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• VC2M4M03

  solve problems involving the duration of time including situations involving ‘am’ and ‘pm’ and conversions between units of time

  Elaborations

  • calculating the amount of time between 2 events, such as the start and finish of a movie, a bus journey or a flight, including cases where the starting and finishing times are written using ‘am’ and ‘pm’ notation
  • converting units of time using relationships between units, such as 60 minutes in an hour and 60 seconds in a minute, to solve problems; for example, creating a daily timetable for an activity such as an athletics carnival or planning an exercise routine with activities and rests
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ explanations of the passing of time through cultural accounts about cyclic phenomena involving the sun, moon and stars

  VC2M4M03 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M5M04

  estimate, construct and measure angles in degrees, using appropriate tools, including a protractor, and relate these measures to angle names

  Elaborations

  • using a protractor to measure angles in degrees and classifying these angles using angle names; for example, an acute angle is less than 90°, an obtuse angle is more than 90° and less than 180°, a right angle is equal to 90° and a reflex angle is more than 180° and less than 360°
  • estimating the size of angles in the environment using a clinometer and describing the angles using angle names
  • using a ruler and protractor to construct triangles, given the angle measures and side lengths
  • using a protractor to measure angles when creating a pattern or string design within a circle
  • recognising the size of angles within shapes that do and do not tessellate, measuring the angles and using the sum of angles to explain why some shapes will tessellate and other shapes do not

  VC2M5M04 | Mathematics | Mathematics Version 2.0 | Level 5 | Measurement

• VC2M3M03

  recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events

  Elaborations

  • estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time
  • planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take
  • reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock
  • using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes
  • exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars

  VC2M3M03 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VCMMG345

  Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

  Elaborations

  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements

  VCMMG345 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning

• VCMMG346

  Solve right-angled triangle problems including those involving direction and angles of elevation and depression

  Elaborations

  • applying Pythagoras's Theorem and trigonometry to problems in surveying and design

  VCMMG346 | Mathematics | Level 10 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG290

  Solve problems involving duration, including using 12- and 24-hour time within a single time zone

  Elaborations

  • identifying regions in Australia and countries in Asia that are in the same time zone

  VCMMG290 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG229

  Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies

  Elaborations

  • understanding which attributes of a shape remain the same or change under the effects of transformations such as size, shape or orientation
  • creating tessellations with simple shapes or simple composite shapes

  VCMMG229 | Mathematics | Level 6 | Measurement and Geometry | Location and transformation

• VC2M6N01

  recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane

  Elaborations

  • extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (−2) and (+2) and their relationship to zero as −2 < 0 < 2
  • using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event
  • using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero (for example, elevators, above and below sea level) and distinguishing a location by referencing the 4 quadrants of the Cartesian plane
  • recognising that the sign (positive or negative) indicates a direction in relation to zero – for example, 30 metres left of the admin block is (−30) and 20 metres right of the admin block is (+20) – and programming robots to move along a number line that is either horizontal or vertical but not both at the same time
  • representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line

  VC2M6N01 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M5N08

  check and explain the reasonableness of solutions to problems, including financial contexts using estimation strategies appropriate to the context

  Elaborations

  • interpreting a series of contextual problems to decide whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
  • recognising the effect of rounding addition, subtraction, multiplication and division calculations, and rounding both numbers up, both numbers down, and one number up and one number down; and explaining which estimation is the best approximation and why
  • considering the type of rounding that is appropriate when estimating the amount of money required; for example, rounding up or rounding down when buying one item from a store using cash, compared to rounding up the cost of every item when buying groceries to estimate the total cost and not rounding when the financial transactions are digital

  VC2M5N08 | Mathematics | Mathematics Version 2.0 | Level 5 | Number

• VC2M4N07

  choose and use estimation and rounding to check and explain the reasonableness of calculations, including the results of financial transactions

  Elaborations

  • using proficiency with basic facts to estimate the result of a calculation and say what amounts the answer will be between; for example, 5 packets of biscuits at $2.60 each will cost between $10 and $15 as 5 × $2 = $10 and 5 × $3 = $15
  • using rounded amounts to complete an estimated budget for a shopping trip or an excursion, explaining why overestimating the amounts is appropriate
  • recognising the effect of rounding in addition and multiplication calculations; rounding both numbers up, both numbers down, and one number up and one number down, and explaining which is the best approximation and why

  VC2M4N07 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M8N05

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

  Elaborations

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

  VC2M8N05 | Mathematics | Mathematics Version 2.0 | Level 8 | Number

• VC2M4N04

  count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines

  Elaborations

  • cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence ‘one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters … eight-quarters or two-wholes ...’
  • subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; and counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines
  • converting mixed numerals into improper fractions and vice versa, and representing mixed numerals on a number line
  • using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one

  VC2M4N04 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VCMNA070

  Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond

  Elaborations

  • understanding that each object must be counted only once, that the arrangement of objects does not affect how many there are, and that the last number counted answers the ‘how many’ question
  • using scenarios to help students recognise that other cultures count in a variety of ways, such as by placing one pebble in a bag to represent one object. For example to count the number of cattle

  VCMNA070 | Mathematics | Foundation Level | Number and Algebra | Number and place value

• VCMNA158

  Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line

  Elaborations

  • converting mixed numbers to improper fractions and vice versa
  • investigating the use of fractions and sharing as a way of managing Country: for example taking no more than half the eggs from a nest to protect future bird populations

  VCMNA158 | Mathematics | Level 4 | Number and Algebra | Fractions and decimals

• 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

• VCMNA309

  Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding midpoint and gradient
  • recognising that the gradient of a line is the same as the gradient of any line segment on that line

  VCMNA309 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• 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