Number

• Identifying, reading, writing, representing, comparing, ordering, and converting between fractions, decimals, and percentages
• Recording, comparing, ordering, and calculating with numbers in scientific notation
• Identifying irrational numbers (e.g. 3 √ 10 , π)
• Generalising about whether square and cube roots of whole numbers are rational or irrational
• Calculating using integer exponents
• Calculating exactly using fractions, roots, and multiples of π
• Using rounding, including to specified significant figures, and estimation to predict results and to check the reasonableness of calculations
• Rounding to the degree of precision required for the context
• Adding, subtracting, multiplying, and dividing positive and negative numbers, including fractions and decimals
• Evaluating positive integer exponents for positive and negative numbers (e.g. 3 5 , (−1) 4 )
• 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
• Applying a proportional increase or decrease to a number
• Calculating the percentage increase or decrease between two numbers (e.g. What is the percentage increase between 50 and 75?)
• Comparing and using ratios and rate (e.g. finding speed, given distance and time)

• Converting New Zealand dollars into other currencies, and vice versa
• Finding proportions of costs (e.g. the price of 400 g of an item, given the cost per kilogram)
• Calculating compound interest on dollar amounts, by calculating simple interest month by month for short time periods (e.g. How much do you have after 3 months if you invest $100 at a 2.5%-per-month interest rate?)

Algebra

• Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by: collecting like terms factorising using common factors factorising quadratic expressions with a leading coefficient of 1 expanding products, including multiplying a single term by a bracketed term, and multiplying two expressions each of the form ax + b , where a and b are integers factorising by grouping (i.e. using the distributive law) (e.g. x 2 + 2 x − 8 = x 2 + 4 x − 2 x − 8 = x ( x + 4) − 2( x + 4) = ( x − 2)( x + 4))
• Forming and solving linear equations and linear inequalities with rational number coefficients (e.g. − 2 — 5 x + 5 ≤ −10), giving exact or rounded solutions, and representing the solution on a number line
• Solving quadratic equations that are factorised or of the form x 2 + c = 0 (where c is an integer), and connecting the solutions to the x -intercepts of the related graph
• Substituting into, rearranging, and simplifying expressions or formulae that involve squares or square roots (e.g. A = π r 2 , c 2 = a 2 + b 2 )
• Interpreting and graphing linear equations in the form y = mx + c , using the gradient and y -intercept
• Calculating the gradient and y -intercept of a line, using a graph
• Comparing the relative magnitude of m in two or more linear graphs, using the concept of steepness and relating it to the magnitude of m
• Finding the equation of a line, given two points or the gradient and a single point
• Determining the effect on graphs in the coordinate plane of changing the coefficient of x 2 and the fixed value c , for a range of quadratic equations of the form y = ax 2 or y = x 2 + c , where a is a positive integer and c is an integer

Measurement

• Estimating, calculating, converting, and accurately representing measurements using significant figures
• Converting between metric units, and using the appropriate prefixes in the metric system (e.g. kilo–, mega–, centi–, milli–, micro–)
• Finding: the area of circles and composite shapes that include circles or semicircles the surface area and volume or capacity of prisms, pyramids, and cylinders
• Deriving the formulae for the area of half and quarter circles from the formula for a full circle
• Deriving the formulae for the surface area of cubes, rectangular prisms, and cylinders
• Calculating the area of half circles and quarter circles
• Calculating the surface area of cubes, rectangular prisms, triangular prisms, cylinders, and composite figures
• Calculating the volume of cylinders and irregular prisms with a consistent cross-sectional area
• Scaling a shape by a factor, and determining the scale factor for the scaled shape’s area or volume
• Using Pythagoras’ theorem to: find the length of an unknown side in a right-angled triangle check if a triangle has a right angle calculate the distance between two points in the coordinate plane, yielding the distance formula d = √ ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2
• Finding speed, distance, or time, given any two of the measurements
• Reasoning about duration using different units of time, including decimal fractions of milliseconds where appropriate

Geometry

• Using the properties of similarity in 2D shapes, including right-angled triangles, to find unknown lengths and angles

• Representing and constructing 3D shapes, including cylinders, from nets
• Transforming 2D shapes, including composite shapes, by resizing them by any scale factor

Statistics

• Planning and collecting multivariate data to respond to a statistical question using a sample or census
• Reasoning why a mean or median would be a better measure of central tendency for a given statistical question

• 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 and with an awareness of variability
• Making an informal inference in comparative situations about what might be happening in the population, based on visual considerations and using the 75%-to-50% comparison rule
• Making informal predictions from scatter plots in relationship situations

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