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• VC2M7M04

  identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons

  Elaborations

  • constructing a pair of parallel lines and a pair of perpendicular lines using their properties, a pair of compasses and a ruler and set squares, or using dynamic geometry software
  • using dynamic geometry software to identify relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal
  • using dynamic geometry software to demonstrate how angles and their properties are involved in the design and construction of scissor lifts, folding umbrellas, toolboxes and cherry pickers
  • using geometric reasoning of angle properties to generalise the angle relationships of parallel lines and transversals, and related properties, such as the size of an exterior angle of a triangle is equal to the sum of the sizes of opposite and non-adjacent interior angles, and the sum of the sizes of interior angles in a triangle in the plane is equal to the size of 2 right angles or 180°

  VC2M7M04 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M7ST01

  acquire data sets for discrete and continuous numerical variables and calculate the range, median, mean and mode; make and justify decisions about which measures of central tendency provide useful insights into the nature of the distribution of data

  Elaborations

  • understanding that summarising data by calculating measures of centre can help make sense of the data, commenting on skewness or symmetry of data and the use of mean and median as representative measures
  • comparing the mean, median, mode and range of displays of data from a given context, and explaining how outliers may affect summary statistics
  • recognising how different data sets can have the same measures of central tendency and experimenting with how varying data affects these measures
  • acquiring continuous numerical data by taking measurement samples during a science experiment, observation or field study, comparing measures of central tendency and identifying any anomalies in the distribution of data

  VC2M7ST01 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• 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

• VC2M7SP01

  represent three-dimensional objects in 2 dimensions; discuss and reason about the advantages and disadvantages of different representations

  Elaborations

  • deconstructing packaging to identify shapes and nets
  • using different nets to construct prisms and determining which nets will make a cube, rectangular prism, triangular prism or pyramid
  • using aerial views of buildings and other three-dimensional structures to visualise the footprint made by the building or structure, identifying prisms that could approximate the structure
  • building objects by interpreting isometric and perspective drawings
  • using isometric and square grid paper to draw views of front, back, side, top and bottom of objects
  • exploring different two-dimensional representations of objects in Aboriginal and/or Torres Strait Islander artworks or cultural maps of Country/Place

  VC2M7SP01 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• 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

• Mathematics Version 2.0: Level 7 description

  In Level 7, 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

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7ST03

  plan and conduct statistical investigations for issues involving discrete and continuous numerical data, and data collected from primary and secondary sources; analyse and interpret distributions of data and report findings in terms of shape and summary statistics

  Elaborations

  • obtaining secondary data from newspapers, the internet or the Australian Bureau of Statistics
  • investigating secondary data relating to the distribution and use of non-renewable resources around the world
  • conducting an investigation to draw conclusions about whether teenagers have faster reaction times than adults
  • conducting an investigation to support claims that a modification of a science, technology, engineering and mathematics (STEM) related design has improved performance
  • using secondary data from the Australian Reconciliation Barometer to conduct and report on statistical investigations relating to Aboriginal and Torres Strait Islander Peoples

  VC2M7ST03 | Mathematics | Mathematics Version 2.0 | Level 7 | Statistics

• VC2M7N10

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts such as ‘best buys’; formulate problems, choosing representations and efficient calculation strategies, designing algorithms and using digital tools as appropriate; interpret...

  Elaborations

  • modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero, or in geography when determining altitude above and below sea level
  • modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of the bottle cost to the recycling refund, proportion of the school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted ‘yes’ to a change of school uniform; and interpreting and communicating answers in terms of the context of the situation
  • modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
  • finding the sum of a set of consecutive numbers using a loop structure
  • constructing geometric patterns such as a honeycomb, using dynamic geometry functionality
  • using mathematical modelling to investigate the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt

  VC2M7N10 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7M03

  describe the relationship between π and the circumference, radius and diameter of a circle

  Elaborations

  • recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter and circumference and using one of radius, diameter or circumference to determine the measure of the other 2; and understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by 2π
  • comparing the circumference of circles in relation to their radius and diameter with materials and measuring, to establish measurement formulas; for example, using a compass to draw several circles, then using string to approximate the circumference, comparing the length of string to the diameter of the circle
  • investigating π as the constant in the proportional relationship between the circumference of a circle and its diameter, and historical approximations from different civilisations, including Egypt, Babylon, Greece, India and China
  • investigating the applications and significance of circles in everyday life of Aboriginal and Torres Strait Islander Peoples, such as in basketry, symbols and architecture, recognising the relationships between the centre, radius, diameter and circumference

  VC2M7M03 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M7N01

  describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems

  Elaborations

  • investigating squares of natural numbers from one to 20, and connecting them to visual representations such as dots arranged in a square pattern
  • using the square and square root notation, and the distributive property and area diagrams, to calculate the squares of two-digit numbers; for example, 432=40+32=402+2×40×3+32=1600+240+9=1849
  • determining between which 2 consecutive natural numbers the square root of a given number lies; for example, 43 is between the square numbers 36 and 49 so 43 is between 36 and 49 and therefore between 6 and 7
  • generating a list of perfect square numbers and describing any emerging patterns, for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
  • using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with 144 square tiles has a perimeter of 48 tile lengths

  VC2M7N01 | Mathematics | Mathematics Version 2.0 | Level 7 | Number