Search results

Result list

• 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

• VC2M10A12

  solve linear equations involving simple algebraic fractions

  Elaborations

  • solving a wide range of linear equations, including those involving one or 2 simple algebraic fractions, and checking solutions by substitution
  • representing word problems, including those involving fractions, as equations and solving them to answer the question

  VC2M10A12 | Mathematics | Mathematics Version 2.0 | Level 10 | 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

• VC2M10A03

  apply the 4 operations to simple algebraic fractions with numerical or single variable denominators

  Elaborations

  • expressing the sum and difference of algebraic fractions with a common denominator
  • using the exponent laws to simplify products and quotients of algebraic fractions

  VC2M10A03 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M6A02

  find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations

  Elaborations

  • using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 × (4 + 6) = □, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication
  • constructing equivalent number sentences involving brackets and combinations of the 4 operations, and explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions
  • finding pairs of unknown values in numerical equations that make the equation hold true; for example, listing possible combinations of natural numbers that make this statement true: 6 + 4 × 8 = 6 × Δ + □

  VC2M6A02 | Mathematics | Mathematics Version 2.0 | Level 6 | Algebra

• VC2M9A01

  apply the exponent laws to numerical expressions with integer exponents and the zero exponent, and extend to variables

  Elaborations

  • representing decimals in exponential form; for example, 0.475 can be represented as 0.475=410+7100+51000=4×10-1+7×10-2+5×10-3 and 0.00023 as 23 × 10^-5
  • simplifying and evaluating numerical expressions, involving both positive and negative integer exponents, explaining why; for example, 5-3=153=(15)3=1125 and connecting terms of the sequence 125, 25, 5, 1, 15, 125, 1125… to terms of the sequence 53, 52,51, 50, 5-1, 5-2, 5-3...
  • relating the computation of numerical expressions involving exponents to the exponent laws and the definition of an exponent; for example, 23÷25=2-2=122=14 and (3×5)2=32×52=9×25=225
  • recognising exponents in algebraic expressions and applying the relevant exponent laws and conventions; for example, for any non-zero natural number a, a0=1, x1=x,  r2=r×r,  h3=h×h×h,  y4=y×y×y×y, and 1w×1w=1w2=w-2
  • relating simplification of expressions from first principles and counting to the use of exponent laws; for example,
    (a2)3=a×a×a×a×a×a=a×a×a×a×a×a=a6;
    b2×b3=b×b×b×b×b=b×b×b×b×b=b5; y4y2=y×y×y×yy×y=y21=y2 and (5a)2=5×a×5×a=5 ×5×a×a=25×a2=25a2 
  • applying the exponent laws to simplifying expressions involving products, quotients, and powers of constants and variables; for example, (2xy)3xy4=8x3y3xy4=8x2y-1
  • relating the prefixes for SI units from pico- (trillionth) to tera- (trillion) to the corresponding powers of 10; for example, one pico-gram = 10^-12 grams and one terabyte = 10¹² bytes

  VC2M9A01 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M5A02

  find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations

  Elaborations

  • using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3 × 5 = 15 and 30 ÷ 2 = 15, then 3 × 5 = 30 ÷ 2, and therefore the solution to 3 × 5 = 30 ÷ □ is 2
  • using relational thinking, and an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6
  • using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not – for example, using arrays to demonstrate that 2 × 3 = 3 × 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 × 2 × 3 = 12 and 2 × 3 × 2 = 12 and 3 × 2 × 2 = 12; and understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8
  • using materials, diagrams or arrays to recognise and explain the distributive property, for example, where 4 × 13 = 4 × 10 + 4 × 3
  • constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 × 4 = 12 and knowing 2 × 2 = 4, then 3 × 4 can be written as 3 × (2 × 2) and, using the associative property, (3 × 2) × 2 so 3 × 4 = 6 × 2 and so 6 is the solution to 3 × 4 = □ × 2

  VC2M5A02 | Mathematics | Mathematics Version 2.0 | Level 5 | Algebra

• VC2M10A04

  expand binomial products and factorise monic quadratic expressions using a variety of strategies

  Elaborations

  • exploring the method of completing the square to factorise quadratic expressions and solve quadratic equations
  • identifying and using common factors, including binomial expressions, to factorise algebraic expressions using the technique of grouping in pairs
  • using the identities for perfect squares and the difference of squares to factorise quadratic expressions

  VC2M10A04 | Mathematics | Mathematics Version 2.0 | Level 10 | Algebra

• VC2M3A01

  recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences

  Elaborations

  • partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)
  • using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36
  • exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place

  VC2M3A01 | Mathematics | Mathematics Version 2.0 | Level 3 | Algebra

• VC2M7A02

  apply the associative, commutative and distributive laws to aid mental and written computation, and formulate algebraic expressions using constants, variables, operations and brackets

  Elaborations

  • simplifying calculations
  • forming simple estimates for calculations involving multiple and/or combined operations
  • generalising arithmetic expressions to algebraic expressions involving constants, variables, operations and brackets; for example, 7+7+7=3×7, x+x+x=3×x noting that 3x includes implied multiplication and recognising the difference between 3x+4 and 3x+4
  • formulating algebraic expressions that represent mathematical relationships; for example, translating from words to symbols in ‘think of a number’ type activities
  • recognising and applying the concept of variable as something that can change in value, investigating the relationships between variables, and the application to processes on Country/Place, including how cultural expressions of Aboriginal and Torres Strait Islander Peoples, such as storytelling, communicate mathematical relationships that can be represented as mathematical expressions

  VC2M7A02 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M1A02

  recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit and recognising the importance of repetition in solving problems

  Elaborations

  • interpreting a repeating pattern sequence created by someone else, noticing and describing the repeating part of the pattern and explaining how they know what comes next in the sequence
  • generalising a repeating pattern by identifying the unit of repeat and representing the elements using numbers, letters or symbols; for example, representing the repeating pattern of stamp, stamp, clap, stamp, clap, pause, stamp, stamp, clap, stamp, clap as SSCSC SSCSC …, recognising the elements that are repeating, describing the unit of repeat as SSCSC and continuing the pattern
  • recognising within the sequencing of natural numbers that 0–9 digits are repeated both in and between the decades and using this pattern to continue the sequence and name two-digit numbers beyond 20
  • identifying the repeating patterns in Aboriginal and/or Torres Strait Islander systems of counting, exploring different ways of representing numbers including oral and gestural language
  • considering how the making of shell or seed necklaces by Aboriginal and/or Torres Strait Islander Peoples includes practices such as sorting shells and beads based on colour, size and shape, and creating a repeating pattern sequence

  VC2M1A02 | Mathematics | Mathematics Version 2.0 | Level 1 | Algebra

• VC2M9A05

  identify and graph quadratic functions, solve quadratic equations graphically and numerically, and use null factor law to solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate

  Elaborations

  • recognising that in a table of values, if the second difference between consecutive values of the dependent variable is constant, then it is a quadratic
  • graphing quadratic functions using digital tools and comparing what is the same and what is different between these different functions and their respective graphs; interpreting features of the graphs such as symmetry, turning point, maximum and minimum values; and determining when values of the quadratic function lie within a given range
  • solving quadratic equations algebraically and comparing these to graphical solutions
  • using graphs to determine the solutions of quadratic equations; recognising that the roots of a quadratic function correspond to the x-intercepts of its graph and that if the graph has no x-intercepts, then the corresponding equation has no real solutions
  • relating horizontal axis intercepts of the graph of a quadratic function to the factorised form of its rule using the null factor law; for example, the graph of the function y=x2-5x+6 can be represented as y=x-2x-3 with x-axis intercepts where either x-2=0 or x-3=0
  • recognising that the equation x2=a, where a>0, has 2 solutions, x=a and x=-a (for example, if x2=39 then x=39=6.245 correct to 3 decimal places, or x=-39=-6.245 correct to 3 decimal places) and representing these graphically
  • graphing percentages of illumination of moon phases in relation to Aboriginal and Torres Strait Islander Peoples’ understandings that describe the different phases of the moon

  VC2M9A05 | Mathematics | Mathematics Version 2.0 | Level 9 | Algebra

• VC2M8A04

  use algorithms and related testing procedures to identify and correct errors

  Elaborations

  • debugging search-and-sort programs
  • testing a number for divisibility

  VC2M8A04 | Mathematics | Mathematics Version 2.0 | Level 8 | Algebra

• VC2M3A03

  recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts

  Elaborations

  • using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts
  • recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives
  • practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts
  • systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns

  VC2M3A03 | Mathematics | Mathematics Version 2.0 | Level 3 | 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

• VC2M10AA09

  solve linear and non-linear simultaneous equations using graphing or systematic guess-check-and-refine with digital tools

  Elaborations

  • using graphs to determine a convergent set of intervals that contain a point of intersection of the graphs of 2 functions
  • using a cobweb diagram to solve simultaneous equations numerically

  VC2M10AA09 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AA01

  investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems

  Elaborations

  • investigating the relationship between algebraic long division and the factor and remainder theorems

  VC2M10AA01 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AA03

  simplify combinations of linear expressions with rational coefficients and the solution of related equations

  Elaborations

  • simplifying sums and differences of linear expressions of the form ax+bc where
    a and b are integers, and c is a non-zero integer, for example, 6x-112-7x4+9-5x3=-5x-3012
  • solving equations involving sums and differences of linear expressions with rational coefficients, for example, -2x3+49= 1157x-1 ⇒-30x+20=693x-99 ⇒x=119723 , and verifying the solution

  VC2M10AA03 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AA07

  factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from a variety of contexts

  Elaborations

  • writing quadratic equations that represent practical problems

  VC2M10AA07 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra

• VC2M10AA08

  use function notation to describe the relationship between dependent and independent variables in modelling contexts

  Elaborations

  • identifying independent and dependent variables in modelling contexts and representing the relation between them using tables, graphs and rules
  • using technology to draw graphs of functions defined using function notation with consideration of domain and range

  VC2M10AA08 | Mathematics | Mathematics Version 2.0 | Level 10A | Algebra