AC9M9M05 Year 9 Mathematics

AC9M9M05 – Year 9 Mathematics: null

Strand

Measurement

Substrand

Measurement

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

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

Elaborations

• modelling situations involving direct proportion such as pro rata pay rates, exchange rates, multiple quotes for a job, conversion between scales or other appropriate science contexts; for example, Hooke’s law and other science contexts involving wave lengths and frequencies
• modelling situations that impact on image editing used in social media and how proportion may not be maintained and can result in distorted images
• modelling situations involving compliance with building and construction standards in design and construction, such as the rise and tread of staircases, and vertical and horizontal components of escalators
• modelling situations involving the application of rates in practical contexts; for example, density, birth, flow or heartbeats
• exploring fire techniques in land management practices used by First Nations Australians that use proportion relationships, including the rate of fire spread in different fuel types to wind speed, temperature and relative humidity

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.