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• 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

• 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

• VC2M8ST01

  distinguish between a population and a sample, and investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the practicalities and implications of obtaining data through sampling, using a variety of investigative processes; for example, investigating situations when random sampling or non-random sampling is used to collect data and the implication of each sampling method
  • discussing how observations, experiments and sampling methods can be impacted by bias; for example, recognising that a sampling bias occurs when certain members of a population are more likely to be selected in a sample than others, such as a survey conducted at a shopping centre, and recognising that environmental conditions may bias the results of scientific investigations if experiments are conducted at different times or under different conditions
  • using digital tools such as simulations and digital measuring devices to observe, measure and record qualitative and quantitative data, discussing precision and the implications of error

  VC2M8ST01 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M8N06

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts involving profit and loss; formulate problems, choosing efficient mental and written calculation strategies and using digital tools where appropriate; interpret and communicate...

  Elaborations

  • modelling situations involving weather and environmental contexts, including temperature or sea depths, by applying operations to positive and negative rational numbers, for example, contexts involving average temperature increases and decreases
  • modelling situations that involve percentage increases or decreases and explaining why it is an increase or decrease, such as mark-ups, discounts, Goods and Services Tax (GST), changes in populations or recycling rates
  • modelling situations involving personal income tax, and interpreting tax tables to determine income tax at various levels of income, including overall percentage of income allocated to tax
  • modelling situations involving percentage increase or decrease such as market trends, effects on population, or effects on the environment over extended time periods

  VC2M8N06 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M8ST03

  compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation

  Elaborations

  • comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
  • using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
  • using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
  • investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
  • investigating Aboriginal and/or Torres Strait Islander ranger groups and other groups’ use of sampling techniques to track biodiversity of species

  VC2M8ST03 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M8SP04

  design and test algorithms involving a sequence of steps and decisions that identify congruency or similarity of shapes, and describe how the algorithm works

  Elaborations

  • listing the properties or criteria necessary to determine if shapes are similar or congruent
  • using the conditions for congruence of triangles and similarity of triangles to develop a sorting algorithm; for example, creating a flow chart
  • evaluating algorithms for accuracy in classifying and distinguishing between similar and congruent triangles

  VC2M8SP04 | Mathematics | Mathematics Version 2.0 | Level 8 | Space

• VC2M8A03

  use mathematical modelling to solve applied problems involving linear relations, including financial contexts involving profit and loss; formulate problems with linear functions, and choose a representation; interpret and communicate solutions in terms of the context, and review the appropriateness...

  Elaborations

  • modelling situations involving linear functions, including practical contexts such as taxi fares involving flag fall fees, motion in a straight line at a constant speed, trade quotes involving call-out fees, cooking that includes resting or cooling times, or water leakage from water tanks, interpreting the constant rate of change and initial value in context, and identifying when values of a model lie within a given range
  • modelling problems in practical situations and interpreting solutions within the context of the problem, including giving attention to all units of measure and whether results are suitable; for example, once a water tank is empty no more water can flow from it
  • modelling financial problems involving pay rates, using a table of values to represent the pay amounts and hours worked using an hourly rate of pay, and graphing the relationship to make inferences
  • modelling patterns on Country/Place and exploring their connections and meaning to linear equations, using the model as a predictive tool and critiquing results by connecting back to Country/Place

  VC2M8A03 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VC2M8M02

  solve problems involving the volume and capacity of right prisms using appropriate units

  Elaborations

  • using models to demonstrate the number of cubic centimetres in a cubic metre and relating this to capacities of millilitres and litres, recognising that one millilitre is equivalent to one cm³
  • solving practical problems involving volume and capacity, for example, optimal packaging and production
  • choosing which measurements are useful to consider when solving practical problems in context; for example, when purchasing a new washing machine, the dimensions are useful when determining whether it will fit in the available space in the laundry and its capacity is useful when considering the maximum washing load it can carry
  • investigating, reasoning and finding solutions to measurement problems involving dimensions, rates, volume and capacity of objects; for example, given the dimensions of a pool and the rate of flow from a tap, determining how long it will take to fill the pool to its normal capacity

  VC2M8M02 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M8N02

  establish and apply the exponent laws with positive integer exponents and the zero exponent, using exponent notation with numbers

  Elaborations

  • recognising the connection between exponent form and expanded form with the exponent laws of product of powers rule, quotient of powers rule, and power of a power rule, for example, 23×22 can be represented as 2×2×2×2×2=25 , and connecting the result to the addition of exponents
  • applying the exponent laws of the product of powers rule, quotient of powers rule, power of a power rule and zero exponent individually and in combination; for example, using exponents to determine the effect on the volume of a 2 centimetre cube when the cube is enlarged to a 6 centimetre cube, 6323= 23×3323=33, so the volume is increased by a factor of 27
  • using digital tools to systematically explore the application of the exponent laws; observing that the bases need to be the same
  • using examples such as 3434=1, and 34-4=30 to illustrate the necessity that for any non-zero natural number n,  n0=1

  VC2M8N02 | Mathematics | Mathematics Version 2.0 | Level 8 | Number