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- - - - Year 8: Choose appropriate units of measurement for area and volume and convert from one unit to another
        
        Year 9 Calculate areas of composite shapes
    - - Year 8: Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites
        
        Year 9: Calculate the surface area and volume of cylinders and solve related problems
        Solve problems involving the surface area and volume of right prisms
        
        Year 10: Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids
        
        10A: Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids
  - - - Year 8: Define congruence of plane shapes using transformations
        Develop the conditions for congruence of triangles
        
        Year 9: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
        Solve problems using ratio and scale factors in similar figures
        
        Year 10: Formulate proofs involving congruent triangles and angle properties
        Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes
        
        10A:Prove and apply angle and chord properties of circles
    - - Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
  - - - Year 10A: Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies
    - - Year 10A: Solve simple trigonometric equations
    - - Year 10: Solve right-angled triangle problems including those involving direction and angles of elevation and depression
        
        10A: Establish the sine, cosine and area rules for any triangle and solve related problems
- - - - Describe probabilities using fractions, decimals and percentages
      - Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies
      - Compare observed frequencies across experiments with expected frequencies
    - - Construct sample spaces for single-step experiments with equally likely outcomes
      - Assign probabilities to the outcomes of events and determine probabilities for events
      - Represent events in two-way tables and Venn diagrams and solve related problems
    - - Identify complementary events and use the sum of probabilities to solve problems
      - Describe events using language of ‘at least’, exclusive ‘or’ (A or B but not both), inclusive ‘or’ (A or B or both) and ‘and’
      - Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians
    - - List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events
      - Calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’ or ‘or’
    - - Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events. Investigate the concept of independence
      - 10 A
        
        Investigate reports of studies in digital media and elsewhere for information on their planning and implementation
  - - - Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
      - Interpret secondary data presented in digital media and elsewhere
    - - Identify and investigate issues involving numerical data collected from primary and secondary sources
      - Construct and compare a range of data displays including
      - stem-and-leaf plots and dot plots
      - Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
      - Describe and interpret data displays using median, mean and range
    - - Investigate techniques for collecting data, including census, sampling and observation
      - practicalities and implications of obtaining data through sampling using a variety of investigative processes
      - Explore the variation of means and proportions of random samples drawn from the same population
      - Investigate the effect of individual data values, including outliers, on the mean and median
    - - Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly and from secondary sources
      - Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’
      - Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
    - - Determine quartiles and interquartile range
      - Construct and interpret box plots and use them to compare data sets
      - Compare shapes of box plots to corresponding histograms and dot plots
      - Use scatter plots to investigate and comment on relationships between two numerical variables
      - Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
      - 10 A
        
        Calculate and interpret the mean and standard deviation of data and use these to compare data sets
        
        Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation
- - - - Investigate index notation and represent whole numbers as products of powers of prime numbers
      - Investigate and use square roots of perfect square numbers
        Apply the associative, commutative and distributive laws to aid mental and written computation
        Compare, order, add and subtract integers
    - - Use index notation with numbers to establish the index laws with positive integral indices and the zero index
      - Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies
  - - - Compare fractions with related denominators and locate and represent them on a number line
  - - - Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line
        
        Solve problems involving addition and subtraction of fractions, including those with unrelated denominators
        
        Multiply and divide fractions and decimals using efficient written strategies and digital technologies
        
        Express one quantity as a fraction of another, with and without the use of digital technologies
      - Round decimals to a specified number of decimal places
      - Connect fractions, decimals and percentages and carry out simple conversions
        Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies
      - Recognise and solve problems involving simple ratios
    - - Investigate terminating and recurring decimals
      - Solve problems involving the use of percentages, including percentage increases and decreases, with and without digital technologies
      - Solve a range of problems involving rates and ratios, with and without digital technologies
      - Investigate the concept of irrational numbers, including π
    - - Apply index laws to numerical expressions with integer indices
        Express numbers in scientific notation
      - Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems
    - - Use the definition of a logarithm to establish and apply the laws of logarithms
      - Define rational and irrational numbers and perform operations with surds and fractional indices
  - - - Year 8: Solve problems involving profit and loss, with and without digital technologies
        
        Year 9:Solve problems involving simple interest
        
        Year 10: Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies
  - - - Year 8: Extend and apply the distributive law to the expansion of algebraic expressions
        
        Year 9 Extend and apply the index laws to variables, using positive integer indices and the zero index
        
        Year 10: Factorise algebraic expressions by taking out a common algebraic factor
        
        10A: Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems
    - - Year 8: Factorise algebraic expressions by identifying numerical factors
        
        Year 9: Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate
        
        Year 10: Simplify algebraic products and quotients using index laws
    - - Year 8: Simplify algebraic expressions involving the four operations
        
        Year 10: Apply the four operations to simple algebraic fractions with numerical denominators
  - - - Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point
        
        Solve simple linear equations
        
        Investigate, interpret and analyse graphs from authentic data
    - - Plot linear relationships on the Cartesian plane with and without the use of digital technologies
      - Solve linear equations using algebraic and graphical techniques. Verify solutions by substitution
    - - Find the distance between two points located on the Cartesian plane using a range of strategies, including graphing software
        
        Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software
        
        Sketch linear graphs using the coordinates of two points and solve linear equations
        
        Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations
    - - Solve problems involving linear equations, including those derived from formulas
        
        Solve linear inequalities and graph their solutions on a number line
        
        Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology
        
        Solve problems involving parallel and perpendicular lines
        
        Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate
        
        Solve linear equations involving simple algebraic fractions
        
        Solve simple quadratic equations using a range of strategies
    - - Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations
        
        Solve simple exponential equations
        
        Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation
        
        Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts