands-on and visual aids as a starting point. In themselves, the discovery, exploration and applications of patterns in mathematics and in creation can awaken feelings of appreciation, pleasure, wonder, and ultimately praise of the Creator. These affective outcomes should be encouraged and modelled. At the same time, mathematical patterns have instrumental value: they enable students to develop and use valuable tools for making sense of observed reality, and for working with it in predictable and effective ways. Good teaching will challenge and help students clarify or refine their understanding of patterns, discard or modify those understandings which are inaccurate or unhelpful, and develop more sophisticated and/or helpful understandings. 2. Proficiency in Mathematics The Australian Curriculum: Mathematics highlights four proficiency strands, describing the breadth of mathematical actions that should be emphasised when students learn and use mathematical understandings and skills: Understanding: Students build a robust knowledge of adaptable and transferable mathematical concepts. They make connections between related concepts and progressively apply the familiar to develop new ideas. They develop an understanding of the relationship between the ‘why’ and the ‘how’ of mathematics. Fluency: Students are fluent when they calculate answers efficiently, when they recognise robust ways of answering questions, when they choose appropriate methods and approximations, when they readily recall and use definitions, facts and standard procedures, and when they can manipulate expressions and equations to find solutions. Problem Solving: Students develop the ability to formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable. Reasoning Mathematically: Students are reasoning mathematically when they explain their thinking, when they deduce and justify strategies used and conclusions reached, when they adapt the known to the unknown, when they transfer learning from one context to another, when they prove that something is true or false and when they compare and contrast related ideas and explain their choices. A year-by-year Overview of Proficiency Strands for the primary years (Foundation to Year 6) is provided in Appendix 2, below. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 17 3. The Learning Environment Success in learning mathematics is strongly associated with student beliefs about mathematics, and about their own ability to “do mathematics”. Students should be encouraged to understand: that mathematics makes sense, that they can make sense of mathematics that mathematics helps them make sense of the world Good teaching requires that students are given the time and opportunity to explore, to think, and to express themselves. They should be given opportunity to make the links between mathematical learning and real-life situations. Success in learning builds confidence in students. However, teachers sometimes explain too much, and intervene too quickly to reduce the risk of error. Where problem solving is seen as integral to mathematical learning, students will begin to understand that making mistakes is a positive and productive part of the learning process. This is likely to reduce anxiety about “getting it wrong”, or of “not being able to do it”, and to promote a willingness to take the risks that are needed for higherorder learning. Teachers should be alert to the secular and consumer-oriented attitudes and lifestyles reflected in numerous mathematics resources. They should arm themselves and their students to deal with that, and if necessary find or design alternative learning strategies or activities. 4. The Language of Mathematics All teachers, including maths teachers, are teachers of language, and all learning, including learning of mathematics, is language learning. Mathematical activity needs to be firmly embedded in language to enable: Exploration of and reflection on mathematical ideas Interaction between learners and teacher, between learners and text, and between learners collaboratively. Clear and precise communication of ideas, findings and conclusions. Students should be taught to understand and use the technical terms and specialist language associated with mathematics. They should also be given frequent opportunities for, and encouraged to use, language interaction as an integral part of their mathematics learning. Development of the effective use of language in mathematics will require sound modelling and scaffolding procedures by the teacher. 5. Student Reflection on Learning At every possible opportunity, students should be asked to reflect on their own learning. This reflection is most effective when goals for learning are clearly presented to them, and when they are asked to think about the links between their own learning and these learning goals. Selfreflection can be oral or written, can be brief or extended, and should focus as much as possible on the mathematical thinking and the problem-solving strategies used. This ought to be done at every level, from K-12, and can range in complexity from: “This is what I was thinking…” “This is how I found the answer to the problem..” through “I think I could also do the problem this way…” “I don’t think this makes sense, because…” “This is hard for me, because I don’t understand…..” to: “This strategy will be most useful when…” “What I have learned in this unit will help me to…” “I need to find out more about…” Students will need to be taught (through modelling and scaffolding) how to perform this kind of reflection, and how it will help them to strengthen and deepen their own learning. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 18 6. ASSESSMENT OF STUDENT LEARNING Assessment of student learning will be referenced to the Achievement Standards of the Australian Curriculum: Mathematics. It will involve a range of assessment practices and activities, grouped around focused observation, products and conversations. The core Mathematics resource chosen for use at individual schools (see 8. below) will incorporate a range of targeted assessment activities that provide a strong starting point for the assessment of teaching and learning. Teaching staff will be expected to use (but not necessarily limit themselves) to these activities. The Western Australian Curriculum and Standards Authority Curriculum and Assessment Outline provides a number of online resources to assist teachers in developing and using appropriate assessment activities. They include: Judging Standards: This is an especially valuable tool for teachers. For each year level from Preprimary to Year 6 it includes: Assessment pointers in a rubric format to provide a point of reference when assigning grades to student activities. They are also useful for giving assessment feedback and for setting the pitch of assessment tasks. For each year level, a number of Annotated Work Samples are provided. These are aligned with the five-point reporting scales set out in the Assessment Pointers. These are examples of student work that illustrate achievement at ‘A’ to ‘D’-grade for each year level. Assessment Principles and Practices: This section provides an overview of the criteria that apply to effective assessment activities across all learning areas. Sample Assessment Activities: These show a range of approaches to assessment. Each activity includes the planning process, showing how teachers developed assessment tasks linked to the Achievement Standards, and teacher reflections summarizing the effectiveness of the assessment activities. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 19 7. SCHOOL-BASED REQUIREMENTS Time Allocations It is expected that teachers will focus on explicitly and systematically teaching numeracy in daily mathematics sessions as well as integrating it with other learning areas. The Australian Curriculum: Mathematics has given indicative time allocations as follows: Preprimary to Year 4: 200 hours per year (4 hours 30 minutes per week) Years 5 – 6: 160 hours per year (4 hours per week) Actual allocations will vary, depending on whether the Mathematics curriculum is to be combined or with other learning areas or presented as integrated learning topics. Some schools or teachers may decide to alternate a term program in History with one, for example, in Geography. Individual schools will discuss and decide specific time allotments at a school based level, with a view to ensuring that the yearly requirements of the Mathematics Learning Area are met. Minimum Standards Each school may discuss and incorporate a set of minimum standards, learning benchmarks or wholeschool agreements for each year level. These will state what students are expected to learn and by when, so that student progress may be charted and suitable intervention or support for students may be arranged if needed. Tracking of Student Learning The goal of student tracking is to assist teachers to establish directions for future numeracy teaching and plan for responsive, differentiated numeracy instruction to meet students’ learning needs. Student data can be collected through: Shared assessment tasks Timely assessments and tests Observations The frequency and type of data that will be collected and the manner in which it will be monitored and tracked will be discussed and decided at an individual school based level. 8. RESOURCES Resources to support the teaching and learning of Mathematics are available in each school. Decisions as to what resources are to be obtained and used will be made at an individual school level. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 20 9. AUDIT AND REVIEW This document was prepared in 2014, for use in the John Calvin Primary Schools operated by the FRSA. It has been agreed to by the Primary School Principals, and was endorsed by the FRSA Board on ________________. It is to be in force from the 2015 school year onward. This document is to be audited and reviewed by the schools during Term 3 of 2016, with a view to ensuring continued compliance with the requirements set out by the School Curriculum and Standards Authority of Western Australia, in a manner consistent with the guiding principles of the schools. Any changes proposed will be considered by the Primary Principals, in consultation with the teaching staff of the schools, and decided upon at a joint meeting of principals. If agreed to, these changes will be will be incorporated in a revision of this document, to take effect at the beginning of the following school year. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 21 APPENDICES: APPENDIX 1: AC MATHEMATICS: OVERVIEW OF CONTENT STRANDS – Foundation to Year 6 APPENDIX 2: AC MATHEMATICS: OVERVIEW OF PROFICIENCY STRANDS – Foundation to Year 6 APPENDIX 3: AC MATHEMATICS: OVERVIEW OF ACHIEVEMENT STANDARDS – Foundation to Year 6 APPENDIX 4: AC MATHEMATICS SCOPE AND SEQUENCE – Year-by-Year Overviews: Foundation to Year 6 John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 22 APPENDICES APPENDIX 1: AC MATHEMATICS: Pre-primary to Year 6 Number and Algebra Strand Pre-primary OVERVIEW OF CONTENT STRANDS – Year 1 Year 2 Year 3 Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012) Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013) Count collections to 100 by partitioning numbers using place value (ACMNA014) Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015) Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences. (ACMNA026) Recognise, model, represent and order numbers to at least 1000 (ACMNA027) Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) Explore the connection between addition and subtraction (ACMNA029) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051) Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053) Recognise and explain the connection between addition and subtraction (ACMNA054) Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055) Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056) Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057) Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016) Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Recognise, describe and order Australian coins according to their value (ACMNA017) Count and order small collections of Australian coins and notes according to their value (ACMNA034) Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059) Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018) Describe patterns with numbers and identify missing elements (ACMNA035) Solve problems by using number sentences for addition or subtraction (ACMNA036) Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060) Number and Place Value Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001) Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) Subitise small collections of objects (ACMNA003) Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289) Represent practical situations to model addition and sharing (ACMNA004) Fractions and Decimals Money and Financial Mathematics Patterns and Algebra Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005) John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 23 Number and Algebra Strand Year 4 Year 5 Year 6 Number and Place Value Investigate and use the properties of odd and even numbers (ACMNA071) Recognise, represent and order numbers to at least tens of thousands (ACMNA072) Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) 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) Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122) Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123) Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124) Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Recognise that the place value system can be extended beyond hundredths (ACMNA104) Compare, order and represent decimals (ACMNA105) Compare fractions with related denominators and locate and represent them on a number line (ACMNA125) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127) Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128) Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129) Multiply and divide decimals by powers of 10 (ACMNA130) Make connections between equivalent fractions, decimals and percentages (ACMNA131) Create simple financial plans (ACMNA106) Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132) Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121) Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133) Explore the use of brackets and order of operations to write number sentences (ACMNA134) Fractions and Decimals Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) Money and Financial Mathematics Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080) Patterns and Algebra Explore and describe 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) Continued… John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 24 AC MATHEMATICS: OVERVIEW Pre-primary to Year 6 Measurement and Geometry Strand Pre-primary Year 1 OF CONTENT STRANDS – (continued): Year 2 Year 3 Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019) Tell time to the half-hour (ACMMG020) Describe duration using months, weeks, days and hours (ACMMG021) Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Compare masses of objects using balance scales (ACMMG038) Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039) Name and order months and seasons (ACMMG040) Use a calendar to identify the date and determine the number of days in each month (ACMMG041) Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061) Tell time to the minute and investigate the relationship between units of time (ACMMG062) Recognise and classify familiar twodimensional shapes and threedimensional objects using obvious features (ACMMG022) Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042) Describe the features of threedimensional objects (ACMMG043) Make models of three-dimensional objects and describe key features (ACMMG063) Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045) Identify and describe half and quarter turns (ACMMG046) Create and interpret simple grid maps to show position and pathways (ACMMG065) Identify symmetry in the environment (ACMMG066) Using Units of Measurement Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language(ACMMG006) Compare and order the duration of events using the everyday language of time(ACMMG007) Connect days of the week to familiar events and actions(ACMMG008) Shape Sort, describe and name familiar two-dimensional shapes and threedimensional objects in the environment (ACMMG009) Location and Transformation Describe position and movement(ACMMG010) Give and follow directions to familiar locations(ACMMG023) Geometric Reasoning Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064) Statistics and Probability Strand Pre-primary Year 1 Year 2 Year 3 Chance Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024) Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067) Data Representation and Interpretation Answer yes/no questions to collect information(ACMSP011) Choose simple questions and gather responses (ACMSP262) Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays (ACMSP263) Identify a question of interest based on one categorical variable. Gather data relevant to the question(ACMSP048) Collect, check and classify data (ACMSP049) Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068) Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069) Interpret and compare data displays (ACMSP070) John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 25 Measurement and Geometry Strand Year 4 Year 5 Year 6 Using Units of Measurement Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084) Compare objects using familiar metric units of area and volume (ACMMG290) Convert between units of time (ACMMG085) Use am and pm notation and solve simple time problems (ACMMG086) Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) Compare 12- and 24-hour time systems and convert between them (ACMMG110) Connect decimal representations to the metric system (ACMMG135) Convert between common metric units of length, mass and capacity (ACMMG136) Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137) Connect volume and capacity and their units of measurement (ACMMG138) Interpret and use timetables (ACMMG139) Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) Construct simple prisms and pyramids (ACMMG140) Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113) Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114) Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115) Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142) Introduce the Cartesian coordinate system using all four quadrants (ACMMG143) Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112) Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141) Shape Compare the areas of regular and irregular shapes by informal means (ACMMG087) Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088) Location and Transformation Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090) Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091) Geometric Reasoning Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089) Statistics and Probability Strand Year 4 Year 5 Year 6 Chance Describe possible everyday events and order their chances of occurring (ACMSP092) Identify everyday events where one cannot happen if the other happens (ACMSP093) Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094) List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116) Recognise that probabilities range from 0 to 1 (ACMSP117) Describe probabilities using fractions, decimals and percentages (ACMSP144) Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145) Compare observed frequencies across experiments with expected frequencies (ACMSP146) Data Representation and Interpretation Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095) 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) Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097) Pose questions and collect categorical or numerical data by observation or survey (ACMSP118) Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119) Describe and interpret different data sets in context (ACMSP120) Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147) Interpret secondary data presented in digital media and elsewhere (ACMSP148) John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 26 APPENDIX 2: AC MATHEMATICS: OVERVIEW OF PROFICIENCY STRANDS – Pre-primary to Year 6 Year P Understanding Fluency connecting names, numerals and quantities counting numbers in sequences readily continuing patterns comparing the lengths of objects directly 1 connecting names, numerals and quantities partitioning numbers in various ways counting number in sequences readily forward and backwards locating numbers on a line naming the days of the week 2 connecting number calculations with counting sequences partitioning and combining numbers flexibly identifying and describing the relationship between addition and subtraction identifying and describing relationship between multiplication and division counting numbers in sequences readily, using units iteratively to compare measurements, listing possible outcomes of chance events describing and comparing time durations 3 connecting number representations with number sequences partitioning and combining numbers flexibly representing unit fractions using appropriate language to communicate times identifying environmental symmetry making connections between representations of numbers partitioning and combining numbers flexibly extending place value to decimals using appropriate language to communicate times using informal units for comparing, and describing properties of symmetrical shapes recalling multiplication facts using familiar metric units to order and compare objects identifying and describing outcomes of chance experiments interpreting maps and communicating positions recalling multiplication tables communicating sequences of simple fractions using instruments to measure accurately creating patterns with shapes and their transformations collecting and recording data making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals representing fractions and decimals in various ways describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways describing connections between fractions and decimals making reasonable estimations choosing appropriate units of measurement for calculation of perimeter and area using estimation to check the reasonableness of answers to calculations using instruments to measure angles 4 5 6 representing negative numbers on a number line calculating simple percentages using brackets appropriately converting between fractions and decimals using operations with fractions, decimals and percentages measuring using metric units interpreting timetables John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 27 Year P 1 2 Problem Solving using materials to model authentic problems sorting objects using familiar counting sequences to solve unfamiliar problems discussing the reasonableness of answers using materials to model authentic problems giving and receiving directions to unfamiliar places using familiar counting sequences to solve unfamiliar problems discussing the reasonableness of answers formulating problems from authentic situations making models and using number sentences that represent problem situations planning routes on maps matching transformations with their original shape 3 formulating and modelling authentic situations involving planning methods of data collection and representation making models of three-dimensional objects using number properties to continue number patterns 4 formulating, modelling and recording authentic situations involving operations, comparing large numbers and time durations, and using properties of numbers to continue patterns 5 formulating and solving authentic problems using numbers and measurements creating transformations identifying line and rotational symmetries 6 formulating and solving authentic problems using numbers and measurements creating similar shapes through enlargements representing secondary data calculating angles Mathematical Reasoning explaining comparisons of quantities creating patterns explaining processes for indirect comparison of length explaining direct and indirect comparisons of length using uniform informal units justifying representations of data explaining patterns that have been created using known facts to derive strategies for unfamiliar calculations comparing and contrasting related models of operations describing connections between 2-D and 3-D representations creating and interpreting simple representations of data using generalising from number properties and results of calculations comparing angles creating and interpreting variations in the results of data collections and data displays using generalising from number properties and results of calculations deriving strategies for unfamiliar multiplication and division tasks comparing angles communicating information using graphical displays evaluating the appropriateness of different displays investigating strategies to perform calculations efficiently creating financial plans interpreting results of chance experiments interpreting data sets explaining mental strategies for performing calculations describing results for continuing number sequences investigating new situations using known properties of angles explaining the transformation of one shape into another inferring from the results of experiments John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 28 APPENDIX 3: AC MATHEMATICS: OVERVIEW OF ACHIEVEMENT STANDARDS – Pre-primary to Year 6 Number and Algebra Strand Pre-primary Year 1 Year 2 Year 3 count to and from 100 locate numbers up to 100 on a number line. partition numbers up to 100 using place value. solve simple addition and subtraction problems using counting strategies count to and from 1000 by grouping, partitioning and rearranging using place value. solve simple addition and subtraction problems using a small range of mental and written strategies represent multiplication and division by grouping into sets. count to and from 10 000 using a range of strategies. recall number facts for single digit numbers. identify odd and even numbers recognise the connection between multiplication and division. solve simple addition and subtraction problems using a range of mental and written strategies with increasing fluency count to and from 100 locate numbers up to 100 on a number line. partition numbers up to 100 using place value. solve simple addition and subtraction problems using counting strategies count to and from 1000 by grouping, partitioning and rearranging using place value. solve simple addition and subtraction problems using a small range of mental and written strategies represent multiplication and division by grouping into sets. count to and from 10 000 using a range of strategies. recall number facts for single digit numbers. identify odd and even numbers recognise the connection between multiplication and division. solve simple addition and subtraction problems using a range of mental and written strategies with increasing fluency recognise Australian coins. associate collections of Australian coins with their value. represent money values in various ways. correctly count out change from financial transactions. continue simple patterns. describe number sequences resulting from skip counting by 2’s, 5’s and 10’s recognise increasing and decreasing number sequences involving 2’, 3’s and 5’s identify the missing element in a number sequence. describe number patterns involving addition and subtraction Number and Place Value count to and from 20 make connections between number names, numerals and quantities up to 20. Fractions and Decimals count to and from 20 make connections between number names, numerals and quantities up to 20. Money and Financial Mathematics Patterns and Algebra order and describe collections group objects based on a common characteristics John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 29 Number and Algebra Strand Year 4 Year 5 Year 6 identify and describe factors and multiples solve simple problems involving the four operations using a range of mental and written strategies, including standard algorithms check the reasonableness of answers using estimation and rounding. locate and represent positive and negative numbers and zero on a number line. describe the use of positive and negative whole numbers and zero in everyday contexts. recognise the properties of special numbers solve problems involving all four operations with whole numbers compare, order and represent decimals and unit fractions perform addition and subtraction of fractions with the same denominator. locate and represent fractions and zero on a number line. calculate a simple fraction of a quantity. solve problems involving the addition and subtraction of related fractions add, subtract and multiply decimals divide decimals where the result is rational. connect fractions, decimals and percentages as different representations of the same number. make connections between the powers of 10 and the multiplication and division of decimals. plan simple budgets. calculate common percentage discounts on sale items. continue patterns by adding and subtracting fractions and decimals. find unknown quantities in equivalent number sentences. describe rules used in sequences involving whole numbers, fractions and decimals. write correct number sentences using brackets and order of operations. describe the four quadrants on the Cartesian plane. Number and Place Value recall multiplication facts to 10X10 and related division facts. use written and mental strategies, including standard algorithms, to solve addition and subtraction problems use appropriate strategies for calculations involving multiplication and division. solve simple problems using the properties of odd and even numbers. Fractions and Decimals locate familiar fractions on a number line. recognise common equivalent fractions in familiar contexts make connections between fraction and decimal notations up to two decimal places. Money and Financial Mathematics solve simple purchasing problems. Patterns and Algebra continue number sequences involving multiples of single digit numbers. describe number patterns resulting from multiplication. use relevant number sentences to solve problems. Continued… John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 30 AC MATHEMATICS: OVERVIEW OF ACHIEVEMENT STANDARDS – Pre-primary to Year 6 Measurement and Geometry Strand Foundation Year 1 (cont): Year 2 Year 3 compare lengths and capacities using informal units tell time to the half hour. describe time duration using hours, days, weeks and months compare and order shapes and objects using informal units. tell the time to the quarter hour. use metric units for length mass and capacity. tell the time to the nearest minute. classify and describe twodimensional shapes and threedimensional objects. draw and describe shapes identify the features of threedimensional objects. describe the features of threedimensional objects use the language of direction to move from place to place. interpret simple maps of familiar locations. explain the effects of one-step transformations. match positions on maps given relevant information. identify symmetrical shapes in real situations. Using Units of Measurement compare objects directly and indirectly using mass, length and capacity. explain the order and duration of events connect events and the days of the week. Shape compare and sort shapes and objects. Location and Transformation Geometric Reasoning Identify angles in real situations. Statistics and Probability Strand Foundation Year 1 Year 2 Year 3 Chance identify outcomes of simple familiar events list outcomes for everyday events. conduct chance experiments and describe possible outcomes collect data from questions create lists, tables and picture graphs. make sense of collected information carry out simple data experiments for categorical variables. interpret and compare data displays Data Representation and Interpretation answer simple questions to collect information collect data by asking questions. draw and describe simple data displays. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 31 Measurement and Geometry Strand Year 4 Year 5 Year 6 use appropriate units of measurement for length, area, volume, capacity and mass calculate perimeter and area of rectangles. convert between 12 and 24 hour time. connect decimal representations to the metric system choose appropriate units of measurement to solve problems. interpret and use timetables. connect three-dimensional objects with twodimensional representations construct simple prisms and pyramids use a grid reference system to describe locations. describe transformations of two-dimensional shapes identify line and rotational symmetry. describe combinations of translations. measure and construct different angles. use the properties of angles to solve problems. Using Units of Measurement use scaled instruments to measure and compare lengths, shapes and objects. convert between units of time. solve problems involving time duration. Shape compare areas of regular and irregular shapes using informal units. Location and Transformation interpret information contained in maps. create symmetrical shapes and patterns. Geometric Reasoning compare and classify angles in relation to a right-angle. Statistics and Probability Strand Year 4 Year 5 Year 6 describe probabilities of everyday events. recognise that probabilities range between 0 and 1 list outcomes of chance experiments. predict and communicate probabilities using simple fractions, decimals and percentages. compare observed and expected frequencies Chance describe probabilities of everyday events identify dependent and independent events. Data Representation and Interpretation describe different methods for data collection, construct data displays evaluate effectiveness of data displays pose questions to gather data construct, describe and interpret different data sets. interpret and compare a variety of data interpret and compare data displays for two categorical variables. evaluate secondary data displayed in the media John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 32 APPENDIX 4: AC MATHEMATICS SCOPE AND SEQUENCE – Foundation to Year 6 Overviews Year Overview: Pre-primary Year Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands including but not necessarily limited to: connecting names, numerals and quantities counting numbers in sequences readily continuing patterns comparing the lengths of objects directly using materials to model authentic problems sorting objects using familiar counting sequences to solve unfamiliar problems discussing the reasonableness of answers explaining comparisons of quantities creating patterns explaining processes for indirect comparison of length Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Number and place value Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001) Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond (ACMNA002) Subitise small collections of objects (ACMNA003) Compare, order and make correspondences between collections, initially to 20, and explain reasoning (ACMNA289) Represent practical situations to model addition and sharing (ACMNA004) count to and from 20 make connections between number names, numerals and quantities up to 20. Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings (ACMNA005) order and describe collections group objects based on a common characteristics Fractions and decimals Money and financial mathematics Patterns and algebra John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 33 Year Overview: Pre-primary Year (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Use direct and indirect comparisons to decide which is longer, heavier or holds more, and explain reasoning in everyday language (ACMMG006) Compare and order the duration of events using the everyday language of time (ACMMG007) Connect days of the week to familiar events and actions (ACMMG008) Sort, describe and name familiar twodimensional shapes and three-dimensional objects in the environment (ACMMG009) compare objects directly and indirectly using mass, length and capacity. explain the order and duration of events connect events and the days of the week. Describe position and movement (ACMMG010) Use appropriate language to describe position and movement. compare and sort shapes and objects. Geometric reasoning Location and transformation STATISTICS AND PROBABILITY Strand: Chance Data representation and interpretation Answer yes/no questions to collect information (ACMSP011) answer simple questions to collect information John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 34 AC MATHEMATICS SCOPE AND SEQUENCE – Year Overview: Year 1 Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands Pre-primary to Year 6 Overviews including but not necessarily limited to: connecting names, numerals and quantities partitioning numbers in various ways counting number in sequences readily forward and backwards locating numbers on a line naming the days of the week using materials to model authentic problems giving and receiving directions to unfamiliar places using familiar counting sequences to solve unfamiliar problems discussing the reasonableness of answers explaining direct and indirect comparisons of length using uniform informal units justifying representations of data explaining patterns that have been created Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero (ACMNA012) Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (ACMNA013) Count collections to 100 by partitioning numbers using place value (ACMNA014) Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts (ACMNA015) Recognise and describe one-half as one of two equal parts of a whole. (ACMNA016) Money and financial mathematics Recognise, describe and order Australian coins according to their value (ACMNA017) recognise Australian coins. Patterns and algebra Investigate and describe number patterns formed by skip counting and patterns with objects (ACMNA018) continue simple patterns. describe number sequences resulting from skip counting by 2’s, 5’s and 10’s Number and place value Fractions and decimals count to and from 100 locate numbers up to 100 on a number line. partition numbers up to 100 using place value. solve simple addition and subtraction problems using counting strategies identify representations of one half. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 35 Year Overview: Year 1 (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Measure and compare the lengths and capacities of pairs of objects using uniform informal units (ACMMG019) Tell time to the half-hour (ACMMG020) Describe duration using months, weeks, days and hours (ACMMG021) Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features (ACMMG022) compare lengths and capacities using informal units tell time to the half hour. describe time duration using hours, days, weeks and months Give and follow directions to familiar locations (ACMMG023) use the language of direction to move from place to place. classify and describe two-dimensional shapes and three-dimensional objects. Geometric reasoning Location and transformation STATISTICS AND PROBABILITY Strand: Chance Identify outcomes of familiar events involving chance and describe them using everyday language such as ‘will happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024) identify outcomes of simple familiar events Data representation and interpretation Choose simple questions and gather responses (ACMSP262) Represent data with objects and drawings where one object or drawing represents one data value. Describe the display (ACMSP263) answer simple questions to collect information John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 36 AC MATHEMATICS SCOPE AND SEQUENCE – Year Overview: Year 2 Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands Pre-primary to Year 6 Overviews including but not necessarily limited to: connecting number calculations with counting sequences partitioning and combining numbers flexibly identifying and describing the relationship between addition and subtraction identifying and describing relationship between multiplication and division counting numbers in sequences readily, using units iteratively to compare measurements, listing possible outcomes of chance events describing and comparing time durations formulating problems from authentic situations making models and using number sentences that represent problem situations planning routes on maps matching transformations with their original shape using known facts to derive strategies for unfamiliar calculations comparing and contrasting related models of operations describing connections between 2-D and 3-D representations creating and interpreting simple representations of data Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Number and place value Fractions and decimals Money and financial mathematics Patterns and algebra Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences (ACMNA026) Recognise, model, represent and order numbers to at least 1000 (ACMNA027) Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) Explore the connection between addition and subtraction (ACMNA029) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Count and order small collections of Australian coins and notes according to their value (ACMNA034) count to and from 1000 by grouping, partitioning and rearranging using place value. solve simple addition and subtraction problems using a small range of mental and written strategies represent multiplication and division by grouping into sets. Describe patterns with numbers and identify missing elements (ACMNA035) Solve problems by using number sentences for addition or subtraction (ACMNA036) recognise increasing and decreasing number sequences involving 2’, 3’s and 5’s identify the missing element in a number sequence. divide collections and shapes into halves quarters and eighths. associate collections of Australian coins with their value. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 37 Year Overview: Year 2 (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Compare masses of objects using balance scales (ACMMG038) Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039) Name and order months and seasons (ACMMG040) Use a calendar to identify the date and determine the number of days in each month (ACMMG041) Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042) Describe the features of three-dimensional objects (ACMMG043) draw and describe shapes identify the features of three-dimensional objects. Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045) Identify and describe half and quarter turns (ACMMG046) interpret simple maps of familiar locations. explain the effects of one-step transformations. compare and order shapes and objects using informal units. tell the time to the quarter hour. Geometric reasoning Location and transformation STATISTICS AND PROBABILITY Strand: Chance Data representation and interpretation Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048) Collect, check and classify data (ACMSP049) Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) list outcomes for everyday events. collect data from questions create lists, tables and picture graphs. make sense of collected information John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 38 AC MATHEMATICS SCOPE AND SEQUENCE – Year Overview: Year 3 Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands Pre-primary to Year 6 Overviews including but not necessarily limited to: connecting number representations with number sequences partitioning and combining numbers flexibly representing unit fractions using appropriate language to communicate times identifying environmental symmetry recalling multiplication facts using familiar metric units to order and compare objects identifying and describing outcomes of chance experiments interpreting maps and communicating positions formulating and modelling authentic situations involving planning methods of data collection and representation making models of three-dimensional objects using number properties to continue number patterns using generalising from number properties and results of calculations comparing angles creating and interpreting variations in the results of data collections and data displays Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Number and place value Fractions and decimals Money and financial mathematics Patterns and algebra Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences (ACMNA026) Recognise, model, represent and order numbers to at least 1000 (ACMNA027) Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) Explore the connection between addition and subtraction (ACMNA029) Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Count and order small collections of Australian coins and notes according to their value (ACMNA034) count to and from 1000 by grouping, partitioning and rearranging using place value. solve simple addition and subtraction problems using a small range of mental and written strategies represent multiplication and division by grouping into sets. Describe patterns with numbers and identify missing elements (ACMNA035) Solve problems by using number sentences for addition or subtraction (ACMNA036) recognise increasing and decreasing number sequences involving 2’, 3’s and 5’s identify the missing element in a number sequence. divide collections and shapes into halves quarters and eighths. associate collections of Australian coins with their value. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 39 Year Overview: Year 3 (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Compare masses of objects using balance scales (ACMMG038) Tell time to the quarter-hour, using the language of 'past' and 'to' (ACMMG039) Name and order months and seasons (ACMMG040) Use a calendar to identify the date and determine the number of days in each month (ACMMG041) Describe and draw two-dimensional shapes, with and without digital technologies (ACMMG042) Describe the features of three-dimensional objects (ACMMG043) draw and describe shapes identify the features of three-dimensional objects. Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG045) Identify and describe half and quarter turns (ACMMG046) interpret simple maps of familiar locations. explain the effects of one-step transformations. list outcomes for everyday events. collect data from questions create lists, tables and picture graphs. make sense of collected information compare and order shapes and objects using informal units. tell the time to the quarter hour. Geometric reasoning Location and transformation STATISTICS AND PROBABILITY Strand: Chance Data representation and interpretation Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048) Collect, check and classify data (ACMSP049) Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 40 AC MATHEMATICS SCOPE AND SEQUENCE – Year Overview: Year 4 Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands Pre-primary to Year 6 Overviews including but not necessarily limited to: making connections between representations of numbers partitioning and combining numbers flexibly extending place value to decimals using appropriate language to communicate times using informal units for comparing, and describing properties of symmetrical shapes recalling multiplication tables communicating sequences of simple fractions using instruments to measure accurately creating patterns with shapes and their transformations collecting and recording data formulating, modelling and recording authentic situations involving operations, comparing large numbers and time durations, and using properties of numbers to continue patterns using generalising from number properties and results of calculations deriving strategies for unfamiliar multiplication and division tasks comparing angles communicating information using graphical displays evaluating the appropriateness of different displays Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Number and place value Fractions and decimals Money and financial mathematics Patterns and algebra Investigate and use the properties of odd and even numbers (ACMNA071) Recognise, represent and order numbers to at least tens of thousands (ACMNA072) Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) 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) Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078) Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080) recall multiplication facts to 10X10 and related division facts. use written and mental strategies, including standard algorithms, to solve addition and subtraction problems use appropriate strategies for calculations involving multiplication and division. solve simple problems using the properties of odd and even numbers. Explore and describe 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) continue number sequences involving multiples of single digit numbers. describe number patterns resulting from multiplication. use relevant number sentences to solve problems. locate familiar fractions on a number line. recognise common equivalent fractions in familiar contexts make connections between fraction and decimal notations up to two decimal places. solve simple purchasing problems. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 41 Year Overview: Year 4 (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Geometric reasoning Location and transformation Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084) Compare objects using familiar metric units of area and volume (ACMMG290) Convert between units of time (ACMMG085) Use am and pm notation and solve simple time problem (ACMMG086) Compare the areas of regular and irregular shapes by informal means (ACMMG087) Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088) Compare angles and classify them as equal to, greater than or less than a right angle (ACMMG089) Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090) Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091) STATISTICS AND PROBABILITY Strand: Chance Describe possible everyday events and order their chances of occurring (ACMSP092) Identify everyday events where one cannot happen if the other happens (ACMSP093) Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094) Data Select and trial methods for data collection, including survey questions and recording sheets representation (ACMSP095) and interpretation 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) Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097) use scaled instruments to measure and compare lengths, shapes and objects. convert between units of time. solve problems involving time duration. compare areas of regular and irregular shapes using informal units. compare and classify angles in relation to a right-angle. interpret information contained in maps. create symmetrical shapes and patterns. describe probabilities of everyday events identify dependent and independent events. describe different methods for data collection, construct data displays evaluate effectiveness of data displays John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 42 AC MATHEMATICS SCOPE AND SEQUENCE – Year Overview: Year 5 Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands Pre-primary to Year 6 Overviews including but not necessarily limited to: making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals representing fractions and decimals in various ways choosing appropriate units of measurement for calculation of perimeter and area using estimation to check the reasonableness of answers to calculations using instruments to measure angles formulating and solving authentic problems using numbers and measurements creating transformations identifying line and rotational symmetries investigating strategies to perform calculations efficiently creating financial plans interpreting results of chance experiments interpreting data sets Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Number and place value Fractions and decimals Money and financial mathematics Patterns and algebra Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Compare and order common unit fractions and locate and represent them on a number line (ACMNA291) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Recognise that the system can be extended beyond hundredths (ACMNA104) Compare, order and represent decimals (ACMNA105) Create simple financial plans (ACMNA106) identify and describe factors and multiples solve simple problems involving the four operations using a range of mental and written strategies, including standard algorithms check the reasonableness of answers using estimation and rounding. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121) continue patterns by adding and subtracting fractions and decimals. find unknown quantities in equivalent number sentences. compare, order and represent decimals and unit fractions perform addition and subtraction of fractions with the same denominator plan simple budgets. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 43 Year Overview: Year 5 (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Geometric reasoning Location and transformation Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) Compare 12- and 24-hour time systems and convert between them (ACMMG110) Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112) Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113) Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114) Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115) STATISTICS AND PROBABILITY Strand: Chance List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116) Recognise that probabilities range from 0 to 1 (ACMSP117) Data Pose questions and collect categorical or numerical data by observation or survey representation (ACMSP118) and interpretation Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119) Describe and interpret different data sets in context (ACMSP120) use appropriate units of measurement for length, area, volume, capacity and mass calculate perimeter and area of rectangles. convert between 12 and 24 hour time. connect three-dimensional objects with twodimensional representations measure and construct different angles. use a grid reference system to describe locations. describe transformations of two-dimensional shapes identify line and rotational symmetry. describe probabilities of everyday events. recognise that probabilities range between 0 and 1 list outcomes of chance experiments. pose questions to gather data construct, describe and interpret different data sets. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 44 AC MATHEMATICS SCOPE AND SEQUENCE – Year Overview: Year 6 Proficiencies Understanding Fluency Problem Solving Mathematical Reasoning Sub-strands Pre-primary to Year 6 Overviews including but not necessarily limited to: describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways describing connections between fractions and decimals making reasonable estimations representing negative numbers on a number line calculating simple percentages using brackets appropriately converting between fractions and decimals using operations with fractions, decimals and percentages measuring using metric units interpreting timetables formulating and solving authentic problems using numbers and measurements creating similar shapes through enlargements representing secondary data calculating angles explaining mental strategies for performing calculations describing results for continuing number sequences investigating new situations using known properties of angles explaining the transformation of one shape into another inferring from the results of experiments Content Descriptions Achievement Standards NUMBER AND ALGEBRA Strand Number and place value Fractions and decimals Money and financial mathematics Patterns and algebra Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101) Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291) Compare and order common unit fractions and locate and represent them on a number line (ACMNA291) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Recognise that the system can be extended beyond hundredths (ACMNA104) Compare, order and represent decimals (ACMNA105) Create simple financial plans (ACMNA106) identify and describe factors and multiples solve simple problems involving the four operations using a range of mental and written strategies, including standard algorithms check the reasonableness of answers using estimation and rounding. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121) continue patterns by adding and subtracting fractions and decimals. find unknown quantities in equivalent number sentences. compare, order and represent decimals and unit fractions perform addition and subtraction of fractions with the same denominator plan simple budgets. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 45 Year Overview: Year 6 (continued): Sub-strands Content Descriptions Achievement Standards MEASUREMENT AND GEOMETRY Strand: Using units of measurement Shape Geometric reasoning Location and transformation Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Calculate the perimeter and area of rectangles using familiar metric units (ACMMG109) Compare 12- and 24-hour time systems and convert between them (ACMMG110) Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112) Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113) Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114) Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115) STATISTICS AND PROBABILITY Strand: Chance List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116) Recognise that probabilities range from 0 to 1 (ACMSP117) Pose questions and collect categorical or Data numerical data by observation or survey representation (ACMSP118) and interpretation Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119) Describe and interpret different data sets in context (ACMSP120) use appropriate units of measurement for length, area, volume, capacity and mass calculate perimeter and area of rectangles. convert between 12 and 24 hour time. connect three-dimensional objects with twodimensional representations measure and construct different angles. use a grid reference system to describe locations. describe transformations of two-dimensional shapes identify line and rotational symmetry. describe probabilities of everyday events. recognise that probabilities range between 0 and 1 list outcomes of chance experiments. pose questions to gather data construct, describe and interpret different data sets. John Calvin Schools – Curriculum Documentation – MATHEMATICS Pre-primary to Year 6 – 2014 Page 46