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• VCMNA214

  Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers

  Elaborations

  • extending whole-number strategies to explore and develop meaningful written strategies for addition and subtraction of decimal numbers to thousandths
  • exploring and practising efficient methods for solving problems requiring operations on decimals, to gain fluency with calculating with decimals and with recognising appropriate operations

  VCMNA214 | Mathematics | Level 6 | Number and Algebra | Fractions and decimals

• VCMNA219

  Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence

  Elaborations

  • identifying and generalising number patterns
  • investigating additive and multiplicative patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern looking for patterns in the way the numbers increase/decrease

  VCMNA219 | Mathematics | Level 6 | Number and Algebra | Patterns and algebra

• VCMNA220

  Explore the use of brackets and order of operations to write number sentences

  Elaborations

  • appreciating the need for rules to complete multiple operations within the same number sentence

  VCMNA220 | Mathematics | Level 6 | Number and Algebra | Patterns and algebra

• VCMNA221

  Design algorithms involving branching and iteration to solve specific classes of mathematical problems

  Elaborations

  • implementing algorithms such as the Euclidean division algorithm
  • devising flowcharts to represent algorithms for a common processes such as adding two fractions

  VCMNA221 | Mathematics | Level 6 | Number and Algebra | Patterns and algebra

• VC2M6P02

  conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials

  Elaborations

  • using digital tools to simulate multiple tosses of a coin or dice and comparing the relative frequency of an outcome as the number of trials increases; and identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
  • using online simulations of repeated random events to recognise emerging patterns, discussing and comparing expected results to the actual results
  • investigating the relative frequencies of all outcomes for a chance experiment and verifying that their sum equals one
  • systematically recording the outcome of large numbers of spins on a spinner and analysing the relative frequencies of outcomes, representing these as percentages

  VC2M6P02 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability

• VC2M6P01

  describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–‍1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals

  Elaborations

  • recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen
  • using a scale of zero to one or 0% to 100% to estimate chances of events
  • listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4
  • recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

  VC2M6P01 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability

• VC2M6SP03

  recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometry software where appropriate

  Elaborations

  • using digital tools to create tessellations of shapes, including paver and tiling patterns, describing the transformations used and discussing why these shapes tessellate; and identifying shapes or combinations of shapes that will or will not tessellate, answering questions such as ‘Do all triangles tessellate?’
  • designing a school or brand logo using the transformation of one or more shapes and describing the transformations used
  • using dynamic geometry software and digital tools to experiment with transformations, for example, to demonstrate when the order of transformations produces different results; and experimenting with transformations and their application to fractals
  • designing an algorithm as a set of instructions to transform a shape, including getting back to where you started from; for example, programming a robot to move around the plane using instructions for movements, such as 2 down, 3 to the right, and combinations of these to transform shapes
  • investigating symmetry, transformation and tessellation in different shapes on Country/Place, including rock formations, insects, and land and sea animals, discussing the purpose or role symmetry plays in their physical structure

  VC2M6SP03 | Mathematics | Mathematics Version 2.0 | Level 6 | Space

• VC2M6SP01

  compare the parallel cross-sections of objects and recognise their relationships to right prisms

  Elaborations

  • using objects made of foam or polystyrene, slicing along different cross-sections, and recording the different shapes of faces that result; and comparing cross-sections of different objects
  • using different pieces of fruit, slicing across different cross-sections, and drawing the cross-section; and reporting back to the class the results of the investigation
  • observing and drawing the shapes resulting from different ways of slicing through familiar objects; for example, slicing carrots at different angles or cutting through playdough models of objects; or using playdough models, fruit or similar to establish which objects can be cut in such a way that the cross-section will always be the same shape
  • understanding that right prisms are objects where parallel cross-sections perpendicular to the base of the prism are the same shape and size
  • connecting different right prisms to the shape of their parallel cross-sections, such as a triangular prism, which can be described as a stack of the same-sized triangles, and a cube or square prism, which can be described as a stack of the same-sized squares
  • investigating the design of Aboriginal and/or Torres Strait Islander Peoples’ dwellings, exploring the relationship between the cross-sections and the dwellings’ construction

  VC2M6SP01 | Mathematics | Mathematics Version 2.0 | Level 6 | Space

• VCMSP234

  Compare observed frequencies across experiments with expected frequencies

  Elaborations

  • predicting likely outcomes from a run of chance events and distinguishing these from surprising results

  VCMSP234 | Mathematics | Level 6 | Statistics and Probability | Chance

• VCMSP232

  Describe probabilities using fractions, decimals and percentages

  Elaborations

  • investigating games of chance popular in different cultures

  VCMSP232 | Mathematics | Level 6 | Statistics and Probability | Chance

• VCMSP235

  Construct, interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables

  Elaborations

  • comparing different student-generated diagrams, tables and graphs, describing their similarities and differences and commenting on the usefulness of each representation for interpreting the data
  • understanding that data can be represented in different ways, sometimes with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgments

  VCMSP235 | Mathematics | Level 6 | Statistics and Probability | Data representation and interpretation

• VCMSP236

  Interpret secondary data presented in digital media and elsewhere

  Elaborations

  • investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
  • identifying potentially misleading data representations in the media, such as graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made, and pie charts in which the whole pie does not represent the entire population about which the claims are made

  VCMSP236 | Mathematics | Level 6 | Statistics and Probability | Data representation and interpretation

• VCMSP233

  Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies

  Elaborations

  • conducting repeated trials of chance experiments, identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials

  VCMSP233 | Mathematics | Level 6 | Statistics and Probability | Chance

• VCMSP237

  Pose and refine questions to collect categorical or numerical data by observation or survey

  Elaborations

  • narrowing or broadening a question to be posed for an observation or survey, for example, ‘which of these ice cream flavours – vanilla or chocolate?’ to ‘do you like ice cream, if yes what is your favourite flavour?’

  VCMSP237 | Mathematics | Level 6 | Statistics and Probability | Data representation and interpretation

• 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

• VC2M6ST01

  interpret and compare data sets for ordinal and nominal categorical, discrete and continuous numerical variables using comparative displays or visualisations and digital tools; compare distributions in terms of mode, range and shape

  Elaborations

  • determining the range for a numerical data set by finding the difference between the highest and the lowest value in the set and comparing the range for different data sets
  • representing acquired numerical data sets using side-by-side column graphs, comparing the spread of each data set using the range, the highest frequency for each data set using the mode, and discussing the shape
  • representing ordinal data collected through surveys, using visualisation tools including dot plots and bar charts, and discussing the distribution of data in terms of shape
  • using technology to access data sets and graphing software to construct side-by-side column graphs or stacked line graphs; and comparing data sets that are grouped by gender, year level, age group or other variables, and discussing findings

  VC2M6ST01 | Mathematics | Mathematics Version 2.0 | Level 6 | Statistics

• VC2M6ST02

  identify statistically informed arguments presented in traditional and digital media; discuss and critique methods, data representations and conclusions

  Elaborations

  • investigating data representations in the media and discussing what they illustrate and the messages the people who created them might want to convey
  • evaluating reports and secondary data relating to the distribution and use of non-renewable resources around the world
  • identifying potentially misleading data representations in the media; for example, graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made and pie charts in which the whole pie does not represent the entire population about which the claims are made
  • investigating both traditional and digital media relating to Aboriginal and Torres Strait Islander Peoples, identifying and critiquing statistically informed arguments

  VC2M6ST02 | Mathematics | Mathematics Version 2.0 | Level 6 | Statistics

• 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