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• 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

• VC2M4A02

  recall and demonstrate proficiency with multiplication facts up to 10 × 10 and related division facts, and explain the patterns in these; extend and apply facts to develop efficient mental and written strategies for computation with larger numbers without a calculator

  Elaborations

  • using arrays on grid paper or created with blocks or counters to develop, represent and explain patterns in multiplication facts up to 10 × 10; and using the arrays to explain the related division facts
  • using materials or diagrams to develop and record multiplication strategies such as doubling, halving, commutativity and adding one more or subtracting from a group to reach a known fact; for example, creating multiples of 3 on grid paper and doubling to find multiples of 6, and recording and explaining the connections to the × 3 and × 6 multiplication facts: 3, 6, 9, … doubled is 6, 12, 18, …
  • using known multiplication facts for 2, 3, 5 and 10 to establish multiplication facts for 4, 6, 7, 8 and 9 in different ways; for example, using multiples of 10 to establish the multiples of 9 as ‘to multiply a number by 9 you multiply by 10 then take the number away’: 9 × 4 = 10 × 4 − 4, so 9 × 4 is 40 − 4 = 36; or using multiples of 3 as ‘to multiply a number by 9 you multiply by 3, and then multiply the result by 3 again’
  • using arrays and known multiplication facts for twos and fives to develop the multiplication facts for sevens, applying the distributive property of multiplication; for example, when finding 6 × 7, knowing that 7 is made up of 2 and 5, and using an array to show that 6 × 7 is the same as 6 × 2 + 6 × 5 = 12 + 30, which is 42

  VC2M4A02 | Mathematics | Mathematics Version 2.0 | Level 4 | Algebra

• 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

• VC2M4M02

  recognise ways of measuring and approximating the perimeter and area of shapes and enclosed spaces, using appropriate formal and informal units

  Elaborations

  • recognising that perimeter is the sum of the lengths that form the boundary of a shape or enclosed space; choosing suitable units from a range of objects to measure around the boundary of a shape such as a garden bed; comparing the results to say which unit was an appropriate choice for the context; and using a piece of string or rope to measure the perimeter of irregular shapes and enclosed spaces, including those that have curved sections
  • creating a range of rectangles representing ‘paddocks’ on grid paper and establishing different methods of working out the length of the boundary fences; and explaining that the more efficient methods involve adding the side lengths rather than counting squares
  • recognising that area is the space enclosed by the boundary of a shape or the surface of an object; measuring and comparing the area of shapes using an array of paper tiles or mosaic squares, including part units to fill gaps at the edge of the shapes; and comparing the total areas by combining the fractional parts to make whole units
  • demonstrating how to use one unit repeatedly to measure the area of a shape (for example, using one paper square to measure and compare the area of a rectangle and a triangle) and recording and explaining how they used part units to give a more accurate measure, and why they needed to ensure there were no gaps or overlaps
  • investigating the ways Aboriginal and/or Torres Strait Islander ranger groups and other groups measure areas of land to make decisions about fire burns to care for Country/Place

  VC2M4M02 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M4M04

  estimate and compare angles using angle names including acute, obtuse, straight angle, reflex and revolution, and recognise their relationship to a right angle

  Elaborations

  • classifying the interior angles of a range of shapes, using examples of angles to identify acute, obtuse, right and reflex angles
  • identifying angles within the environment and estimating whether they are acute, obtuse, right or reflex
  • creating a right-angle template using cardboard or a double-folded piece of paper and using it to compare angles in the environment, commenting on whether they are smaller than or greater than a right angle
  • using different measuring tools such as a spirit level or set squares to determine whether lines or objects are straight, square or perpendicular (at right angles)

  VC2M4M04 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VC2M4M01

  use scaled and digital instruments to interpret unmarked and partial units to measure and compare lengths, masses, capacities, durations and temperatures, using appropriate units

  Elaborations

  • reading the mass of objects measured with digital and analog kitchen scales and explaining what unit of mass the lines on the analog scales refer to
  • deciding on which attribute, unit and measuring instrument to use to compare the length and mass of various things, such as the distance travelled by an object in a science investigation; and explaining the use of units such as grams or millimetres to give accurate measures when needed
  • using scaled instruments such as tape measures, measuring jugs, kitchen scales and thermometers to record measures using whole units (for example, 560 millimetres) or whole and part units (for example, 5.25 metres, 1.75 litres, 2.5 kilograms, 28.5° Celsius)
  • reading and interpreting the scale of an analog clock without marked minutes to estimate the time to the nearest minute and to determine the duration of time between events
  • using the timer or alarm function of a clock to alert when a specified duration has elapsed from a given starting time, for example, for the different activities of an exercise routine
  • making a scaled measuring instrument such as a tape measure, ruler, sand timer, sundial or measuring cup using scaled instruments and direct comparisons
  • exploring the different types of scaled instruments used by Aboriginal and/or Torres Strait Islander ranger groups and other groups to make decisions about caring for Country/Place, and modelling these in local contexts

  VC2M4M01 | Mathematics | Mathematics Version 2.0 | Level 4 | Measurement

• VCMMG173

  Create symmetrical patterns, pictures and shapes with and without digital technologies

  Elaborations

  • using stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art

  VCMMG173 | Mathematics | Level 4 | Measurement and Geometry | Location and transformation

• VCMMG172

  Use simple scales, legends and directions to interpret information contained in basic maps

  Elaborations

  • identifying the scale used on maps of cities and rural areas in Australia and a city in Indonesia and describing the difference
  • using directions to find features on a map

  VCMMG172 | Mathematics | Level 4 | Measurement and Geometry | Location and transformation

• VCMMG165

  Use scaled instruments to measure and compare lengths, masses, capacities and temperatures

  Elaborations

  • reading and interpreting, to the nearest graduation, the graduated scales on a range of measuring instruments

  VCMMG165 | Mathematics | Level 4 | Measurement and Geometry | Using units of measurement

• VCMMG174

  Compare angles and classify them as equal to, greater than or less than a right angle

  Elaborations

  • creating angles and comparing them to a right angle using digital technologies

  VCMMG174 | Mathematics | Level 4 | Measurement and Geometry | Geometric reasoning

• VCMMG168

  Use am and pm notation and solve simple time problems

  Elaborations

  • calculating the time spent at school during a normal school day
  • calculating the time required to travel between two locations
  • determining arrival time given departure time

  VCMMG168 | Mathematics | Level 4 | Measurement and Geometry | Using units of measurement

• VCMMG170

  Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies

  Elaborations

  • identifying common two-dimensional shapes that are part of a composite shape by re-creating it from these shapes
  • creating two-dimensional shapes from verbal or written instructions

  VCMMG170 | Mathematics | Level 4 | Measurement and Geometry | Shape

• VCMMG166

  Compare objects using familiar metric units of area and volume

  Elaborations

  • comparing areas using grid paper
  • comparing volume using centicubes
  • recognising that metric units are not the only units used throughout the world, for example measuring the area of floor space using tatami mats (Japan), using squares for room and house area (Australia)

  VCMMG166 | Mathematics | Level 4 | Measurement and Geometry | Using units of measurement

• VCMMG169

  Compare the areas of regular and irregular shapes by informal means

  Elaborations

  • comparing areas using metric units, such as counting the number of square centimetres required to cover two areas by overlaying the areas with a grid of centimetre squares

  VCMMG169 | Mathematics | Level 4 | Measurement and Geometry | Shape

• VCMMG167

  Convert between units of time

  Elaborations

  • identifying and using the correct operation for converting units of time

  VCMMG167 | Mathematics | Level 4 | Measurement and Geometry | Using units of measurement

• VCMMG171

  Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects

  Elaborations

  • describing the similarities and differences between two-dimensional shapes and three-dimensional objects
  • recognising two-dimensional shapes that are the faces for three-dimensional objects such as prisms, pyramids and platonic solids (including tetrahedrons, cubes and dodecahedrons)

  VCMMG171 | Mathematics | Level 4 | Measurement and Geometry | Shape

• 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

• VC2M4N10

  follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns

  Elaborations

  • creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely
  • creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and recording the sequence of numbers generated; and checking results and describing any emerging patterns
  • using a multiplication formula in a spreadsheet and the ‘fill down’ function to generate a sequence of numbers (for example, entering the number ‘1’ in the cell A1, using ‘fill down’ to cell A100, entering the formula ‘=A1*4’ in the cell B1 and using the ‘fill down’ function to generate a sequence of 100 numbers) and describing emerging patterns
  • creating an algorithm that will generate number sequences involving multiples of one to 10, using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely

  VC2M4N10 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M4N05

  solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits

  Elaborations

  • using physical or virtual materials to demonstrate the multiplicative relationship between the places
  • using materials such as place value charts, numeral expanders or sliders to recognise and explain why multiplying by 10 moves the digits one place to the left and dividing by 10 moves digits one place to the right
  • using a calculator or other digital tools to recognise and develop an understanding of the effect of multiplying or dividing numbers by tens, hundreds and thousands, recording sequences in a place value chart, in a table or spreadsheet, generalising the patterns noticed and applying them to solve multiplicative problems without a calculator

  VC2M4N05 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M4N09

  use mathematical modelling to solve practical problems that involve additive and multiplicative situations, including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate...

  Elaborations

  • modelling and solving a range of practical additive problems using materials, part-part-whole diagrams and/or a bar model, and writing addition and/or subtraction number sentences, based on whether a part or the whole is missing; and explaining how each number in their number sentence is connected to the situation
  • modelling practical problems with division, interpreting and representing the situation using a diagram or array to represent what is unknown (the number of groups, or the number per group); and writing a division number sentence to represent the situation and choosing an efficient calculation strategy
  • modelling practical problems involving money (such as a budget for a large event) that require either addition, subtraction, multiplication or division and justifying the choice of operation in relation to the situation
  • modelling and solving multiplication problems involving money, such as buying 5 toy scooters for $96 each, using efficient mental strategies and written jottings to keep track if needed; for example, rounding $96 up to $100 and subtracting 5 × $4 = $20, so 5 × $96 is the same as 5 × $100 less $20, giving the answer $500 − $20 = $480
  • modelling situations by formulating comparison problems using number sentences, comparison models and arrays; for example, ‘Ariana read 16 books for the “readathon”; Maryam read 4 times as many books. How many books did Maryam read?’ using the expression 4 × 16 and using place value partitioning, basic facts and an array, thinking 4 × 10 = 40 and 4 × 6 = 24, so 4 × 16 can be written as 40 + 24 = 64

  VC2M4N09 | Mathematics | Mathematics Version 2.0 | Level 4 | Number