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• 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

• 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

• VCMNA255

  Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point

  Elaborations

  • plotting points from a table of integer values and recognising simple patterns, such as points that lie on a straight line

  VCMNA255 | Mathematics | Level 7 | Number and Algebra | Linear and non-linear relationships

• VCMNA256

  Solve simple linear equations

  Elaborations

  • solving equations using concrete materials, such as the balance model, and explain the need to do the same thing to each side of the equation using substitution to check solutions
  • investigating a range of strategies to solve equations

  VCMNA256 | Mathematics | Level 7 | Number and Algebra | Linear and non-linear relationships

• VCMNA257

  Investigate, interpret and analyse graphs from real life data, including consideration of domain and range

  Elaborations

  • using travel graphs to investigate and compare the distance travelled to and from school
  • interpreting features of travel graphs such as the slope of lines and the meaning of horizontal lines
  • using graphs of evaporation rates to explore water storage
  • describing and comparing temperature during a day at different times of the year from the corresponding graphs

  VCMNA257 | Mathematics | Level 7 | Number and Algebra | Linear and non-linear relationships

• VCMNA240

  Apply the associative, commutative and distributive laws to aid mental and written computation and make estimates for these computations

  Elaborations

  • simplifying calculations
  • forming simple estimates for calculations involving multiple and/or combined operations

  VCMNA240 | Mathematics | Level 7 | Number and Algebra | Number and place value

• VCMNA241

  Compare, order, add and subtract integers

  Elaborations

  • using a variety of models to represent, add and subtract integers

  VCMNA241 | Mathematics | Level 7 | Number and Algebra | Number and place value

• VCMNA251

  Introduce the concept of variables as a way of representing numbers using letters

  Elaborations

  • understanding that arithmetic laws are powerful ways of describing and simplifying calculations and that using these laws leads to the generality of algebra

  VCMNA251 | Mathematics | Level 7 | Number and Algebra | Patterns and algebra

• VCMNA250

  Investigate and calculate 'best buys', with and without digital technologies

  Elaborations

  • applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g

  VCMNA250 | Mathematics | Level 7 | Number and Algebra | Money and financial mathematics

• VCMNA239

  Investigate and use square roots of perfect square numbers

  Elaborations

  • investigating square numbers such as 25 and 36 and developing square-root notation
  • investigating between which two whole numbers a square root lies

  VCMNA239 | Mathematics | Level 7 | Number and Algebra | Number and place value

• VCMNA252

  Create algebraic expressions and evaluate them by substituting a given value for each variable

  Elaborations

  • using authentic formulas to perform substitutions

  VCMNA252 | Mathematics | Level 7 | Number and Algebra | Patterns and algebra

• VCMNA238

  Investigate index notation and represent whole numbers as products of powers of prime numbers

  Elaborations

  • defining and comparing prime and composite numbers and explaining the difference between them
  • applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation

  VCMNA238 | Mathematics | Level 7 | Number and Algebra | Number and place value

• VCMNA253

  Extend and apply the laws and properties of arithmetic to algebraic terms and expressions

  Elaborations

  • identifying order of operations in contextualised problems, preserving the order by inserting brackets in numerical expressions, then recognising how order is preserved by convention
  • moving fluently between algebraic and word representations as descriptions of the same situation

  VCMNA253 | Mathematics | Level 7 | Number and Algebra | Patterns and algebra

• VCMNA254

  Design and implement mathematical algorithms using a simple general purpose programming language

  Elaborations

  • finding the sum of a set of consecutive numbers using a loop structure
  • constructing geometric patterns such as a honeycomb, using dynamic geometry functionality

  VCMNA254 | Mathematics | Level 7 | Number and Algebra | Patterns and algebra

• VC2M7P01

  identify the sample space for single-stage experiments; assign probabilities to the possible outcomes and predict relative frequencies for related experiments.

  Elaborations

  • discussing the meaning of probability terminology, for example, ‘probability’, ‘sample space’, ‘favourable outcome’, ‘trial’, ‘experiment’ and ‘event’
  • listing sample spaces for games involving throwing a coin or a dice, spinners, or lucky dip
  • assigning the probability for throwing a 6 on a dice and using this to predict the number of times a 6 will occur when a dice is thrown multiple times

  VC2M7P01 | Mathematics | Mathematics Version 2.0 | Level 7 | Probability

• VC2M7P02

  conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predicted with observed results, explaining the differences and the effect of sample size on the outcomes 

  Elaborations

  • developing an understanding of the law of large numbers through using experiments and simulations to conduct large numbers of trials for seemingly random events and discussing findings
  • conducting simulations using online simulation tools and comparing the combined results of a large number of trials to predicted results
  • exploring and observing Aboriginal and/or Torres Strait Islander children’s instructive games – for example, Koara from the Jawi and Bardi Peoples of Sunday Island in Western Australia – to investigate probability, predicting outcomes for an event and comparing with increasingly larger numbers of trials, and comparing observed and expected results

  VC2M7P02 | Mathematics | Mathematics Version 2.0 | Level 7 | Probability

• 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

• VC2M7SP03

  describe the effect of transformations of a set of points using coordinates in the Cartesian plane, including translations, reflections in an axis, and rotations about the origin

  Elaborations

  • using digital tools to transform shapes in the Cartesian plane, describing and recording the transformations
  • describing patterns and investigating different ways to produce the same transformation, such as using 2 successive reflections to provide the same result as a translation
  • experimenting with, creating and re-creating patterns using combinations of translations, reflections and rotations, using digital tools

  VC2M7SP03 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VC2M7SP04

  design algorithms involving a sequence of steps and decisions that will sort and classify sets of shapes according to their attributes, and describe how the algorithms work

  Elaborations

  • creating a classification scheme for triangles based on sides and angles, using a flow chart that uses sequences and decisions
  • creating a flow chart or hierarchy for quadrilaterals that shows the relationships between trapeziums, parallelograms, rhombuses, rectangles, squares and kites
  • creating a classification scheme for regular, irregular, concave or convex polygons that are sorted according to the number of sides

  VC2M7SP04 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VCMSP269

  Construct and compare a range of data displays including stem-and-leaf plots and dot plots

  Elaborations

  • understanding that some data representations are more appropriate than others for particular data sets, and answering questions about those data sets
  • 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

  VCMSP269 | Mathematics | Level 7 | Statistics and Probability | Data representation and interpretation