VIEWS: 7 PAGES: 30 POSTED ON: 8/15/2011
Mt Tarampa State School Mathematics Program Mt Tarampa State School Page 1 of 30 Our beliefs about teaching mathematics The staff of Mt Tarampa State School believe that mathematics: is highly important for successful life beyond schooling should be taught everyday focuses on the development of higher order thinking within our students includes the explicit teaching of mathematical strategies and ways of working incorporates the use of materials at all year levels should be connected to the students’ real lives includes opportunities for teachers to continue learning. Teaching mathematics at Mt Tarampa State School includes: a balanced mathematical learning approach which consists of o learning basic facts o applying basic facts and procedures to solve familiar problems o solving specific problems in novel situations o investigating issues and problem situations differentiated learning to meet the varied needs of our students embedding the effective use of information and communication technologies embedding Indigenous perspectives focusing on all forms of computation (mental, written and technology-assisted) First steps in mathematics strategies. Cross-curricular priorities Numeracy We improve the numerate capabilities of students at Mt Tarampa State School by: fostering students to be confident in their use of mathematics encouraging students to be flexible in their mathematical thinking promoting higher-order thinking through a working mathematically approach applying mathematics through a range of contexts and key learning areas encouraging risk-taking in the use of mathematical knowledge, skills and thinking instilling persistence when problem-solving in mathematics. Literacy We improve the literacy capabilities of students at Mt Tarampa State School by: explicitly identifying and teaching the language demands of mathematics at all year levels ensuring students are exposed to and taught the conventions used by mathematicians applying skills learned at literacy training to the interpretation of word problems in mathematics (in particular, functional grammar) identifying the different visual representations used in mathematics e.g. number lines, tables, graphs, maps, networks, nets and 3D objects (refer to notes in the term breakdown for further details). Our Maths Program Structure The Mathematics program has been structured as follows: there will be a single curriculum focus for each year level during any teaching period Ways of working are embedded throughout the Teaching Focus section of the school mathematics program Mathematics will be allocated 5 hours per week Term programs work on 9 weeks to allow for other commitments such as assessment, review, consolidation and interruptions eg excursions, sports days Mt Tarampa State School Page 2 of 30 Pedagogy At Mt Tarampa State School we encourage learning as an active process, and have designed our mathematics program around the inclusion of interesting, fun and relevant learning experiences that will help students develop a positive disposition towards mathematics. To meet this aim, our program, planning, teaching and assessment include: a range and balance of learning experiences from focused skill development activities through to open-ended investigations and inquiry the provision of multiple opportunities for students to explore concepts so they can develop a deep knowledge and understanding planning units and lessons that are relevant and responsive to the needs, interests and capabilities of our students. This is achieved by starting with real world problems materials and representations language symbolic representations and abstract concepts an emphasis on challenging problems that promote higher order thinking skills, and the critical analysis of data and issues teaching a range of calculation strategies, such as mental computation, formal and informal jottings, calculators, computers and written algorithms a range and balance of teaching approaches, such as whole class–directed lessons, group/team work and individual work an embedded use of ICTs into all classrooms Indigenous perspectives embedded into all classrooms explicit teaching of specific mathematics language, diagrams, models and conventions used by mathematicians the provision of multiple opportunities for students to confidently, willingly and capably transfer their mathematics learning to a variety of contexts explicit advice to students about expected standards of achievement. Assessment and reporting Monitoring learning Monitoring of student learning is integral to informing our planning so we develop students that have a deep understanding of the concepts that make up number, algebra, measurement, chance and data, and space. At Mt Tarampa State School, monitoring occurs in the following ways: classroom observations checklists homework diagnostic tasks anecdotal records knowledge gained from assessment for reporting. Immediate feedback to students is a priority, as this builds student confidence and a positive disposition. It also assists students to manage their own learning. Assessment for reporting (assessment of learning) We believe that to learn mathematics, children must construct concepts, and relationships among concepts, in their own minds. To do this, we must allow our children to explore and investigate, and discuss and justify. As such, we have designed our teaching and assessment programs using these tenants. The assessable elements (knowledge and understanding, thinking and reasoning, communicating, reflecting) are considered, but not all are assessed on every task. Each semester in each year level, we aim to have a range and balance of different types of tasks. As such, our minimum assessment requirements for each class are listed below. Mt Tarampa State School Page 3 of 30 School-based assessment requirements Assessment type Frequency Assessable elements Short answer tests 1 per topic Knowledge and understanding Communicating Open-ended 1 per term Thinking and reasoning investigation Communicating Reflecting Report 2 per year Knowledge and understanding Thinking and reasoning Communicating Reflecting QCAT (semester 2 1 per year As per QCAT design brief — this will vary every only) second year External assessment requirements NAPLAN To be completed in May of each year This data is to be included in the student’s portfolio so that progress can be tracked. Notes: In the early years of schooling, there will be a greater emphasis on the use of oral presentations, portfolios and checklists. As students progress through the school, there will be more balance between spoken and written forms of assessment. National Assessment Program — Literacy and Numeracy (NAPLAN) data will be used to review our program, and identify strengths and weaknesses, and professional development priorities for staff and resource purchasing. Students that require targeted teaching can be identified. 2009 NAPLAN results (Reading, writing, spelling, grammar and punctuation, and numeracy results for Years 3, 5, 7 and 9) Numeracy Year 3 Year 5 Year 7 Avg. score for Mt Tarampa SS 275.5 456.2 513.6 Avg. score for Australia 393.9 486.8 543.6 Percentage of students at Mt Tarampa SS above benchmark 50 100 90.9 Year 2 Diagnostic Net Results (2008): Percentage of students not requiring additional support in Number: 100% Reporting At Mt Tarampa State School, we will report student achievement and learning to parents on a regular basis. This will include both written and oral reporting. Specifically: quarterly written reports on a 5-point scale (end of each term) thrice yearly oral reporting (end of Terms 1, 2 and 3) informal reporting to parents (on a needs basis for those students requiring special programs, such as intervention or extension) Note: Special programs may take a variety of forms (i.e. intensive and specialised teaching within the classroom, targeted programs with specialist teachers or intensive one-to-one tutoring). Mt Tarampa State School Page 4 of 30 Mathematics Overview ~ Year P-3 Semester 1 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) PATTERNS Algebra Simple relationships between objects or numbers Patterns Patterns can be described in terms of order, sequence - patterns in our daily lives - repeating and non-repeating patterns and arrangement - repeating patterns including actions, both number patterns and pictorial Number patterns and sequences based on sounds and objects patterns simple rules involve repetition, order and regular recognises the pattern recognises the pattern increases or decreases. continues or extends the pattern identifies the repeating part identifies the repeating part continues the pattern creates a repeating pattern identifies the missing part determines the missing part MONEY Number Money can be used to buy goods and services. Knowledge Knowledge Transactions for goods and services can use - coins and notes – sort; relative value of - coins and notes - relationship between different combinations of notes and coins of notes and coins (notes have more different coins and notes; justifies equivalent value. value than coins); visual recognition of thinking coins and notes - represents values in a variety of ways - language – cost, price and names of e.g. $5 can be made up of 2 $2 coins coins and notes and 1 $1 coin or 5 $1 coins Financial decisions Financial decisions - Uses of money - Uses of money Mt Tarampa State School Page 5 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) CHANCE Chance and Data Predictions about chance events can be made Likelihood Likelihood using simple statements. - concept of likelihood linked to - concept of likelihood linked to appropriate language appropriate language - language – will happen, won’t happen, - language – likely, unlikely, certain, always, sometimes, never, will, will not, impossible might happen, maybe Judgements Judgements - uses language to describe different - Classifications of the likelihood of daily situations e.g. pulling a green marble events out of the bag, the chance of rain tomorrow etc. TIME Number Simple fractions, including half and quarter, and Fraction Fraction mixed numbers can be represented in different - parts of a whole (equal parts & not - half is one of two-equal parts of the ways. equal parts) whole and quarter is one of four-equal Measurement - half = 1 of 2 equal parts parts of the whole Hour, half-hour, and quarter-hour times and five- Point in time - identify half and quarter on a clock face minute intervals are read using analogue clocks - identify and sequence familiar daily Duration of time and all times are read using digital clocks. events - analogue and digital clocks. - sequence daily events - read and record hour, half-hour and - language – start, finish, later, earlier, quarter-hour times and five-minute slow, longer, shorter intervals on analogue clocks and all Duration of time times on digital clocks - comment if something takes a long time or not Mt Tarampa State School Page 6 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) 3D OBJECTS Space Geometric names and properties are used to Shape - 3D objects Shape - 3D objects sort, describe and construct common 2D shapes - recognition and identification of objects - identification of object as prism, including squares, rectangles, triangles and - classification of everyday objects (see pyramid, cone, cylinder, sphere circles, and 3D objects, including prisms, list in Essentials) - using verbal and written pyramids, cones, cylinders and spheres. - grouping boxes, cones and balls representations to identify and according to their properties (including communicate the properties of different justification) objects - construction of models using play Visualisation dough - identification of 2D shapes as faces of visualisation 3D object - description of properties (shapes, - construct 3D objects according to faces, pointy, smooth, rolling, sliding) criteria - draw 3D shapes to show depth VOLUME Measurement Standard units, including centimetre, metre, Understanding volume and associated Understanding volume and associated kilogram (half and quarter) and litre (half and units units quarter), and non-standard units of - concept of volume - concept of volume measurement can be used to measure attributes Direct comparisons - non-standard units e.g. cups, cans, of shapes and objects. - empty, full buckets Measurements of length, area, volume and - order and sequence objects according - standard units - litre including a half mass of shapes and objects are compared and to volume and a quarter ordered, using instruments - ways to measure volume Direct comparisons - determining appropriateness of standard or non-standard units - order objects based on their volume - measure volume using standard and non-standard units depending on accuracy required Mt Tarampa State School Page 7 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) LENGTH AND AREA Measurement Standard units, including centimetre, metre, Understanding length and area and Understanding length, area and kilogram (half and quarter) and litre (half and associated units associated units quarter), and non-standard units of measurement - concept of length - concept of length and perimeter can be used to measure attributes of shapes and - non-standard units for length e.g. - standard units - metres, centimetres objects. pencil, rake, foot - relationship between metres and Measurements of length, area, volume and Direct comparisons centimetres mass of shapes and objects are compared and - bigger, smaller, longer, taller, shorter, - conventions – m, cm ordered, using instruments wider, longest, tallest, shortest, widest, - concept of area same length, near, far - non-standard units e.g. post-its, tiles, - order and sequence objects according counters to length Direct comparisons - ways to measure length - determining appropriateness of standard or non-standard units for length - order objects based on their length - order objects based on their area - measure or estimate length using standard and non-standard units depending on accuracy required Indirect measures - problem solving involving the perimeter of a range of 2D shapes Mt Tarampa State School Page 8 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) MULTIPLICATIVE Number THINKING Multiplication and division of whole numbers to Number concepts Number concepts 10 can be calculated using arrays, skip counting, - groups of - conventions used to write number doubles, double doubles, turnarounds and - equal sharing sentences involving grouping and sharing of concrete materials Numeration sharing - counting in twos and fives Numeration Number facts and strategies - skip counting - using arrays to show groups of Number facts and strategies Problem solving - arrays - representation of groups of and sharing - doubles, double doubles, … problems using materials - multiplication facts for 1, 2, 5 and 10 - writing number sentences (using words Problem solving and symbols e.g. 5 groups of 2 = 10) to - solving problems involving describe thinking multiplication and division using basic facts and materials as appropriate for the situation and size of the numbers - writing number sentences (using words and symbols e.g. 5 groups of 2 = 10) to describe thinking Mt Tarampa State School Page 9 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) EQUATIONS Number Number concepts Addition and subtraction involving 2-digit whole Number concepts - place value numbers can be calculated using concrete - number representations - words, Numeration materials, mental computation and written symbols, pictorial and materials - comparing and ordering strategies. Numeration Number facts and strategies Multiplication and division of whole numbers to - grouping of items using blocks - doubles, double doubles, skip counting, 10 can be calculated using arrays, skip counting, Number facts and strategies turnarounds doubles, double doubles, turnarounds and - counting - on and back in 1s, 2s, and - mental computation sharing of concrete materials. 3s Problem solving strategies that involve a Problems involving operations can be explored - simple addition and subtraction facts to single operation using concrete materials, sketches and 10 e.g. 4+4=8 and 5+3=8 - sketches and diagrams diagrams. Problem solving - inverse relationship between +/- and Problems using a single operation can be - problem solving with the use of x/ planned and solved. materials - using materials Algebra - written methods Inverse relationships between addition and - check for reasonableness subtraction can be applied to find unknowns and - addition and subtraction problems maintain equivalence in equations involving 2-digit whole numbers - multiplication and division Mt Tarampa State School Page 10 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) EQUIVALENCE Number Whole numbers (to 999) have position on a Numeration Numeration number line and each digit has place value - using a number line to order number (to - using a number line to order numbers Algebra 10) (to 999) Simple relationships between objects or Number facts and strategies Number facts and strategies numbers, including equivalence, can be - counting on and counting back in 1s, 2s - relationships between equations e.g. 6 represented using concrete and pictorial and 3s - using materials, mentally and + 3 = 9, 9 – 6 = 3 and 9 – 3 = 6 materials in written form Problem solving Problem solving - justification of thinking - representations of numbers using - representations of numbers and pictorial and concrete material e.g. 5 equations of equivalence using pictorial can be made up of 3 blue and 2 red and concrete material representations markers or 4 blue and 1 red marker e.g. 14 + 8 = 10 + 12 without changing the total number - recording equations (addition and - justification of thinking subtraction) using written, pictorial and concrete representations Mt Tarampa State School Page 11 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) DATA Chance and Data Data can be collected using simple surveys and Collecting data Collecting data observations to respond to questions. - Gather a small amount of data to - surveys and how to conduct one Data can be organised in lists, tables, picture support a class decision (hands up for - determine data needed to support graphs and bar graphs. this decision, counts the hands) hypothesis e.g. if we survey the Data can be explored for variation and adequacy. - Observation to collect data to resolve students at our school on what their questions, issues of interest favourite ice-cream flavour is, is it Displaying data appropriate to comment that this is our - Class generated data recording sheets town’s favourite ice-cream flavour or do - Can develop written observations: lists, we need more evidence? data displays, pictures Displaying data Analysing data - read and record results as a list, table, - Classifies and sorts objects and picture graph or bar graph. pictures and discusses the basis for - differences and similarities between their classification lists, tables, picture graphs and bar graphs Analysing data - compare data in a graph to analyse variation Mt Tarampa State School Page 12 of 30 Mathematics Overview ~ Year P-3 Semester 2 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) MISCELLANEOUS Review Measurement Review areas in need of assistance with Angles particular emphasis on Number - concept of angles in relation to turns - comparison of angles using non- standard units e.g. arms, right-angle checker (corner of a piece of paper) TIME Measurement Calendars can be used to identify specific Duration of time Duration of time information about days and dates. - names of months in the year - names and sequence of the days in a - names of days in the week week and months in the year. - record familiar events on a simple - names and sequence of the seasons calendar - read calendars e.g. identify the dates of - names and characteristics of the all the Thursdays in a given month seasons. Time intervals - fortnight, annual, monthly etc. - calculate the date that is a week later, or earlier. SYMMETRY Space Flips, slides and turns are particular ways of Visualisation Transformations moving shapes to explore symmetry. - making mental images of 2D shapes - language - slide, turn and 3D objects - application of flip, slides, turns to Transformations shapes and objects - turn simple shapes to match other - develop repeating patterns based on shapes. flip, slide, turn - fold shapes that have line symmetry - simple visual puzzles e.g. a drawing of a heart with a line of symmetry down the middle - use materials including pattern blocks to demonstrate flips and turns Mt Tarampa State School Page 13 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) POSITION IN SPACE Space Obvious features in everyday environments can Location, direction and movement Location, direction and movement be represented and located on simple maps and - simple sketches to represent objects - construct birds-eye view to show plans. e.g. can look at a drawing of 3 bottles positions within a given area (e.g. Directions can be given for moving and for and place them in the correct order in bedroom, classroom etc) locating features within and environment. real-life - follow and give directions to move - Birds-eye view to show relative position forwards, backwards, left, right, half, full - language – over, under, up, down, left, and quarter turns (three-quarter turns) right, forwards, backwards, sideways, on, below, between, beside, near, before, after, full turn, half turn - simple directions - move forwards, backwards, left and right - non-verbal information (gestures) to give directions MASS Measurement Standard units, including centimetre, metre, Understanding mass and associated units Understanding mass and associated units kilogram (half and quarter) and litre (half and - concept of mass - concept of mass quarter), and non-standard units of measurement Direct comparisons - non-standard units e.g. centicubes, can be used to measure attributes of shapes and - bigger, smaller, heavy, light, heavier, marbles objects. lighter, heaviest, lightest - standard units - kilogram including a Measurements of length, area, volume and mass - order and sequence objects according half and a quarter of shapes and objects are compared and to mass Direct comparisons ordered, using instruments - ways to measure mass - determining appropriateness of - determining which object is lighter or standard or non-standard units heavier by hefting - order objects based on their mass - measure mass using standard and non-standard units depending on accuracy required Mt Tarampa State School Page 14 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and TEACHING FOCUS P – 1 TEACHING FOCUS 2-3 Understandings) 2D SHAPES Space Geometric names and properties are used to Shape – 2D shapes(see list in Essentials) Shape – 2D shapes (see list in Essentials) sort, describe and construct common 2D shapes - recognition and identification of 2D - properties of shapes e.g. right angles, including squares, rectangles, triangles and shapes number of straight sides circles, and 3D objects, including prisms, - recognition of straight and curved lines, - identify 2D shapes in different pyramids, cones, cylinders and spheres. number of sides and corners orientations - names of shapes Visualisation Visualisation - draw 2D shapes and identify properties - make 2D shapes learnt with cord or of the shape pipe cleaners - draw 2D shapes according to criteria EQUIVALENCE Number Whole numbers (to 999) have position on a Numeration Numeration number line and each digit has place value - using a number line to order number (to - using a number line to order numbers Algebra 10) (to 999) Simple relationships between objects or Number facts and strategies Number facts and strategies numbers, including equivalence, can be - counting on and counting back in 1s, 2s - relationships between equations e.g. 6 represented using concrete and pictorial and 3s - using materials, mentally and + 3 = 9, 9 – 6 = 3 and 9 – 3 = 6 materials in written form Problem solving Inverse relationships between addition and Problem solving - justification of thinking subtraction can be applied to find unknowns and - representations of numbers using - representations of numbers and maintain equivalence in equations pictorial and concrete material e.g. 5 equations of equivalence using pictorial can be made up of 3 blue and 2 red and concrete material representations markers or 4 blue and 1 red marker e.g. 14 + 8 = 10 + 12 without changing the total number - recording equations (addition and - justification of thinking subtraction) using written, pictorial and concrete representations VOLUME MULTIPLICATIVE THINKING Review areas in need of assistance EQUATIONS DATA Mt Tarampa State School Page 15 of 30 Mathematics Overview ~ Year 4/5 Semester 1 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 EQUATIONS Number Place value of digits in whole numbers and decimal fractions Number concepts changes when they are multiplied and divided by 10 and 100. - factors including prime numbers and composite numbers Whole numbers (to thousands) and decimal fractions (to Numeration hundredths) can be calculated using addition and subtraction. - investigates the effect of multiplying a number by 10 and by 100 Whole numbers can be multiplied and divided by whole numbers to Number facts and strategies 10 - mental computation strategies that rely on commutative, Whole numbers have factors, prime numbers have only two distinct associative, distributive and inverse laws e.g. 27 + 52 + 3 = 27 + factors and composite numbers have more than two factors. 3 + 52 = 30 + 52 = 82 Problems can be made manageable by using strategies involving - adds and subtracts with and without regrouping estimation, inverse operations, doubles, double doubles and halving - multiplication facts to 10 Algebra Problem solving Rules can be developed to interpret a pattern and predict further - reinforce problem solving strategies (refer to Year 2-3 notes) elements - discuss other strategies that could be used for solving problems Generalisations associated with the four operations are built upon Patterns commutative, associative and distributive properties and inverse - Growing patterns - identifies the rule; and continues the pattern operations. Mt Tarampa State School Page 16 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 TIME Measurement Analogue and digital clocks can be used to read time to the nearest Duration of time minute. - hours, minutes and seconds Timelines, clocks, calendars and timetables are used to sequence, - read and record times on analogue and digital clocks to the schedule and calculate timed events. nearest minute Standard units, including centimetre, metre, square centimetre, - real-life applications of timelines, clocks, calendars and timetables square metre, gram, kilogram, minute, degree, millilitre and litre, Time intervals and a range of instruments are used to measure and order attributes - calculate the amount of time between one event and another of objects, including length, area, volume, mass, time, and angles using timelines, clocks, calendars and timetables Links exist between different ways of recording the same - calculate the time of given events using hours, minutes and measurement. seconds Reasonable estimates can be made using strategies that suit the - estimate times taken for different situations e.g. I know it takes 2 situation. hours to travel 212km so I estimate it will take 1hour to travel 100km 2D SHAPES Space Geometric features, including parallel and perpendicular lines, acute, Shape - 2D shapes right, obtuse and reflex angles, and vertex, edge and base, can be - grouping shapes according to their properties (see list in used to sort shapes and objects into broad family groups. Essentials) Defining features, including edges, angle sizes and parallel lines, are - parallel sides, congruent sides used to make accurate representations of 2D shapes and 3D - using verbal and written representations to identify and objects. communicate the properties of different shapes - drawing accurate representations using appropriate tools Visualisation - draw 2D shapes according to criteria and using appropriate conventions MASS Measurement Standard units, including centimetre, metre, square centimetre, Understanding mass and associated units square metre, gram, kilogram, minute, degree, millilitre and litre, - standard units - kilogram and gram and a range of instruments are used to measure and order attributes - relationship between kilograms and grams of objects, including length, area, volume, mass, time, and angles. - conventions to represent mass e.g. kg, g Links exist between different ways of recording the same Direct comparisons measurement. - measure or estimate mass depending on accuracy required Reasonable estimates can be made using strategies that suit the situation. Mt Tarampa State School Page 17 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 MULTIPLICATIVE Number THINKING Common and mixed fractions involving denominators to tenths can Fractions be represented as a collection of objects, on number lines and as - unit fractions to tenths parts of measure to solve problems - non-unit fractions - mixed numbers - compare and order common fractions and mixed numbers - operating with fraction problems with related denominators e.g. 1/2 + 3/4 - problem solving involving fractions MISCELLANEOUS Measurement Standard units, including centimetre, metre, square centimetre, Angles square metre, gram, kilogram, minute, degree, millilitre and litre, and - concept of angles a range of instruments are used to measure and order attributes of - types of angles - acute, right, obtuse, straight and reflex objects, including length, area, volume, mass, time, and angles. - standard units – degrees including the fact that there are 360 degrees in a circle - measures and calculates angles using appropriate technologies (protractor) MONEY Number Financial records and simple spending and saving plans are ways to Knowledge check on available money and income. - savings - methods of saving; interest may be earned on savings Money can be saved and borrowed, and interest and fees may - borrowing - methods of borrowing; interest is applied to money apply. borrowed - income - money coming in - expenditure - money going out - ways to record these transaction amounts appropriately Financial decisions - decisions based on income and expenditure - borrowing - implications interest has on individuals Mt Tarampa State School Page 18 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 CHANCE Chance and Data The likelihood of outcomes of events involving chance can be Likelihood described using terms including “likely”, “more likely”, “most likely” - concept of likelihood linked to appropriate language and “never”. - language – likely, more likely, most likely, never Data collected from experiments or observations can be organised - relate fractions to likelihood in tables and graphs and used to respond to questions about the Judgements likelihood of possible outcomes of events. - uses appropriate language to describe different situations - experiments of likelihood - collect data and discuss the likelihood of different events occurring e.g. pull a marble out of a bag 10 times and comment on the likelihood of choosing a blue one next - represent data collected in a table and/or graph VOLUME Measurement Standard units, including centimetre, metre, square centimetre, Understanding volume and associated units square metre, gram, kilogram, minute, degree, millilitre and litre, - standard units - litres and millilitres and a range of instruments are used to measure and order attributes - relationship between litres and millilitres of objects, including length, area, volume, mass, time, and angles. - conventions to represent volume e.g. L, mL Links exist between different ways of recording the same Direct comparisons measurement. - measure or estimate volume depending on accuracy required Reasonable estimates can be made using strategies that suit the situation. 3D OBJECTS Space Geometric features, including edges, angle sizes and parallel lines, Shape – 3D objects are used to make accurate representations of 2D shapes and 3D - language - edge, angle size, and parallel lines objects. - classify objects, in appropriate context, according to properties 3D objects can be visualised or constructed using nets. and using appropriate language/terminology to justify classifications Visualisation - nets - construct objects from a net; identify object that matches a given net - draw 2D representations of 3D objects Mt Tarampa State School Page 19 of 30 Mathematics Overview ~ Year 4/5 Semester 2 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 SYMMETRY Space Symmetry and transformations involving flips, slides, turns, Visualisation enlargements and reductions provide a basis for creating patterns, - visualise single flips, slides and turns designs and tessellations. Transformations - demonstrate understanding of flip, slide, turn - enlarging and reducing shapes and patterns - investigating tessellating 2D shapes POSITION IN SPACE Space Mapping conventions, including symbols, scales, legends and Location, direction and movement alphanumeric grids, are used to represent and interpret movements - mapping conventions including symbols, scales, legends, and to identify locations on maps and plans. alphanumeric grids. Mapping conventions, including the four major compass points, are - create maps that use mapping conventions used to give direction and movement and can be linked to turns. - calculate real-life distances from scale (e.g. 1cm is 1 km in real life therefore, 3cm is 3km in real life etc) - use a map to follow directions - relationship between North, South, East and West and quarter, half and three quarter turns PATTERNS Algebra Simple relationships are used to predict results of change Patterns Rules can be developed to interpret a pattern and predict further - repeating and non-repeating number patterns elements. recognises the pattern identifies the rule e.g. 5, 7, 9, 11, …adds on 2 uses the rule to continue the pattern TIME Measurement Timelines, clocks, calendars and timetables are used to sequence, Duration of time schedule and calculate timed events. - real-life applications of timelines, clocks, calendars and timetables Links exist between different ways of recording the same Time intervals measurement. - problem solving using timelines, clocks, calendars and timetables Reasonable estimates can be made using strategies that suit the - 12 months = 1 year, 52 weeks = 1 year, 26 fortnights = 1 year, 10 situation. years = 1 decade, 100 years = 1 century etc. Mt Tarampa State School Page 20 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 DATA Chance and Data Data collected from experiments or observations can be organised Collecting data in tables and graphs and used to respond to questions about the - experiments, simulations, surveys, research likelihood of possible outcomes of events. - determine data needed to justify statements or predictions (e.g. Collected data can be used to justify statements and predictions. more children in our town like riding motorbikes than horses) Sets of data may contain expected or unexpected variation, and this - new questions are developed as we collect data and these new may mean that additional data are needed. questions also need to be investigated Displaying data - record data appropriately in tables, bar graphs, line graphs Analysing data - interpret data in tables, bar graphs, line graphs - compare data in tables or graphs to analyse variation LENGTH AND AREA Measurement Understanding length, area and associated units Standard units, including centimetre, metre, square centimetre, - standard units – metres, centimetres, millimetres, kilometres square metre, gram, kilogram, minute, degree, millilitre and litre, - relationship between metres, centimetres, millimetres and and a range of instruments are used to measure and order attributes kilometres of objects, including length, area, volume, mass, time, and angles. - conventions to represent length e.g. m, cm, mm, km Links exist between different ways of recording the same - standard units – square centimetres, square metres measurement. - relationship between square centimetres and square metres Reasonable estimates can be made using strategies that suit the - conventions – cm2, m2 situation. Direct comparisons - determining appropriateness of standard or non-standard units for area - measure or estimate area depending on accuracy required Indirect measures - problem solving involving the perimeter or area of a range of 2D shapes - rules for calculating the perimeter of square and rectangle Mt Tarampa State School Page 21 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 4-5 EQUIVALENCE Number Whole numbers (to 9999), decimal fractions (to at least hundredths), Numeration and common and mixed fractions have positions on a number line - using a number line to represent and order numbers on a number Equivalent fractions have easily related denominators that are used line - whole numbers; common and decimal fractions; mixed to assist mental calculations numbers Algebra Fractions Patterns in space and number, and relationships between quantities, - numerators and denominators including equivalence, can be represented using concrete and - using related denominators to determine equivalence pictorial materials, lists, tables and graphs Number facts and strategies Generalisations associated with the four operations are built upon - mental computation strategies commutative, associative and distributive properties and inverse Problem solving operations - equivalence can be applied to quantities of measurement – these can be calculated and recorded in a variety of methods. - equations of equivalence can be represented using all four operations. - appropriate symbols can be used to represent relations of equivalence Mt Tarampa State School Page 22 of 30 Mathematics Overview ~ Year 6/7 Semester 1 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 EQUATIONS Number Estimation strategies including rounding, and estimates based on Number concepts powers of 10, assist in checking for reasonableness of calculations - place value relating to large numbers and decimals involving whole numbers and common and decimal fractions. Numeration Problems can be interpreted and solved by selecting from the four - comparing and ordering operations and mental, written and technology-assisted strategies. - representing numbers (place value) Algebra Number facts and strategies Expressions and relationships, including formulas and simple - order of operations equations, can be demonstrated using words, diagrams, materials Problem solving involving more than one operation and symbols to represent variables. - estimating - strategies for working with whole numbers, decimals The order of operations identifies the appropriate sequence of and fractions operations used in calculations to obtain solutions. - reasonableness of answer when problem solving Tables of values for functions using input-output rules can be - connecting written words, numerical equations and pictorial forms constructed and the resulting ordered pairs graphed. of the same problem - representing problems in words, as a numerical equation and in pictorial formats EQUIVALENCE Number Whole numbers, including positive and negative numbers, and Numeration common and decimal fractions can be ordered and compared using - using a number line to order and compare whole numbers, a number line common and decimal fractions both positive and negative Common fractions can be represented as equivalent fractions, Fractions decimals and percentages for different purposes - relationship between common fractions, decimals and Algebra percentages Equations and expressions involving addition, subtraction and Number facts and strategies multiplication can be solved to establish equivalence - Mental computation Problem solving - Solve equations using addition, subtraction and multiplication to establish equivalence - Use appropriate symbols to represent equivalence in equations Mt Tarampa State School Page 23 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 2-D SHAPES Space Geometric conventions, including length, angle size and Shape – 2D shapes relationships between faces, are used to classify 2D shapes and 3D - properties of shapes and the similarities and differences between objects, including part and composite shapes. these (e.g. types of triangles, quadrilaterals etc) 2D shapes can be sketched or accurately represented, using Visualisation drawing instruments and software, to reflect their geometric - sketch and draw accurate representations of 2D shapes using properties. appropriate tools and software Congruent shapes are the same shape and size and can be Transformations superimposed on one another through a sequence of - language - congruent, reflections, rotations, translations transformations, involving reflections, rotations and translations. - identifying congruent shapes TIME Measurement Timetables and duration of events involving both 12- and 24-hour Duration of time time cycles and Australian time zones can be calculated. - read and record times in both 12- and 24-hour times Appropriate instruments, technologies and scale are used when - read a clock even though not all graduations are labelled exploring measurement of length, area, volume, mass, time and - time-zones angles where not all of the graduations are numbered. Time intervals Estimation strategies are used to identify a reasonable range of - problem solve using both 12- and 24-hour times values for a measurement. - problem solving involving the time taken to complete events on that use different time-zones e.g. the time taken to fly from the East coast to the West coast of Australia - estimation strategies Mt Tarampa State School Page 24 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 DATA Chance and Data Data may be discrete and can be allocated to categories or Collecting data numbered. - terminology – discrete, continuous, bias Data may be continuous and described as distributions of quantities. - collection methods for discrete and continuous data Sample data drawn from a given population can be summarised, - identify bias in samples compared and represented in a variety of ways. Displaying data Measures of location such as mean, median and mode, and - representations - two-way tables, pie charts, bar graphs, line frequency and relative frequency, can be used to explore graphs distributions of sample data. - determine display/s most appropriate for discrete and continuous Variation and possible causes of bias can be identified in data data collections. Analysing data - terminology - mean, median, mode, frequency, relative frequency - measures of central tendency – mean, median, mode - measures of spread - range - effects of central tendency and spread on distributions MISCELLANEOUS Measurement Appropriate instruments, technologies and scale are used when Angles exploring measurement of length, area, volume, mass, time and - concept of angles angles where not all of the graduations are numbered. - types of angles - acute, right, obtuse, straight and reflex Measurement involves error, which can be reduced through the - standard units – degrees selection and use of appropriate instruments and technologies. - conventions - o Estimation strategies are used to identify a reasonable range of - geometric properties - 360 degrees in a circle, sum of angles in a values for a measurement. triangle equal 180o, sum of angles in a quadrilateral equal 360o - measures the size of given angles using a protractor - calculates the size of given angles using knowledge of angles, circles, triangles and quadrilaterals Mt Tarampa State School Page 25 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 MULTIPLICATIVE Number THINKING Percentages, rate, ratio and proportion can be used to describe Number concepts relationships between quantities and to solve problems in practical - key percentages situations involving money, time and other measures - concept of rate - concept of ratio - conventions for rate and ratio e.g. km/h, km per h, 1:4, 1/4 - concept of proportion as two or more equal ratios Numeration - compare and order percentages - estimating involving percentage problems Number facts and strategies - relationship between key percentages, common fractions and decimals - order of operations Problem solving - calculating involving percentage, rate, ratio and proportion in practical situations MONEY Number Financial decisions and transactions are influenced by a range of Knowledge factors, including value for money, discounts, method of payment, - language - value for money, discount, method of payment, and available income or savings. income, savings, budget, cheque, EFTPOS, credit card, debit Budgets and financial records are used to monitor income, savings card, money order and spending. - accessing money or the equivalent – discount; interest ; ATMs Cashless transactions include the use of cheques, EFTPOS, credit Financial decisions and debit cards, and money orders. - budgeting including saving and borrowing - developing a budget on given figures - managing personal budgets with reference to bank statements, ATM slips, credit card statements, etc. Mt Tarampa State School Page 26 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 POSITION IN SPACE Space Maps and plans can be constructed and interpreted to identify a Location, direction and movement specific location, to plan movement from one location to another, - mapping conventions including coordinates (ordered pairs), scale and to calculate distance between locations. (1:20) Mapping conventions, including coordinates, compass points and - relationship between the 8 key compass points and amount of scale, are used to specify and identify locations on maps and plans. turn - construct maps and plans to identify a specific location, plan movement from one location to another, and to calculate distance between locations - identify the best route to follow within parameters e.g. most direct route, most scenic route, longest route etc Mt Tarampa State School Page 27 of 30 Mathematics Overview ~ Year 6/7 Semester 2 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 LENGTH AND AREA Measurement Understanding length, area and associated units Appropriate instruments, technologies and scale are used when - International System of measures and relationships between units exploring measurement of length, area, volume, mass, time and e.g. metres, kilometre, millimetre, square centimetre, square angles where not all of the graduations are numbered. metre, hectare, etc. Relationships exist within the International System (SI) of measures, Direct comparisons including between mm, cm, m and km; kg and t; cm2 and m2; cm3 - measure accurately using standard units and m3. - estimate length or area when appropriate Relationships between attributes of regular 2D shapes and 3D Indirect measure objects can be used to develop rules that allow perimeter, area and - problem solving involving perimeter and/or area including the use volume to be calculated. of ratio in scales Measurement involves error, which can be reduced through the - the relationship between the perimeter and area of a given shape selection and use of appropriate instruments and technologies. e.g. rectangle, triangle Estimation strategies are used to identify a reasonable range of - rules for calculating the perimeter and area of common 2D values for a measurement shapes 3D OBJECTS Space Geometric conventions, including length, angle size and Shape – 3D objects relationships between faces, are used to classify 2D shapes and 3D - language - length, angle size, faces objects, including part and composite shapes. - classify 3D objects 3D objects can be constructed from plans, nets and isometric Visualisation diagrams. - plans, nets and isometric diagrams - construct models based on plans, nets and isometric diagrams (e.g. main street of town, school buildings etc) Mt Tarampa State School Page 28 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 CHANCE Chance and Data Events have different likelihoods of occurrence and estimates of Likelihood probability can be expressed as percentages, common fractions or - express probability on a scale from 0 to 1 decimal fractions between 0 and 1. - express probability as a percentage, common fraction or decimal Experimental data for chance events can be compared with - theoretical vs experimental probability theoretical probability. - list the sample space for theoretical probability of an event Judgements - demonstrates understanding of experimental data and theoretical probability by conducting an experiment and commenting on the results e.g. tosses a coin 20 times and records the answers for experimental data whereas the theoretical probability states you should toss 10 heads and 10 tails PATTERNS Algebra Tables of values for functions using input-output rules can be Functions constructed and the resulting ordered pairs graphed. - input – output machines displays input and outputs in a table uses the input and the rule to find the output uses the output and the rule to find the input uses the inputs and outputs to find the rule - displays of data and their relationships – tables, graphs, rules MASS Measurement Appropriate instruments, technologies and scale are used when Understanding mass and associated units exploring measurement of length, area, volume, mass, time and - concept of mass angles where not all of the graduations are numbered. - International System of measures and relationships between units Relationships exist within the International System (SI) of measures, e.g. gram, kilogram, tonne including between mm, cm, m and km; kg and t; cm2 and m2; cm3 Direct comparisons and m3. - measure accurately using standard units Measurement involves error, which can be reduced through the - estimate mass when appropriate selection and use of appropriate instruments and technologies. Indirect measure Estimation strategies are used to identify a reasonable range of - problem solving involving the concept of mass values for a measurement Mt Tarampa State School Page 29 of 30 FOCUS CONCEPTS ESSENTIAL LEARNINGS (Knowledge and Understandings) TEACHING FOCUS 6-7 VOLUME Measurement Appropriate instruments, technologies and scale are used when Understanding volume and associated units exploring measurement of length, area, volume, mass, time and - concept of volume angles where not all of the graduations are numbered. - International System of measures and relationships between units Relationships exist within the International System (SI) of measures, e.g. litres, millilitres, megalitres including between mm, cm, m and km; kg and t; cm2 and m2; cm3 Direct comparisons and m3. - measure accurately using standard units Relationships between attributes of regular 2D shapes and 3D - estimate volume when appropriate objects can be used to develop rules that allow perimeter, area and Indirect measure volume to be calculated. - problem solving involving the concept of volume Measurement involves error, which can be reduced through the selection and use of appropriate instruments and technologies. Estimation strategies are used to identify a reasonable range of values for a measurement. DATA Chance and Data Data may be discrete and can be allocated to categories or Collecting data numbered. - terminology – discrete, continuous, bias Data may be continuous and described as distributions of quantities. - collection methods for discrete and continuous data Sample data drawn from a given population can be summarised, - identify bias in samples compared and represented in a variety of ways. Displaying data Measures of location such as mean, median and mode, and - representations - two-way tables, pie charts, bar graphs, line frequency and relative frequency, can be used to explore graphs distributions of sample data. - determine display/s most appropriate for discrete and continuous Variation and possible causes of bias can be identified in data data collections. Analysing data - terminology - mean, median, mode, frequency, relative frequency - measures of central tendency – mean, median, mode - measures of spread - range - effects of central tendency and spread on distributions SYMMETRY Space Points, lines and planes of symmetry can be identified in shapes and Transformations objects and can be related to transformations and tessellations of - points, lines and planes of symmetry suitable shapes in the plane. - identify congruent shapes Mt Tarampa State School Page 30 of 30