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• VC2M10A08

  solve linear inequalities and graph their solutions on a number line

  Elaborations

  • representing word problems with simple linear inequalities and solving them to answer questions
  • graphing regions corresponding to inequalities in the Cartesian plane (for example, graphing $2x+3y<24)\mathrm{ }$and verifying using a test point such as (0, 0)

  VC2M10A08 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M9A03

  sketch linear graphs of equations in various algebraic forms, using the coordinates of 2 points, and solve linear equations

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs, and describing them using both words and algebra

  VC2M9A03 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M10AA09

  solve linear and non-linear simultaneous equations using graphing or systematic guess-check-and-refine with digital tools

  Elaborations

  • using graphs to determine a convergent set of intervals that contain a point of intersection of the graphs of 2 functions
  • using a cobweb diagram to solve simultaneous equations numerically

  VC2M10AA09 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VCMNA257

  Investigate, interpret and analyse graphs from real life data, including consideration of domain and range

  Elaborations

  • using travel graphs to investigate and compare the distance travelled to and from school
  • interpreting features of travel graphs such as the slope of lines and the meaning of horizontal lines
  • using graphs of evaporation rates to explore water storage
  • describing and comparing temperature during a day at different times of the year from the corresponding graphs

  VCMNA257 | Mathematics | Level 7 | Number and Algebra | Linear and non-linear relationships

• VC2M9A05

  identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

  Elaborations

  • recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
  • graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values; and determining when values of the quadratic function lie within a given range
  • solving quadratic equations algebraically and comparing these to graphical solutions
  • using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the $x$-intercepts of its graph and that if the graph has no $x$-intercepts, then the corresponding equation has no real solutions
  • relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function $y=x^2-5x+6$ can be represented as $y=\left(x-2\right)\left(x-3\right)$ with $x$-axis intercepts where either $\left(x-2\right)=0$ or $\left(x-3\right)=0$
  • recognising that the equation $x^2=a$, where $a>0$, has 2 solutions, $x=\sqrt[]{a}$ and $x=-\sqrt[]{a}$ (for example, if $x^2=39$ then $x=\sqrt[]{39}=6.245$ correct to 3 decimal places, or $x=-\sqrt[]{39}=-6.245$ correct to 3 decimal places) and representing these graphically
  • graphing percentages of illumination of moon phases in relation to Aboriginal and Torres Strait Islander Peoples’ understandings that describe the different phases of the moon

  VC2M9A05 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A07

  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 interpreting the effects of these transformations using digital tools; for example,
    $y=x\to y=2x$ (vertical enlargement as $a>1$) $\to y=2x-1$ (vertical translation) and
    $y=x\to y=\frac{1}{2}x$(vertical compression as $0<a<1$) $\to y=-\frac{1}{2}x$ (reflection in the horizontal axis) $\to y=-\frac{1}{2}x+3$ (vertical translation)
  • investigating transformations of the parabola $y=x^2$to the graph of $y=a{\left(x-h\right)}^2+b$ 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,
    $y=x^2\to y=\frac{1}{3}{x}^2$ (vertical compression as $0<a<1$) $\to y=\frac{1}{3}{(x-5)}^2$ (horizontal translation) $\to y=\frac{1}{3}{(x-5)}^2+7$ (vertical translation) or
    $y=x^2\to y=2x^2$ (vertical enlargement as $a>1$) $\to y=-2x^2$ (reflection in the horizontal axis) $\to y=-2{(x+6)}^2$ (horizontal translation) $\to y=-2{\left(x+6\right)}^2+10$ (vertical translation)
  • experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal $y=\frac{1}{x}$, square root $y=\sqrt[]{x}$, cubic $y=x^3$ and exponential functions$y=2^x, y={\left(\frac{1}{2}\right)}^x$, identifying patterns

  VC2M9A07 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VCMNA336

  Solve linear inequalities and graph their solutions on a number line

  Elaborations

  • representing word problems with simple linear inequalities and solving them to answer questions

  VCMNA336 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA285

  Plot graphs of non-linear real life data with and without the use of digital technologies, and interpret and analyse these graphs

  Elaborations

  • investigating different combinations of length and width of a rectangle for a fixed area, and drawing the corresponding graph
  • using graphs to analysing change in the value of a currency against another currency over a specified period

  VCMNA285 | Mathematics | Level 8 | Number and Algebra | Linear and non-linear relationships

• VC2M9A04

  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

  VC2M9A04 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M1M03

  describe the duration and sequence of events using years, months, weeks, days and hours

  Elaborations

  • naming, listing and using familiar units of time, such as hours, days, weeks and years
  • comparing the number of days in the months of the year and explaining how the months cycle from one year to the next
  • sequencing familiar events, including representing time, on pictorial timelines
  • discussing events and activities and deciding whether they would take closer to an hour, a day, a week, a month or a year; for example, it takes a day for the sun to rise and fall and rise again, but it takes less than an hour for me to walk to school
  • investigating durations of time represented in Aboriginal and/or Torres Strait Islander seasonal calendars

  VC2M1M03 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VCEALC633

  Locate specific information from subject-based diagrams, graphs and charts

  Elaborations

  • identifying a sentence that describes a graph or image, for example ‘More than half of the class walks to school’
  • using labels or captions to identify specific features on a diagram, illustration or map

  VCEALC633 | Curriculum content | English as an Additional Language (EAL) | Level C2 | Reading and Viewing | Communication

• VCEALC697

  Extract information from a range of visual representations, including tables, graphs and diagrams

  Elaborations

  • connecting information in visual representations and print texts
  • using captions, labels and topic knowledge to identify specific features on a diagram or illustration
  • interpreting bar, column and pie charts to compare different results

  VCEALC697 | Curriculum content | English as an Additional Language (EAL) | Level C3 | Reading and Viewing | Communication

• VCMNA310

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

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs and describing them using both words and algebra

  VCMNA310 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMSP128

  Create displays of data using lists, table and picture graphs and interpret them

  Elaborations

  • creating picture graphs to represent data using one-to-one correspondence
  • comparing the usefulness of different data displays

  VCMSP128 | Mathematics | Level 2 | Statistics and Probability | Data representation and interpretation

• VCMSP149

  Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies

  Elaborations

  • exploring meaningful and increasingly efficient ways to record data, and representing and reporting the results of investigations
  • collecting data to investigate features in the natural environment

  VCMSP149 | Mathematics | Level 3 | Statistics and Probability | Data representation and interpretation

• VC2M10A11

  explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital tools as appropriate

  Elaborations

  • sketching graphs of parabolas, and circles
  • applying translations, reflections and stretches to parabolas and circles
  • sketching the graphs of exponential functions using transformations
  • plotting graphs of families of relations where the product of 2 variables is equal to a fixed constant

  VC2M10A11 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VCMSP179

  Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values

  Elaborations

  • exploring ways of presenting data and showing the results of investigations
  • investigating data displays using many-to-one correspondence

  VCMSP179 | Mathematics | Level 4 | Statistics and Probability | Data representation and interpretation

• VCEALC504

  Understand simple visual elements of texts, including basic charts, graphs and other images

  Elaborations

  • matching a short description to an illustration, for example ‘It is green, with big eyes’
  • using visual clues to locate information on a map, for example finding ‘the city marked with a green dot’

  VCEALC504 | Curriculum content | English as an Additional Language (EAL) | Level CL | Reading and Viewing | Communication

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VCMMG368

  Use the unit circle to define trigonometric functions as functions of a real variable, and graph them with and without the use of digital technologies

  Elaborations

  • establishing the symmetrical properties of trigonometric functions
  • investigating angles of any magnitude
  • understanding that trigonometric functions are periodic and that this can be used to describe motion
  • identifying points on the unit circle via arc lengths in radians, which correspond to specified values of the circular functions sine, cosine and tangent

  VCMMG368 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry