AC9M9A03 Year 9 Mathematics

AC9M9A03 – Year 9 Mathematics: null

Strand

Algebra

Substrand

Algebra

This Content Descriptor from Year 9 Mathematics provides the specific knowledge and skills students should learn. Use it to plan lessons, create learning sequences, and design assessments that align with the Australian Curriculum v9.

Content Descriptor

find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

Elaborations

• recognising that the gradient of a line is calculated using the gradient of a line segment on that line and is  independent of which \(2\)  distinct points on the line are used for this calculation
• using digital tools and transformations to illustrate that parallel lines in the Cartesian plane have the same gradient and that the relationship between the gradients of pairs of perpendicular lines is that their product is (-\(1\))
• using Pythagoras’ theorem to establish the distance between \(2\) points in the Cartesian plane and applying this using horizontal and vertical distances and coordinates
• investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between \(2\) points
• using dynamic graphing software and superimposed images; for example, playground equipment, ramps and escalators, to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts
• investigating how coordinate geometry and aspects of linear algebra play a fundamental role in machine learning and predictive algorithms; for example, object detection and navigation by autonomous vehicles

Achievement Standard This Supports

This Content Descriptor contributes to the following Achievement Standard:

Year 9 ASMATY9

Year 9 Mathematics Achievement Standard

By the end of Year 9, students recognise and use rational and irrational numbers to solve problems. They extend and apply the exponent laws with positive integers to variables. Students expand binomial products, and factorise monic quadratic expressions. They find the distance between 2 points on the Cartesian plane, and the gradient and midpoint of a line segment. Students use mathematical modelling to solve problems involving change in financial and other applied contexts, choosing to use linear and quadratic functions. They graph quadratic functions and solve monic quadratic equations with integer roots algebraically. Students describe the effects of variation of parameters on functions and relations, using digital tools, and make connections between their graphical and algebraic representations. They apply formulas to solve problems involving the surface area and volume of right prisms and cylinders. Students solve problems involving ratio, similarity and scale in two-dimensional situations. They determine percentage errors in measurements. Students apply Pythagoras’ theorem and use trigonometric ratios to solve problems involving right-angled triangles. They use mathematical modelling to solve practical problems involving direct proportion, ratio and scale, evaluating the model and communicating their methods and findings. Students express small and large numbers in scientific notation. They apply the enlargement transformation to images of shapes and objects, and interpret results. Students design, use and test algorithms based on geometric constructions or theorems. They compare and analyse the distributions of multiple numerical data sets, choose representations, describe features of these data sets using summary statistics and the shape of distributions, and consider the effect of outliers. Students explain how sampling techniques and representation can be used to support or question conclusions or to promote a point of view. They determine sets of outcomes for compound events and represent these in various ways. Students assign probabilities to the outcomes of compound events. They design and conduct experiments or simulations for combined events using digital tools.