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Math
Measurement and Geometry
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Shape
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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
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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
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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
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Year 10A: Apply Pythagoras’ Theorem and trigonometry to solving
three-dimensional problems in right-angled triangles
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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Statistics & Probability
Chance ![GCO-STIK01-550x550](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABCAYAAAAfFcSJAAAAAXNSR0IArs4c6QAAAAtJREFUCB1jYAACAAAFAAGNu5vzAAAAAElFTkSuQmCC)
Year 6
Describe probabilities using fractions, decimals and percentages
Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies
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Year 8
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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
Data Representation & Interpretation
Year 6
Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
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Year 7
Identify and investigate issues involving numerical data collected from primary and secondary sources
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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
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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
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Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
10 A
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Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line to describe the relationship allowing for variation
Number & Algebra
Number and Place Value
Year 7
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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
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Real Numbers
Year 7
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
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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
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Year 8
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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
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Year 9
Apply index laws to numerical expressions with integer indices
Express numbers in scientific notation
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Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems
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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
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Patterns and algebra:
Year7: Introduce the concept of variables as a way of representing numbers using letters :
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Year 7: Create algebraic expressions and evaluate them by substituting a given value for each variable
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Year 10: Expand binomial products and factorise monic quadratic expressions using a variety of strategies
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Linear and non-linear relationships
Year 7:
Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point
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Investigate, interpret and analyse graphs from authentic data
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Year 9
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
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Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations
Year 10
Solve problems involving linear equations, including those derived from formulas
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Solve linear simultaneous equations, using algebraic and graphical techniques, including using digital technology
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Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate
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10A
Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations
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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