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• Mathematics Version 2.0: Level 2 achievement standards

  By the end of Level 2, students order and represent numbers to at least 1000; apply knowledge of place value to partition, rearrange and rename two- and three-digit numbers in terms of their parts; and regroup partitioned numbers to assist in calculations. They use mathematical modelling...

  Level description | Mathematics | Mathematics Version 2.0 | Level 2

• VC2M7N04

  round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of computations

  Elaborations

  • identifying the interval between a pair of consecutive integers that includes a given rational number
  • choosing and applying conventions for rounding correct to a specified number of decimal places based upon the context
  • checking that the accuracy of rounding is suitable for context and purpose; for example, for the amount of paint required or the cost estimate for renovating a house, purchasing 2 litres of paint to paint the bedroom even though 1.89 litres is the exact answer or estimating a renovation budget to the nearest $100

  VC2M7N04 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VCMNA133

  Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

  Elaborations

  • recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers
  • extending strategies for addition and subtraction such as 14 + 8 + 6 = 14 + 6 + 8 = 28 and 54 – 28 = 2 + 20 + 4
  • combining knowledge of addition and subtraction facts and partitioning to aid computation. For example, 57 + 19 = 57 + 20 – 1

  VCMNA133 | Mathematics | Level 3 | Number and Algebra | Number and place value

• VC2M9ST02

  analyse how different sampling methods, and different samples using the same method, can affect the results of surveys and how choice of representation can be used to support a particular point of view

  Elaborations

  • investigating and analysing different visualisations of data such as infographics found in the media and commenting on the strengths, weaknesses and possible biases of particular examples
  • discussing the impact of decreased landline usage or an increased aversion to answering calls from unknown numbers on survey data 
  • exploring potential cultural bias relating to Aboriginal and Torres Strait Islander Peoples by critically analysing sampling techniques in statistical reports 

  VC2M9ST02 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• VCMSP295

  Describe events using language of 'at least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or both) and 'and'

  Elaborations

  • posing 'and', 'or' and 'not' probability questions about objects or people

  VCMSP295 | Mathematics | Level 8 | Statistics and Probability | Chance

• VC2M2N05

  multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays and partitioning to support a variety of calculation strategies

  Elaborations

  • making and naming arrays and using bar models to solve simple multiplication or sharing problems; for example, making different arrays to represent 12 and naming them as ‘3 fours’, ‘2 sixes’, ‘4 threes’ and ‘6 twos’, using physical or virtual materials to make arrays or using bar models to demonstrate that ‘3 fours’ is equal to ‘4 threes’
  • finding the total number represented in an array by partitioning the array using subitising and number facts; for example, describing how they determined the total number of dots arranged in a ‘3 fives’ array by saying, ‘I saw 2 fives, which is 10, and then 5 more, which makes 15’
  • recognising problems that can be solved using division and identifying the difference between dividing a set of objects into 3 equal groups and dividing the same set of objects into groups of 3
  • using a Think Board to solve partition and quotition division problems; for example, sharing a prize of $36 between 4 people, using materials, a diagram and skip counting to find the answer, and explaining whether the answer ‘9’ refers to people or dollars
  • using materials or diagrams, and skip counting, to solve repeated equal-quantity multiplication problems; for example, writing a repeated addition number sentence and using skip counting to solve the problem ‘Four trays of biscuits with 6 on each tray – how many biscuits are there?’

  VC2M2N05 | Mathematics | Mathematics Version 2.0 | Level 2 | Number

• VC2M5N09

  use mathematical modelling to solve practical problems involving additive and multiplicative situations, including simple financial planning contexts; formulate the problems, choosing operations and efficient mental and written calculation strategies, and using digital tools where appropriate;...

  Elaborations

  • modelling an everyday situation and determining which operations can be used to solve it using materials, diagrams, arrays and/or bar models to represent the problem; formulating the situation as a number sentence; and justifying their choice of operations in relation to the situation
  • modelling a series of contextual problems, deciding whether an exact answer or an approximate calculation is appropriate, and explaining their reasoning in relation to the context and the numbers involved
  • modelling financial situations such as creating financial plans; for example, creating a budget for a class fundraising event, using a spreadsheet to tabulate data and perform calculations
  • investigating how mathematical models involving combinations of operations can be used to represent songs, stories and/or dances of Aboriginal and Torres Strait Islander Peoples

  VC2M5N09 | Mathematics | Mathematics Version 2.0 | Level 5 | 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

• VC2M7N02

  represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation

  Elaborations

  • relating the sequences 10, 100, 1000, 10 000 … and 10¹, 10², 10³, 10⁴ …
  • applying and explaining the connections between place value and expanded notations, for example, $7000=7\times {10}^3$ and $3750=3\times {10}^3+7\times {10}^2+5\times {10}^1$
  • applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees, for example, $48=6\times 8=2\times 3\times 2\times 2\times 2=3^1\times 2^4=3\times 2^4$
  • developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation

  VC2M7N02 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• Mathematics: Level 9 achievement standards

  Number and Algebra

  Students apply the index laws using integer indices to variables and numbers, express numbers in scientific notation, solve problems involving very small and very large numbers, and check the order of magnitude of calculations. They solve problems involving simple interest. Students...

  Level description | Mathematics | Level 9

• Mathematics: Level 2 description

  In Level 2, students use grouping partitioning and re-arrangement to apply place value and extend the range of numbers they use and apply to thousands.

  Students recognise, model and order numbers to at least 1000 and use a variety of strategies to count efficiently, including skip counting forwards...

  Level description | Mathematics

• Mathematics: Level 5 description

  In Level 5, students extend decimal fractions to thousandths, and explore the ideas of factors, multiples and divisibility.

  Students use estimation and rounding for all four operations, with and without the use of technology for calculation. They solve multiple digit problems involving addition...

  Level description | Mathematics

• Mathematics: Level 9 description

  In Level 9, students develop familiarity with a broader range of non-linear and linear functions and relations, and related algebra and graphs.

  Students apply index laws with integer indices to a range of numerical expressions and extend this to algebraic expressions involving numbers and pro-numerals...

  Level description | Mathematics

• Mathematics Version 2.0: Foundation Level description

  In Foundation, learning in Mathematics builds on each student’s prior learning and experiences, including the learning opportunities acquired through the implementation of the Victorian Early Years Learning and Development Framework (VEYLDF). Students engage in a range of approaches to the...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 9 achievement standards

  By the end of Level 9, students recognise and use rational and irrational numbers to solve problems.

  Students extend and apply the exponent laws with positive integers and the zero exponent to variables. They expand binomial products and factorise monic quadratic expressions. They...

  Level description | Mathematics | Mathematics Version 2.0 | Level 9

• VC2M9A02

  simplify algebraic expressions, apply the distributive law to expand algebraic expressions including binomial products, and factorise monic quadratic expressions

  Elaborations

  • expanding combinations of binomials such as $\left(x+7\right)\left(x+8\right), \left(x+7\right)\left(x-8\right),$$\left(x-7\right)\left(x+8\right), (x-7)(x-8)$ to identify expansion and factorisation patterns related to $\left(x+a\right)\left(x+b\right)=x^2+\left(a+b\right)x+ab$, where $a$ and $b$ are integers
  • using manipulatives such as algebra tiles or area models to expand or factorise algebraic expressions with readily identifiable binomial factors; for example, $\left(x+1\right)\left(x+3\right)=x^2+4x+3$, ${(x-5)}^2=x^2-10x+25$ or ${(x-3)}^2+4=x^2-6x+9+4=x^2-6x+13$
  • recognising the relationship between expansion and factorisation, and using digital tools to systematically explore the factorisation of $x^2+mx+n$ where $m$ and $n$are integers

  VC2M9A02 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M10AA10

  experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns

  Elaborations

  • applying a bisection algorithm to determine the approximate location of the horizontal axis intercepts of the graph of a quadratic function such as $f\left(x\right)=2x^2-3x-7$
  • applying transformations to the graph of $x^2+y^2=1$
  • identifying the coordinates of any points of intersection of the graph of a linear function with the graph of a quadratic function or a circle
  • identifying intervals on the real number line over which a given quadratic function is positive or negative
  • using a table of values to determine when an exponential growth or decay function exceeds or falls below a given value, such as monitoring the trend in value of a share price in a context of exponential growth or decay

  VC2M10AA10 | Mathematics | Mathematics Version 2.0 | Level 10A | 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

• VC2M1N05

  use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials; use calculation strategies to solve the problem

  Elaborations

  • modelling problems involving addition and subtraction presented in stories, using a Think Board to represent the problem, solving the problem using physical materials and explaining the connections between any materials used, the Think Board diagram and the numbers within the story
  • modelling simple money problems involving addition and subtraction using whole dollar amounts; for example, setting up a shop and role-playing practical problems of buying and selling goods, using addition and subtraction with play money and prices in whole dollar amounts; or solving the problem ‘I had $14 and was given $15 for my birthday’ using addition to answer the problem
  • modelling a variety of different additive situations to solve practical problems; for example, keeping track of the number of people on a bus as it stops to pick up and drop off passengers or the number of people entering a lift

  VC2M1N05 | Mathematics | Mathematics Version 2.0 | Level 1 | Number