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• Mathematics | Mathematics Version 2.0: Learning in Mathematics Version 2.0

  Learning in Mathematics emphasises the importance of providing opportunities for students to develop proficiency in mathematics. This development of proficiency is achieved in how content is explored or developed, that is, how students experience the thinking and doing of mathematics.

  Proficiency...

  Overview material | Mathematics Version 2.0

• Mathematics | Mathematics Version 2.0: Structure

  Mathematics is presented in 11 levels, from Foundation to Level 10.

  Level 10 also includes Level 10A, which provides opportunities for students to extend their exploration of mathematical notions and further their mathematical studies.

  Strands

  The curriculum is organised into 6 interrelated...

  Overview material | Mathematics Version 2.0

• 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 8 achievement standards

  By the end of Level 8, students recognise irrational numbers as numbers that cannot develop from the division of integer values by natural numbers and terminating or recurring decimals. They apply the exponent laws to calculations with numbers involving positive integer exponents. Students...

  Level description | Mathematics | Mathematics Version 2.0 | Level 8

• Mathematics Version 2.0: Level 10 achievement standards

  By the end of Level 10, students recognise the effect of approximations of real numbers in repeated calculations.

  Students use mathematical modelling to solve problems involving growth and decay in financial and other applied situations, applying linear, quadratic and exponential...

  Level description | Mathematics | Mathematics Version 2.0 | Level 10

• Mathematics Version 2.0: Level 10A description

  Level 10A provides optional, additional content to extend students in their mathematical studies in number, algebra, function, geometry, probability and statistics.

  Level 10A does not include an achievement standard and does not require reporting.

  Students may extend...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 10 description

  In Level 10, learning in Mathematics builds on each student’s prior learning and experiences and provides the basis for a sound background in number, algebra, function, geometry and statistics. Students engage in a range of approaches to the learning and doing of mathematics that...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 1 description

  In Level 1, 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...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 2 description

  In Level 2, 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...

  Level description | Mathematics | Mathematics Version 2.0

• Mathematics Version 2.0: Level 8 description

  In Level 8, learning in Mathematics builds on each student’s prior learning and experiences. Students engage in a range of approaches to the learning and doing of mathematics that develop their understanding of and fluency with concepts, procedures and processes by making connections...

  Level description | Mathematics | Mathematics Version 2.0

• VC2M10A15

  use mathematical modelling to solve applied problems involving inverse proportion, growth and decay, including in financial contexts to establish the compound interest formula as repeated applications of simple interest; formulate problems, choosing to apply linear, quadratic or exponential models...

  Elaborations

  • modelling problems involving inverse proportion in real-life contexts such as travel time decreasing with increased travel speed, the brightness of luminous objects decreasing with distance, or household expenditure and savings, and solving related equations
  • modelling situations and choosing between linear, quadratic and exponential models by representing relationships in a table of values and recognising that linear functions have constant first differences, quadratic functions have constant second differences and exponential functions have a constant ratio between consecutive values of the dependent variable
  • modelling situations involving exponential growth and decay, and contrasting this with linear growth or decay, for example, situations involving constant percentage change and constant ratio, and determining doubling time and half-life and approximate intervals for which the values of the model lie within a given range
  • modelling situations that involve working with authentic information, data and interest rates to calculate compound interest and solve related problems
  • modelling and investigating how exponential equations are used in carbon dating to estimate the age of Aboriginal and Torres Strait Islander artefacts or material culture
  • modelling situations involving the growth of native animal populations on Country/Place with varying reproductive behaviour, using exponential functions and critiquing their applicability to real-world situations

  VC2M10A15 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M7A05

  generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

  Elaborations

  • plotting points from a table of values generated using simple linear functions and recognising patterns, such as the points lie on a straight line
  • discussing and using variables to create a general rule and using the rule to determine the value of the dependent variable for any given value of the independent variable; for example, plotting the value of the circumference of a circle for varying values of radius
  • using function machines to generate a table of ordered pairs using input and output values, plotting the relationships on a Cartesian plane and describing the graph in terms of shape
  • using diagrams and manipulatives to form linear growth patterns, representing these patterns in tables and describing the relationship in terms of the way the pattern is growing and in the context of the situation

  VC2M7A05 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M10A14

  solve simple exponential equations

  Elaborations

  • investigating exponential equations derived from authentic mathematical models based on population growth
  • recognising that in a table of values, if the ratio between consecutive values of the dependent variable is constant, then it is an exponential relation
  • investigating the links between algebraic and graphical representations of exponential functions using graphing software
  • using digital tools with symbolic manipulation functionality to systematically explore exponential relations
  • investigating Aboriginal and/or Torres Strait Islander ranger groups’ and other groups’ programs that attempt to eradicate feral animals for survival of native animals on Country/Place, exploring the competition between feral and native animals and their impact on natural resources by formulating exponential equations for population growth for each animal species 

  VC2M10A14 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A13

  solve simple quadratic equations using a range of strategies, including null factor law

  Elaborations

  • using techniques to solve quadratic equations, including grouping like terms, completing the square, the quadratic formula and null factor law, and choosing 2 integers with the required product and sum
  • using digital tools to explore the conditions for solutions to exist
  • using digital tools to explore both graphically and algebraically the link between the value of the discriminant and the number of real solutions to a quadratic equation

  VC2M10A13 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M5A01

  recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts

  Elaborations

  • using materials or diagrams to develop and explain division strategies, such as halving, using the inverse relationship to turn division into a multiplication
  • using arrays, multiplication tables, and physical and virtual materials to develop families of facts, for example, 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3
  • demonstrating multiplicative partitioning using materials, diagrams or arrays and recording 2 multiplication and 2 division facts for each grouping (for example, 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4), explaining how each grouping is different from and connected to other groupings in the materials, diagrams or arrays
  • using materials, diagrams or arrays to recognise and explain the inverse relationship between multiplication and division (for example, solving 240 ÷ 20 = □ by thinking 20 × □ = 240) and using the inverse to make calculations easier (for example, solving 17 × □ = 221 using division, □ = 221 ÷ 17)

  VC2M5A01 | Mathematics | Mathematics Version 2.0 | Level 5 | Algebra

• VC2M2A03

  recall and demonstrate proficiency with multiplication facts for twos; extend and apply facts to develop the related division facts using doubling and halving

  Elaborations

  • recognising and relating terms such as ‘double’, ‘twice’ and ‘multiply by 2’, and ‘halve’ and ‘divide by 2’ using physical and virtual materials; for example, colouring numbers on a hundreds chart to represent doubles and using it to recognise halves or recognising the doubling pattern and applying the pattern to find related facts such as ‘For 8 twos, think 2 eights’
  • doubling and halving collections to practise and develop fluency with multiplication and division facts for twos, leading to recall of these facts
  • establishing an understanding of doubles and near doubles using physical or virtual manipulatives; for example, using manipulatives to establish that doubling 5 gives you 10, then extending this doubling fact to respond to the question ‘How can you use this fact to double 6 or double 4?’
  • developing fluency with doubling and halving numbers within 20 using physical or virtual materials and playing doubling and halving games; for example, using a physical or virtual dice and choosing whether to double or halve to reach a target number 

  VC2M2A03 | Mathematics | Mathematics Version 2.0 | Level 2 | 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 fx=2x2-3x-7
  • applying transformations to the graph of x2+y2=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

• VC2MFN06

  represent practical situations that involve equal sharing and grouping with physical and virtual materials and use counting or subitising strategies

  Elaborations

  • using materials to role-play equal sharing; for example, sharing pieces of fruit or a bunch of grapes between 4 people and discussing how you would know they have been shared equally; or, when playing card games where each player is dealt the same number of cards, counting the number of cards after the deal to ensure they have the same amount
  • representing situations that involve counting several items; for example, starting with 9 beads or 6 $1 coins and then sharing them equally between 3 people by subitising or counting each group by ones to decide how many beads or coins each person will receive
  • exploring instructive games of Aboriginal and/or Torres Strait Islander Peoples that involve sharing; for example, playing Yangamini of the Tiwi Peoples of Bathurst Island to investigate and discuss equal sharing

  VC2MFN06 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFN04

  partition and combine collections up to 10 using part-part-whole relationships and subitising to recognise and name the parts

  Elaborations

  • recognising numbers represented in physical or virtual ten-frames, and describing their reasoning: ‘It’s 7 because there is 5 there and 2 more’
  • partitioning collections of up to 10 objects in different ways and saying the part-part-whole relationship; for example, partitioning a collection of 6 counters into 4 counters and 2 counters and saying, ‘6 is 4 and 2 more, it’s 2 and 4’, then partitioning the same collection into 5 and 1 or 3 and 3
  • representing part-part-whole relationships in numbers up to 10 using physical or virtual materials; for example, identifying numbers represented by dots in standard number configurations such as on dominoes and dice by recognising parts that form the whole
  • exploring number groupings in Aboriginal and/or Torres Strait Islander Peoples’ counting systems and the different ways of representing these groupings to form and partition numbers, applying this to quantify collections of objects in the environment on Country/Place up to 10

  VC2MFN04 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number

• VC2MFN03

  quantify and compare collections to at least 20 using counting and explain or demonstrate reasoning

  Elaborations

  • establishing the language and process of counting, and 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 question of ‘How many?’; for example, saying numbers in sequence while playing and performing actions
  • using counting to compare the size of 2 or more collections of like items to justify which collection contains more or fewer items
  • using counting and one-to-one correspondence to quantify the number of items required for a purpose; for example, when asked to collect enough scissors for each member of their group to have a pair, counting each member and using the total count to know how many to collect
  • discussing how different cultures may have alternative ways of representing the count; for example, discussing how some people of the Asia region use an abacus or Chinese hand gestures
  • using body-tallying that involves body parts and one-to-one correspondence from counting systems of Aboriginal and/or Torres Strait Islander Peoples to count to 20

  VC2MFN03 | Mathematics | Mathematics Version 2.0 | Foundation Level | Number