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• VC2M6SP02

  locate points in the 4 quadrants of the Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane

  Elaborations

  • understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin
  • understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose
  • understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate
  • using the Cartesian plane to draw lines and polygons, listing coordinates in the correct order to complete a polygon
  • investigating and connecting land or star maps used by Aboriginal and Torres Strait Islander Peoples with the Cartesian plane through a graphical or visual way of describing location

  VC2M6SP02 | Mathematics | Mathematics Version 2.0 | Level 6 | Space

• 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

• 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

• VC2M7SP03

  describe the effect of transformations of a set of points using coordinates in the Cartesian plane, including translations, reflections in an axis, and rotations about the origin

  Elaborations

  • using digital tools to transform shapes in the Cartesian plane, describing and recording the transformations
  • describing patterns and investigating different ways to produce the same transformation, such as using 2 successive reflections to provide the same result as a translation
  • experimenting with, creating and re-creating patterns using combinations of translations, reflections and rotations, using digital tools

  VC2M7SP03 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VC2M6M04

  identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning

  Elaborations

  • using protractors or dynamic geometry software to measure and generalise about the size of angles formed when lines are crossed, and combinations of angles that meet at a point, including combinations that form right or straight angles
  • demonstrating the meaning of language associated with properties of angles, including right, complementary, complement, straight, supplement, vertically opposite, and angles at a point
  • using the properties of supplementary and complementary angles to represent spatial situations with number sentences and solving to find the size of unknown angles

  VC2M6M04 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• Mathematics | Mathematics Version 2.0: Learning in Mathematics Version 2.0

  Learning in Mathematics emphasises the importance of providing opportunities for students to develop proficiency in mathematics. This development of proficiency is achieved in how content is explored or developed, that is, how students experience the thinking and doing of mathematics.

  Proficiency...

  Overview material | Mathematics Version 2.0

• VC2M9ST02

  analyse how different sampling methods, and different samples using the same method, can affect the results of surveys and how choice of representation can be used to support a particular point of view

  Elaborations

  • investigating and analysing different visualisations of data such as infographics found in the media and commenting on the strengths, weaknesses and possible biases of particular examples
  • discussing the impact of decreased landline usage or an increased aversion to answering calls from unknown numbers on survey data 
  • exploring potential cultural bias relating to Aboriginal and Torres Strait Islander Peoples by critically analysing sampling techniques in statistical reports 

  VC2M9ST02 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VC2M8ST04

  plan and conduct statistical investigations involving samples of a population; use ethical and fair methods to make inferences about the population and report findings, acknowledging uncertainty

  Elaborations

  • using data such as electricity consumption to draw conclusions about the impacts of events, such as pandemics, on households or business
  • identifying situations where the collection of data from a sample is necessary due to efficiency, cost or restricted time for collection of data, and is sufficiently reliable for making inferences about a population
  • exploring progress in reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, investigating and evaluating sampling techniques and methods to gather relevant data to measure progress

  VC2M8ST04 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• Mathematics | Mathematics Version 2.0: Scope and Sequence

  The curriculum sets out what students are expected to learn and is designed as a continuum of learning. The curriculum is being presented in a scope and sequence chart to support teachers to easily see the progression and assist in planning teaching and learning programs to meet the diverse...

  Overview material | Mathematics Version 2.0

• VC2M10A06

  implement algorithms that use data structures using pseudocode or a general purpose programming language

  Elaborations

  • using two-dimensional arrays such as matrices to represent and implement sequences of transformations of sets of points in the plane
  • using pointers in algorithms

  VC2M10A06 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• Mathematics Version 2.0: Level 9 achievement standards

  By the end of Level 9, students recognise and use rational and irrational numbers to solve problems.

  Students extend and apply the exponent laws with positive integers and the zero exponent to variables. They expand binomial products and factorise monic quadratic expressions. They...

  Level description | Mathematics | Mathematics Version 2.0 | Level 9

• 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

• VC2M10AM02

  explore the effect of increasingly small changes in the value of variables on the average rate of change and in relation to limiting values

  Elaborations

  • using the gradient of the line segment between 2 distinct points as a measure of rate of change to obtain numerical approximations to instantaneous speed and interpreting ‘tell me a story’ piecewise linear position-time graphs

  VC2M10AM02 | Mathematics | Mathematics Version 2.0 | Level 10A | Measurement

• Mathematics Version 2.0: Level 6 achievement standards

  By the end of Level 6, students use integers to represent points on a number line and on the Cartesian plane. They solve problems using the properties of prime, composite, square and triangular numbers. Students order common fractions, giving reasons, and add and subtract fractions with...

  Level description | Mathematics | Mathematics Version 2.0 | Level 6

• Mathematics Version 2.0: Level 6 description

  In Level 6, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections...

  Level description | Mathematics | Mathematics Version 2.0

• VC2M10ASP01

  prove and apply relationships between angles and various lines associated with circles (radii, diameters, chords, tangents)

  Elaborations

  • identifying and proving relationships, for example, angles between tangents and chords, angles subtended by a chord with respect to the centre of a circle and angles subtended by a chord with respect to a point on the circumference of a circle, including using dynamic geometry software
  • exploring how deductive reasoning and diagrams are used in proving geometric theorems related to circles

  VC2M10ASP01 | Mathematics | Mathematics Version 2.0 | Level 10A | Space

• VC2M7A05

  generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

  Elaborations

  • plotting points from a table of values generated using simple linear functions and recognising patterns, such as the points lie on a straight line
  • discussing and using variables to create a general rule and using the rule to determine the value of the dependent variable for any given value of the independent variable; for example, plotting the value of the circumference of a circle for varying values of radius
  • using function machines to generate a table of ordered pairs using input and output values, plotting the relationships on a Cartesian plane and describing the graph in terms of shape
  • using diagrams and manipulatives to form linear growth patterns, representing these patterns in tables and describing the relationship in terms of the way the pattern is growing and in the context of the situation

  VC2M7A05 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• Mathematics | Mathematics Version 2.0: Structure

  Mathematics is presented in 11 levels, from Foundation to Level 10.

  Level 10 also includes Level 10A, which provides opportunities for students to extend their exploration of mathematical notions and further their mathematical studies.

  Strands

  The curriculum is organised into 6 interrelated...

  Overview material | Mathematics Version 2.0

• Mathematics Version 2.0: Level 7 achievement standards

  By the end of Level 7, students represent natural numbers in expanded form and as products of prime factors, using exponent notation. They solve problems involving squares of numbers and square roots of perfect square numbers. Students solve problems involving addition and subtraction...

  Level description | Mathematics | Mathematics Version 2.0 | Level 7

• VC2M6ST03

  plan and conduct statistical investigations by posing and refining questions to collect categorical or numerical data by observation or survey, or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation

  Elaborations

  • selecting and using appropriate peripherals; for example, using a scientific probe to collect data about changing soil moisture for plants, interpreting the data and sharing the results as a digital chart
  • using a spreadsheet to record and analyse data, recognising the difference between cell formats in spreadsheets; for example, changing the default general format to numerical, text or date as needed
  • investigating the daily water usage by a student in the home compared to the World Health Organization claim that between 50 and 100 litres of clean water is needed per person per day
  • collecting sample sets of ‘discrete numerical data’ (for example, the number of cars or pets in a household), where the class is surveyed, then other classes are surveyed, and data is analysed and compared, discussing findings
  • collecting ordinal categorical data through the use of a survey; for example, surveying each member of the class, by asking them to indicate their preference on a five-point scale for a particular graphic and colour combination of a proposed school logo
  • collecting ordinal data for ranking nominees for school captain with respect to several criteria, contrasting the use of a five-point scale compared with using a four-point scale

  VC2M6ST03 | Mathematics | Mathematics Version 2.0 | Level 6 | Statistics