Search results

Result list

• 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

• VC2M1M02

  measure the length of shapes and objects using informal units, recognising that units need to be uniform and used end-to-end

  Elaborations

  • using 2 different units (for example, icy pole sticks and pencils) to measure the length of an object (for example, a desk), and explaining why the number of units used may be different
  • comparing the length of 2 objects, such as a desk and a bookshelf, by laying multiple copies of a unit and counting to say which is longer and how much longer; and explaining why they should not have gaps or overlaps between the units, as this will change the length of the unit
  • measuring the distance between 2 locations using footsteps, comparing the results and explaining why there may be different results, for example, referring to the different lengths of footsteps as using different units
  • measuring and comparing the length of objects using blocks; for example, comparing the height of 2 toys by stacking blocks one on top of the other and counting how many it takes to reach the height of each object to decide which is taller

  VC2M1M02 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• Mathematics Version 2.0: Level 3 description

  In Level 3, 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

• VC2M6ST03

  plan and conduct statistical investigations by posing and refining questions to collect categorical or numerical data by observation or survey, or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation

  Elaborations

  • selecting and using appropriate peripherals; for example, using a scientific probe to collect data about changing soil moisture for plants, interpreting the data and sharing the results as a digital chart
  • using a spreadsheet to record and analyse data, recognising the difference between cell formats in spreadsheets; for example, changing the default general format to numerical, text or date as needed
  • investigating the daily water usage by a student in the home compared to the World Health Organization claim that between 50 and 100 litres of clean water is needed per person per day
  • collecting sample sets of ‘discrete numerical data’ (for example, the number of cars or pets in a household), where the class is surveyed, then other classes are surveyed, and data is analysed and compared, discussing findings
  • collecting ordinal categorical data through the use of a survey; for example, surveying each member of the class, by asking them to indicate their preference on a five-point scale for a particular graphic and colour combination of a proposed school logo
  • collecting ordinal data for ranking nominees for school captain with respect to several criteria, contrasting the use of a five-point scale compared with using a four-point scale

  VC2M6ST03 | Mathematics | Mathematics Version 2.0 | Level 6 | Statistics

• VC2M8ST01

  distinguish between a population and a sample, and investigate techniques for data collection including census, sampling, experiment and observation, and explain the practicalities and implications of obtaining data through these techniques

  Elaborations

  • identifying situations where data can be collected by census and those where a sample is appropriate
  • investigating the practicalities and implications of obtaining data through sampling, using a variety of investigative processes; for example, investigating situations when random sampling or non-random sampling is used to collect data and the implication of each sampling method
  • discussing how observations, experiments and sampling methods can be impacted by bias; for example, recognising that a sampling bias occurs when certain members of a population are more likely to be selected in a sample than others, such as a survey conducted at a shopping centre, and recognising that environmental conditions may bias the results of scientific investigations if experiments are conducted at different times or under different conditions
  • using digital tools such as simulations and digital measuring devices to observe, measure and record qualitative and quantitative data, discussing precision and the implications of error

  VC2M8ST01 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• VC2M10M02

  interpret and use logarithmic scales in applied contexts involving small and large quantities and change 

  Elaborations

  • understanding that the logarithmic scale is calibrated in terms of order of magnitude, for example, doubling or powers of 10
  • identifying and interpreting data representations (charts and graphs) that use logarithmic scales (for example, graphs representing percentage change, a wide range of values or exponential growth) and discussing when it is appropriate to use this type of scale and when it is not appropriate
  • investigating and interpreting logarithmic scales used in real-world contexts (for example, Richter, decibel and sensitivity scales or growth in investments, timescales and the spread of microorganisms and disease) and describing reasons for choosing to use a logarithmic scale rather than a linear scale
  • investigating dating methods of geological sites to provide evidence of Aboriginal and Torres Strait Islander Peoples’ presence in Australia, including the Madjedbebe dig in the Northern Territory, that use logarithmic scales, scientific notation and measurement accuracy in the dating

  VC2M10M02 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M4ST01

  acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created

  Elaborations

  • investigating many-to-one data displays using digital tools and graphical software, interpreting and discussing key features
  • understanding that data can be represented with one symbol representing more than one piece of data, and that it is important to read all information about a representation before making judgements
  • constructing graphs of data collected through observation during science experiments, recording, interpreting and discussing the results in terms of the scientific study
  • acquiring samples of data using practical activities, observations or repeated chance experiments; recording data using tally charts, digital tables or spreadsheets; and graphing, discussing and comparing the results using a column graph
  • using secondary data of fire burns to construct data displays that assist Aboriginal and/or Torres Strait Islander ranger groups and other groups to care for Country/Place

  VC2M4ST01 | Mathematics | Mathematics Version 2.0 | Level 4 | Statistics

• 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

• 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

• VC2M7A01

  recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown

  Elaborations

  • linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length × width as
    A=l×w; or using p=6g+b to describe a total of points expressed as goals (worth 6 points) and behinds (worth one point)
  • interpreting and using formulas obtained from other sources, for example, maximum heart rates and target heart rates for moderate exercise
  • substituting numerical values for variables when using formulas and calculating the value of an unknown in practical situations; for example, calculating weekly wage W given base wage b and overtime hours h at 1.5 times rate r, W=b+1.5 ×h ×r, using values for mass m and volume v to determine density d of a substance where d=mv
  • using everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables

  VC2M7A01 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M4A01

  find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations

  Elaborations

  • demonstrating the commutative properties of addition using materials, diagrams and number lines; for example, using number lines to demonstrate that 5 + 2 = 2 + 5, and demonstrating that 2 + 2 + 3 = 7 and 2 + 3 + 2 = 7 and 3 + 2 + 2 = 7
  • using balance scales and informal uniform units to create addition or subtraction number sentences showing equivalence, such as 7 + 8 = 6 + 9, and to find unknowns in equivalent number sentences, such as 6 + 8 = □ + 10
  • using relational thinking and knowledge of equivalent number sentences to explain whether equations involving addition or subtraction are true; for example, explaining that 27 − 14 = 17 − 4 is true and using a number line to show the common difference is 13

  VC2M4A01 | Mathematics | Mathematics Version 2.0 | Level 4 | Algebra

• VC2M3A01

  recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences

  Elaborations

  • partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)
  • using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place

  VC2M3A01 | Mathematics | Mathematics Version 2.0 | Level 3 | Algebra

• VC2M4N01

  recognise and extend the application of place value to tenths and hundredths and use the conventions of decimal notation to name and represent decimals

  Elaborations

  • using a bar to represent the whole, dividing it into 10 equal pieces with each piece representing 0.1 or one-tenth of the whole length and understanding that 2 pieces are 0.2 or two-tenths of the whole
  • using materials to show the multiplicative relationship between the whole, tenths and hundredths; for example, using a bundle of 10 straws to represent the whole, one straw as the tenth, and cutting the tenth into 10 parts to show the hundredths; or using deci-pipes to represent tenths
  • recognising that one is the same as ten-tenths and one-tenth is the same as ten-hundredths and using this relationship to rename decimals; for example, renaming 0.25 as two-tenths and five-hundredths or twenty-five-hundredths
  • making models of measurement attributes to show the relationship between the base unit and parts of the unit, for example, 1.5 metres is one metre and five-tenths of the next metre; 1.75 units is one unit and seventy-five-hundredths of the next unit
  • counting large quantities of mixed notes and coins, writing the total using dollars and cents, and recognising the cents as parts of the next dollar
  • comparing the way money and measures are read and said, and explaining how they are the same and different; for example, explaining that $2.75 is said ‘two dollars seventy-five’ and 2.75 metres is said ‘two point seven five metres’, and recognising that the 7 means seven-tenths and the 5 means five-hundredths in both

  VC2M4N01 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• 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