Year 9 Curriculum

Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems.

Apply index laws to numerical expressions with integer indices.

Express numbers in scientific notation.

Solve problems involving simple interest.

Extend and apply the index laws to variables, using positive integer indices and the zero index.

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate.

Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software.

Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software.

Sketch linear graphs using the coordinates of two points and solve linear equations.

Graph simple non­linear relations with and without the use of digital technologies and solve simple related equations.

Calculate the areas of composite shapes.

Calculate the surface area and volume of cylinders and solve related problems.

Solve problems involving the surface area and volume of right prisms.

Investigate very small and very large time scales and intervals.

Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar.

Solve problems using ratio and scale factors in similar figures.

Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles.

Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right­ angled triangles.

Apply trigonometry to solve right-angled triangle problems.

List all outcomes for two­step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events.

Calculate relative frequencies from given or collected data to estimate probabilities of events.

Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians.

Identify everyday questions and issues involving at least one numerical and at least one categorical variable and collect data directly from secondary sources.

Construct back-to-back stem and leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’.

Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread.

End of year 9 achievement standard

Number and Algebra

Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students use the distributive law to expand algebraic expressions, including binomial expressions, and simplify a range of algebraic expressions. They find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment using a range of strategies including the use of digital technology. Students sketch and draw linear and nonlinear relations, solve simple related equations and explain the relationship between the graphical and symbolic forms, with and without the use of digital technology.

Measurement and Geometry

Students solve measurement problems involving perimeter and area of composite shapes, surface area and volume of rectangular prisms and cylinders, with and without the use of digital technology. They relate three­dimensional objects to two­ dimensional representations. Students explain similarity of triangles, interpret ratios and scale factors in similar figures, and apply Pythagoras’s theorem and trigonometry to solve problems involving angles and lengths in right­angled triangles.

Statistics and Probability

Students compare techniques for collecting data from primary and secondary sources, and identify questions and issues involving different data types. They construct histograms and back­to­back stem­and­leaf plots with and without the use of digital technology. Students identify mean and median in skewed, symmetric and bi­modal displays and use these to describe and interpret the distribution of the data. They calculate relative frequencies to estimate probabilities. Students list outcomes for two­step experiments and assign probabilities for those outcomes and related events.

*Extracted from referencing the Victorian Essential Learning Standards within the Australian Curriculum.