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• VC2M3A02

  extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator

  Elaborations

  • partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore 15 − 7 = 8 and 15 − 8 = 7
  • using partitioning to develop and record facts systematically (for example, ‘How many ways can 12 monkeys be spread among 2 trees?’, 12 = 12 + 0, 12 = 11 + 1, 12 = 10 + 2, 12 = 9 + 3, …), explaining how they know they have found all possible partitions
  • understanding basic addition and related subtraction facts and using extensions to these facts; for example, 6 + 6 = 12, 16 + 6 = 22, 6 + 7 = 13, 16 + 7 = 23, and 60 + 60 = 120, 600 + 600 = 1200

  VC2M3A02 | Mathematics | Mathematics Version 2.0 | Level 3 | 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

• VC2M3A03

  recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts

  Elaborations

  • using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts
  • recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives
  • practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts
  • systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns

  VC2M3A03 | Mathematics | Mathematics Version 2.0 | Level 3 | Algebra

• VC2M3M01

  identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates

  Elaborations

  • examining the packaging on supermarket items to determine the metric unit used to describe the mass or volume of the contents
  • identifying items that have a mass of one kilogram or 500 grams, or a capacity of one litre or 500 millilitres, and using these benchmarks to estimate the mass or capacity of other things, explaining their reasoning
  • estimating the height of a tree by comparing it to the height of their friend and quoting the result as ‘The tree is about 3 times as tall’; and estimating the capacity of a fish tank by using a litre milk carton as a benchmark
  • choosing and using metres to estimate the dimensions of the classroom

  VC2M3M01 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M3M05

  identify angles as measures of turn and use right angles as a reference to compare angles in everyday situations

  Elaborations

  • using quarter, half and three-quarter turns and comparing them to a right angle, for example, a quarter turn is the same as a right angle; a half a turn is greater than a right angle and is the same as 2 right angles; a three-quarter turn is greater than a right angle and is the same as 3 right angles
  • recognising that right angles occur at the corners of many everyday objects, for example, books, windows, tabletops and whiteboards
  • identifying angles that are bigger than, smaller than and the same as a right angle in the environment; for example, opening doors partially and fully and comparing the angles created to a right angle
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games to investigate angles as measures of turn, for example, in the game Waayin from the Datiwuy People in the northern part of the Northern Territory

  VC2M3M05 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M3M04

  describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute

  Elaborations

  • representing and reading the time on an analog clock using the markings and the positions of the hands, to the nearest minute mark or 5-minute interval
  • reading and connecting analog and digital time, interpreting times, and recognising and using the language of time, for example, 12:15 as a quarter past 12, or 15 minutes past 12; 12:45 as a quarter to one or 15 minutes before one o’clock; and 10:05 as 5 minutes past 10
  • reading analog clocks throughout the day, and noticing and connecting the position of the hour hand and the distance the minute hand has travelled during the current hour

  VC2M3M04 | Mathematics | Mathematics Version 2.0 | Level 3 | Measurement

• VC2M3M02

  measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings

  Elaborations

  • making a measuring tape using metric units of length and using it to measure and compare things, for example, the girth of a tree; and explaining that the lines on a ruler show the beginning and end of each unit
  • using a strip of one-centimetre grid paper to measure and compare the length of objects, connecting this with centimetre units on a ruler and using fractions of a graduation to give a more accurate measure
  • discussing how the capacity of a container or object usually refers to the amount of liquid it can hold, measured in millilitres and litres, and comparing the capacity of different sizes of familiar drinks (for example, 600-millilitre, one-litre, 2-litre and 3-litre milk containers)
  • measuring and comparing the mass of objects and capacity of containers, using measuring jugs and kitchen or other scales and standard metric units of millilitres, litres, grams and kilograms; and interpreting and explaining what the lines on the measuring jug or scales mean
  • comparing the capacity of different beakers used in science lessons and using the numbered graduations to measure out different capacities of liquid

  VC2M3M02 | Mathematics | Mathematics Version 2.0 | Level 3 | 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

• VCMMG141

  Tell time to the minute and investigate the relationship between units of time

  Elaborations

  • recognising there are 60 minutes in an hour and 60 seconds in a minute

  VCMMG141 | Mathematics | Level 3 | Measurement and Geometry | Using units of measurement

• VCMMG140

  Measure, order and compare objects using familiar metric units of length, area, mass and capacity

  Elaborations

  • recognising the importance of using common units of measurement
  • recognising and using centimetres and metres, square centimetres, grams and kilograms, and millilitres and litres
  • measuring the area of rectangles (including squares) by counting the number of square centimetres

  VCMMG140 | Mathematics | Level 3 | Measurement and Geometry | Using units of measurement

• VCMMG142

  Make models of three-dimensional objects and describe key features

  Elaborations

  • exploring the creation of three-dimensional objects, including prisms and pyramids, using origami

  VCMMG142 | Mathematics | Level 3 | Measurement and Geometry | Shape

• 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

• VCMMG143

  Create and interpret simple grid maps to show position and pathways

  Elaborations

  • creating a map of the classroom or playground

  VCMMG143 | Mathematics | Level 3 | Measurement and Geometry | Location and transformation

• VCMMG146

  Identify angles as measures of turn and compare angle sizes in everyday situations

  Elaborations

  • opening doors partially and fully and comparing the size of the angles created
  • recognising that analogue clocks use the turning of arms to indicate time, and comparing the size of angles between the arms for familiar times

  VCMMG146 | Mathematics | Level 3 | Measurement and Geometry | Geometric reasoning

• VCMMG145

  Identify and describe slides and turns found in the natural and built environment

  Elaborations

  • recognising and representing slides and turn used in brickwork around the school
  • recognising and representing slides and turn used in sporting activities

  VCMMG145 | Mathematics | Level 3 | Measurement and Geometry | Location and transformation

• VC2M3N06

  estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations

  Elaborations

  • estimating how much space a grid paper representation of a large number such as 20 200 will take up on the wall and how much paper will be required
  • estimating the number of people in a large gathering (for example, a school assembly) using known numbers (such as how many students per class)
  • choosing which place value they would estimate to for different situations; for example, choosing to estimate to the nearest ten when estimating how many dots on a ladybird or choosing to estimate to the nearest thousand when estimating crowd sizes at a venue
  • checking the reasonableness of an addition calculation by using two- and three-digit numbers to the nearest ten or hundred to estimate; for example, using 200 + 400 = 600 to estimate and check the solution to the calculation 219 + 385

  VC2M3N06 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M3N01

  identify, explain and use the properties of odd and even numbers

  Elaborations

  • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
  • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
  • explaining why some materials can be shared evenly between 2 people without leaving a remainder and some cannot
  • explaining the patterns involved in adding, subtracting and multiplying odd and even numbers (for example, even + even = even, odd + even = odd, odd + odd = even) and using this to decide whether answers to addition, subtraction and multiplication calculations are correct or not
  • following an algorithm consisting of a flow chart with a series of instructions and decisions to determine whether a number is even or odd; and using the algorithm to identify which elements of a set of numbers are divisible by 2

  VC2M3N01 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M3N09

  follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns

  Elaborations

  • following or creating an algorithm to generate number patterns formed by doubling and halving using technology to assist, where appropriate, and identifying and describing emerging patterns
  • following or creating an algorithm that determines whether a given number is a multiple of 2, 5 or 10, identifying and discussing emerging patterns
  • creating an algorithm as a set of instructions that a classmate can follow to generate multiples of 3 using the rule ‘To multiply by 3 you double the number and add on one more of the number’ (for example, for 3 threes, you double 3 and add on 3 to get 9; for 3 fours you double 4 and add one more 4 to get 12 …)
  • creating a sorting algorithm that will sort a collection of 5-cent and 10-cent coins and providing the total value of the collection by applying knowledge of multiples of 5 and 10

  VC2M3N09 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M3N04

  add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator

  Elaborations

  • using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written ‘jottings’ to keep track of the numbers if necessary
  • using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations, for example, to calculate 214 + 325, representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones, resulting in 5 groups of 100, 3 groups of 10 and 9 ones, which is 539
  • choosing between standard and non-standard place value partitions to assist with calculations, for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850
  • solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 − 395, adding 5 to both numbers to make 539 − 400 = 139
  • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems
  • applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week

  VC2M3N04 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M3N08

  use mathematical modelling to solve practical problems involving additive and multiplicative situations, including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms...

  Elaborations

  • modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation
  • modelling additive problems using a bar model to represent the problem; for example, modelling the problem ‘I had 75 tomatoes and then picked some more. Now I have 138. How many did I pick?’
  • modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation
  • modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences, and explaining how the 2 number sentences are connected to the problem
  • modelling the problem of deciding how to share an amount equally (for example, 48 horses into 2, 4, 6 or 8 paddocks), representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions

  VC2M3N08 | Mathematics | Mathematics Version 2.0 | Level 3 | Number