AC9M9N01 Year 9 Mathematics

AC9M9N01 – Year 9 Mathematics: null

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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

recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools

Elaborations

• investigating the real number system by representing the relationships between irrationals, rationals, integers and natural numbers and discussing the difference between exact representations and approximate decimal representations of irrational numbers
• using a real number line to indicate the solution interval for inequalities of the form \(ax+bc\); for example, \(1.2x-5.4>10.8\)
• using positive and negative rational numbers to solve problems; for example, for financial planning such as budgeting
• solving problems involving the substitution of real numbers into formulas, understanding that solutions can be represented in exact form or as a decimal approximation, such as calculating the area of a circle using the formula \(A=\mathrm{π}r^2\) and specifying the answer in terms of \(π\) as an exact real number; for example, the circumference of a circle with diameter \(5\) units is \(5\mathrm\pi\) units, and the exact area is \(\mathrm\pi(\frac52)^2=\frac{25}4\mathrm\pi\) square units which rounds to \(19.63\) square units, correct to \(2\) decimal places
• investigating the position of rational and irrational numbers on the real number line, using geometric constructions to locate rational numbers and square roots on a number line; for example, \(\sqrt2\) is located at the intersection of an arc and the number line, where the radius of the arc is the length of the diagonal of a one-unit square

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.