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• VCMSP322

  Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or'

  Elaborations

  • using Venn diagrams or two-way tables to calculate relative frequencies of events involving ‘and’, ‘or’ questions
  • using relative frequencies to find an estimate of probabilities of ‘and’, ‘or’ events

  VCMSP322 | Mathematics | Level 9 | Statistics and Probability | Chance

• 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

• 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 $\frac{ax+b}{c}$ where
    $a$ and $b$ are integers, and $c$ is a non-zero integer, for example, $\frac{6x-11}{2}-\frac{7x}{4}+\frac{9-5x}{3}=\frac{-5x-30}{12}$
  • solving equations involving sums and differences of linear expressions with rational coefficients, for example, $\frac{-2x}{3}+\frac{4}{9}=\mathrm{ }\frac{11}{5}\left(7x-1\right)\mathrm{ }$$\Rightarrow -30x+20=693x-99\mathrm{ }$$\Rightarrow x=\frac{119}{723}\mathrm{ }$, and verifying the solution

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

• VCMNA021

  Make comparison between items using appropriate language such as ‘same’ or ‘different’

  Elaborations

  • comparing two collections using one to one correspondence within the context of everyday situations
  • responding to questions about group comparison for example ‘Are they the same?’ ‘Or different?’ verbally or by indicating through augmentative and alternative communication, actions or eye gaze

  VCMNA021 | Mathematics | Level B | Number and Algebra | Number and place value

• VCMNA053

  Recognise number name, numerals and quantities, initially up to five and beyond

  Elaborations

  • responding to key vocabulary and questions about ‘how many’
  • using one-to-one matching of number words, sign or augmentative and alternative communication (AAC) representation for objects to five
  • matching numerals to the correct number of items initially to five using number games, software, cards and everyday situations

  VCMNA053 | Mathematics | Level D | Number and Algebra | Number and place value

• VC2M9P02

  calculate relative frequencies from given or collected data to estimate probabilities of events involving ‘and’, inclusive ‘or’ and exclusive ‘or’

  Elaborations

  • understanding that relative frequencies from large data sets or long-run experiments can provide reliable measures of probability and can be used to make predictions of decisions 
  • using Venn diagrams or two-way tables to estimate frequencies of events involving ‘and’ and ‘or’ questions

  VC2M9P02 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability

• VC2M10ST03

  construct two-way tables and discuss possible relationship between categorical variables

  Elaborations

  • using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents, for example, junior students’ responses compared to senior students’ responses to a survey question
  • recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
  • conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week (as canteen specials might lead to different types of litter) or the weather (due to hot days leading to more icy poles and cold drinks being sold)

  VC2M10ST03 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M10ST05

  plan and conduct statistical investigations of situations that involve bivariate data, including where the independent variable is time; evaluate and report findings with consideration of limitations of any inferences

  Elaborations

  • designing statistical investigations that collect bivariate data over time through observation, experiment or measurement; graphing, interpreting and analysing data; and reporting within the context of the statistical investigation question
  • investigating and comparing anecdotal claims with data collected from well-constructed surveys, including those concerning climate, housing affordability and natural resources, with consideration of data validity and limitations of interpolation or extrapolation
  • using a statistical investigation to address the question ‘Is there a relationship between vaccines and immunity from a virus?’
  • investigating biodiversity changes in Australia before and after colonisation by comparing related bivariate numerical data, discussing and reporting on associations

  VC2M10ST05 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M7N01

  describe the relationship between perfect square numbers and square roots, and use squares of numbers and square roots of perfect square numbers to solve problems

  Elaborations

  • investigating squares of natural numbers from one to 20, and connecting them to visual representations such as dots arranged in a square pattern
  • using the square and square root notation, and the distributive property and area diagrams, to calculate the squares of two-digit numbers; for example, ${43}^2={\left(40+3\right)}^2={40}^2+2\times 40\times 3+3^2=1600+240+9=1849$
  • determining between which 2 consecutive natural numbers the square root of a given number lies; for example, 43 is between the square numbers 36 and 49 so $\sqrt[]{43}$ is between $\sqrt[]{36}\mathrm{ }\text{and }\sqrt[]{49}$ and therefore between 6 and 7
  • generating a list of perfect square numbers and describing any emerging patterns, for example, the last digit of perfect square numbers, or the difference between consecutive square numbers, and recognising the constant second difference
  • using the relationship between perfect square numbers and their square roots to determine the perimeter of a square tiled floor using square tiles; for example, an area of floor with 144 square tiles has a perimeter of 48 tile lengths

  VC2M7N01 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M9ST05

  plan and conduct statistical investigations involving the collection and analysis of different kinds of data; report findings and discuss the strength of evidence to support any conclusions

  Elaborations

  • planning and conducting an investigation using questions together with analysis of a secondary data set collected from online databases such as the Australian Bureau of Statistics
  • planning and conducting an investigation relating to consumer spending habits; and modelling market research on what teenagers are prepared to spend on technology compared to clothing, with consideration of sample techniques and potential sources of bias
  • investigating where would be the best location for a tropical fruit plantation, by conducting a statistical investigation comparing different variables such as the annual rainfall in various parts of Australia, Indonesia, New Guinea and Malaysia, land prices and associated farming costs
  • posing statistical questions; collecting, representing and interpreting data from different sources in relation to reconciliation between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians; and considering the relationships between variables

  VC2M9ST05 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics

• 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

• VC2M6N08

  approximate numerical solutions to problems involving rational numbers and percentages, using appropriate estimation strategies

  Elaborations

  • using familiar fractions, decimals and percentages to approximate calculations, such as 0.3 of 180 is about $\frac{1}{3}$of 180, or 52% is about $\frac{1}{2}$
  • choosing appropriate estimation strategies including rounding to the nearest whole number, knowledge of multiples of 2, 5 or 10 and partitioning numbers, in contexts such as measuring or cost per unit
  • recognising the effect of rounding on calculations involving fractions or decimals and saying what numbers the answer will be between
  • recognising the usefulness of estimation to check calculations for contexts such as dividing wood into a number of lengths, calculating cost per unit, reducing a recipe or dividing the cost of dinner for a group into individual amounts
  • verifying solutions by estimating percentages in suitable contexts, such as discounts, using common percentages of 10%, 25%, 30%, 50% and 1%
  • investigating estimation strategies to make decisions about steam cooking in ground ovens by Aboriginal and/or Torres Strait Islander Peoples, including catering for different numbers of people and resources needed for cooking

  VC2M6N08 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VCMNA020

  Explore the concept of ‘none’, ‘one’ and ‘more’

  Elaborations

  • recognising a change in a collection’s size within the context of familiar, everyday objects, for example a group of cars, toys, lollies, fruit, vegetables, coins, books, materials or tools
  • demonstrating an understanding of one by selecting, giving or taking one object
  • responding to questions about group composition (for example ‘Which group has more?’ ‘Which group has none?’) verbally or by indicating through augmentative and alternative communication, actions or eye gaze

  VCMNA020 | Mathematics | Level B | Number and Algebra | Number and place value

• VC2M3P02

  conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation

  Elaborations

  • identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial, and then responding to the questions ‘How did your results vary for each trial?’ and ‘How do the results vary across the class?’
  • conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, or using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials

  VC2M3P02 | Mathematics | Mathematics Version 2.0 | Level 3 | Probability

• VC2M7SP02

  classify triangles, quadrilaterals and other polygons according to their side and angle properties; identify and reason about relationships

  Elaborations

  • using strips of paper with parallel sides to make triangles and quadrilaterals, and contrasting the rigidity of triangles with the flexibility of quadrilaterals
  • constructing triangles with 3 given side lengths and discussing the question ‘Can any 3 lengths be used to form the sides of a triangle?’
  • identifying and communicating about side and angle properties of scalene, isosceles, equilateral, right-angled, acute and obtuse triangles using geometric conventions
  • describing, comparing and contrasting squares, rectangles, rhombuses, parallelograms, kites and trapeziums, explaining the relationships between these shapes

  VC2M7SP02 | Mathematics | Mathematics Version 2.0 | Level 7 | Space

• VC2M6N09

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and using efficient mental and written calculation strategies, and using digital tools where appropriate; interpret and...

  Elaborations

  • modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation, for example, purchasing items during a sale
  • modelling situations involving earning money and budgeting, asking questions such as ‘Can I afford it?’, ‘Do I need it?’ and ‘How much do I need to save for it?’ and developing a savings plan or budget for an upcoming event or personal purchase
  • modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals

  VC2M6N09 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M8A02

  graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution

  Elaborations

  • recognising that in a table of values, if the first difference between consecutive values of the dependent variable is constant, then it is a linear relation
  • graphing linear functions and relations of the form $x=a$ , $y=a$ , $x \le a$ , $x>a$ , $y \le a$ , $y>a$ on the Cartesian plane for known values of $a$
  • completing a table of values, plotting the resulting points on the Cartesian plane and determining whether the relationship is linear
  • graphing the linear relationship $ax+b=c$for given values of $a, b$and $c$ and identifying from the graph where $ax+b <c$ or where $ax+b >c$
  • solving linear equations of the form $ax+b=c$ and one-variable inequalities of the form $ax+b <c$ or $ax+b >c$ where $a$ > 0 using inverse operations and digital tools, and checking solutions by substitution
  • solving linear equations such as $3x+7=6x-9 ,$representing these graphically, and verifying solutions by substitution

  VC2M8A02 | Mathematics | Mathematics Version 2.0 | Level 8 | 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

• VC2M9ST04

  choose appropriate forms of display or visualisation for a given type of data; justify selections and interpret displays for a given context

  Elaborations

  • comparing data displays using mean, median and range to describe and interpret numerical data sets in terms of centre and spread using histograms, dot plots or stem-and-leaf plots
  • choosing the type of representations based on the data type: categorical (nominal or ordinal) or numerical (discrete or continuous)
  • using different visualisations of data, including non-standard representations such as infographics, and discussing their purpose and intended audience, and evaluating how well they communicate responses to statistical questions of interest
  • comparing and interpreting stacked bar charts, area charts and line graphs, discussing how they represent larger categories that can be subdivided into smaller categories and how information that can be obtained from these displays can be used for comparison

  VC2M9ST04 | Mathematics | Mathematics Version 2.0 | Level 9 | Statistics