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Australian Curriculum Docs Year 6 Achievement standard Year 7 Achievement standard Year 8 Achievement standard By the end of Year 6, students are able to work with numbers including fractions and decimals to thousandths and apply their place value understanding to establish equivalences. They confidently solve realistic problems including those involving rate and ratio choosing appropriately written and mental strategies or calculators. They use estimation strategies to predict and check reasonableness of calculations. Students represent data choosing appropriate displays including stem and leaf plots and distinguish between sample and population data. They are beginning to quantify probability. Students can visualise and connect two- and three-dimensional shapes and objects. Their facility with maps extends to the use and interpretation of scales and legends. They are beginning to connect algebra and measurement, understanding the basis for formulas for perimeter, area and volume of simple polygons and rectangular prisms. By the end of Year 7, students work fluently with index notation. They are able to use the operations to calculate accurately with integers, fractions and decimals, choosing appropriate operations when solving problems, and correctly applying the order of operations. They extend this understanding to algebraic representations, selecting and applying formulas for area and volume and begin to generalise arithmetic patterns, including linear functions, representing them algebraically and graphically. Students conduct systematic data-based enquiry using univariate and bivariate data, choosing appropriate graphs, calculating measures of spread and centre and drawing conclusions. They identify equally likely outcomes and calculate probabilities and relative frequencies from data. Students have a sound understanding of the geometric properties of angles, triangles and quadrilaterals and twodimensional views of three-dimensional objects. They are beginning to construct logical geometric arguments about properties of triangles and quadrilaterals. By the end of Year 8, students are able to use number, algebraic conventions and formulas and apply this understanding to problem solving with ratios and scale, percentage increase and decrease, perimeters and areas of triangles, quadrilaterals and circles and volumes of triangular prisms. Students readily connect tabular, graphical and algebraic representations of linear functions, and choose appropriate models for solving real life problems. They use numerical and graphical summaries of data, interpret these to draw conclusions and calculate probabilities. They apply mathematical reasoning including congruence and transformations to solve geometric problems and generalise formulas for the perimeter for triangles and rectangles to other quadrilaterals and develop understanding of the volumes of simple prisms. They are able to visualise three-dimensional objects from two-dimensional representations including isometric drawing and plans. 1 Number and Algebra Year 6 Number and Algebra Year 7 Number and Algebra Year 8 1. Integers Read, represent, write, interpret and order positive and negative integers 1. Indices Understand and work fluently with index notation and represent whole numbers as a product of powers of prime numbers 1. Ratio and rate Solve problems involving use of percentages, rates and ratios, including percentage increase and decrease and the unitary method and judge reasonableness of results 2. Decimals Recognise and represent numbers involving thousandths, read, write and order those numbers, and connect them to fractions 3. Place value Justify uses of the place value system to describe decimal numbers, and to partition and regroup those numbers to assist calculation and solve problems 4. Multiplication and division Apply multiplication and related division facts to solve realistic problems efficiently using mental and written strategies and calculators justifying the reasonableness of answers and explaining reasoning. 5. Ratio and rate Recognise and solve problems involving unit ratio and everyday rates and check for reasonableness of answers 6. Decimals Understand and work fluently with decimal numbers to thousandths, and multiply and divide numbers including decimals by whole numbers to solve additive problems, including using technology 2. Integers Order, add and subtract integers fluently and identify patterns for multiplication and division including using ICT 3. Calculation Understand and become fluent with written, mental and calculator strategies for all four operations with fractions, decimals and percentages 2. Index laws Understand, describe and use generalisations of the index laws with positive integral indices 3. Calculation Solve problems involving fractions, decimals and percentages, including those requiring converting and comparing, and judge the reasonableness of results using techniques such as rounding 4. Variables Apply the associative, commutative and distributive laws and the order of operations to mental and written computation and generalise these processes using variables 4. Algebra Generalise the distributive law to expansion and factorisation of simple algebraic expressions and use the four operations with algebraic expressions 5. Linear equations Use symbols to represent linear relationships and solve problems involving linear relationships where there is only one occurrence of a variable 5. Linear equations Create, solve and interpret linear equations, including those using realistic contexts using algebraic and graphical techniques 6. Coordinates Plot points on the Cartesian plane using all four quadrants 6. Coordinates Plot graphs of linear functions and use these to find solutions of equations including using ICT 7. Fractions Understand and work fluently with and solve additive problems involving fractions with unrelated denominators, compare and contrast fractions using equivalence 8. Estimation Estimate the outcomes of calculations involving decimal numbers and justify the reasonableness of answers 9. Number properties Identify and describe properties of numbers including prime, composite and square numbers 2 Statistics and Probability Year 6 Statistics and Probability Year 7 Statistics and Probability 1. Data representation Construct, read and interpret tables and graphs including ordered stem and leaf plots, and construct pie charts and other simple data displays including using technology 1. Data measures Determine mean, median, and range and use these measures to compare data sets explaining reasoning including using ICT 1. Statistical measures Use a mean or median from a sample to estimate the mean or median of a population and to recognise the limitations of samples 2. Data investigation Investigate questions involving the collection of univariate and simple bivariate data, including the use of back-to-back stem plots and scatter plots 2. Data investigation Collect samples and construct tables and graphs including frequency column graphs with and without technology for grouped data, and to select and justify the choice of measure of centre and spread used 2. Data interpretation Interpret secondary data presented in the media and elsewhere, identifying misleading representations and distinguishing between samples and populations 3. Variation Explore concepts of variation and error by collecting repeated measurements 4. Chance List all outcomes for chance events and quantify probabilities using simple fractions, decimals and percentages 3. Sample space Construct sample spaces for singlestep experiments with equally likely outcomes and use them to assign probabilities 4. Relative frequency Calculate relative frequencies, and recognise variation between results of chance experiments 3 3. Probability Identify complementary events and use the facts that probabilities range between 0 and 1 and sum to 1 over the sample space to check probabilities 4. Representing probability Use Venn diagrams or two-way tables to illustrate ’and’, ‘or’, ‘given’ and ‘not’ criteria, and to calculate simple probabilities Measurement and Geometry Year 6 Measurement and Geometry Year 7 Measurement and Geometry Year 8 1. Geometry Visualise and solve problems relating to packing and stacking 1. Geometry Describe the properties of parallel and perpendicular lines, triangles and quadrilaterals to classify them and make geometric constructions including angle bisectors and perpendicular bisectors 1. Congruence Identify properties and conditions for congruence of plane figures, and use coordinates to describe transformations 2. Measurement Solve problems involving comparison of length, area, volume and other attributes using appropriate tools, scales and metric units 3. Metric System Work fluently with the metric system to convert between metric units of length, capacity and mass, using whole numbers and commonly used decimals 4. Angles Estimate, compare and measure angles 5. Time Create, interpret and use timetables and timelines including calculating elapsed time 6. Measurement formulas Understand and use the formulas for calculating perimeters and areas of rectangles, and volumes of rectangular prisms 7. Transformation and symmetry Describe patterns in terms of reflection and rotational symmetry, and translations including identifying equivalent transformations using ICT 2. Measurement formulas Relate the formula for calculating the area of triangles to the formula for rectangles and parallelograms, to develop the formula for the volume of rectangular prisms, and use these to solve problems 3. Transformations Visualise, demonstrate and describe translations, reflections, rotations and symmetry in the plane, including using coordinates and ICT 4. Time Calculate duration using 12- and 24-hour time, explain and use time zones 5. Location Interpret and create maps and plans, including using legends and scales, describe relative position, and plan journeys 8. Location Describe and interpret locations and give and follow directions, using scales, legends, compass points, including directions such as NE and SW, distances, and grid references 2. Measurement formulas Generalise from the formulas for perimeter and area of triangles and rectangles to investigate relationships between the perimeter and area of special quadrilaterals and volumes of triangular prisms and use these to solve problems 3. Circles Investigate the relationship between features of circles such as circumference, area, radius and diameter and generalise these to solve problems involving circumference and area 4. Congruence Explain properties for congruence of triangles and apply these to investigate properties of quadrilaterals 5. Location Solve problems involving interpreting and creating maps and plans using scales 6. Visualisation Create, interpret and use twodimensional representations of three-dimensional objects, including projections, isometric views and plans 7. Pythagoras Use Pythagoras theorem to solve simple problems involving right-angled triangles 4