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DEPARTMENT OF EDUCATION C2C Year Level Plan Mathematics Year 6 Year level description Curriculum intent The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content across the three strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or developed. They provide the language to build in the developmental aspects of the learning of mathematics. At this year level: Understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations Fluency includes representing integers 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, and interpreting timetables Problem Solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays, and finding the size of unknown angles Reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another, explaining why the actual results of chance experiments may differ from expected results Achievement standard By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They evaluate secondary data displayed in the media. Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate probabilities using simple fractions, decimals and percentages. C2C adapted with permission by NT DoE © The State of Queensland 1 of 8 www.det.nt.gov.au Unit outline Semester 1 Sequencing the teaching and learning Term 1 Unit 1 Students have opportunities to develop understandings of: Properties of numbers: factors, multiples, prime and composite numbers Fractions: related denominators, comparing, adding, subtracting Measurement: metric system, connection to decimals, length, mass and capacity 3 dimensional objects: prisms, pyramids, geometric features, nets, constructing. Term 2 Unit 2 Students have opportunities to develop understandings of: Properties of numbers: identify properties of square, triangular, prime and composite numbers Fractions and decimals: add and subtract decimals to thousandths, use estimation and rounding to check reasonableness of answers Data: collect, display and interpret. Unit 3 Students have opportunities to develop understandings of: Integers: properties of numbers, investigating positive and negative numbers Fractions, decimals and percentages: calculating equivalent fractions, decimals and percentages Decimals and the metric system: units of measurement, identifying relationships between metric units Time: interpreting and using timetables Unit 4 Students have opportunities to develop understandings of: Data interpretation: interpreting a variety of data displays, including unfamiliar display types Addition and subtraction (whole numbers and decimals): applying appropriate mental and written strategies and digital technologies to solve problems involving addition and subtraction and solving problems involving decimals to thousandths using a variety of mental and written strategies Addition and subtraction (fractions): adding and subtracting fractions with the same and related denominators Chance: representing probability as a fraction, decimal or percentage between 0 and 1 Order of operations: exploring the order of operations in problems and in equations. General capabilities and Cross-curriculum priorities Opportunities to engage with: C2C adapted with permission by NT DoE © The State of Queensland Opportunities to engage with: 2 of 8 www.det.nt.gov.au Unit outline Semester 2 Sequencing the teaching and learning Term 3 Term 4 Unit 5 Students have opportunities to develop understandings of: Properties of numbers: exploring the properties of prime, composite, square and triangular numbers and using prime factors to identify greatest common factors and lowest common multiples Four operations: adding and subtracting whole numbers and decimals, multiplying by two digit whole numbers and decimals and dividing by two digit whole numbers and decimals with terminating remainders Patterns: creating and continuing number patterns involving whole numbers, fractions and decimals and using a table of values to write a rule to describe the pattern 3 dimensional shapes: drawing nets of prisms and pyramids and constructing 3D objects using concrete materials and nets. Unit 6 Students have opportunities to develop understandings of: Chance: expressing probability as a fraction, decimal and/or percentage and comparing observed frequencies with expected frequencies Patterns and algebra: applying the order of operations to complete multiple operations within the same number sentence Fractions and money: making connections between equivalent representations of the same number, finding fractions of a quantity and calculating percentage discounts Data representation and interpretation: investigating representations of data in the media, influences on data and misleading data. Unit 7 Students have opportunities to develop understandings of: Transformations: combining transformations to create shapes and tessellations Angles: classifying and measuring angles and establishing generalisations about vertically opposite angles, adjacent angles on a straight line and angles at a point Measurement: converting between equivalent units of measure and exploring the relationship between the length of the sides and the area of the rectangles Volume and capacity: exploring volume and capacity and the relationship between the two and measuring and estimating volume and capacity. Unit 8 Students have opportunities to develop understandings of: Cartesian coordinate system: introducing the four quadrants of a Cartesian plane, plotting coordinates on the Cartesian plane, designing and evaluating a game involving plotting coordinates on the Cartesian plane Chance: describing probabilities on a scale from 0 to 1, comparing expected and observed frequencies and exploring the effect of the number of trials (in a chance experiment) on the outcomes Fractions, decimals and percentages: revising the connections between fractions, decimals and percentages, adding and subtracting fractions and decimals and finding a percentage discount Operations: revising strategies to estimate, add, multiply and divide when operating with whole numbers, and choosing and using the most appropriate operations to solve problems. General capabilities and Cross-curriculum priorities Opportunities to engage with: Opportunities to engage with: Key to General capabilities and Cross-curriculum priorities Literacy Numeracy Personal and social Intercultural understanding competence C2C adapted with permission by NT DoE © The State of Queensland ICT competence Critical and creative thinking Ethical behaviour Aboriginal and Torres Strait Asia and Australia’s Sustainability Islander histories and cultures engagement with Asia 3 of 8 www.det.nt.gov.au Assessment Semester 1 Teachers and children organise evidence of learning in individual folios. The individual folio is constructed jointly by a teacher, a child, parents/carers and other partners. It becomes a dynamic record of examples of a child’s learning and development. Term 1 Term 2 Unit 2: Identifying properties of whole numbers Short answer questions Students identify, describe and sequence whole numbers according to their properties. Unit 3: Sporting skills Assignment/Project Unit 4: Data decoder Short answer questions Students perform a number of tasks, recording their scores for each task. Students convert these scores to equivalent fractions and decimals to demonstrate their understanding of the relationship between the three representations of the same number. Students make decisions informed by interpreting and comparing a range of data displays. Unit 3: Rodeo round-up Short answer questions Students use and interpret more than one transport timetable when organising a trip to a rodeo. Students use available information to make informed decisions about the suitability of each transport option. Making consistent judgements / Feedback Curriculum leaders will randomly sample student work to check for consistency of Teachers will moderate to identify A-E samples before marking practical demonstration tasks. They will participate in on-going moderation conversations teacher judgments. to achieve consensus and consistency of judgments. Teachers will co-mark the assignment/project to achieve consensus and consistency of judgments. Curriculum leaders will randomly sample student work to check for consistency of teacher judgments. C2C adapted with permission by NT DoE © The State of Queensland 4 of 8 www.det.nt.gov.au Assessment Semester 2 Teachers and children organise evidence of learning in individual folios. The individual folio is constructed jointly by a teacher, a child, parents/carers and other partners. It becomes a dynamic record of examples of a child’s learning and development. Term 3 Unit 5: Year 6 mathematics QCAT Written Term 4 Unit 6: Is it fair? Written Unit 7: Transformations and tessellations Assignment/Project The QCAT gathers evidence about how Students apply knowledge of chance well students apply the proficiency events, variation and bias to develop strands to: arguments and improve game fairness. identify and describe the properties of special numbers create sequences of whole numbers and describe the rules used to create them use mathematical reasoning to solve simple and multi-step problems involving nets and all four operations with whole numbers and decimals. Students use a combination of transformations to create a shape that can be used in a tessellating pattern. Making consistent judgments/ Feedback Teachers will co-mark the QCAT to achieve consensus and consistency of judgments. Year level teachers will moderate the QCATs to identify A-E samples to take to cluster moderation in Term 4. C2C adapted with permission by NT DoE © The State of Queensland Teachers will moderate to identify A-E samples before marking design and practical demonstration tasks. They will participate in on-going moderation conversations to achieve consensus and consistency of judgments. Curriculum leaders will randomly sample student work to check for teacher consistency of judgments. Year level teachers will participate in cluster moderation of the QCATs. 5 of 8 www.det.nt.gov.au Balance and coverage of content descriptions Year 6 Number and Algebra Term Number and place value 1 Identify and describe properties of prime, composite, square and triangular numbers. 1 2 3 Term Measurement and Geometry 4 5 Using units of measurement 1 2 Connect decimal representations to the metric system. 1 3 Statistics and Probability 4 Chance 3 7 2 3 4 Describe probabilities using fractions, decimals and percentages. 4 6 8 3 7 Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies. 4 6 8 Solve problems involving the comparison of lengths and areas using appropriate units. 7 Compare observed frequencies across experiments with expected frequencies. 4 6 8 Connect volume and capacity and their units of measurement. 7 2 Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers. 4 Investigate everyday situations that use positive and negative whole numbers and zero. Locate and represent these numbers on a number line. 3 5 8 Convert between common metric units of length, mass and capacity. Interpret and use timetables. Fractions and decimals Compare fractions with related denominators and locate and represent them on a number line. 1 Solve problems involving addition and subtraction of fractions with the same or related denominators. 1 Shape Construct simple prisms and pyramids. 1 C2C adapted with permission by NT DoE © The State of Queensland 8 6 of 8 1 3 5 2 4 Term Data representation and interpretation Interpret and compare a range of data displays, including side-byside column graphs for two categorical variables. 2 Interpret secondary data presented in digital media and elsewhere. 4 6 www.det.nt.gov.au Balance and coverage of content descriptions Year 6 Number and Algebra Fractions and decimals cont. Term 1 Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies. Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers. 2 2 3 3 6 4 Multiply decimals by whole numbers and perform divisions that result in terminating decimals, with and without digital technologies. Term Measurement and Geometry Statistics and Probability Term 4 8 5 Multiply and divide decimals by powers of 10. 3 5 Make connections between equivalent fractions, decimals and percentages. 3 6 Money and financial mathematics Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies. 6 C2C adapted with permission by NT DoE © The State of Queensland 8 8 4 7 8 Location and transformation 1 2 Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies. Introduce the Cartesian coordinate system using all four quadrants. 7 of 8 3 www.det.nt.gov.au Balance and coverage of content descriptions Year 6 Number and Algebra Term Patterns and algebra 1 Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence. 1 Explore the use of brackets and order of operations to write number sentences. 2 3 5 2 4 Term Measurement and Geometry 4 Geometric reasoning 1 2 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. 6 3 Statistics and Probability Term 4 7 References http://www.australiancurriculum.edu.au/ Australian Curriculum Version 3.0 dated 23 January 2012 Copyright © The State of Queensland (represented by the Department of Education and Training) Copyright in this work is owned by or licensed to the State of Queensland (acting through the Department of Education and Training), PO Box 15033 City East QLD 4002 Australia and is reproduced with its permission. No part may be further reproduced in hardcopy form by anyone outside the Northern Territory Department of Education without the express permission of the Queensland Department of Education and Training. C2C adapted with permission by NT DoE © The State of Queensland 8 of 8 www.det.nt.gov.au