Number

• Reading, writing comparing, and ordering whole numbers and decimals using positive and negative powers of 10
• Representing whole numbers and decimals in expanded form using powers of 10 (e.g. 3.61 = 3 × 10 0 + 6 × 10 −1 + 1 × 10 −2 )
• Representing negative powers of 10 as a fraction and a decimal, and vice-versa (e.g. 0.01 = 1 — 100 = 10 −2 )
• Using exponents and identifying cube roots for cube numbers up to at least 125
• Using radicals (√ and 3 √) to represent square and cube roots
• Evaluating square and cube roots for perfect squares and cubes and using a calculator to approximate them for other numbers
• Representing composite numbers as products of their prime factors, using exponents to summarise repeated factors (e.g. 36 = 2 × 2 × 3 × 3 = 2 2 × 3 2 )
• Locating negative and positive numbers on a number line
• Comparing and ordering negative and positive numbers using a number line (e.g. −3.4 < −3)
• Evaluating expressions involving negative numbers, addition, and subtraction (e.g. 3 + −7)
• Using rounding, estimation, and benchmarks to predict results and to check the reasonableness of calculations (e.g. 14.7 × 5 must be between 14 × 5 = 70 and 15 × 5 = 75)
• Rounding whole numbers to any specified power of 10, and rounding decimals to the nearest whole number, tenth, hundredth, or thousandth
• Multiplying and dividing whole numbers (e.g. 327 ÷ 15 = 21.8 or 21 4 — 5 )
• Evaluating expressions with integers, using the order of operations
• Identifying, reading, writing, and representing fractions, decimals, and percentages
• Comparing, ordering, and converting between fractions, decimals, and percentages
• Multiplying whole numbers by fractions, including by improper fractions, by mixed numbers, and by first converting to an improper fraction
• Multiplying fractions and representing the answer in its simplest form
• Multiplying and dividing numbers by powers of 10
• Multiplying positive decimals (e.g. 2.3 × 45)
• Finding a fraction of a whole number, including when the result is a mixed number or improper fraction (e.g. for 2 — 5 of 42, 2 — 5 × 42 = 84 — 5 = 16 4 — 5 )
• Finding a whole amount when given a fraction, including when the whole set is a mixed number or improper fraction (e.g. if 8 is 3 — 5 of a set, 8 × 5 — 3 = 13 1 — 3 )
• Finding percentages of whole numbers
• Finding the whole (100%) when given a percentage (e.g. 3% is 27)
• Identifying percentage equivalence in calculations (e.g. 45% of 20 is equal to 20% of 45)
• Dividing a quantity into two parts, given the part:part or part:whole ratio
• Expressing the division of quantity into two parts as a ratio

• Creating and comparing weekly, monthly, and yearly finance plans (e.g. for saving plans, phone plans, budgets, and ‘buy now, pay later’ services)
• Applying percentage discounts (e.g. a 35% discount on $180 will give a new price of $180 − (0.35 × $180) = $117)

Algebra

• Forming and solving linear equations with rational solutions (e.g. t + 7 = 6.5, 5 s + 9 = −18)
• Forming and solving linear inequalities and representing the solution on a number line (e.g. t − 3 ≥ −5)
• Using substitution to find the value of an expression or formula (e.g. calculating w + 12 given w = 4)
• Rearranging known formulae using one or two steps
• Simplifying algebraic expressions involving sums, products, differences, and single brackets, and collecting like terms (e.g. 2( x + 3) + 1 = 2 x + 6 + 1 = 2 x + 7)
• Factorising simple algebraic expressions (e.g. 5 x − 35 = 5( x − 7))
• Identifying and plotting points in the four quadrants of the coordinate plane, using ordered pairs and values from a table
• Using tables, graphs in the coordinate plane, and diagrams to recognise the relationship between the ordinal position and its corresponding element in a linear pattern, develop a rule for the pattern in words, and make 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 using the equation to make conjectures
• Investigating the patterns of triangular numbers, square numbers, and cube numbers, extending the patterns, creating tables of values, and plotting the values on the coordinate plane

Measurement

• Estimating and measuring length, area, volume, capacity, mass (weight), temperature, time, and angle, using appropriate units
• Converting between metric units of area (mm 2 , cm 2 , m 2 , and km 2 ) and volume (mm 3 , cm 3 and m 3 )
• Converting between different volume units (cm 3 , m 3 , mL, L)
• Calculating the area of a parallelogram and a trapezium
• Calculating the area of a shape, given some lengths and its perimeter, and vice versa
• Calculating lengths of quadrilaterals, given their area and other sufficient information
• Calculating the volume of triangular prisms
• Calculating the volume of composite figures made up of cubes, rectangular prisms, and/or triangular prisms
• Reading, interpreting, and using timetables, charts and results that present information about duration.
• Converting times to a given unit (e.g. hours and minutes to minutes)

Geometry

• Identifying and describing the parts of a circle: the radius, diameter, and circumference

• Transforming 2D shapes on the coordinate plane, including composite shapes, by a combination of translations, reflections, rotations, and scaling by any factor
• Proving that the interior angle sum of a triangle is 180°, and generalising a rule for the interior angle sum and exterior angles for any polygon
• Reasoning about unknown angles in situations involving internal and external angles of polygons

• Using map scales, compass points, distance, and turn to interpret and communicate positions and pathways in coordinate systems and grid reference systems

Statistics

• Planning and collecting data in order to respond to a statistical question (e.g. Are our feet the same length?)
• Calculating the mean, median, and mode for numerical data
• Calculating the range for numerical data

• For a given set of data, choosing and constructing an appropriate data visualisation according to the data type (e.g. a dot plot, bar graph, time-series graph)
• Noticing and explaining outliers in a given set of data

• Responding to statistical questions by calculating an appropriate measure of central tendency and range for a variety of data tables and data visualisations
• Interpreting data visualisations, including those from contemporary media
• Identifying when a data visualisation cannot be interpreted accurately due to missing information
• Identifying outliers by eye and taking them into account when using range as a measure of spread

Probability

• Carrying out a chance experiment and calculating the experimental probability of each outcome
• Comparing experimental probability (using at least 30 trials) to theoretical probability, 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

• Calculating probabilities for events as decimals, fractions, and percentages
• Comparing the likelihood of different events
• Calculating probabilities for complementary events