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• VCMNA308

  Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding distance between two points
  • using Pythagoras' theorem to calculate distance between two points

  VCMNA308 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA337

  Solve simultaneous linear equations, using algebraic and graphical techniques including using digital technology

  Elaborations

  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs

  VCMNA337 | Mathematics | Level 10 | Number and Algebra | Linear and non-linear relationships

• VCMNA306

  Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate

  Elaborations

  • understanding that the distributive law can be applied to algebraic expressions as well as numbers
  • understanding the relationship between expansion and factorisation and identifying algebraic factors in algebraic expressions

  VCMNA306 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra

• VCMNA277

  Solve a range of problems involving rates and ratios, including distance-time problems for travel at a constant speed, with and without digital technologies

  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
  • calculating population growth rates in Australia and Asia and explaining their difference
  • finding one of distance travelled, time taken or average speed given the other two quantities

  VCMNA277 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMNA276

  Solve problems involving the use of percentages, including percentage increases and decreases and percentage error, with and without digital technologies

  Elaborations

  • using percentages to solve problems, including those involving mark-ups, discounts, and GST
  • using percentages to calculate population increases and decreases
  • using percentage error to compare relative size of error in calculations involving a given or actual value, and an estimated or measured value

  VCMNA276 | Mathematics | Level 8 | Number and Algebra | Real numbers

• VCMNA184

  Solve problems involving division by a one digit number, including those that result in a remainder

  Elaborations

  • using the fact that equivalent division calculations result if both numbers are divided by the same factor
  • using rounding and making estimates for computations
  • interpreting and representing the remainder in division calculations sensibly for the context

  VCMNA184 | Mathematics | Level 5 | Number and Algebra | Number and place value

• VCMNA136

  Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole

  Elaborations

  • partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes
  • locating unit fractions on a number line
  • recognising that in English the term ‘one third’ is used (order: numerator, denominator) but in other languages, such as Japanese for example, this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator)

  VCMNA136 | Mathematics | Level 3 | Number and Algebra | Fractions and decimals

• VCMNA089

  Represent and solve simple addition and subtraction problems using a range of strategies including counting on, partitioning and rearranging parts

  Elaborations

  • developing a range of mental strategies for addition and subtraction problems

  VCMNA089 | Mathematics | Level 1 | Number and Algebra | Number and place value

• VCMNA114

  Apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction

  Elaborations

  • using technology to construct a sequence of numbers based on constant addition or subtraction from a given starting value
  • sharing a set of objects equally between a small number of groups

  VCMNA114 | Mathematics | Level 2 | Number and Algebra | Patterns and algebra

• 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

• VCMSP206

  Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies

  Elaborations

  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations

  VCMSP206 | Mathematics | Level 5 | Statistics and Probability | Data representation and interpretation

• 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

• VCMSP349

  Determine quartiles and interquartile range and investigate the effect of individual data values, including outliers on the interquartile range

  Elaborations

  • finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the box plot, as tools for both numerically and visually comparing the centre and spread of data sets
  • exploring the effect of varying data values, including outliers, on the interquartile range for different sets of data

  VCMSP349 | Mathematics | Level 10 | Statistics and Probability | Data representation and interpretation

• VCMSP297

  Distinguish between a population and a sample and investigate techniques for collecting data, including census, sampling and observation

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the differences between convenience, judgemental and simple random sampling from a population

  VCMSP297 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VCMMG144

  Identify symmetry in the environment

  Elaborations

  • identifying symmetry in Aboriginal rock carvings or art
  • identifying symmetry in the natural and built environment

  VCMMG144 | Mathematics | Level 3 | Measurement and Geometry | Location and transformation

• VCMMG291

  Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology

  Elaborations

  • understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures
  • establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles are equal
  • exploring tiling patterns in art and design

  VCMMG291 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VCMSP372

  Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation

  Elaborations

  • using the standard deviation to describe the spread of a set of data
  • using the mean and standard deviation to compare numerical data sets
  • constructing distributions for the mean and standard deviation of simple random samples from a population

  VCMSP372 | Mathematics | Level 10A | Statistics and Probability | Data representation and interpretation

• VCMSP325

  Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’

  Elaborations

  • using stem-and-leaf plots to compare two like sets of data such as the heights of girls and the heights of boys in a class
  • describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’ and 'symmetric' and 'bi-modal'

  VCMSP325 | Mathematics | Level 9 | Statistics and Probability | Data representation and interpretation

• 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

• VCMNA185

  Use efficient mental and written strategies and apply appropriate digital technologies to solve problems

  Elaborations

  • choosing between mental, written and a technology-based computation depending on the nature of the problems and the purpose for computation
  • using technology to solve problems and check the reasonableness of answers

  VCMNA185 | Mathematics | Level 5 | Number and Algebra | Number and place value