Number

• Reading, writing comparing, and ordering whole numbers using powers of 10 (e.g. 10,000 = 10 4 , 1000 < 10 4 )
• Representing numbers in expanded form using powers of 10 (e.g. 34,506 = 3 × 10 4 + 4 × 10 3 + 5 × 10 2 + 6)
• Using exponents and identifying square roots for square numbers up to at least 144
• Using radicals (√) to represent square roots
• Using divisibility rules to identify numbers that are divisible by 2, 3, 4, 5, 6, 8, 9, and 10
• Identifying prime numbers to 100
• Finding the highest common factor (HCF) of two numbers under 100, and finding the least common multiple (LCM) of two numbers under 10
• Locating integers on a number line
• Ordering whole negative and positive numbers using a number line
• Identifying the additive inverse of any number
• Representing addition and subtraction of integers using a number line
• Using negative numbers to solve problems in a range of contexts, including the measurement of temperature and finance
• Using rounding and estimation to predict results and to check the reasonableness of calculations (e.g. 0.73 + 0.8 + 0.999 must be less than 3 since each are close to but less than 1)
• Rounding whole numbers to any specified power of 10, and rounding decimals to the nearest whole number, tenth, or hundredth
• Multiplying whole numbers
• Dividing whole numbers by one- or two-digit divisors (e.g. 327 ÷ 5 = 65.4 or 65 2 — 5 )
• Evaluating expressions using the order of operations
• Identifying, reading, writing, and representing fractions, decimals, and percentages
• Comparing, ordering, and converting between fractions, decimals, and percentages
• Finding equivalent fractions and representing fractions in their simplest form
• Adding and subtracting fractions, including improper fractions and mixed numbers, and representing the answer in its simplest form
• Adding and subtracting decimals
• Multiplying and dividing numbers by powers of 10
• Multiplying whole numbers by fractions and representing the answer in its simplest form
• Multiplying decimals by whole numbers (e.g. 0.7 × 5 and 0.7 × 50, which both relate to knowing 7 × 5 = 35)
• Dividing fractions by whole numbers and representing the answer in its simplest form
• Dividing a whole number by a unit fraction
• Finding a fraction of a whole number (e.g. 5 — 3 of 186)
• Finding a whole amount when given a fraction (e.g. 5 — 4 of the set is 85, what is the whole set?)
• Finding common percentages of whole numbers
• Finding the whole (100%) when given a percentage (e.g. 40% is 28)
• Using proportional reasoning to explore multiplicative relationships between quantities (e.g. “If there are 3 red for every 7 blue balls, how many balls are there altogether when there are 18 red balls?”)

• Calculating the total cost and change for a transaction involving any amount of money
• Applying percentage discounts to whole dollar amounts (e.g. in a 20%-off sale)

Algebra

• Forming and solving one- and two-step linear equations with integer solutions (e.g. t + 7 = 12, 5 s + 3 = 18)
• Checking the truth of and completing number sentences involving all four operations and including the use of inequalities (e.g. 0.8 × 12 ≤ 8 × 0.5 + 8, true or false?)
• 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 (e.g. making w the subject of A = lw )
• Simplifying expressions involving any of the four operations by collecting like terms (e.g. 3 a + a + a = 5 a , 3 b − 2 b = b )
• 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

Measurement

• Selecting and using an appropriate base measure (e.g. metre, gram, litre) within the metric system, along with a prefix (e.g. kilo–, centi–) to show the size of units
• Using formulae to find unknown measurements related to perimeter (e.g. the length of the unknown sides of a square given its perimeter, the length of an unknown side in a composite shape given its perimeter)
• Using formulae to find unknown measurements related to area (e.g. the base of a triangle given its area and height, the area of a figure composed of a triangle and rectangle, given side lengths)
• Using formulae to find unknown measurements related to volume (e.g. the dimensions of a cube given its volume, the volume of a rectangular prism given side lengths)
• Reading, interpreting, and using timetables and charts that present information about duration

Geometry

• Classifying triangles by both their angle and side properties

• Transforming 2D shapes in the coordinate plane by a single translation, reflection across a given mirror line, or a rotation about a given point by a multiple of 90 degrees
• Identifying the 2D shapes that compose 3D shapes
• Drawing nets for prisms and pyramids
• Reasoning about unknown angles in situations involving perpendicular lines, parallel lines, and transversals
• Solving for an unknown angle in a diagram by setting up and solving a multi-step equation based on supplementary, complementary, vertical, and adjacent angle relationships

• Interpreting and communicating the location of positions and pathways using coordinates, angle measures, and the eight main and halfway compass points (e.g. NE, which is 45° E from N)

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