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Mathematics Scope and Sequence Manunda Terrace Primary School Year 5: Number and Algebra…………………... 3 - 9 Measurement and Geometry….….10 – 15 Statistics and Probability……………16 - 18 Key: Red text: Identifies achievement standards and strand connections Blue text: T-9 Literacy and Numeracy Net Australian Curriculum NT School Year 5 - 1 of 21 Manunda Terrace Primary Foreword In 2011, Manunda Terrace Primary School was the focus of three major projects. Firstly, it was selected to be a Pilot School to trial the Australian Mathematics Curriculum. Secondly, Manunda Terrace Primary School received funding through the National Partnership Smarter Schools Project, Maximising Improvement in Literacy and Numeracy, to support improved numeracy learning outcomes. Thirdly, Manunda Terrace Primary was extremely fortunate to have a Numeracy Coach from the Department of Education Darwin Regional Curriculum Team, Carolyn Clark, based part time on-site for the first half of 2011 to support changed mathematical pedagogy. After familiarisation with the Australian Mathematics Curriculum, teachers determined the need to unpack the specific content of the Australian Curriculum content descriptions. Small teams of teachers researched various documents, including the Northern Territory Curriculum Framework and T-9 Literacy and Numeracy Net. They also examined various resources including Count Me in Too and First Steps to extrapolate and make explicit content knowledge, aligned with quality pedagogical practice. This exercise has resulted in the publication of the Manunda Terrace Primary School Mathematics Scope and Sequence. Parallel to this process, staff engaged in developing mathematics resources, participated in various professional learning experiences, and applied this knowledge to writing units of work using the Australian Curriculum mathematics learning area with improved teaching practice. We wish to acknowledge and thank: The hard work of Manunda Terrace Primary School teaching staff of 2011 Carolyn Clark’s outstanding support and contribution (Numeracy Coach, Darwin Regional Curriculum Team) Department of Education and Training support through the Darwin Regional Curriculum Team National Partnership Project funding, through Maximising Improvements in Literacy and Numeracy Curriculum Teaching and Phases of Learning Australian Curriculum pilot We believe that our own staff will continue to develop and improve pedagogy, through the use of this document to ensure best learning outcomes for our students. We hope that this document will be useful for other schools as a starting point for their own journey in pedagogy, curriculum and assessment in mathematics teaching. Sally Winch Principal Australian Curriculum NT School Lisa Hirschausen Assistant Principal Year 5 - 2 of 21 Manunda Terrace Primary Mathematics Scope and Sequence Number and Algebra Achievement Standards Proficiency Strands Understandings: By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect threedimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Skills: Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes as probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data. Understanding includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry Fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles Problem Solving includes formulating and solving authentic problems using whole numbers and measurements, and creating financial plans Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals , interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets Achievement Standard Work Samples http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10 Number and Place Value AC Content Descriptor AC Elaborations Identify and describe factors and multiples of whole numbers and use them to solve problems Use estimation and rounding to check the reasonableness of answers to calculations So learning will include Year 5 – Number and Algebra Using models investigate factors in multiplication, eg manipulate arrays to find out how many different arrays can be made with a given product, and record and explain reasoning as to how many ways the arrays can be described? eg o for product 24 outlined or cut out arrays could be: 2 x 12 array, 12 x 2 array, 6 x 4 array, 1 x 24 array ... (Leading to identifying and understanding factors for a given product), o Online factors and arrays activity http://illuminations.nctm.org/ActivityDetail.aspx?id=64 Investigate ways of recording factors of products using, eg factor trees http://nzmaths.co.nz/resource/factor-trees , hundred charts Predict what a sequence ‘down the line’ might be in investigating multiplicative patterns products (multiples); find the missing part/s of multiple sequence and justify and explain outcomes; investigate and record patterns made, using 100 charts Use multiple and factor knowledge to estimate and check reasonableness of answers when solving problems Investigate ways of compare and displaying factors of multiples to find common ones, eg o factors of 2 2 4 6 8 or o factors of 2 2 4 6 8 10 12 14 o factors of 4 4 8 12 o factors of 3 3 6 9 12 15 o factors of 8 8 First Steps Number: Book 2: RNP – KU6 Use estimation and rounding to check the reasonableness of answers to calculations Recognising the usefulness of estimation to check calculations Applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load Australian Curriculum NT School Estimate money totals using strategies such as inverse operations and rounding, eg estimate cost of five children’s movie tickets then two adult tickets to determine whether $100 will be enough, and if the sellers ‘change’ is correct. Continue to develop efficient mental strategies (as listed in Year 4 strategies find the face ) for solving real context problems but with larger numbers, and o use estimation and rounding to check reasonableness of answers; fluently round numbers to nearest 10, 100, 1000 First Steps Number: Book 2: Cal – KU8, KU10 Year 5 - 3 of 21 Manunda Terrace Primary AC Elaborations Solve problems involving multiplication of large numbers by one or two-digit numbers using efficient mental, written strategies and appropriate digital technologies Exploring techniques for multiplication such as the area model, the Italian lattice method or partitioning of numbers Year 5 – Number and Algebra AC Content Descriptor Applying the distributive law using arrays to model multiplication and explain calculation strategies Number and Place Value So learning will include Investigate and solve real context large numbers by 1 and 2 digit, multiplication problems, using a variety of techniques including area models (First Steps Number, names model as Multiplication Grids), Italian lattice methods, and partitioning with base ten columns in tradition multiplication algorithms Investigate the ‘distributive property of multiplication over addition’ using real context larger number scenarios eg model to visually show on an array, 4 x 587 = (4 x 500) + (4 x 80) + (4 x 7) Solve real context problems, using a variety of problem solving methods, and use models to explain what they did and why it makes sense, eg think boards that could include, words, pictures, diagrams, numbers including algorithms Investigate different problem types, eg o Equal grouping problems: with ‘repeated addition’ or rate type problems (eg cost, measurement, length) for multiplication. Problems exploring both ‘how many groups?’ and ‘how many in each group?’, eg If chocolate frogs cost 75 cents each, how much did Jeff pay for a bag of 25 frogs? o Comparison type problems: where the product is unknown, (multiplication), eg Ali picked 26 oranges; Sally picked 16 times as many as Ali. How many did she pick? o Combination type problems: where problems involve counting the number of possible pairings that can be made between two sets, eg buying 3 tops and 5 shorts and investigating how many different combinations could be made, eg models for investigations could be arrays, tree diagrams o Product of Measure problems: eg the area of a rectangle is 95cm² and has one side that is 20cm long. How long is the adjacent side? (Refer: First Steps Number: Book 2 page 90) Investigate how multiplication models equate to different algorithm processes; explain and justify the choice of approach for particular scenarios Determine the relationship between pairs of values in a table and predict values not represented by generalising, eg predict the revenue from a class enterprise selling friendship bands from a table, find the cost of ? bands Number of Bands Money 5 10 $ 1 0 $20 15 20 25 o Display data from a table of values in a graph and investigate the ‘shape of the graph’; make conjectures about why it has this type of shape; construct other multiple type values tables (as in example above) and investigate their graph ‘shapes’. Discuss and explain similarities and differences in terms of the multiples of numbers used Italian lattice multiplication - link http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathsco ntinuum/number/N40002ma.htm Area model multiplication -link http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathsco ntinuum/number/N40002P.htm First Steps Number: Book 2: Cal – KU1, KU3, KU4, KU5, KU6; RNP – KU4, KU5 Australian Curriculum NT School Year 5 - 4 of 21 Manunda Terrace Primary Number and Place Value AC Content Descriptor Year 5 – Number and Algebra Solve problems involving division by a one-digit number, including those that result in a remainder AC Elaborations So learning will include Using the fact Estimate simple problems requiring division by one digit numbers using known that equivalent facts, eg 9 people share $300 so they’ll get $30 each since 300 ÷ 10 = 30 division Solve real context word problems by dividing; use larger numbers by 1 digit with calculations result remainders; eg use models to explain what they did and why it makes sense if both numbers such as think boards; could include, words, pictures, diagrams, numbers and are divided by the algorithms same factor Include problem types such as, eg o Equal grouping problems: with ‘fair sharing or rate type problems (cost , Interpreting and measurement, length) for partitioning division , eg ‘How many groups? and representing the ‘How many in each group? remainder in o Comparison type problems: where the group size is unknown, (partition division division) or measurement division, eg Mia has 17 shells; how many times as calculations many shells does Tegan have, if she has 95? sensibly for the o Combination type problems: eg there are three types of ice-cream cones and context various ice cream flavours. If 18 different ice creams can be made, how many different flavours are there? (Refer: First Steps Number Number: Book 2 pg 90) Solve real scenario problems to investigate how remainders can be expressed in different ways; explain why that way of expressing remainder has been chosen. Remainder types include; o ‘left over’ remainder, eg 24 lollies equally shared between 7 friends o remainder partitioned as a fraction, eg each can holds 200mls. If the jug holds 1L and 300mL, how many cans would that be? (6 ½ cans) o remainder is discarded, eg if a skipping rope is 25m long, how many 3m length ropes can be made? ( 8 ) o forced to next whole number, eg a boat can hold 6 people. How many trips needed to carry 21 people across a river? (4) o remainder is rounded to give an approximate result, eg a family of 6 share a packet of 40 snakes. About how many snakes do they get each? (about 7) First Steps Number: Book 2: Cal – KU1, KU3, KU4, KU5; RNP – KU4, KU5 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems Using calculators to check the reasonableness of answers Applying known facts and strategies Continue to develop efficient mental and written strategies (refer Year 4 listed strategies ) for solving real context problems that require the use of all four operations Read, say, write in words and digits, compare and order whole numbers to hundred millions and enter these numbers into a calculator for practical purposes, eg make comparisons of populations of different cities or states Use efficient mental, written and calculator strategies to add, subtract, multiply and divide (including decimal numbers) to solve multi step word problems, eg add costs of items and then work out change from a defined amount Use place value knowledge to partition numbers mental in order to simplify computation, eg to multiply 23 x 4 think 2 tens and 3 ones multiplied by 4, = 8 tens and 12 ones = 9 tens and 2 = 92; or thinks, 23 x 4 = 11 x 4 doubled + 4; or 25 x 4 – 8 First Steps Number: Book 2: Cal – KU1, KU3, KU4, KU5; RNP – KU4, KU5 Australian Curriculum NT School Year 5 - 5 of 21 Manunda Terrace Primary Patterns and Algebra Year 5 – Number and Algebra AC Content Descriptor Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction AC Elaborations Using the number line to create patterns involving fractions or decimals So learning will include Know and explain the repeated pattern of hundreds, tens and ones across the place value ‘groups’ of ones, thousands and millions, eg 657 432 156 = 657 million, 432 thousand and 156 ones Use models to investigate patterns by copying, creating, extending and determining them when adding or subtracting decimal and fractional notion, eg use marked or empty number lines, use table of values (as illustrated in Number and Place Value substrand above), pattern making using matchsticks, popsticks, straws Use models to investigate the patterns that eventuate from adding or subtracting a given amount, such as ½ to or from ½, ¼, 1/8, 1/3, 1/6 sequences, and describe and record the patterns formed; identify and explain the pattern rule eg use marked number line, fraction walls, value tables Investigate the relationship in patterns between fractions and decimals; explain patterns created and record findings, eg use models such as fraction walls and 100 x 100 grids, fraction circles and hundredth discs First Steps Number: Book 2: RNP – KU1, KU3, KU4, KU5, KU6 Hundredth disc BLM 28: http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,3547876-,00.html Use equivalent number sentences involving multiplication & division to find unknown quantities Using relevant problems to develop number sentences Use a variety of problem types to make equivalent multi step multiplication and division number sentences and justify reasoning as to why they are equivalent or not. Use symbols to show the relationship of operations on either side of an equal sign, eg o Investigate given multiplication and division number sentences in terms of equivalence using’ true or false’ statements, and justify decision choice, eg 3 x 46 = 6 x 23 or 52 ÷ 12 = 26 ÷ 6 (problem should challenge and encourage the move towards relational thinking instead of computation; for example above numbers have been doubled or halved) o Solve’ open sentences’ multiplication and division problems using partitioning and combining (part part whole relationships), eg 20 x 48 = ∆ = 24 ; use models such as number lines to justify reasoning, leading to discussions on relational thinking First Steps Number: Book 2: UO – KU7, KU8; Cal – KU1, KU3, KU4, KU5, KU6; RNP – KU3, KU4 Australian Curriculum NT School Year 5 - 6 of 21 Manunda Terrace Primary Year 5 – Number and Algebra Fractions and Decimals AC Content Descriptor AC Elaborations So learning will include Compare and order common unit fractions and locate and represent them on a number line Recognising the connection between the order of unit fractions and their denominator Count in fractions indicating the different names and representations, eg one third, two thirds, three thirds or one; four thirds or one and a third; five thirds or one and 2 thirds..., place each fraction 1/2, ¼ , 1/8, 1/3 and 1/6 on marked or empty 0 – 1 number lines Investigate and compare different sized models (including measurement attributes of mass and volume) to find fractions that are relative to that particular whole, eg explain that one quarter of the family size pizza is more than half of the small pizza; ½ the weight of the bag of marbles is more than ¾ the weight of the shoe box of foam bricks State what the numerator and denominator mean in numerical representation of fractions, eg ‘ the bottom number says how many parts in the whole, the top number says how many of those parts we have’ (vinculum: the horizontal line placed over the top of denominator indicates that it’s to be considered as a group) Estimate the shaded fraction on geometric shapes, and order and record the fractions on a number line marked 0-1 Order familiar unit fractions and explain why they are larger or smaller, eg use models to verify and justify which is bigger and why Use a 0-2 number line (with random points marked on it) and write the fraction indicated by each point. Justify why fraction representation has been chosen, in particular noting the choice of denominator. Note equivalent fractions First Steps Number: Book 1: UFN- KU5 Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator Modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes Using different strategies, investigate everyday occurrences of adding and subtracting fractions and consider the relevance of equally divided and shared parts and the relevance of size of the whole; record using models, proving and justifying outcomes, eg o share 3 pancakes between 4 people o eating family sized pizzas in comparison to mega sized pizzas to feed the family. Add together everyone’s shares; or subtract for the number of pieces eaten by each member from the whole number of pizzas bought; prove and justify what is the best sized pizza for value, for the family needs Investigate strategies to solve fraction addition and subtraction problems, and justify the strategies used eg o Use models to add and subtract simple fractions with the same denominator, eg use jumps on marked or empty number lines to verify order sequence and explain outcomes investigate addition and subtraction scenarios using, eg fraction walls First Steps Number: Book 1: UFN – KU5; Book 2: Cal – KU7 Recognise that the place value system can be extended beyond hundredths Use knowledge of place value and division by 10 to extend the number system to thousandths and beyond Recognising the equivalence of one thousandth and 0.001 Australian Curriculum NT School Count, read, write, say and order sequences of decimal numbers to thousandths Count number sequences forwards and backwards by decimal numbers, and read and say numbers with two decimal places correctly, eg say ‘point three two’, or ‘thirty two hundredths’, NOT ‘point thirty two’, read and say 9.263 as nine point two six three, not nine point two hundred and sixty three (understanding that the cyclic pattern of ones, tens, and hundreds used in saying whole numbers, does not apply to decimals) Investigate where and why decimals to the thousandths and beyond are found in real contexts, eg timing in sports statistics, measuring, science connections Relate decimals usage to everyday experiences, eg o investigate decimals using real context measurement scenarios with length, mass, area, volume, capacity and money; comparing similarities and differences, and explaining the relationships of measurement unit conversions to decimal numbers, eg mm to cm to m Use real context scenarios to investigate multiplication and division by 10, to connect understandings that numbers both sides of the decimal point have a 10 to 1 ratio, and thousandths is equivalent to 0.001, eg o using measuring metric system conversions with length, mass, area, volume, capacity and money Year 5 - 7 of 21 Manunda Terrace Primary Fractions and Decimals Year 5 – Number and Algebra AC Content Descriptor AC Elaborations So learning will include Understand that base ten place value knowledge extends to even smaller values of thousandths and beyond as part of the numbers less than one; use models such as explaining the relationship between tens, ones and tenths using objects such as a bundle of 10 straws where one straw is 1, eg show 14.2 using one bundle of 10 straws, 4 single straws and 2 pieces of a straw cut into 10 equal pieces; take examples (such as above) through to thousandths understandings using technology models Use the constant function on a calculator to investigate counting by hundredths and thousandths, eg o press 0.01 =, = … Predict what will happen next after 0.09 and justify by proving outcome using other models. Investigate, record and compare how many presses it takes to get from one whole number to the next with tenths, hundredths and thousandths Round decimals up or down to the nearest tenth and hundredth to estimate numbers for calculating and check reasonableness of calculations and can say which two whole numbers the answer will be between, eg 4.1 x 4.5 will be between 15 and 17 because 4 x 4 is less than 4 x 5 First Steps Number: Book 1: UWDN – KU3, KU7, KU8 ; UFN – KU6 Compare, order and represent decimals Locating decimals on a number line Compare and order numbers up to two decimal places knowing that the number of decimal places or length does not reflect the value of the number, eg explains why 0.4 is greater than 0.32 Connect decimal, fraction and word representations, eg know 0.2 and 2/10 both represent two tenths, write decimals to thousandths in expanded form Use models to compare order and represent decimal places to thousandths such as using marked, empty or broken number lines (also CMIT washing line), eg o to place a decimal between an identified pair of decimal numbers, eg 4 4.2 x? 4.8 5 o to identify the closest whole number to a given decimal o to place given decimals (eg 0.007 and 0.7) on the correct/best estimate points of a marked number line 0 to 1 o to decide which decimals are smaller or bigger (4.3, 4.07, 4.301) o to place decimals that have ‘friendly fractions’ (halves, fifths, fourths and eighths that more easily connect conceptually to decimal equivalents) on an unlabelled but fractionally segmented number line (fourths, fifths) and provide the fraction equivalent for each placed decimal; investigate and discuss similarities and differences in the way both decimals and fractions are written First Steps Number: Book 1: UWDN – KU3, KU7, KU8 ; UFN – KU6 Australian Curriculum NT School Year 5 - 8 of 21 Manunda Terrace Primary Money and Financial Matters Year 5 – Number and Algebra AC Content Descriptor Create simple financial plans Australian Curriculum NT School AC Elaborations So learning will include Creating a simple budget for a class fundraising event Use real scenarios to investigate the concepts of calculating, predicting and manipulating ingoing and outgoing money in order to effectively finance a real or simulated event, and make conjectures about how personal or group decisions made influence the end result Use calculators to enter, read and calculate money transactions and know that a display of 5.3 means $5.30 Understand that the GST (Goods and Services Tax) is a 10% government tax included in the purchase price of many goods and services, and investigate it’s prevalence, eg collect shopping brochures, newspapers, magazine advertisements Investigate the interrelatedness of the term ‘percent’ and the term ‘hundredth’, understanding that percent is a new notation not a new concept, and is represented by the symbol % Calculate 50%, 25% and 75% by mentally using fractional equivalents, eg finds 25% by halving and halving again (Year 6 Australian Curriculum content descriptor) and identify the 10% GST component of collected invoices and receipts Identifying the GST component of invoices and receipts Teaching Financial Literacy link http://www.teaching.financialliteracy.gov.au/home.html Year 5 - 9 of 21 Manunda Terrace Primary Resources Year 5 – Number and Algebra Maths manipulatives resources– Manunda PS library Scootle - Learning Objects http://www.scootle.edu.au/ec/p/home First Steps Number Number: Book 1: UWDNT – Understand Whole and Decimal Numbers; UFN – Understand Fractional Numbers; Book 2: UO – Understand Operations; Cal – Calculate; RNP – Reason about Number Patterns Teaching Financial Literacy link http://www.teaching.financialliteracy.gov.au/home.html Number lines: marked ( with sequenced numbers), empty (no numbers ), broken (a segment that is marked but doesn’t begin at zero, eg __15__________________56_) Number expanders http://www.education.vic.gov.au/studentlearning/teachingresources/ maths/mathscontinuum/number/numberexpander.htm National Library of Virtual Manipulatives http://nlvm.usu.edu/ http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,354787 6-,00.html Gay West resource file Maths 300 Username: (check administration for username and password) Collections: include any items that can be handled, from commercially made maths resources (eg counters, link blocks, geo shapes, small objects collections - mini people / teddy bears / fruit), to environmentally collected items (eg leaves, shells), to art items (eg popsticks, coloured papers, beads, pipe cleaners) Model: has been used to describe actions using manipulatives, games and strategies to show a process of understanding Problem Solving Strategies Making a table Drawing a graph Pictorial representation Use of algorithms Guess and check Act out problem (Further information on Problem Solving) Key Mathematical Language (EAL/D) Number and Place Value Rounding, estimating, increasing, decreasing, divide, addition, sum, total, difference, difference between, compare, ascending order, descending order, differences, lower, higher Patterns and Algebra Sequence, position, number, array, multiples, vertical, horizontal, row, column, double, increase, decrease, sum, difference Fractions and Decimals Percent, denominator, numerator, equal, tenths, hundredths, the fraction equivalent, constant function on a calculator Money and Financial Matters Goods and Services Tax as GST, budget, income, payment, the symbol %, interest, bank account, wage, salary, deposit, withdrawal, borrow, loan Australian Curriculum NT School Year 5 - 10 of 21 Manunda Terrace Primary Mathematics Scope and Sequence Measurement and Geometry Achievement Standards Proficiency Strands Understandings: By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect threedimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Skills: Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes as probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data. Understandings: By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect threedimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Skills: Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes as probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data. Achievement Standard Work Samples Achievement Standard Work Samples http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10 http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10 Year 5 - Measurement and Geometry Using Units of Measurement AC Content Descriptor AC Elaborations So learning will include Choose appropriate units of measurement for length, area, volume, capacity and mass Investigating alternative measures of scale to demonstrate that these vary between countries and change over time, eg temperature measurement in Australia, Indonesia, Japan and USA Know that some tasks require measuring different attributes (length, area, volume, mass and temperature) and more accurate measurement than others, eg more accuracy required when measuring water for cooking bread than for making cordial Know the relationships between km, m, cm, and mm and use visualisation of each unit in order to estimate length at a glance Measure mass accurately to the nearest graduation in kg, g, by first choosing an appropriate measuring instrument that allows for the level of precision needed for the purpose, eg chooses bathroom scales to weigh their luggage before travelling on a plane Investigate the relationship of the size of ‘measurement units’ in length, area, volume, capacity and mass, to the object/area being measured, and use and justify choice of measuring units eg o for measuring with accuracy or for approximation purposes o when measuring very small to very large objects/spaces, eg using mm for measuring insects, km for distances between places In real context scenarios understand and use standard metric measurement symbols when recording measurements o square metres – 1m2 = 10 000 square cm o square centimetres 1cm2 = 100 square mm o cubic metre – 1m3 = 100cm x 100cm x 100cm o cubic centimetres – 1cm3 = 10mm x 10mm x 10mm o Kilometres – 1km = 1 000m o Hectares – 1ha = 10 000 square metres ( 100m x 100m) o Investigate imperial measurement units, the geographical locations where these are used, or historically have been used, and compare and contrast these to the metric system of measurement, eg knows historical relationships between inches and centimetres, feet and yards to metres, acres and hectares Recognising that some units of measurement are better suited for some tasks than others, eg kilometres rather than metres to measure the distance between two towns First Steps Measurement: Book 1: UU – KU2, KU5, KU6, KU7, KU8; DM – KU4, KU5 Australian Curriculum NT School Year 5 - 11 of 21 Manunda Terrace Primary Using Units of Measurement AC Content Descriptor AC Elaborations Calculate the perimeter and Exploring efficient area of rectangles using ways of calculating familiar metric units the perimeters of rectangles such as adding the length and width together and doubling the result Year 5 - Measurement and Geometry Exploring efficient ways of finding the areas of rectangles So learning will include Understand the concept/meaning of perimeter, area and volume writing a description of each and giving examples of where measuring these attributes might be needed, eg water in a fish tank, distance around the school boundary fence, size of cloth needed to fully cover a table or bird cage Investigate measuring a rectangular area by placing identical square units in rows or columns over the surface without overlays or gaps, investigating the relationship of these units to the concept of a multiplication array (leading to understand a row of squares (determined by the length of the side) can be seen as a single row unit that can be replicated by multiplication/repeated addition; (how many times being determined by the length (number of units) of the other side- or Width of the rectangle) Investigate and describe ways of calculating the area of a rectangle using the array concept and explain reasoning as to which description is the most efficient eg Area = column of 8 + column of 8 + column of 8; Area = columns of 8 (length) x rows of 3 (width); A = L x W Devise a method to calculate the approximate area of a large region; use, verify, and justify its efficiency, recognising the need for larger units of area; hectare and square kilometre Investigate and identify areas that are less than, about the same as and larger than a square metre and understand that a square metre area can be various shapes, eg a rectangle Investigate and describe ways of calculating perimeter and explain reasoning as to which description is the most efficient, including strategies to measure curved boundaries eg Perimeter = side 1+side 2 + side 3 + side 4; Perimeter = (L x 2) + (W x 2); Perimeter = L + W x 2 First Steps Measurement: Book 1: UU – KU2, KU5, KU6, KU7, KU8; DM KU4, KU5 Compare 12 and 24 hour time systems and convert between them Investigating the ways time was and is measured in different Aboriginal Country such as using tidal change Using units hours, minutes and seconds Investigate and make generalisations about where and why 12 or 24 hour representations of time occur in the environment, eg find example in newspapers, TV schedules, tide times, plane timetables Write , draw and explain scenarios that show a need to understand the use of 12 and 24 hour time notation, eg catching a plane Use real context scenarios to investigate the relationships between 12 and 24 hour and am and pm understandings; eg o convert between 12 and 24 hour representations of time that use hours, minutes and seconds when reading and interpreting 12 and 24 hour timetables to work out travel plans (bus and train timetables – schedule or online) Research ways different indigenous groups across Australia measure time Calculate elapsed time from a timetable, eg reads a bus timetable and says the next bus will come in 25 minutes and takes 30 minutes to get into town, its 3pm now, so I’ll get there at 3:55 if I catch it and can identify assumptions such as bus on time, and bus won’t break down Investigate different strategies when using clock faces or timelines to calculate time durations, eg use the ‘jump’ method to find time from 8:15 to 10:50. to do this, eg set as a table - 8.15 to 9.00 is 45mins, 9.00 to 10.00 is 60mins, 10.00 to 10.50 is 50 mins, so add mins and convert (Note: 24 hour time is written 0525 or 1418, not 05:25; no colon) First Steps Measurement: Book 1: DM – KU6 Australian Curriculum NT School Year 5 - 12 of 21 Manunda Terrace Primary Shape AC Elaborations So learning will include Connect three-dimensional objects with their nets and other two-dimensional representations Identifying the shape and relative position of each face of a solid to determine the net of the solid, including prisms and pyramids Using models investigate how key property features of cubes, cylinders, cones, and rectangular prisms relate to each object, particularly noting the placement and 2D shape of faces; and recording findings, eg o constructing and deconstructing the nets (flat 2D pattern) of shapes eg by cutting open a variety of shaped boxes; using geo shapes, polydrons, cardboard/paper, isometric and grid paper o investigate how many different nets can be made for a ‘given’ shape, predicting, constructing and justifying findings, eg Maths 300 #116 cube nets o investigate the nets of various sized, but same 3D objects, and predict and make generalisations about the key features, eg investigate different sized rectangular prisms noting whether size of length, width or height changes the 2D shapes in the nets o identify and record by drawing different views and representations of 3D objects including nets perspective drawings (showing length, width and height representation), isometric drawings – 3D shapes drawn on isometric grids (shows a 90º angle drawn as a 30ºangle) orthogonal views, eg build simple 3D shapes with cubes, then represent the top, front, back and side views as 2D shape drawings, eg http://nzmaths.co.nz/resource/winning-ways, use card matching sets cross sections, eg oblique cut cross section of a cylinder shows an oval Use card sets to match 3D objects with different 2 D representations, eg using cards set of photos of regular and irregular 3D objects from different view points, and card sets of related 2D representations such as isometric drawings, orthogonal views, perspective drawings and nets; and justify matching of cards checking on a real 3D model Predict and test which pentomino nets can be folded to make an open box and which are symmetrical Make tessellations with pentominos and explain strategy used Year 5 - Measurement and Geometry AC Content Descriptor Representing twodimensional shapes such as photographs, sketches and images created by digital technologies First Steps Measurement: Book 2: RS – KU1, KU2, KU3 Australian Curriculum NT School Year 5 - 13 of 21 Manunda Terrace Primary Location and Transformation AC Content Descriptor Use a grid reference system to describe locations. Describe routes using landmarks and directional language AC Elaborations Comparing aerial views of Country, desert paintings and maps with grid references Year 5 - Measurement and Geometry Creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another So learning will include Interpret and use simple scales, eg one grid square length equals ten km, coordinates, eg 2B and keys on maps and plans (such as a street directory or map of their town) when locating features or giving directions Match photographs of a scene to the positions , shown on a plan, from which the photographs were taken Play coordinate grid games eg Hurkle http://www.aimsedu.org/aimskids/ipuzzles/hurkle/index.html Construct a map or plan of a familiar location that includes a key of significant items and a simple coordinate grid Give or follow instructions to move involving turning through a given rotation clockwise or anticlockwise or moving a given number of steps N,S, E, W (with compass points shown) Use a coordinate grid system on a local street map to identify/record specific items or places given the coordinates Interpret and create maps and plans involving positive coordinates and intermediate compass points Calculate the distance between two locations or coordinates on a map given a simple scale. Investigate ‘Google Earth’ site First Steps Measurement: Book 2: RL KU1, KU2, KU3 Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetry Identifying and describing the line and rotational symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies Identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies Using models investigate and compare by predicting outcomes, then manipulating 2D shapes to find and explore, if and how many points of rotational symmetry they have, (ie the 2D shape or ‘footprint’ rotated about a point (without flipping it over) lands in a position exactly matching the footprint. The ‘order of rotational symmetry’ is the number of times the shape matches the footprint in a full turn); explain and record results, eg an equilateral triangle has a rotational symmetry of order 3, (3 points) Use models of 2D shapes to investigate the relationship of symmetry and rotational symmetry properties, eg a parallelogram has no lines of symmetry but two points of rotational symmetry; create words having line or rotational symmetry using uppercase letters that exhibit symmetry Classify triangles and quadrilaterals according to side length, shape and symmetry Use dynamic geometry software to create tessellation patterns where 2D shapes are manipulated through line and rotational symmetry, eg o describe the Tetris shapes and how they fit together o GeoGebra http://www.geogebra.org/cms/ Investigate the angle properties of tessellating 2D shapes First Steps Measurement: Book 2: RT – KU1, KU2, KU3, KU4; RG – KU1 Apply the enlargement transformation to familiar two-dimensional shapes and explore the properties of the resulting image compared with the original Using digital technologies to enlarge shapes Using a grid system to enlarge a favourite image or cartoon Investigate the connections between proportional reasoning and the geometric concept of similarity by enlarging and reducing dimensions of 2D shapes, eg take photos of everyday objects in the classroom; print photo and work out the scale of the photo to the object use a variety of grid papers such as 1cm or 2cm to create or use given ratios, (eg 1cm square = to 3cm squares, or 1:3) when drawing 2D shapes, comparing original drawing with the transformed (enlarged or reduced) drawing informally use 1 point perspective over a grid to create enlarged and reduced transformations use dynamic geometry software to explore the idea of ratio, eg GeoGebra http://www.geogebra.org/cms/ First Steps Measurement: Book 2: RT – KU1, KU2, KU3, KU4; RG – KU1 Australian Curriculum NT School Year 5 - 14 of 21 Manunda Terrace Primary Geometric Reasoning Year 5 - Measurement and Geometry AC Content Descriptor Estimate, measure and compare angles using degrees. Construct angles using a protractor Australian Curriculum NT School AC Elaborations So learning will include Measuring and constructing angles using both 180° and 360° protractors recognising that angles have arms and a vertex, and that size is the amount of turn required for one arm to coincide with the other Draw and accurately measure angles to the nearest degree using a variety of tools to measure real context and on-screen angles, eg using protractors and electronic protractors, cardboard angle wheels (100th disc / 2 spliced circles together) Understand and use ‘degree’ º notation to label measurements Investigate angles properties of polygons by direct measurement and through the use of dynamic geometric software, eg sum of interior angles of a rectangle Explore angle size by cutting up shapes and putting corners (angles) together Name angle type, use standard geometrical marks to identify equal sides of shapes, equal angles and right angles Classify angles using terms, acute, right, obtuse, straight, reflex and mark on a full circle Understand and use 180º and 360º protractors to make comparative measures of different angles and relate amount of turn to degrees, eg 90º, 180º, 270º and 360º, eg labelling a protractor drawing with greater than and less than angles named and marked around the circle; use interactive sites such as the Banana Game Make creative patterns and designs using 2D shapes; explain the shape and angles in your design Year 5 - 15 of 21 Manunda Terrace Primary Year 5 - Measurement and Geometry Resources First Steps Measurement: Book 1: UU – Understand Units; DM – Direct Measure; Book 2: IM – Indirect Measure; E – Estimate; RL – Represent Location; RS – Represent Shape; RT – Represent Transformation; RG – Reason Geometrically http://www.brainpop.com/ (check administration for username and password) http://nrich.maths.org/public/ http://www.amathsdictionaryforkids.com/dictionary.html maths dictionary National Library of Virtual Manipulatives http://nlvm.usu.edu/ Collections: include any items that can be handled, from commercially made maths resources (eg counters, link blocks, geo shapes, small objects collections - mini people / teddy bears / fruit), to environmentally collected items (eg leaves, shells), to art items (eg popsticks, coloured papers, beads, pipe cleaners) Model: has been used to describe actions using manipulatives, games and strategies to show a process of understanding Problem Solving Strategies Guess and check Create an organized list Looking for a pattern (further information on problem solving) Key Mathematical Language (EAL/D) Using Units of Measurement conversion, convert, area, columns, rows, array, surface region, perimeter, square metres, square centimetres, square kilometres, hectares, length, width, breadth, cubic centimetre, volume, litre, millimetre, millilitres, metric, kilogram, grams, half a kilogram, quarter of a kilogram, second, analogue, digital, timetable, am, pm, Shape vertex/vertices, front, top, side views, depth, cross-section, apex, cuboid, regular shape, irregular shape, decagon, heptagon, pentominoes, right angle, perpendicular lines, parallel lines, intersecting lines, tetromino, tetrix Location and Transformation degree, clockwise, half turn, quarter turn, anticlockwise, tessellation, cross-section, route, North, South, East, West, boundary Geometric Reasoning right angle, perpendicular lines, parallel lines, acute, right, obtuse, straight, reflex angles Australian Curriculum NT School Year 5 - 16 of 21 Manunda Terrace Primary Mathematics Scope and Sequence Statistics and Probability Achievement Standards Proficiency Strands Understandings: By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets. Skills: Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely outcomes as probabilities between 0 and 1. Students pose questions to gather data, and construct data displays appropriate for the data. Achievement Standard Work Samples http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10 Understanding includes making connections between representations of numbers, using fractions to represent probabilities, comparing and ordering fractions and decimals and representing them in various ways, describing transformations and identifying line and rotational symmetry Fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the reasonableness of answers to calculations and using instruments to measure angles Problem Solving includes formulating and solving authentic problems using whole numbers and measurements, and creating financial plans Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data sets Year 5 – Statistics and Probability Chance AC Content Descriptor AC Elaborations So learning will include List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions Commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (rockpaper-scissors) Use in context, understand, calculate and explain that in chance experiments probability can be express as the number of successful trials (one action in an experiment) divided by the total number of the trials, eg 5 tails in 20 flips of the coin, 5 divided by 20 Use and devise games or models to investigate chance events where the likely hood of occurrences is known (theoretical probability) and compare, discuss and explain what happens in trials using fractional representations; record outcomes of the trials, and analyse data to make conjectures about winning strategies eg o Predict, play, discuss, record and analyse outcomes in ‘equal chance’ games, eg a spinner with two colours on each half has a 50 – 50 chance or ½ a chance of coming up; using one coin to toss heads or tails; the winner of a race between two children of equal ability o Devise and conduct repeated trials to investigate the relationships between numerical ‘randomness’ of criteria and the likelihood of chance event, eg, 6 has more chance of coming up when tossing a 6 sided dice (1 in 6 chance), than if you tossed a 20 sided dice (1 in 20 chance); on a ¾ blue and ¼ red spinner, blue is more likely to be spun because it covers ¾ of the spinner o Play and analyse outcomes of games such as Greedy pig or Heads and Tails as described in Year 4, and use this to make conjectures about probability of chance - expressed as fractions, and about winning strategies; explain reasoning Rank discrete events from most likely to least likely based on the numerical probability involved, eg drawing cards at random from a 52 pack of cards, an ace has a less likely chance at 1 in13 (1/13 of being picked than a red card, at an equal chance or ½ chance Says which events have more chance, equal chance or less chance by reading and understanding the context, eg knows that the more raffle tickets they buy in a raffle the more chance they have of winning or getting a prize and can relate this to the number of tickets sold says: I have one chance in 5 thousand of winning which is better than one chance in a million (For some events the exact probability can be determined by an analysis of the event itself, eg six sided dice toss – 1 in 6 chance. A probability determined in this manner is call a theoretical probability) First Steps Chance and Data: UC – KU4, KU5 Australian Curriculum NT School Year 5 - 17 of 21 Manunda Terrace Primary Chance AC Content Descriptor AC Elaborations Recognise that probabilities Investigating the range from 0 to 1 probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1 So learning will include Use models to investigate and understand that probability is expressed as a numerical value, where ‘impossibility’ indicates 0 and certainty indicates 1, eg on a 0 – 1 number line, eg given an event such as ‘there will be a crocodile story on the cover of NT News this month’, mark a point on the number line to indicate how likely the event will be Investigate and understand the numerical value of probability, 0 and 1, also relates to common fractions and percentage, eg a spinner with two colours one on each half has an even or 50 – 50 chance, or ½ a chance, or a 50% chance; a one coloured blue spinner has a zero chance of spinning red, so 0 – impossible or 0%; and an all red spinner will spin red, so is a ‘certain chance ’ or 1, or 100% Use common percentages to describe likelihood of real context investigation outcomes, eg 50%, 25%, 75%, 100% chance Utilises graphic organisers, eg tree diagrams, to identify possible outcomes Investigate, predicts and records possible outcomes of an event using the numerical value 0 to 1, a fractional value, and percentage, eg describe the likelihood of outcomes, eg 1 in 4 chance so ¼ or 25% chance First Steps Chance and Data: UC – KU4, KU5 Australian Curriculum NT School Year 5 - 18 of 21 Manunda Terrace Primary Data representation and interpretation AC Content Descriptor Year 5 – Statistics and Probability Pose questions and collect categorical or numerical data by observation or survey AC Elaborations So learning will include Posing questions about insect diversity in the playground, collecting data by taping a onemetre-square piece of paper to the playground and observing the type and number of insects on it over time Investigate, design (including using IT) and effectively choose and use data collection methods that best suit the context eg questionnaires, surveys, sampling techniques, tables, lists, observations, experiments, simulations Using given or chosen contexts, pose questions that will elicit numerical and categorical data about element/s of that context; design collection strategies; justify which are the most effective and efficient in eliciting and collecting data, eg o for life in the playground, collect categorical (types of insects) and numerical (number of insects in each type group) data on insect diversity in the playground using a sampling over time strategy o pose a question in response to a localised issue, such as information needed to take to School Council about playground facilities such as, ‘Does our school playground meet every child’s needs?’ observe and collect data on the density (numerical data), of children over time in various parts of the playground (categorical data) survey to find out age of children using specific spaces in the playground using snapshot over time approach, (categorical data) survey children by Year level (numerical and categorical data) to find out their preferred space (categorical data) Consider questions such as what variables need to be considered when designing data collection strategies and why? eg, time of data collection and possible impact on results Investigate posing ‘What is the likelihood of................?’ or ‘How many items could you draw out......? type questions and design simple experiments using the most effective data collection strategy to answer questions, eg o How many blue marbles are you likely to draw out of a container holding the same number of green and blue marbles in ten draws? Design a sampling technique that is based on long trial understandings and explain reasoning in choosing that data collection strategy Collect data to answer a question in their own context, eg what sort of litter do students at the school leave behind? What proportion of students in the school are from different cultural groups/ by first deciding what data they need and how they might collect it First Steps Chance and Data: CPDA – KU1, KU2 Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies Identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations Construct data displays, investigating the effect that the choice of display type (hand and technology generated) has on the ease of interpreting data, to answer a focus question; explain reasoning, represent collected data on a suitable graph (including using technology) and justify the choice of graph, eg o use a variety of data displays such as column and bar graphs and histographs o simple line graph (A graph that uses points connected by lines to show how something changes in value as time goes by or as something else happens, eg temperature over time in degrees) o dot plots (similar to a bar chart, with the bars replaced by a series of dots each one representing a fixed number of elements. For continuous data, the dot plot is similar to a histogram, with the rectangles replaced by dots. A dot plot can also help detect any unusual observations (outliers), or any gaps in the data set.), eg activities such as http://nzmaths.co.nz/resource/fridge-pickers http://nzmaths.co.nz/resource/winning-dots o diagrams and tables, eg Venn diagrams and Carroll diagrams (two way tables) Year 1’s Year 4’s Bike to school 3 14 Car to school 15 5 o Investigate situations and the data displays involving permutations, (ordered arrangements of a set of objects/symbols) and describe discoveries, eg How many different combinations can you make from 4 different flavoured ice creams and 3 different types on cones o Resource: Choosing appropriate graphical displays http://www.education.vic.gov.au/studentlearning/teachingresources/mat hs/mathscontinuum/mcd/M37508P.htm#a3 Understand and uses key features of data displays, eg labels, titles, and x and y axis and scales First Steps Chance and Data: CPDB – KU1, KU2, Ku3, KU4, KU5 Australian Curriculum NT School Year 5 - 19 of 21 Manunda Terrace Primary Data representation and interpretation AC Content Descriptor Year 5 – Statistics and Probability Describe and interpret different data sets in context AC Elaborations Using and comparing data representations for different data sets to help decision making So learning will include (Graphs and charts tell about information; and different types of representations tell different things about the same data) Investigate ways of analysing displays of data to generate inferences about the focus question, i.e. the reason for the data collection, focussing on the variability of the data, the centre of the data (clustering) and the ‘shape’ of the data, (how spread out or clustered the data is, using questions (☻) like, eg o What do the numbers tell us about...? o If we asked another ‘group’ how would our data look? What if we asked a larger group, how would it look then? o How do the numbers in this graph (about a group) compare to another groups’ graph? o Where is the data ‘clustering’? How much of the data is or is not in the cluster? o What kinds of variability might need to be considered in interpreting this data? o Would this data be different if ...? (change of sample, group or setting) o What does the graph not tell us? What might we infer? o What new questions could come out of this data? (J A Van De Walle, K S Karp, J M Bay-Williams; 2004, pg 453) Investigate ways of analysing and comparing data and displays; make statements and predictions about the information using data displays to support their arguments, eg o interpret sampling data to predict fairly accurately the height of a new child joining their class next week o sketch the shape of data in a graph (without using any specific data) by matching the sketch to a written or orally described situation; match a data display from a selection of different types, to match a written or orally described situation o read and use data shown in published tables to help make decisions, eg reads a menu or price list or compare tables in mobile phone plans to help make a choice of which one to buy o interpret expected or unexpected variations in data displays and reason as to the cause and the effect eg variation in data showing how many children line up at the canteen as soon as the lunch bell goes, or at later times during lunch; on Tuesday, 16 children from the class bought their lunch at the canteen Understand, identify and compare variability shown in and across data displays, and investigate the most effective data display to show the variability of data for a particular context, eg o Variability within and between groups (detailed in Year 4) o Sampling variability, eg collect data from a coin tossed 10 times that might show 5 heads and 5 tails, or many other combinations (variables) Understand and use different data sources to interpret and compare information, eg o real-life applications like graphs and tables found in newspapers or online o advertising information sheets Interpret data displays and make statements, predictions and conclusions from it including about the mode if appropriate, eg says paper is the most common rubbish that we leave behind, and concludes most of the trees in the school ground are eucalypts First Steps Chance and Data: ID – KU1, KU2, KU3 Australian Curriculum NT School Year 5 - 20 of 21 Manunda Terrace Primary Year 5 – Statistics and Probability Resources First Steps: UC – Understand Chance; CPDA – Collect and Process Data Part A; CPDB – Collect and Process Data Part B; ID - Interpret Data Spinners: Spinners can be easily designed using colours segments or number ranges, and have multiple uses in maths across all strands. They can be made from a spinner printout, a pen and a paperclip. They do not require assembly. ‘Talking Namba – Scaffolded foundational numeracy approach’ – has a short video clip at this link, showing how a spinner is made and used. http://ourcourses.ntschools.net/course/view.php?id=271 National Library of Virtual Manipulatives http://nlvm.usu.edu http://www.amathsdictionaryforkids.com/dictionary.html maths dictionary Collections: include any items that can be handled, from commercially made maths resources (eg counters, link blocks, geo shapes, small objects collections - mini people / teddy bears / fruit), to environmentally collected items (eg leaves, shells), to art items (eg popsticks, coloured papers, beads, pipe cleaners) Model: has been used to describe actions using manipulatives, games and strategies to show a process of understanding Problem Solving Strategies Guess and check Create an organized list Looking for a pattern (more information on problem solving) Key Mathematical Language (EAL/D) Chance most likely, least likely, experimental data, occurrence, prediction, investigations, judgements, possible, impossible, certain, fair, odds-on, favourite, perhaps, 50-50, outcomes, equally likely, chance, even chance, equal chance, combinations, frequency, table, random, never, possibility, analyse, predict, order, probability, tally, experiment, probable, event, trial. Data representation and interpretation tally, bar graph, column graph, axis, heading, labels (graph), table Australian Curriculum NT School Year 5 - 21 of 21 Manunda Terrace Primary