Number

• Identifying, reading, writing, representing, comparing, ordering, and converting between fractions, decimals, and percentages
• Recording, comparing, and ordering whole and decimal numbers using scientific notation (e.g. 3.14 × 10 3 )
• Finding equivalent fractions, simplifying fractions, and converting between improper fractions and mixed numbers
• Expressing remainders from division as fractions or decimals, depending on the context
• Identifying powers of 2 through to 2 10
• Converting between negative powers and unit fractions (e.g. 3 −2 = 1 — 9 )
• Approximately locating roots on the number line with reference to the closest perfect square (e.g. √ 48 is between √ 36 = 6 and √ 49 = 7, but closer to 7)
• Using rounding and estimation to predict results and to check the reasonableness of calculations
• Rounding to the degree of precision required for the context
• Generalising about exponents of 0 and 1
• Adding, subtracting, multiplying, and dividing integers
• Generalising the rule for dividing by a fraction by starting with dividing a whole number by a fraction
• Adding, subtracting, multiplying, and dividing fractions and decimals
• Connecting multiplying or dividing decimals with multiplying or dividing fractions (e.g. 0.3 × 0.15 = 3 — 10 × 15 — 100 ).
• Checking for equivalence in expressions involving negative numbers (e.g. (−3) 2 ≠ −3 2 , −2 + 3 = 3 + (−2), 2 × (−3) = (−3) × 2 = (−2) × 3, 2 — −3 = −2 — 3 = − 2 — 3
• Finding a fraction or percentage of a number
• Finding the whole amount, given a fraction or percentage (e.g. 20% of an amount is 30. What is the original amount?)
• Expressing a number as a fraction or percentage of another number
• Increasing or decreasing a number by a given proportion
• Representing proportional relationships using whole-number ratios, including reducing the ratios to their simplest form
• Dividing a quantity into two parts, given the part:part or part:whole ratio
• Finding equivalent ratios and rates by scaling up or down

• Applying percentage mark-ups and discounts
• Calculating simple interest and GST on dollar amounts (e.g. finding 15% GST on $432)

Algebra

• Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by: collecting like terms factorising using common factors expanding products, including multiplying a single term by a bracketed term.
• Generalising the properties of operations with variables (e.g. multiplication is distributive over subtraction)
• Multiplying or dividing by −1 in inequalities (e.g.−3 < 5)
• Forming and solving linear equations with rational number coefficients and linear inequalities with positive coefficients
• Using substitution to find the value of an expression or a formula, given the values of its variables
• Rearranging formulae (e.g. solving P = 2 l + 2 w for w )
• Interpreting rules of the form y = mx + c and using a combination of substitution and tables to plot points from the linear graph, connecting the points to form a line
• Identifying the sign of m from tables of values, and linear graphs
• Identifying the value of c for a straight line, from tables of values and from linear graphs
• Using tables and graphs in the coordinate plane (showing all four quadrants), and diagrams to recognise the relationship between the ordinal position and its corresponding element in a linear pattern developing a rule for the pattern in words and making conjectures about further elements in the pattern
• Identifying the constant increase or decrease in a linear pattern, using variables and algebraic notation to represent the rule in an equation, and drawing on the rule to make conjectures

Measurement

• Estimating, calculating, converting, and accurately representing measurements
• Selecting and using appropriate measurement units for a given context, converting between metric units if necessary and using appropriate prefixes
• Finding: the perimeter of 2D shapes the circumference of circles the area of parallelograms, trapeziums, and kites, relating the formulae used to the formula for a rectangle
• Deriving the formulae for the perimeter of half and quarter circles from the formula for a full circle
• Calculating the perimeter of half circles and quarter circles
• Using Pythagoras’ theorem to: verify that given side lengths in a right-angled triangle satisfy the theorem find the length of the hypotenuse in a right-angled triangle, given the lengths of the other two sides
• Proving Pythagoras’ theorem (e.g. by rearranging four congruent right-angled triangles into a square)
• Finding another Pythagorean triple from a given Pythagorean triple
• Finding distance, given speed and time
• Finding time, given distance and speed
• Reasoning about duration using different units of time, including decimal fractions of milliseconds where appropriate

Geometry

• Identifying and describing parts of a circle (e.g. a chord; the diameter, radius, and circumference) and how they relate to each other
• Reasoning about unknown angles in situations involving intersecting and parallel lines and transversals.
• Verifying that two lines are parallel, using angles at the intersections of a transversal

• Representing and constructing 3D shapes, including rectangular and triangular prisms and pyramids, from nets and plan views drawings
• Transforming 2D shapes in the coordinate plane by translation, reflection about a given line of symmetry, and rotation about a given point by a multiple of 90 degrees

Statistics

• Planning and collecting multivariate data to respond to a statistical question and where at least one variable is categorical and at least one is numerical
• Calculating the five-point-summary for numerical data: the minimum value the value of quartile 1, or Q 1 the value of the median or quartile 2, or Q 2 the value of quartile 3, or Q 3 the maximum value
• Calculating the interquartile range as IQR = Q 3 − Q 1

• Creating multiple data visualisations for an investigation
• Selecting appropriate scales for data
• For relationship investigations, drawing an eyeballed line or curve of best fit to predict possible y-values (the response variable) for given x-values (the explanatory variable)

• Critically considering data visualisations, including those from contemporary media, to see if they support or misrepresent the data
• Communicating findings in context to answer an investigative question, using evidence
• Providing possible explanations for findings
• Comparing findings to initial conjectures or assertions and existing knowledge
• Evaluating findings and data-collection methods to check whether claims or statements are supported by the data

Probability

• Carrying out a chance experiment, including running simulations for a large number of trials using digital tools
• Systematically listing outcomes for the sample space
• Comparing experimental probability (from at least 30 trials) to theoretical probability for a chance experiment, and explaining why they differ and how increasing the number of trials reduces this difference
• Carrying out chance experiments of at least 100 trials and comparing the experimental probability of each individual outcome to its theoretical probability, in order to demonstrate the Law of Large Numbers
• Creating and describing data visualisations for the distribution of observed outcomes from a chance experiment
• Calculating probability estimates for different outcomes