Stage Three



Year Six Maths Scope and Sequence- Term One Overview of Key IdeasOUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasIdentify and describe properties of prime, composite, square and triangular numbers (ACMNA122)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)OUTCOMESSUBSTRANDMA3-9MG LENGTHMA3-13MGTIMEMA3-14MG3D SPACEMA3-18SPDATAKey IdeasConnect decimal representations to the metric system (ACMMG135)Convert between common metric units of length (ACMMG136)Solve problems involving the comparison of lengths using appropriate units (ACMMG137)Interpret and use timetables (ACMMG139)Construct simple prisms and pyramids (ACMMG140)Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)Find a simple fraction of a quantity where the result is a whole number, with and without the use of digital technologies (ACMNA127)OUTCOMESSUBSTRANDMA3-10MG AREAMA3-15MG2D SPACEMA3-16MGANGLESMA3-17MG POSITIONKey IdeasSolve problems involving the comparison of areas using appropriate units (ACMMG137)Construct simple prisms and pyramids (ACMMG140)LINKED TO ANGLESInvestigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)LINKED TO 2D SPACEUse a grid-reference system to describe locations (ACMMG113)Describe routes using landmarks and directional language (ACMMG113)Year Six Maths Scope and Sequence - Term One Weeks 1-5 (Number)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONKey IdeasIdentify and describe properties of prime, composite, square and triangular numbers (ACMNA122)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Related Contentdetermine whether a number is prime, composite or neither explain whether a whole number is prime, composite or neither by finding the number of factors, eg '13 has two factors (1 and 13) and therefore is prime', '21 has more than two factors (1, 3, 7, 21) and therefore is composite', '1 is neither prime nor composite as it has only one factor, itself' (Communicating, Reasoning)explain why a prime number, when modelled as an array, can have only one row (Communicating, Reasoning)model square and triangular numbers and record each number group in numerical and diagrammatic form explain how square and triangular numbers are created (Communicating, Reasoning) explore square and triangular numbers using arrays, grid paper or digital technologies (Communicating, Problem Solving) recognise and explain the relationship between the way each pattern of numbers is created and the name of the number group (Communicating, Reasoning) solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) use the term 'operations' to describe collectively the processes of addition, subtraction, multiplication and divisioninvestigate and establish the order of operations using real-life contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 × 10 + 2 × 4 but, to obtain the total cost, multiplication must be performed before addition write number sentences to represent real-life situations (Communicating, Problem Solving) recognise that the grouping symbols and are used in number sentences to indicate operations that must be performed first OUTCOMESSUBSTRANDMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasCompare fractions with related denominators and locate and represent them on a number line (ACMNA125)Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)Related Contentmodel, compare and represent fractions with denominator of 2, 3, 4, 5, 6, 8, 10, 12 and 100 of a whole object, a whole shape and a collection of objectscompare the relative size of fractions drawn on the same diagram, eg (Reasoning) compare and order simple fractions with related denominators using strategies such as diagrams, the number line, or equivalent fractions, eg?write and in ascending orderfind equivalent fractions by re-dividing the whole, using diagrams and number lines, eg record equivalent fractions using diagrams and numeralscontinue and create number patterns, with and without the use of?digital technologies, using whole numbers, fractions and decimals, eg? or 1.25, 2.5, 5,?… describe how number patterns have been created and how they can be continued (Communicating, Problem Solving) create simple geometric patterns using concrete materials, eg complete a table of values for a geometric pattern and describe the pattern in words, eg describe the number pattern in a variety of ways and record descriptions using words, eg 'It looks like the multiplication facts for four'determine the rule to describe the pattern by relating the bottom number to the top number in a table, eg 'You multiply the number of squares by four to get the number of matches'use the rule to calculate the corresponding value for a larger number, eg 'How many matches are needed to create 100 squares?'Year Six Maths Scope and Sequence - Term One Weeks 1-5 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-9MG LENGTHMA3-13MGTIMEMA3-14MG3D SPACEMA3-18SPDATAKey IdeasConnect decimal representations to the metric system (ACMMG135)Convert between common metric units of length (ACMMG136)Solve problems involving the comparison of lengths using appropriate units (ACMMG137)Interpret and use timetables (ACMMG139)Construct simple prisms and pyramids (ACMMG140)Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)Related Contentrecognise the equivalence of whole-number and decimal representations of measurements of length, eg 165 cm is the same as 1.65 minterpret decimal notation for lengths and distances, eg 13.5 cm is 13 centimetres and 5 millimetresrecord lengths and distances using decimal notation to three decimal places, eg?2.753?kmconvert between metres and kilometresconvert between millimetres, centimetres and metres to compare lengths and distancesexplain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg?'More metres than kilometres will be needed to measure the same distance, and so to convert from kilometres to metres, I need to multiply' (Communicating, Reasoning) investigate and compare perimeters of rectangles with the same area determine the number of different rectangles that can be formed using whole-number dimensions for a given area (Problem Solving, Reasoning) solve a variety of problems involving length and perimeter, including problems involving different units of length, eg 'Find the total length of three items measuring 5 mm, 20 cm and 1.2 m' read, interpret and use timetables from real-life situations, including those involving 24-hour time use bus, train, ferry and airline timetables, including those accessed on the internet, to prepare simple travel itineraries interpret timetable information to solve unfamiliar problems using a variety of strategies (Problem Solving) create prisms and pyramids using a variety of materials, eg?plasticine, paper or cardboard nets, connecting cubesconstruct as many rectangular prisms as possible using a given number of connecting cubes (Problem Solving) construct three-dimensional models of prisms and pyramids and sketch the front, side and top viewsdescribe to another student how to construct or draw a three-dimensional object (Communicating) interpret data presented in two-way tables create a two-way table to organise data involving two categorical variables, eg Year Six Maths Scope and Sequence - Term One Weeks 6-10 (Number)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Related Contentrecognise the location of negative whole numbers in relation to zero and place them on a number lineuse the term 'integers' to describe positive and negative whole numbers and zero solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) OUTCOMESSUBSTRANDMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSKey IdeasExplore the use of brackets and the order of operations to write number sentences (ACMNA134)Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)Find a simple fraction of a quantity where the result is a whole number, with and without the use of digital technologies (ACMNA127)Related Contentrecognise that if more than one pair of grouping symbols are used, the operation within the innermost grouping symbols is performed firstperform calculations involving grouping symbols without the use of digital technologies, eg apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies, eg - addition and subtraction only, therefore work from left to right- multiplication and division only, therefore work from left to right- perform operation in grouping symbols first - perform operation in grouping symbols first- perform multiplication before addition investigate whether different digital technologies apply the order of operations (Reasoning) recognise when grouping symbols are not necessary, eg?32?+?(2?×?4) has the same answer as 32?+?2?×?4develop mental strategies for generating equivalent fractions, such as multiplying or dividing the numerator and the denominator by the same number,eg , ie explain or demonstrate why two fractions are or are not equivalent (Communicating, Reasoning) write fractions in their 'simplest form' by dividing the numerator and the denominator by a common factor, eg?recognise that a fraction in its simplest form represents the same value as the original fraction (Reasoning)apply knowledge of equivalent fractions to convert between units of time, eg?15?minutes is the same as ?of an hour, which is the same as ?of an hour (Problem Solving)calculate unit fractions of collections, with and without the use of digital technologies, eg calculate of 30 describe the connection between finding a unit fraction of a collection and the operation of division (Communicating, Problem Solving) calculate a simple fraction of a collection/quantity, with and without the use of digital technologies, eg?calculate of 30 explain how unit fractions can be used in the calculation of simple fractions of collections/quantities, eg 'To calculate of a quantity, I found of the collection first and then multiplied by 3' (Communicating, Reasoning) solve word problems involving a fraction of a collection/quantity Year Six Maths Scope and Sequence - Term One Weeks 6-10 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-10MG AREAMA3-15MG2D SPACEMA3-16MGANGLESMA3-17MG POSITIONKey IdeasSolve problems involving the comparison of areas using appropriate units (ACMMG137)Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)Use a grid-reference system to describe locations (ACMMG113)Describe routes using landmarks and directional language (ACMMG113)Related Contentinvestigate the area of a triangle by comparing the area of a given triangle to the area of the rectangle of the same length and perpendicular height, eg use a copy of the given triangle with the given triangle to form a rectangleexplain the relationship between the area of a triangle and the area of the rectangle of the same length and perpendicular height (Communicating, Reasoning) establish the relationship between the base length, perpendicular height and area of a triangle record, using words, the method for finding the area of any triangle, eg?'Area of triangle = × base × perpendicular height' investigate and compare the areas of rectangles that have the same perimeter, eg?compare the areas of all possible rectangles with whole-number dimensions and a perimeter of 20 centimetres determine the number of different rectangles that can be formed using whole-number dimensions for a given perimeter (Problem Solving, Reasoning) solve a variety of problems involving the areas of rectangles (including squares) and triangles identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90° once and then reflected once'construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software predict the next translation, reflection or rotation in a pattern, eg 'The arrow is being rotated 90° anti-clockwise each time'choose the correct pattern from a number of options when given information about a combination of transformations (Reasoning) identify and name angle types formed by the intersection of straight lines, including right angles, 'angles on a straight line', 'angles at a point' that form an angle of revolution, and 'vertically opposite angles' recognise right angles, angles on a straight line, and angles of revolution embedded in diagrams (Reasoning)identify the vertex and arms of angles formed by intersecting lines (Communicating)recognise vertically opposite angles in different orientations and embedded in diagrams (Reasoning)find locations on maps, including maps with legends, given their grid references describe particular locations on grid-referenced maps, including maps with a legend, eg?'The post office is at E4'find a location on a map that is in a given direction from a town or landmark, eg?locate a town that is north-east of Broken Hill describe the direction of one location relative to another, eg?'Darwin is north-west of Sydney' follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map use a given map to plan and show a route from one location to another, eg?draw a possible route to the local park or use an Aboriginal land map to plan a route use a street directory or online map to find the route to a given location (Problem Solving) describe a route taken on a map using landmarks and directional language, including compass directions, eg?'Start at the post office, go west to the supermarket and then go south-west to the park' Year Six Maths Scope and Sequence- Term Two Overview of Key IdeasOUTCOMESSUBSTRANDMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasSelect and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)OUTCOMESSUBSTRANDMA3-11MGVOLUME AND CAPACITYMA3-13MGTIMEMA3-14MG3D SPACEMA3-15MG2D SPACEKey IdeasConnect volume and capacity and their units of measurement (ACMMG138)Convert between common metric units of capacity (ACMMG136)Calculate the volumes of rectangular prisms (ACMMG160)Draw and interpret timelines using a given scaleConstruct simple prisms and pyramids (ACMMG140)Identify and name parts of circlesOUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)OUTCOMESSUBSTRANDMA3-18SPDATAMA3-19SPCHANCEMA3-12MGMASSMA3-14MG3D SPACEMA3-15MG2D SPACEKey IdeasInterpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)Compare observed frequencies across experiments with expected frequencies (ACMSP146)Connect decimal representations to the metric system (ACMMG135)Convert between common metric units of mass (ACMMG136)Investigate the diagonals of two-dimensional shapes Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)Year Six Maths Scope and Sequence - Term Two Weeks 1-5 (Number)OUTCOMESSUBSTRANDMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONKey IdeasSelect and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)Related Contentsolve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbersselect and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainderestimate solutions to problems and check to justify solutions (Problem Solving, Reasoning) use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiplesOUTCOMESSUBSTRANDMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasSolve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)Related Contentadd and subtract fractions, including mixed numerals, where one denominator is the same as, or a multiple of, the other, eg , , convert an answer that is an improper fraction to a mixed numeral (Communicating)use knowledge of equivalence to simplify answers when adding and subtracting fractions (Communicating, Reasoning)recognise that improper fractions may sometimes make calculations involving mixed numerals easier (Communicating)solve word problems involving the addition and subtraction of fractions where one denominator is the same as, or a multiple of, the other, eg?'I ate ?of a cake and my friend ate ?of the cake. What fraction of the cake remains?' multiply simple fractions by whole numbers using repeated addition, leading to a rule,eg? leading to Image not found complete a table of values for number patterns involving one operation (including patterns that decrease) and describe the pattern in words, eg describe the pattern in a variety of ways and record descriptions in words, eg 'It goes up by ones, starting from four'determine a rule to describe the pattern from the table, eg 'To get the value of the term, you add three to the position in the pattern'use the rule to calculate the value of the term for a large position number, eg 'What is the 55th term of the pattern?'explain why it is useful to describe the rule for a pattern by describing the connection between the 'position in the pattern' and the 'value of the term' (Communicating, Reasoning) interpret explanations written by peers and teachers that accurately describe geometric and number patterns (Communicating) make generalisations about numbers and number relationships, eg?'If you add a number and then subtract the same number, the result is the number you started with' Year Six Maths Scope and Sequence - Term Two Weeks 1-5 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-11MGVOLUME AND CAPACITYMA3-13MGTIMEMA3-14MG3D SPACEMA3-15MG2D SPACEOUTCOMESSUBSTRANDMA3-11MGVOLUME AND CAPACITYMA3-13MGTIMEMA3-14MG3D SPACEMA3-15MG2D SPACEKey IdeasConnect volume and capacity and their units of measurement (ACMMG138)Convert between common metric units of capacity (ACMMG136)Calculate the volumes of rectangular prisms (ACMMG160)Draw and interpret timelines using a given scaleConstruct simple prisms and pyramids (ACMMG140)Identify and name parts of circlesRelated Contentselect the appropriate unit to measure volume and capacitydemonstrate that a cube of side 10 cm will displace 1 litre of water demonstrate, by using a medicine cup, that a cube of side 1 cm will displace 1 mL of waterequate 1?cubic centimetre to 1?millilitre and 1000?cubic centimetres to 1?litreconvert between millilitres and litresexplain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg?'Fewer litres than millilitres will be needed to measure the same capacity, and so to convert from millilitres to litres, I need to divide' (Communicating, Reasoning) describe the 'length', 'width' and 'height' of a rectangular prism as the 'dimensions' of the prism construct rectangular prisms using cubic-centimetre blocks and count the blocks to determine the volumes of the prismsconstruct different rectangular prisms that have the same volume (Problem Solving) explain that objects with the same volume may be different shapes (Communicating, Reasoning) describe rectangular prisms in terms of layers, eg?'There are 3 layers of 8 cubic-centimetre blocks' (Communicating)use repeated addition to find the volumes of rectangular prisms, eg 'My rectangle has 3 layers of 6 cubes, so the total number of cubes is 6 plus 6 plus 6, or 18'establish the relationship between the number of cubes in one layer, the number of layers, and the volume of a rectangular prism explain that the volume of a rectangular prism can be found by finding the number of cubes in one layer and multiplying by the number of layers (Communicating, Reasoning) determine a suitable scale and draw an accurate timeline using the scale, eg represent events using a many-to-one scale of 1?cm?=?10?yearsinterpret a given timeline using the given scale create prisms and pyramids using a variety of materials, eg?plasticine, paper or cardboard nets, connecting cubesconstruct as many rectangular prisms as possible using a given number of connecting cubes (Problem Solving) create skeletal models of prisms and pyramids, eg?using toothpicks and modelling clay or straws and tape connect the edges of prisms and pyramids with the construction of their skeletal models (Problem Solving)create a circle by finding points that are all the same distance from a fixed point (the centre)identify and name parts of a circle, including the centre, radius, diameter, circumference, sector, semicircle and quadrant Year Six Maths Scope and Sequence - Term Two Weeks 6-10 (Number)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)Add and subtract decimals, with and without the use of digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)Related Contentinterpret integers in everyday contexts, eg temperatureinvestigate negative whole numbers and the number patterns created when counting backwards on a calculatorrecognise that negative whole numbers can result from subtraction (Reasoning)ask 'What if' questions, eg 'What happens if we subtract a larger number from a smaller number on a calculator?' (Communicating) solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) solve word problems involving multiplication and division, eg?'A recipe requires 3 cups of flour for 10 people. How many cups of flour are required for 40 people?' use appropriate language to compare quantities, eg 'twice as much as', 'half as much as' (Communicating) use a table or similar organiser to record methods used to solve problems (Communicating, Problem Solving) recognise symbols used to record speed in kilometres per hour, eg 80 km/h solve simple problems involving speed, eg 'How long would it take to travel 600 km if the average speed for the trip is 75 km/h?' add and subtract decimals with the same number of decimal places, with and without the use of?digital technologies add and subtract decimals with a different number of decimal places, with and without the use of?digital technologies relate decimals to fractions to aid mental strategies (Communicating)round a number of up to three decimal places to the nearest whole numberuse estimation and rounding to check the reasonableness of answers when adding and subtracting decimals describe situations where the estimation of calculations with decimals may be useful, eg?to check the total cost of multiple items when shopping (Communicating, Problem Solving)solve word problems involving the addition and subtraction of decimals, with and without the use of?digital technologies, including those involving money use selected words to describe each step of the solution process (Communicating, Problem Solving) interpret a calculator display in the context of the problem, eg 2.6 means $2.60 (Communicating)Year Six Maths Scope and Sequence - Term Two Weeks 6-10 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-18SPDATAMA3-19SPCHANCEMA3-12MGMASSOUTCOMESSUBSTRANDMA3-18SPDATAMA3-19SPCHANCEMA3-12MGMASSKey IdeasInterpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)Compare observed frequencies across experiments with expected frequencies (ACMSP146)Connect decimal representations to the metric system (ACMMG135)Convert between common metric units of mass (ACMMG136)Related Contentinterpret side-by-side column graphs for two categorical variables, eg?favourite television show of students in Year?1 compared to that of students in Year?6 interpret and compare different displays of the same data set to determine the most appropriate display for the data setcompare the effectiveness of different student-created data displays (Communicating)discuss the advantages and disadvantages of different representations of the same data (Communicating) explain which display is the most appropriate for interpretation of a particular data set (Communicating, Reasoning) compare representations of the same data set in a side-by-side column graph and in a two-way table (Reasoning) use the term 'frequency' to describe the number of times a particular outcome occurs in a chance experiment distinguish between the 'frequency' of an outcome and the 'probability' of an outcome in a chance experiment (Communicating) compare the expected frequencies of outcomes of chance experiments with observed frequencies, including where the outcomes are not equally likelyrecognise that some random generators have outcomes that are not equally likely and discuss the effect on expected outcomes, eg on this spinner, green is more likely to occur than red or grey or blue (Reasoning)discuss the 'fairness' of simple games involving chance (Communicating, Reasoning) explain why observed frequencies of outcomes in chance experiments may differ from expected frequencies (Communicating, Reasoning) recognise the equivalence of whole-number and decimal representations of measurements of mass, eg 3 kg 250 g is the same as 3.25 kginterpret decimal notation for masses, eg?2.08 kg is the same as 2 kilograms and 80 gramsmeasure mass using scales and record using decimal notation of up to three decimal places, eg 0.875 kgconvert between kilograms and grams and between kilograms and tonnesexplain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg?'More grams than kilograms will be needed to measure the same mass, and so to convert from kilograms to grams, I need to multiply' (Communicating, Reasoning) solve problems involving different units of mass, eg find the total mass of three items weighing 50 g, 750 g and 2.5 kg relate the mass of one litre of water to one kilogramOUTCOMESSUBSTRANDMA3-14MG3D SPACEMA3-15MG2D SPACEKey IdeasConstruct simple prisms and pyramids (ACMMG140)Investigate the diagonals of two-dimensional shapesRelated Contentcreate prisms and pyramids using a variety of materials, eg?plasticine, paper or cardboard nets, connecting cubesconstruct as many rectangular prisms as possible using a given number of connecting cubes (Problem Solving) construct three-dimensional models of prisms and pyramids, given drawings of different viewsidentify and name 'diagonals' of convex two-dimensional shapes recognise the endpoints of the diagonals of a shape as the vertices of the shape (Communicating) determine and draw all the diagonals of convex two-dimensional shapescompare and describe diagonals of different convex two-dimensional shapes use measurement to determine which of the special quadrilaterals have diagonals that are equal in length (Problem Solving)determine whether any of the diagonals of a particular shape are also lines (axes) of symmetry of the shape (Problem Solving)Year Six Maths Scope and Sequence- Term Three Overview of Key IdeasOUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasIdentify and describe properties of prime, composite, square and triangular numbers (ACMNA122)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)Multiply and divide decimals by powers of 10 (ACMNA130)Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)OUTCOMESSUBSTRANDMA3-19SPCHANCEMA3-9MG LENGTHMA3-13MGTIMEMA3-15MG2D SPACEMA3-16MGANGLESKey IdeasConduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)Connect decimal representations to the metric system (ACMMG135)Convert between common metric units of length (ACMMG136)Solve problems involving the comparison of lengths using appropriate units (ACMMG137)Interpret and use timetables (ACMMG139)Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)LINKED TO ANGLESInvestigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)LINKED TO 2D SPACEOUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)OUTCOMESSUBSTRANDMA3-10MG AREAMA3-15MG2D SPACEMA3-17MG POSITIONKey IdeasSolve problems involving the comparison of areas using appropriate units (ACMMG137)Identify and name parts of circlesUse a grid-reference system to describe locations (ACMMG113)Describe routes using landmarks and directional language (ACMMG113)Year Six Maths Scope and Sequence - Term Three Weeks 1-5 (Number)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONKey IdeasIdentify and describe properties of prime, composite, square and triangular numbers (ACMNA122)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Related Contentdetermine whether a number is prime, composite or neither explain whether a whole number is prime, composite or neither by finding the number of factors, eg '13 has two factors (1 and 13) and therefore is prime', '21 has more than two factors (1, 3, 7, 21) and therefore is composite', '1 is neither prime nor composite as it has only one factor, itself' (Communicating, Reasoning)explain why a prime number, when modelled as an array, can have only one row (Communicating, Reasoning)model square and triangular numbers and record each number group in numerical and diagrammatic form explain how square and triangular numbers are created (Communicating, Reasoning) explore square and triangular numbers using arrays, grid paper or digital technologies (Communicating, Problem Solving) recognise and explain the relationship between the way each pattern of numbers is created and the name of the number group (Communicating, Reasoning) solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) use the term 'operations' to describe collectively the processes of addition, subtraction, multiplication and divisioninvestigate and establish the order of operations using real-life contexts, eg 'I buy six goldfish costing $10 each and two water plants costing $4 each. What is the total cost?'; this can be represented by the number sentence 6 × 10 + 2 × 4 but, to obtain the total cost, multiplication must be performed before addition write number sentences to represent real-life situations (Communicating, Problem Solving) recognise that the grouping symbols and are used in number sentences to indicate operations that must be performed first OUTCOMESSUBSTRANDMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasMultiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)Multiply and divide decimals by powers of 10 (ACMNA130)Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)Related Contentuse mental strategies to multiply simple decimals by single-digit numbers, eg 3.5 × 2multiply decimals of up to three decimal places by whole numbers of up to two digits, with and without the use of digital technologies, eg 'I measured three desks. Each desk was 1.25 m in length, so the total length is 3 × 1.25 = 3.75 m' recognise the number patterns formed when decimals are multiplied and divided by 10,?100?and 1000 multiply and divide decimals by 10, 100 and 1000use a calculator to explore the effect of multiplying and dividing decimals by multiples of 10 (Reasoning)recognise that the number plane (Cartesian plane) is a visual way of describing location on a gridrecognise that the number plane consists of a horizontal axis (x-axis) and a vertical axis (y-axis), creating four quadrants recognise that the horizontal axis and the vertical axis meet at right angles (Reasoning)identify the point of intersection of the two axes as the origin, having coordinates (0,?0) Year Six Maths Scope and Sequence - Term Three Weeks 1-5 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-19SPCHANCEMA3-9MG LENGTHKey IdeasConduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)Connect decimal representations to the metric system (ACMMG135)Convert between common metric units of length (ACMMG136)Solve problems involving the comparison of lengths using appropriate units (ACMMG137)Related Contentassign expected probabilities to outcomes in chance experiments with random generators, including digital simulators, and compare the expected probabilities with the observed probabilities after both small and large numbers of trials determine and discuss the differences between the expected probabilities and the observed probabilities after both small and large numbers of trials (Communicating, Reasoning) explain what happens to the observed probabilities as the number of trials increases (Communicating, Reasoning) use samples to make predictions about a larger 'population' from which the sample comes, eg?take a random sample of coloured lollies from a bag, calculate the probability of obtaining each colour of lolly when drawing a lolly from the bag, and use these probabilities and the total number of lollies in the bag to predict the number of each colour of lolly in the bag discuss whether a prediction about a larger population, from which a sample comes, would be the same if a different sample were used (Communicating, Reasoning) recognise the equivalence of whole-number and decimal representations of measurements of length, eg 165 cm is the same as 1.65 minterpret decimal notation for lengths and distances, eg 13.5 cm is 13 centimetres and 5 millimetresrecord lengths and distances using decimal notation to three decimal places, eg?2.753?kmconvert between metres and kilometresconvert between millimetres, centimetres and metres to compare lengths and distancesexplain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg?'More metres than kilometres will be needed to measure the same distance, and so to convert from kilometres to metres, I need to multiply' (Communicating, Reasoning) investigate and compare perimeters of rectangles with the same area determine the number of different rectangles that can be formed using whole-number dimensions for a given area (Problem Solving, Reasoning) solve a variety of problems involving length and perimeter, including problems involving different units of length, eg 'Find the total length of three items measuring 5 mm, 20 cm and 1.2 m' OUTCOMESSUBSTRANDMA3-13MG TIMEMA3-15MG2D SPACEMA3-16MGANGLESKey IdeasInterpret and use timetables (ACMMG139)Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)Investigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)Related Contentread, interpret and use timetables from real-life situations, including those involving 24-hour time use bus, train, ferry and airline timetables, including those accessed on the internet, to prepare simple travel itineraries interpret timetable information to solve unfamiliar problems using a variety of strategies (Problem Solving) identify whether a two-dimensional shape has been translated, reflected or rotated, or has undergone a number of transformations, eg 'The parallelogram has been rotated clockwise through 90° once and then reflected once'construct patterns of two-dimensional shapes that involve translations, reflections and rotations using computer software predict the next translation, reflection or rotation in a pattern, eg 'The arrow is being rotated 90° anti-clockwise each time'choose the correct pattern from a number of options when given information about a combination of transformations (Reasoning) investigate, with and without the use of digital technologies, adjacent angles that form a right angle and establish that they add to 90°investigate, with and without the use of digital technologies, adjacent angles on a straight line and establish that they form a straight angle and add to 180°investigate, with and without the use of digital technologies, angles at a point and establish that they form an angle of revolution and add to 360°use the results established for adjacent angles that form right angles, straight angles and angles of revolution to find the size of unknown angles in diagrams explain how the size of an unknown angle in a diagram was calculated (Communicating, Reasoning) Year Six Maths Scope and Sequence - Term Three Weeks 6-10 (Number)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Related Contentrecognise the location of negative whole numbers in relation to zero and place them on a number lineuse the term 'integers' to describe positive and negative whole numbers and zero solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) recognise that if more than one pair of grouping symbols are used, the operation within the innermost grouping symbols is performed firstperform calculations involving grouping symbols without the use of digital technologies, eg apply the order of operations to perform calculations involving mixed operations and grouping symbols, without the use of digital technologies, eg - addition and subtraction only, therefore work from left to right- multiplication and division only, therefore work from left to right- perform operation in grouping symbols first - perform operation in grouping symbols first- perform multiplication before addition investigate whether different digital technologies apply the order of operations (Reasoning) recognise when grouping symbols are not necessary, eg?32?+?(2?×?4) has the same answer as 32?+?2?×?4OUTCOMESSUBSTRANDMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasMultiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without the use of digital technologies (ACMNA129)Make connections between equivalent fractions, decimals and percentages (ACMNA131)Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)Related Contentdivide decimals by a one-digit whole number where the result is a terminating decimal, eg 5.25 ÷ 5 = 1.05solve word problems involving the multiplication and division of decimals, including those involving money, eg determine the 'best buy' for different-sized cartons of cans of soft drink represent simple fractions as decimals and as percentagesinterpret and explain the use of fractions, decimals and percentages in everyday contexts, eg??hour = 45 minutes, percentage of trees in the local area that are native to Australia (Communicating, Reasoning) represent decimals as fractions and percentages, eg?plot and label points, given coordinates, in all four quadrants of the number plane plot a sequence of coordinates to create a picture (Communicating) identify and record the coordinates of given points in all four quadrants of the number planerecognise that the order of coordinates is important when locating points on the number plane, eg (2,?3) is a location different from (3,?2) (Communicating)Year Six Maths Scope and Sequence - Term Three Weeks 6-10 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-10MGAREAMA3-15MG2D SPACEMA3-17MG POSITIONKey IdeasSolve problems involving the comparison of areas using appropriate units (ACMMG137)Identify and name parts of circlesUse a grid-reference system to describe locations (ACMMG113)Describe routes using landmarks and directional language (ACMMG113)Related Contentinvestigate the area of a triangle by comparing the area of a given triangle to the area of the rectangle of the same length and perpendicular height, eg use a copy of the given triangle with the given triangle to form a rectangleexplain the relationship between the area of a triangle and the area of the rectangle of the same length and perpendicular height (Communicating, Reasoning) establish the relationship between the base length, perpendicular height and area of a triangle record, using words, the method for finding the area of any triangle, eg?'Area of triangle = × base × perpendicular height' investigate and compare the areas of rectangles that have the same perimeter, eg?compare the areas of all possible rectangles with whole-number dimensions and a perimeter of 20 centimetres determine the number of different rectangles that can be formed using whole-number dimensions for a given perimeter (Problem Solving, Reasoning) solve a variety of problems involving the areas of rectangles (including squares) and triangles create a circle by finding points that are all the same distance from a fixed point (the centre)identify and name parts of a circle, including the centre, radius, diameter, circumference, sector, semicircle and quadrant find locations on maps, including maps with legends, given their grid references describe particular locations on grid-referenced maps, including maps with a legend, eg?'The post office is at E4'find a location on a map that is in a given direction from a town or landmark, eg?locate a town that is north-east of Broken Hill describe the direction of one location relative to another, eg?'Darwin is north-west of Sydney' follow a sequence of two or more directions, including compass directions, to find and identify a particular location on a map use a given map to plan and show a route from one location to another, eg?draw a possible route to the local park or use an Aboriginal land map to plan a route use a street directory or online map to find the route to a given location (Problem Solving) describe a route taken on a map using landmarks and directional language, including compass directions, eg?'Start at the post office, go west to the supermarket and then go south-west to the park' Year Six Maths Scope and Sequence- Term Four Overview of Key IdeasOUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Make connections between equivalent fractions, decimals and percentages (ACMNA131)OUTCOMESSUBSTRANDMA3-18SPDATAMA3-19SPCHANCEMA3-11MGVOLUME AND CAPACITYMA3-13MGTIMEMA3-15MG2D SPACEMA3-16MGANGLESKey IdeasInterpret secondary data presented in digital media and elsewhere (ACMSP148)LINKED TO CHANCEDescribe probabilities using fractions, decimals and percentages (ACMSP144)LINKED TO DATAConnect volume and capacity and their units of measurement (ACMMG138)Connect decimal representations to the metric system (ACMMG135)Calculate the volumes of rectangular prisms (ACMMG160)Draw and interpret timelines using a given scaleInvestigate the diagonals of two-dimensional shapesLINKED TO ANGLESInvestigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)LINKED TO 2D SPACEOUTCOMESSUBSTRANDMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasSelect and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Explore the use of brackets and the order of operations to write number sentences (ACMNA134)Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without the use of?digital technologies (ACMNA132)Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)OUTCOMESSUBSTRANDMA3-12MG MASSMA3-14MG3D SPACEKey IdeasConnect decimal representations to the metric system (ACMMG135)Convert between common metric units of mass (ACMMG136)Construct simple prisms and pyramids (ACMMG140)Year Six Maths Scope and Sequence - Term Four Weeks 1-5 (Number)OUTCOMESSUBSTRANDMA3-4NAWHOLE NUMBERMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONMA3-7NAFRACTIONS AND DECIMALSKey IdeasInvestigate everyday situations that use integers; locate and represent these numbers on a number line (ACMNA124)Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)Make connections between equivalent fractions, decimals and percentages (ACMNA131)Related Contentinterpret integers in everyday contexts, eg temperatureinvestigate negative whole numbers and the number patterns created when counting backwards on a calculatorrecognise that negative whole numbers can result from subtraction (Reasoning)ask 'What if' questions, eg 'What happens if we subtract a larger number from a smaller number on a calculator?' (Communicating) solve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) select and use efficient mental and written strategies, and digital technologies, to multiply whole numbers of up to four digits by one- and two-digit numbersselect and use efficient mental and written strategies, and digital technologies, to divide whole numbers of up to four digits by a one-digit divisor, including where there is a remainderestimate solutions to problems and check to justify solutions (Problem Solving, Reasoning) use mental strategies to multiply and divide numbers by 10, 100, 1000 and their multiplesrecognise that the symbol % means 'percent' represent common percentages as fractions and decimals, eg '25% means 25 out of 100 or or 0.25'recognise fractions, decimals and percentages as different representations of the same value (Communicating)recall commonly used equivalent percentages, decimals and fractions, eg 75%, 0.75, (Communicating)Year Six Maths Scope and Sequence - Term Four Weeks 1-5 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-18SPDATAMA3-19SPCHANCEMA3-11MG VOLUME AND CAPACITYKey IdeasInterpret secondary data presented in digital media and elsewhere (ACMSP148)Describe probabilities using fractions, decimals and percentages (ACMSP144)Connect volume and capacity and their units of measurement (ACMMG138)Connect decimal representations to the metric system (ACMMG135)Calculate the volumes of rectangular prisms (ACMMG160)Related Contentinterpret data representations found in digital media and in factual texts interpret tables and graphs from the media and online sources, eg?data about different sports teams (Reasoning) identify and describe conclusions that can be drawn from a particular representation of data (Communicating, Reasoning) critically evaluate data representations found in digital media and related claims discuss the messages that those who created a particular data representation might have wanted to convey (Communicating) identify sources of possible bias in representations of data in the media by discussing various influences on data collection and representation, eg?who created or paid for the data collection, whether the representation is part of an advertisement (Communicating, Reasoning) identify misleading representations of data in the media, eg broken axes, graphics that are not drawn to scale (Reasoning) list the outcomes for chance experiments where the outcomes are not equally likely to occur and assign probabilities to the outcomes using fractionsuse knowledge of equivalent fractions, decimals and percentages to assign probabilities to the likelihood of outcomes, eg?there is a 'five in ten', , 50%, 0.5 or 'one in two' chance of a particular event occurringuse probabilities in real-life contexts, eg?'My football team has a 50% chance of winning the game' (Communicating, Reasoning)design a spinner or label a die so that a particular outcome is more likely than another and discuss the probabilities of the outcomes (Communicating, Problem Solving) find the volumes of irregular solids in cubic centimetres using a displacement strategyrecognise the equivalence of whole-number and decimal representations of measurements of capacities, eg?375 mL is the same as 0.375 Linterpret decimal notation for volumes and capacities, eg?8.7 L is the same as 8 litres and 700 millilitresrecord volume and capacity using decimal notation to three decimal places, eg 1.275 Lrecord, using words, the method for finding the volumes of rectangular prisms, eg'Volume of rectangular prism = number of cubes in one layer × number of layers' calculate the volumes of rectangular prisms in cubic centimetres and cubic metresrecognise that rectangular prisms with the same volume may have different dimensions (Reasoning) record calculations used to find the volumes of rectangular prismsOUTCOMESSUBSTRANDMA3-13MGTIMEMA3-15MG2D SPACEMA3-16MGANGLESKey IdeasDraw and interpret timelines using a given scaleInvestigate the diagonals of two-dimensional shapesInvestigate, with and without the use of digital technologies, angles on a straight line, angles at a point, and vertically opposite angles; use the results to find unknown angles (ACMMG141)Related Contentdetermine a suitable scale and draw an accurate timeline using the scale, eg represent events using a many-to-one scale of 1?cm?=?10?yearsinterpret a given timeline using the given scale identify and name 'diagonals' of convex two-dimensional shapes recognise the endpoints of the diagonals of a shape as the vertices of the shape (Communicating) determine and draw all the diagonals of convex two-dimensional shapescompare and describe diagonals of different convex two-dimensional shapes use measurement to determine which of the special quadrilaterals have diagonals that are equal in length (Problem Solving)determine whether any of the diagonals of a particular shape are also lines (axes) of symmetry of the shape (Problem Solving)investigate, with and without the use of digital technologies, vertically opposite angles and establish that they are equal in sizeuse the equality of vertically opposite angles to find the size of unknown angles in diagramsYear Six Maths Scope and Sequence - Term Four Weeks 6-10 (Number)OUTCOMESSUBSTRANDMA3-5NAADDITION AND SUBTRACTIONMA3-6NAMULTIPLICATION AND DIVISIONKey IdeasSelect and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving addition and subtraction with whole numbers (ACMNA123)Select and apply efficient mental and written strategies, and appropriate digital technologies, to solve problems involving multiplication and division with whole numbers (ACMNA123)Related Contentsolve addition and subtraction word problems involving whole numbers of any size, including problems that require more than one operation, eg 'I have saved $40 000 to buy a new car. The basic model costs $36 118 and I add tinted windows for $860 and Bluetooth connectivity for $1376. How much money will I have left over?' select and apply appropriate mental and written strategies, with and without the use of digital technologies, to solve unfamiliar problems (Problem Solving) explain how an answer was obtained for an addition or subtraction problem and justify the selected calculation method (Communicating, Problem Solving, Reasoning) reflect on their chosen method of solution for a problem, considering whether it can be improved (Communicating, Reasoning) give reasons why a calculator was useful when solving a problem (Communicating, Reasoning)record the strategy used to solve addition and subtraction word problems use selected words to describe each step of the solution process (Communicating, Problem Solving) solve word problems involving multiplication and division, eg?'A recipe requires 3 cups of flour for 10 people. How many cups of flour are required for 40 people?' use appropriate language to compare quantities, eg 'twice as much as', 'half as much as' (Communicating) use a table or similar organiser to record methods used to solve problems (Communicating, Problem Solving) recognise symbols used to record speed in kilometres per hour, eg 80 km/h solve simple problems involving speed, eg 'How long would it take to travel 600 km if the average speed for the trip is 75 km/h?' OUTCOMESSUBSTRANDMA3-7NAFRACTIONS AND DECIMALSMA2-8NAPATTERNS AND ALGEBRAKey IdeasInvestigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without the use of?digital technologies (ACMNA132)Continue and create sequences involving whole numbers, fractions and decimals; describe the rule used to create the sequence (ACMNA133)Related Contentequate 10% to , 25% to and 50% to calculate common percentages (10%, 25%, 50%) of quantities, with and without the use of?digital technologies choose the most appropriate equivalent form of a percentage to aid calculation, eg (Problem Solving) use mental strategies to estimate discounts of 10%, 25% and 50%, eg?'50% off the price of $122.70: 50% is the same as , so the discount is about $60' calculate the sale price of an item after a discount of 10%, 25% and 50%, with and without the use of?digital technologies, recording the strategy and result continue and create number patterns, with and without the use of?digital technologies, using whole numbers, fractions and decimals, eg? or 1.25, 2.5, 5,?… describe how number patterns have been created and how they can be continued (Communicating, Problem Solving) create simple geometric patterns using concrete materials, eg complete a table of values for a geometric pattern and describe the pattern in words, eg describe the number pattern in a variety of ways and record descriptions using words, eg 'It looks like the multiplication facts for four'determine the rule to describe the pattern by relating the bottom number to the top number in a table, eg 'You multiply the number of squares by four to get the number of matches'use the rule to calculate the corresponding value for a larger number, eg 'How many matches are needed to create 100 squares?'complete a table of values for number patterns involving one operation (including patterns that decrease) and describe the pattern in words, eg describe the pattern in a variety of ways and record descriptions in words, eg 'It goes up by ones, starting from four'determine a rule to describe the pattern from the table, eg 'To get the value of the term, you add three to the position in the pattern'use the rule to calculate the value of the term for a large position number, eg 'What is the 55th term of the pattern?'explain why it is useful to describe the rule for a pattern by describing the connection between the 'position in the pattern' and the 'value of the term' (Communicating, Reasoning) interpret explanations written by peers and teachers that accurately describe geometric and number patterns (Communicating) make generalisations about numbers and number relationships, eg?'If you add a number and then subtract the same number, the result is the number you started with' Year Six Maths Scope and Sequence - Term Four Weeks 1-5 (Measurement/ Data and Statistics)OUTCOMESSUBSTRANDMA3-12MG MASSMA3-14MG3D SPACEKey IdeasConnect decimal representations to the metric system (ACMMG135)Convert between common metric units of mass (ACMMG136)Construct simple prisms and pyramids (ACMMG140)Related Contentrecognise the equivalence of whole-number and decimal representations of measurements of mass, eg 3 kg 250 g is the same as 3.25 kginterpret decimal notation for masses, eg?2.08 kg is the same as 2 kilograms and 80 gramsmeasure mass using scales and record using decimal notation of up to three decimal places, eg 0.875 kgconvert between kilograms and grams and between kilograms and tonnesexplain and use the relationship between the size of a unit and the number of units needed to assist in determining whether multiplication or division is required when converting between units, eg?'More grams than kilograms will be needed to measure the same mass, and so to convert from kilograms to grams, I need to multiply' (Communicating, Reasoning) solve problems involving different units of mass, eg find the total mass of three items weighing 50 g, 750 g and 2.5 kg relate the mass of one litre of water to one kilogramcreate prisms and pyramids using a variety of materials, eg?plasticine, paper or cardboard nets, connecting cubesconstruct as many rectangular prisms as possible using a given number of connecting cubes (Problem Solving) create skeletal models of prisms and pyramids, eg?using toothpicks and modelling clay or straws and tape connect the edges of prisms and pyramids with the construction of their skeletal models (Problem Solving)construct three-dimensional models of prisms and pyramids and sketch the front, side and top viewsdescribe to another student how to construct or draw a three-dimensional object (Communicating) construct three-dimensional models of prisms and pyramids, given drawings of different views ................
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