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• 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

• 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

• VC2M6M03

  measure, calculate and compare elapsed time; interpret and use timetables and itineraries to plan activities and determine the duration of events and journeys

  Elaborations

  • planning a trip involving one or more modes of public transport
  • developing a timetable of daily activities for a planned event, for example, a sports carnival
  • investigating different ways duration is represented in timetables and using different timetables to plan a journey

  VC2M6M03 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• VC2M6N05

  solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions

  Elaborations

  • representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes
  • determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems
  • calculating the addition or subtraction of fractions in the context of real-world problems (for example, using part cups or spoons in a recipe), using the understanding of equivalent fractions
  • understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators

  VC2M6N05 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• 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

• VC2M6N09

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

  Elaborations

  • modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale
  • modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase
  • modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals

  VC2M6N09 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6N04

  apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers

  Elaborations

  • applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
  • applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
  • working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic Games in the women’s long jump or shot-put and comparing school records to the Olympic records
  • deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 − 0.0035 or 2.345 + 1.4999

  VC2M6N04 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• 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