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• VCMMG265

  Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning

  Elaborations

  • constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
  • defining and identifying the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal

  VCMMG265 | Mathematics | Level 7 | Measurement and Geometry | Geometric reasoning

• 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

• 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

• VC2M7A05

  generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

  Elaborations

  • plotting points from a table of values generated using simple linear functions and recognising patterns, such as the points lie on a straight line
  • discussing and using variables to create a general rule and using the rule to determine the value of the dependent variable for any given value of the independent variable; for example, plotting the value of the circumference of a circle for varying values of radius
  • using function machines to generate a table of ordered pairs using input and output values, plotting the relationships on a Cartesian plane and describing the graph in terms of shape
  • using diagrams and manipulatives to form linear growth patterns, representing these patterns in tables and describing the relationship in terms of the way the pattern is growing and in the context of the situation

  VC2M7A05 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7M01

  establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem-solving

  Elaborations

  • building on the understanding of the area of rectangles to develop formulas for the area of triangles
  • establishing that the area of a triangle is half the area of an appropriate rectangle
  • using area formulas for rectangles and triangles to solve problems involving areas of surfaces

  VC2M7M01 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VCMMG258

  Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving

  Elaborations

  • building on the understanding of the area of rectangles to develop formulas for the area of triangles
  • establishing that the area of a triangle is half the area of an appropriate rectangle
  • using area formulas for rectangles and triangles to solve problems involving areas of surfaces

  VCMMG258 | Mathematics | Level 7 | Measurement and Geometry | Using units of measurement

• VCMSP271

  Describe and interpret data displays using median, mean and range

  Elaborations

  • using mean and median to compare data sets and explaining how outliers may affect the comparison
  • locating mean, median and range on graphs and connecting them to real life

  VCMSP271 | Mathematics | Level 7 | Statistics and Probability | Data representation and interpretation

• VC2M7A02

  apply the associative, commutative and distributive laws to aid mental and written computation, and formulate algebraic expressions using constants, variables, operations and brackets

  Elaborations

  • simplifying calculations
  • forming simple estimates for calculations involving multiple and/or combined operations
  • generalising arithmetic expressions to algebraic expressions involving constants, variables, operations and brackets; for example, 7+7+7=3×7, x+x+x=3×x noting that 3x includes implied multiplication and recognising the difference between 3x+4 and 3x+4
  • formulating algebraic expressions that represent mathematical relationships; for example, translating from words to symbols in ‘think of a number’ type activities
  • recognising and applying the concept of variable as something that can change in value, investigating the relationships between variables, and the application to processes on Country/Place, including how cultural expressions of Aboriginal and Torres Strait Islander Peoples, such as storytelling, communicate mathematical relationships that can be represented as mathematical expressions

  VC2M7A02 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VCMNA249

  Recognise and solve problems involving simple ratios

  Elaborations

  • understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem

  VCMNA249 | Mathematics | Level 7 | Number and Algebra | Real numbers

• VCMSP270

  Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data

  Elaborations

  • understanding that summarising data by calculating measures of centre and spread can help make sense of the data

  VCMSP270 | Mathematics | Level 7 | Statistics and Probability | Data representation and interpretation

• VC2M7A06

  manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables

  Elaborations

  • experimenting with different sets of tables of values from formulas; for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height
  • using spreadsheets and the formula function to recognise the effect of changing parameters on the entries in cells
  • analysing distance travelled for different combinations of average speed and time of travel using a table of values and the distance formula

  VC2M7A06 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VCMNA247

  Connect fractions, decimals and percentages and carry out simple conversions

  Elaborations

  • justifying choices of written, mental or calculator strategies for solving specific problems including those involving large numbers
  • understanding that quantities can be represented by different number types and calculated using various operations, and that choices need to be made about each
  • calculating the percentage of the total local municipal area set aside for parkland, manufacturing, retail and residential dwellings to compare land use

  VCMNA247 | Mathematics | Level 7 | Number and Algebra | Real numbers

• VC2M7SP02

  classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

  Elaborations

  • using strips of paper with parallel sides to make triangles and quadrilaterals, and contrasting the rigidity of triangles with the flexibility of quadrilaterals
  • constructing triangles with 3 given side lengths and discussing the question ‘Can any 3 lengths be used to form the sides of a triangle?’
  • identifying and communicating about side and angle properties of scalene, isosceles, equilateral, right-angled, acute and obtuse triangles using geometric conventions
  • describing, comparing and contrasting squares, rectangles, rhombuses, parallelograms, kites and trapeziums, explaining the relationships between these shapes

  VC2M7SP02 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• 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

• VC2M7N08

  compare, order and solve problems involving addition and subtraction of integers

  Elaborations

  • using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as -5<+2; -3>-6
  • discussing language such as ‘addition’, ‘subtraction’, ‘magnitude’, ‘difference’ and ‘sign’ and synonyms of these terms
  • ordering, adding and subtracting integers using a number line

  VC2M7N08 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N06

  use the 4 operations with positive rational numbers, including fractions and decimals, to solve problems using efficient mental and written calculation strategies

  Elaborations

  • solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
  • choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 18, 0.125 or 1251000
  • developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 23 of 12 , giving 12 of 23=13
  • solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
  • developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
  • carrying out calculations to solve problems using the representation that makes computations efficient, such as 12.5% of 96 is more efficiently calculated as 18 of 96, including contexts such as comparing land use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases or decreases in energy accounts each account cycle

  VC2M7N06 | Mathematics | Mathematics Version 2.0 | Level 7 | Number