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• 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

• VC2M4N06

  develop efficient mental and written strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder

  Elaborations

  • using and choosing efficient calculation strategies for addition and subtraction problems involving larger numbers, for example, place value partitioning, inverse relationship, compatible numbers, jump strategies, bridging tens, splitting one or more numbers, extensions to basic facts, algorithms and digital tools where appropriate
  • using physical or virtual materials to demonstrate doubling and halving strategies for solving multiplication problems; for example, for 5 × 18, using the fact that double 5 is 10 and half of 18 is 9; or using 10 × 18 = 180, then halving 180 to get 90; or applying the associative property of multiplication, where 5 × 18 becomes 5 × 2 × 9, then 5 × 2 × 9 = 10 × 9 = 90 so that 5 × 18 = 90
  • using an array to represent a multiplication problem, connecting the idea of how many groups and how many in each group with the rows and columns of the array, and writing an associated number sentence
  • using materials or a diagram to solve a multiplication or division problem, by writing a number sentence and explaining what each of the numbers within the number sentence refers to
  • representing a multiplicative situation using materials, array diagrams and/or a bar model, and writing multiplication and/or division number sentences, based on whether the number of groups, the number per group or the total is missing, and explaining how each number in their number sentence is connected to the situation
  • using place value partitioning, basic facts and an area or region model to represent and solve multiplication problems; for example, for 16 × 4, thinking 10 × 4 and 6 × 4, then 40 + 24 = 64, or a double double strategy where double 16 is 32, double this is 64, so 16 × 4 is 64

  VC2M4N06 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M4N08

  solve problems involving purchases and the calculation of change to the nearest 5 cents with and without digital tools

  Elaborations

  • recognising that not all countries use dollars and cents; for example, India uses rupees
  • carrying out calculations in another currency as well as in dollars and cents, and identifying both as decimal systems

  VC2M4N08 | Mathematics | Mathematics Version 2.0 | Level 4 | 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

• VC2M4N03

  find equivalent representations of fractions using related denominators and make connections between fractions and decimal notation

  Elaborations

  • extending fraction families within collections of materials, for example, by seeing 34 as 3 in each 4, showing this within related fractions like 68 or seeing that 25 means 2 in each 5 so it can be shown within 410
  • creating models of equivalent fractions by subdividing capacity measures into smaller fractions; for example, half a cup of flour could be shown as two-quarters or four-eighths of a cup of flour
  • folding paper to show equivalence between different fractions; for example, folding A4 paper in half and half again, repeating to form eighths and demonstrating that 48=24=12 ; or folding paper strips into fifths and tenths, and recording as both fractions and decimals
  • identifying and using the connection between fractions of metres and decimals; for example, finding 14 of a metre and connecting this to 0.25 metres or 25 centimetres, or finding 110 of a metre and connecting this with 0.10 metres or 10 centimetres
  • using array diagrams to show the relationship between fractions and division and multiplication of natural numbers, for example, 3 × 4 = 12, 12 ÷ 4 = 3, 14 of 12 is 3, 13 of 12 is 4

  VC2M4N03 | Mathematics | Mathematics Version 2.0 | Level 4 | Number

• VC2M4N02

  investigate number sequences involving multiples of 3, 4, 6, 7, 8 and 9

  Elaborations

  • recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences

  VC2M4N02 | Mathematics | Mathematics Version 2.0 | Level 4 | 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

• VCMNA152

  Recognise, represent and order numbers to at least tens of thousands

  Elaborations

  • reproducing five-digit numbers in words using their numerical representations, and vice versa

  VCMNA152 | Mathematics | Level 4 | Number and Algebra | Number and place value

• VCMNA154

  Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9

  Elaborations

  • recognising that number sequences can be extended indefinitely, and determining any patterns in the sequences

  VCMNA154 | Mathematics | Level 4 | 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

• 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

• 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