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• VCMNA189

  Recognise that the place value system can be extended beyond hundredths

  Elaborations

  • using knowledge of place value and division by 10 to extend the number system to thousandths and beyond
  • recognising the equivalence of one thousandths and 0.001

  VCMNA189 | Mathematics | Level 5 | Number and Algebra | Fractions and decimals

• VCMNA303

  Express numbers in scientific notation

  Elaborations

  • representing extremely large and small numbers in scientific notation, and numbers expressed in scientific notation as whole numbers or decimals

  VCMNA303 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCMNA159

  Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation

  Elaborations

  • using division by 10 to extend the place-value system
  • using knowledge of fractions to establish equivalences between fractions and decimal notation

  VCMNA159 | Mathematics | Level 4 | Number and Algebra | Fractions and decimals

• VCMSP179

  Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values

  Elaborations

  • exploring ways of presenting data and showing the results of investigations
  • investigating data displays using many-to-one correspondence

  VCMSP179 | Mathematics | Level 4 | Statistics and Probability | Data representation and interpretation

• VCMNA092

  Recognise, describe and order Australian coins according to their value

  Elaborations

  • showing that coins are different in other countries by comparing Asian coins to Australian coins
  • understanding that the value of Australian coins is not related to size
  • describing the features of coins that make it possible to identify them

  VCMNA092 | Mathematics | Level 1 | Number and Algebra | Money and financial mathematics

• VCMMG315

  Investigate very small and very large time scales and intervals

  Elaborations

  • investigating the usefulness of scientific notation in representing very large and very small numbers

  VCMMG315 | Mathematics | Level 9 | Measurement and Geometry | Using units of measurement

• VCMNA111

  Count and order small collections of Australian coins and notes according to their value

  Elaborations

  • identifying equivalent values in collections of coins or notes, such as two five-cent coins having the same value as one 10-cent coin
  • counting collections of coins or notes to make up a particular value, such as that shown on a price tag

  VCMNA111 | Mathematics | Level 2 | Number and Algebra | Money and financial mathematics

• 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

• VCMNA088

  Count collections to 100 by partitioning numbers using place value

  Elaborations

  • understanding partitioning of numbers and the importance of grouping in tens
  • understanding two-digit numbers as being comprised of tens and ones/units

  VCMNA088 | Mathematics | Level 1 | Number and Algebra | Number and place value

• VCMSP300

  Investigate the effect of individual data values including outliers, on the range, mean and median

  Elaborations

  • using displays of data to explore and investigate effects
  • exploring the effect of outliers on the range for different sets of data by comparing its value with and without outliers included

  VCMSP300 | Mathematics | Level 8 | Statistics and Probability | Data representation and interpretation

• VCMNA153

  Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

  Elaborations

  • recognising and demonstrating that the place-value pattern is built on the operations of multiplication or division of tens

  VCMNA153 | Mathematics | Level 4 | Number and Algebra | Number and place value

• VCMNA137

  Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents

  Elaborations

  • recognising the relationship between dollars and cents, and that not all countries use these denominations and divisions. For example, the Japanese Yen

  VCMNA137 | Mathematics | Level 3 | Number and Algebra | Money and financial mathematics

• VCMNA333

  Substitute values into formulas to determine an unknown and re-arrange formulas to solve for a particular term

  Elaborations

  • solving simple equations arising from formulas
  • re-arranging expressions to make a specified variable the subject such as calculating the radius of a sphere to produce a given volume

  VCMNA333 | Mathematics | Level 10 | Number and Algebra | Patterns and algebra

• VCMNA131

  Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

  Elaborations

  • recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones
  • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations

  VCMNA131 | Mathematics | Level 3 | Number and Algebra | Number and place value

• 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

• VCMSP102

  Represent data with objects and drawings where one object or drawing represents one data value. Describe the displays

  Elaborations

  • understanding one-to-one correspondence
  • describing displays by identifying categories with the greatest or least number of objects

  VCMSP102 | Mathematics | Level 1 | Statistics and Probability | Data representation and interpretation

• VCMSP180

  Evaluate the effectiveness of different displays in illustrating data features including variability

  Elaborations

  • interpreting data representations in the media and other forums in which symbols represent more than one data value
  • suggesting questions that can be answered by a given data display and using the display to answer questions

  VCMSP180 | Mathematics | Level 4 | Statistics and Probability | Data representation and interpretation

• 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

• VCMMG368

  Use the unit circle to define trigonometric functions as functions of a real variable, and graph them with and without the use of digital technologies

  Elaborations

  • establishing the symmetrical properties of trigonometric functions
  • investigating angles of any magnitude
  • understanding that trigonometric functions are periodic and that this can be used to describe motion
  • identifying points on the unit circle via arc lengths in radians, which correspond to specified values of the circular functions sine, cosine and tangent

  VCMMG368 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• 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