TeaCheese Achievement Standards Content Descriptors Blog About
Descriptors›Mathematics›Year 9›Algebra›Algebra›AC9M9A06
AC9M9A06: Year 9 Mathematics Content Descriptor – Algebra
AC9M9A06 Year 9 Mathematics

AC9M9A06 – 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

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

Elaborations

  • • investigating transformations of the graph of \(y=x\) to the graph of \(y=ax+b\) by systematic variation of \(a\) and \(b\) and interpretating the effects of these transformations using digital tools; for example, \(y=x\rightarrow y=2x\) (vertical enlargement as \(a>1\)) \(\rightarrow y=2x-1\) (vertical translation) and \(y=x\rightarrow y=\frac12x\) (vertical compression as \(a<1\)) \(\rightarrow y=\)-\(\frac12x\) (reflection in the horizontal axis) \(\rightarrow y=\)-\(\frac12x+3\) (vertical translation)
  • • investigating transformations of the parabola \(y=x^2\) in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example, \(y=x^2\rightarrow y=\frac13x^2\) (vertical compression as \(a<1\)) \(\rightarrow y=\frac13(x-5)^2\) (horizontal translation) \(\rightarrow y=\frac13(x-5)^2+7\) (vertical translation) or \(y=x^2\rightarrow y=2x^2\) (vertical enlargement as \(a>1\)) \(\rightarrow y=\)-\(2x^2\) (reflection in the horizontal axis) \(\rightarrow y=\)-\(2(x+6)^2\) (horizontal translation) \(\rightarrow y=\)-\(2(x+6)^2+10\) (vertical translation)
  • • experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal \(y=\frac1x\), square root \(y=\sqrt x\), cube \(y=x^3\) and exponential functions, \(y=2^x\), \(y=(\frac12)^x\), identifying patterns
  • • investigating how experimenting with the effects of the variation of parameters of related functions can provide artificial intelligence researchers insights into the predictive behaviour of artificial intelligence models

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.