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• 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

• VC2M10A06

  implement algorithms that use data structures using pseudocode or a general purpose programming language

  Elaborations

  • using two-dimensional arrays such as matrices to represent and implement sequences of transformations of sets of points in the plane
  • using pointers in algorithms

  VC2M10A06 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M8A01

  create, expand, factorise, rearrange and simplify linear expressions, applying the associative, commutative, identity, distributive and inverse properties

  Elaborations

  • rearranging and simplifying linear expressions involving variables with integer coefficients and constants; and using manipulatives such as algebra tiles to support calculations, for example, using manipulatives to demonstrate that 2x+4=2x+2 , 3a-b=3a-3b, or 5m+2n+3m-4n= 5m+10n+3m-4n=8m+6n
  • demonstrating the relationship between factorising and expanding linear expressions using manipulatives, such as algebra tiles or area models, and describing with mathematical language
  • using the distributive, associative, commutative, identity and inverse properties to expand and factorise algebraic expressions using strategies such as the area model

  VC2M8A01 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VC2M9A03

  sketch linear graphs of equations in various algebraic forms, using the coordinates of 2 points, and solve linear equations

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs, and describing them using both words and algebra

  VC2M9A03 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M10A11

  explore the connection between algebraic and graphical representations of relations such as simple quadratic, reciprocal, circle and exponential, using digital tools as appropriate

  Elaborations

  • sketching graphs of parabolas, and circles
  • applying translations, reflections and stretches to parabolas and circles
  • sketching the graphs of exponential functions using transformations
  • plotting graphs of families of relations where the product of 2 variables is equal to a fixed constant

  VC2M10A11 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M7A01

  recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown

  Elaborations

  • linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length × width as
    A=l×w; or using p=6g+b to describe a total of points expressed as goals (worth 6 points) and behinds (worth one point)
  • interpreting and using formulas obtained from other sources, for example, maximum heart rates and target heart rates for moderate exercise
  • substituting numerical values for variables when using formulas and calculating the value of an unknown in practical situations; for example, calculating weekly wage W given base wage b and overtime hours h at 1.5 times rate r, W=b+1.5 ×h ×r, using values for mass m and volume v to determine density d of a substance where d=mv
  • using everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables

  VC2M7A01 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M10A07

  solve problems involving linear equations, including those derived from formulas

  Elaborations

  • representing word problems with simple linear equations and solving them to answer questions

  VC2M10A07 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• 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

• VC2M10A08

  solve linear inequalities and graph their solutions on a number line

  Elaborations

  • representing word problems with simple linear inequalities and solving them to answer questions
  • graphing regions corresponding to inequalities in the Cartesian plane (for example, graphing 2x+3y<24) and verifying using a test point such as (0, 0)

  VC2M10A08 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M9A06

  use mathematical modelling to solve applied problems involving change, including financial contexts involving simple interest; formulate problems, choosing to use either linear or quadratic functions or other simple variations; interpret solutions in terms of the context; evaluate the model and...

  Elaborations

  • modelling practical contexts using linear functions such as cooking times that include resting or cooling times, or water leakage from water tanks, using tables and graphs or digital tools and algebraically
  • modelling measurement situations and determining the perimeter and areas of rectangles where the length, l, of the rectangle is a linear function of its width, w; for example, l=w,  l=w+5,  l=3w,  l=2w+7
  • modelling practical contexts (for example, area, paths of projectiles, parabolic mirrors, satellite dishes) using simple quadratic functions, tables and graphs (hand drawn or using digital tools) and, algebraically, interpreting features of the graphs such as the turning point and intercepts in context; for example, area, paths of projectiles, parabolic mirrors, satellite dishes
  • modelling and solving problems involving financial contexts using linear functions, for example, combinations of purchases of different items when they have a set amount of money to spend, profit/loss situations and trade quotes involving call-out fees
  • modelling situations involving change, for example, change in daily temperature during the ski season, fluctuation of speed above and below the speed limit, and acceleration and deceleration of a car coming to and moving off from a set of traffic lights
  • modelling the hunting techniques of Aboriginal and Torres Strait Islander Peoples using quadratic functions and exploring the effect of increasing the number of hunters to catch more prey 

  VC2M9A06 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M9A04

  find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane

  Elaborations

  • recognising that the gradient of a line is calculated using the gradient of a line segment on that line and is independent of which 2 distinct points on the line are used for this calculation
  • using digital tools and transformations to illustrate that parallel lines in the Cartesian plane have the same gradient and that the relationship between the gradients of pairs of perpendicular lines is that their product is (−1)
  • using Pythagoras’ theorem to establish the distance between 2 points in the Cartesian plane and applying this using horizontal and vertical distances and coordinates
  • investigating graphical and algebraic techniques for finding the midpoint and gradient of the line segment between 2 points
  • using dynamic graphing software and superimposed images (for example, playground equipment, ramps and escalators) to investigate gradients in context and their relationship to rule of a linear function, and interpret gradient as a constant rate of change in linear modelling contexts

  VC2M9A04 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• 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

• VC2M10A10

  solve problems involving gradients of parallel and perpendicular lines

  Elaborations

  • solving problems using the fact that parallel lines have the same gradient and conversely that if 2 lines have the same gradient then they are parallel
  • solving problems using the fact that the product of the gradients of perpendicular lines is −1 and conversely that if the product of the gradients of 2 lines is −1 then they are perpendicular

  VC2M10A10 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M10A09

  solve simultaneous linear equations, using algebraic and graphical techniques including using digital tools

  Elaborations

  • investigating situations involving simultaneous linear equations in context (such as multiple quotes for a job, or profit and loss) and solving the equations graphically, giving solutions in everyday language (such as ‘break-even point’ or ‘point to change providers’ for the job)
  • describing the solution of simultaneous equations within the context of the situation
  • using the algebraic methods of substitution and elimination, with and without the use of digital tools, and identifying which technique is the most efficient for a given pair of equations
  • associating the solution of simultaneous equations with the coordinates of the intersection of their corresponding graphs
  • investigating the strategies inherent in Aboriginal and/or Torres Strait Islander children’s instructive games, for example, Weme from the Warlpiri Peoples of central Australia, and their connection to strategies to solve simultaneous linear equations in 2 variables

  VC2M10A09 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M9A07

  experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns 

  Elaborations

  • investigating transformations of the graph of y=x to the graph of y=ax+b by systematic variation of a and b and interpreting the effects of these transformations using digital tools; for example,
    y=x→y=2x (vertical enlargement as a>1) →y=2x-1 (vertical translation) and
     y=x→y=12x (vertical compression as 0<a<1) →y=-12x (reflection in the horizontal axis) →y=-12x+3 (vertical translation)
  • investigating transformations of the parabola y=x2 to the graph of y=ax-h2+b in the Cartesian plane using digital tools to determine the relationship between graphical and algebraic representations of quadratic functions, including the completed square form; for example,
    y=x2→y=13x2 (vertical compression as 0<a<1) →y=13(x-5)2 (horizontal translation) →y=13(x-5)2+7 (vertical translation) or
    y=x2→y=2x2 (vertical enlargement as a>1) →y=-2x2 (reflection in the horizontal axis) →y=-2(x+6)2 (horizontal translation) →y=-2x+62+10 (vertical translation)
  • experimenting with digital tools by applying transformations to the graphs of functions, such as reciprocal y=1x, square root y=x, cubic y=x3 and exponential functions y=2x, y=(12)x, identifying patterns

  VC2M9A07 | Mathematics | Mathematics Version 2.0 | Level 9 | 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

• VC2M10A02

  simplify algebraic products and quotients using exponent laws

  Elaborations

  • applying knowledge of exponent laws to algebraic terms, and simplifying algebraic expressions using both positive and negative integral indices

  VC2M10A02 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M2A04

  apply repetition in arithmetic operations, including multiplication as repeated addition and division as repeated subtraction

  Elaborations

  • using technology to construct a sequence of numbers based on constant addition or subtraction from a given starting value
  • sharing a set of objects equally between a small number of groups

  VC2M2A04 | Mathematics | Mathematics Version 2.0 | Level 2 | Algebra

• VC2M6A01

  recognise and use rules that generate visually growing patterns and number patterns involving rational numbers

  Elaborations

  • investigating patterns such as the number of tiles in a geometric pattern, or the number of dots or other shapes in successive repeats of a strip or border pattern, looking for patterns in the way the numbers increase or decrease
  • using a calculator or spreadsheet to experiment with number patterns that result from multiplying or dividing; for example, 1 ÷ 9, 2 ÷ 9, 3 ÷ 9 …, 210 × 11, 211 × 11, 212 × 11 …, 111 × 11, 222 × 11, 333 × 11 …, or 100 ÷ 99, 101 ÷ 99, 102 ÷ 99 …
  • creating an extended number sequence that represents an additive pattern using decimals; for example, representing the additive pattern formed as students pay their $2.50 for an incursion as 2.50, 5.00, 7.50, 10.00, 12.50, 15.00, 17.50 …
  • investigating the number of regions created by successive folds of a sheet of paper (one fold, 2 regions; 2 folds, 4 regions; 3 folds, 8 regions) and describing the pattern using everyday language
  • creating a pattern sequence with materials, writing the associated number sequence and then describing the sequence with a rule so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles using 3 for one triangle, 5 for 2 triangles and 7 for 3 triangles and describing the pattern as ‘Multiply the number of triangles by 2 and then add one for the extra toothpick in the first triangle’

  VC2M6A01 | Mathematics | Mathematics Version 2.0 | Level 6 | Algebra