Math
Measurement and Geometry
Statistics & Probability
Chance
Data Representation & Interpretation
Year 6
Describe probabilities using fractions, decimals and percentages
Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies
Year 7
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
Year 8
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
Year 9
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’
Year 10
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
Year 6
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
Year 7
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
Year 8
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
Year 9
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
Year 10
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
Units of Measurement
Year 7: Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving
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 7: Calculate volumes of rectangular prisms
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: Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving circumference and area
Year 8: Develop formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving Year volume
Year 8: Solve problems involving duration, including using 12- and 24-hour time within a single time zone
Shape
Year 7 Draw different views of prisms and solids formed from combinations of prisms
Location and Transformation
Year 7 Describe translations, reflections in an axis and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries
Geometric Reasoning
Year 7: Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal
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 7 Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning
Year 7: Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Pythagoras and trigonometry
Year 9: Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles
Year 10A: Use the unit circle to define trigonometric functions, and graph them with and without the use of digital technologies
Year 9 Apply trigonometry to solve
right-angled triangle problems
Year 10A: Solve simple trigonometric equations
Year 10A: Apply Pythagoras’ Theorem and trigonometry to solving
three-dimensional problems in right-angled triangles
Number & Algebra
Number and Place Value
Year 7
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
Year 8
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
Fractions and Decimals
Year 6:
Compare fractions with related denominators and locate and represent them on a number line
Real Numbers
Year 7
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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
Year 8
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
Year 9
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
10A
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
Money and financial mathematics
Year 7: Investigate and calculate ‘best buys’, with and without digital technologies
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
Patterns and algebra:
Year7: Introduce the concept of variables as a way of representing numbers using letters :
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 7: Create algebraic expressions and evaluate them by substituting a given value for each variable
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 7: Extend and apply the laws and properties of arithmetic to algebraic terms and expressions
Year 8: Simplify algebraic expressions involving the four operations
Year 10: Apply the four operations to simple algebraic fractions with numerical denominators
Year 10: Expand binomial products and factorise monic quadratic expressions using a variety of strategies
Year 10: Substitute values into formulas to determine an unknown
Linear and non-linear relationships
Year 7:
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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
Year 8
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
Year 9
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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
Year 10
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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
10A
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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
Year 9: Investigate Pythagoras’ Theorem and its application to solving simple problems involving right-angled triangles
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
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