That the real number system includes the rational numbers and...
recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools
Year 9 Maths
Choose a unit below. Every green Live label marks a complete learning path with the same eight questions used in Worksheet, Practice and Test.
Elaborations are curriculum teaching examples. Coverage points show how many curriculum ideas guide the unit.
recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools
apply the exponent laws to numerical expressions with integer exponents and extend to variables
simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions
find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane
identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate
use mathematical modelling to solve applied problems involving change including financial contexts; formulate problems, choosing to use either linear or quadratic functions; interpret solutions in terms of the situation; evaluate the model and report methods and findings
experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns
solve problems involving the volume and surface area of right prisms and cylinders using appropriate units
solve problems involving very small and very large measurements, time scales and intervals expressed in scientific notation
solve spatial problems, applying angle properties, scale, similarity, Pythagoras’ theorem and trigonometry in right-angled triangles
calculate and interpret absolute, relative and percentage errors in measurements, recognising that all measurements are estimates
use mathematical modelling to solve practical problems involving direct proportion, rates, ratio and scale, including financial contexts; formulate the problems and interpret solutions in terms of the situation; evaluate the model and report methods and findings
recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity
apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change
design, test and refine algorithms involving a sequence of steps and decisions based on geometric constructions and theorems; discuss and evaluate refinements
analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians
analyse how different sampling methods can affect the results of surveys and how choice of representation can be used to support a particular point of view
represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures
choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context
plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions
list all outcomes for compound events both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes
calculate relative frequencies from given or collected data to estimate probabilities of events involving “and”, inclusive “or” and exclusive “or”
design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results