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• Mathematics Version 2.0: Level 10A description

  Level 10A provides optional, additional content to extend students in their mathematical studies in number, algebra, function, geometry, probability and statistics.

  Level 10A does not include an achievement standard and does not require reporting.

  Students may extend...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 10 achievement standards

  By the end of Level 10, students recognise the effect of approximations of real numbers in repeated calculations.

  Students use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential...

  Level description | Mathematics | Mathematics Version 2.0 | Level 10

• VC2M8SP01

  identify the conditions for congruence and similarity of triangles and explain the conditions for other sets of common shapes to be congruent or similar, including those formed by transformations

  Elaborations

  • developing an understanding of what it means for shapes to be congruent or similar
  • using the enlargement transformation and digital tools to develop sets of similar shapes
  • investigating sufficient conditions to establish that 2 triangles are congruent
  • applying logical reasoning and tests for congruence and similarity, to problems and proofs involving plane shapes
  • comparing angle and side measurements of shapes under transformation to answer questions such as ‘What changes?’ and ‘What stays the same?’
  • establishing that 2 shapes are congruent if one lies exactly on top of the other after one or more transformations, including translations, reflections and rotations, and recognising that the matching sides and the matching angles are equal

  VC2M8SP01 | Mathematics | Mathematics Version 2.0 | Level 8 | Space

• VC2M10M01

  solve problems involving the surface area and volume of composite objects using appropriate units

  Elaborations

  • determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
  • estimating the surface area and volume of composite objects in practical contexts
  • using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a rooftop and the optimal shape and dimensions for rainwater storage based on where it will be located on a property, or determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community

  VC2M10M01 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M9M01

  solve problems involving the volume and surface area of right prisms, cylinders and composite objects using appropriate units

  Elaborations

  • analysing nets of objects to generate short cuts and establish formulas for surface area 
  • determining the amount of material needed to make can-coolers for a class fundraising project and working out the most cost-efficient way to cut out the pieces
  • finding different prisms that have the same volume but different surface areas, making conjectures as to what type of prism would have the smallest or largest surface area
  • investigating objects and technologies of Aboriginal and Torres Strait Islander Peoples, analysing and connecting surface area and volume, and exploring their relationship to their capacity

  VC2M9M01 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• 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

• Mathematics Version 2.0: Level 10 description

  In Level 10, learning in Mathematics builds on each student’s prior learning and experiences and provides the basis for a sound background in number, algebra, function, geometry and statistics. Students engage in a range of approaches to the learning and doing of mathematics that...

  Level description | Mathematics | Mathematics Version 2.0

• 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

• VC2M5ST02

  interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made

  Elaborations

  • reading and interpreting different line graphs, discussing how the horizontal axis represents measures of time such as days of the week or times of the day, and the vertical axis represents numerical quantities or ordinal categorical variables such as percentages, money, measurements or ratings such as fire hazard ratings
  • interpreting real-life data represented as a line graph showing how measurements change over a period of time, and make simple inferences
  • matching unlabelled line graphs to the context they represent based on the stories of the different contexts
  • interpreting the data represented in a line graph, making inferences; for example, reading line graphs that show the varying temperatures or ultraviolet (UV) rates over a period of a day and discussing when would be the best time to hold an outdoor assembly

  VC2M5ST02 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M10M02

  interpret and use logarithmic scales in applied contexts involving small and large quantities and change 

  Elaborations

  • understanding that the logarithmic scale is calibrated in terms of order of magnitude, for example, doubling or powers of 10
  • identifying and interpreting data representations (charts and graphs) that use logarithmic scales (for example, graphs representing percentage change, a wide range of values or exponential growth) and discussing when it is appropriate to use this type of scale and when it is not appropriate
  • investigating and interpreting logarithmic scales used in real-world contexts (for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of microorganisms and disease) and describing reasons for choosing to use a logarithmic scale rather than a linear scale
  • investigating dating methods of geological sites to provide evidence of Aboriginal and Torres Strait Islander Peoples’ presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales, scientific notation and measurement accuracy in the dating

  VC2M10M02 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M10P02

  describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine probabilities of events; investigate the concept of independence

  Elaborations

  • recognising that a subsequent event can be dependent, and that this will affect the way its probability is calculated, for example, cards chosen from a standard deck without replacement, conditional selection problems from a fixed sample size, or the Bertrand’s box paradox

  VC2M10P02 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• VC2M10AM01

  solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids

  Elaborations

  • using formulas to solve problems
  • using authentic situations to apply knowledge and understanding of surface area and volume

  VC2M10AM01 | Mathematics | Mathematics Version 2.0 | Level 10A | Measurement

• VC2M9M02

  solve problems involving very small and very large measurements, timescales and intervals expressed in scientific notation

  Elaborations

  • representing very large and very small real numbers in scientific notation, converting real numbers expressed in scientific notation into decimal form; for example, the approximate geological age of Earth is 4.6 × 10⁹ years, and the mass of a glucose molecule is 2.99 × 10⁻²² grams
  • using knowledge of place value and applying exponent laws to operate with numbers expressed in scientific notation in applied contexts; for example, performing calculations involving extremely small numbers in scientific and other contexts
  • examining the degree of accuracy that different measurement instruments provide in a science laboratory, such as a measuring cylinder compared with a pipette, and recording data values to the correct degree of accuracy using appropriate scientific notation

  VC2M9M02 | Mathematics | Mathematics Version 2.0 | Level 9 | Measurement

• VC2M10P01

  use the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such language, and describe and interpret situations involving conditional probability; design and conduct simulations using digital tools to model...

  Elaborations

  • using two-way tables and Venn diagrams to understand conditional statements using the language of ‘if … then …’, ‘given’, ‘of’ and ‘knowing that’ and identifying common mistakes in interpreting such language
  • using arrays and tree diagrams to represent, interpret and compare probabilities of dependent and independent events 
  • using samples of different sizes with and without replacement from a population to identify when the difference in methods becomes negligible
  • using simulations to gather data on frequencies for situations involving chance that appear to be counterintuitive, such as the three-door problem or the birthday problem
  • identifying situations in real life where probability simulations are used for decision-making, such as supply and demand of product, insurance risk and queueing 
  • using simulation to predict the number of people likely to be infected with a strain of flu or virus

  VC2M10P01 | Mathematics | Mathematics Version 2.0 | Level 10 | Probability

• 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

• 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

• VC2M5SP03

  describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries

  Elaborations

  • understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not its shape or size
  • using pattern blocks and paper, tracing around a shape and then conducting a series of one-step transformations and tracing each resulting image, and then finally copying the original position and end position on a new sheet of paper
  • demonstrating how different combinations of transformations can produce the same resulting image
  • challenging classmates to select a combination of transformations to move from an original image to the final image, noting the different combinations by using different colours to trace images
  • investigating how animal tracks can be interpreted by Aboriginal and Torres Strait Islander Peoples using the transformation of their shapes, to help determine and understand animal behaviour

  VC2M5SP03 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VC2M7ST02

  create different types of displays of numerical data, including dot plots and stem-and-leaf plots, using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode

  Elaborations

  • using ordered stem-and-leaf plots to record and display numerical data collected in a class investigation, such as constructing a class plot of height in centimetres on a shared stem-and-leaf plot for which the stems 12, 13, 14, 15, 16 and 17 have been produced
  • comparing variation in attributes by category using split stem-and-leaf plots or dot plots; interpreting the shape of the distribution using qualitative terms to describe ‘symmetry’, ‘skewness’ and ‘average’ in terms of the mean, median and mode, and the amount of variation based on qualitative descriptions of the spread of the data
  • connecting features of the data display (for example, highest frequency, clusters, gaps, symmetry or skewness) to the mode, range and median, and the question in context; describing the shape of distributions using terms such as ‘positive skew’, ‘negative skew’, ‘symmetric’ and ‘bi-modal’ and discussing the location of the median and mean on these distributions
  • using mean and median to compare data sets, identifying possible outliers and explaining how these may affect the comparison; recognising how different displays make specific information about data more evident, including proportions, and measures of mean, mode or median, spread and extreme values; understanding that the median and the mean will be the same or similar for symmetric distributions but different for distributions that are skewed
  • comparing the mean and median of data with and without extremes; for example, estimation of standard measures for length or mass, informally considering for a given set of data what might constitute an unexpected, unusual or extreme data value

  VC2M7ST02 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• VC2M8M05

  recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure

  Elaborations

  • identifying examples of rates in the real world, including constant rates, rate of pay, cost per kilogram, recipes, simple interest and average rates
  • applying rates to solve problems involving the conversion between different units of measure; for example, using a conversion rate to convert distances from miles to kilometres, or using currency exchange rates to determine the price of items
  • applying rates to calculate solutions to problems in different contexts, for example, required run rates in cricket, dilution of concentrated chemicals and comparing the petrol consumption rates of different vehicles
  • using taxation tables to calculate an individual's annual income tax
  • investigating the application of rates in Aboriginal and Torres Strait Islander Peoples’ land management practices, including the rate of fire spread under different environmental conditions such as fuel types, wind speed, temperature and relative humidity; the conservation of water by Aboriginal and Torres Strait Islander Peoples by estimating rates of water evaporation based on surface area and climatic conditions

  VC2M8M05 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• 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