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• Mathematics Version 2.0: Level 6 achievement standards

  By the end of Level 6, students use integers to represent points on a number line and on the Cartesian plane. They solve problems using the properties of prime, composite, square and triangular numbers. Students order common fractions, giving reasons, and add and subtract fractions with...

  Level description | Mathematics | Mathematics Version 2.0 | Level 6

• Mathematics Version 2.0: Level 6 description

  In Level 6, 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

• VC2M6A03

  design and use algorithms involving a sequence of steps and decisions that use rules to generate sets of numbers; identify, interpret and explain emerging patterns

  Elaborations

  • using an algorithm to create extended number sequences involving rational numbers, using a rule and digital tools, and explaining any emerging patterns
  • designing an algorithm to model operations, using the concept of input and output, describing and explaining relationships and any emerging patterns; for example, using function machines to model operations and recognising and comparing additive and multiplicative relationships
  • designing an algorithm or writing a simple program to generate a sequence of numbers based on the user’s input and a chosen operation, discussing any emerging patterns; for example, generating a sequence of numbers and comparing how quickly the sequences are growing in comparison to each other using the rule ‘add 2 to the input number’ compared to multiplying the input number by 2

  VC2M6A03 | Mathematics | Mathematics Version 2.0 | Level 6 | 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

• 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

• VC2M6M01

  convert between common metric units of length, mass and capacity; choose and use decimal representations of metric measurements relevant to the context of a problem

  Elaborations

  • recognising the significance of the prefixes in units of measurement
  • identifying and using the correct operations when converting between units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
  • recognising the equivalence of measurements, such as 1.25 metres is the same as 125 centimetres

  VC2M6M01 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• VC2M6M03

  measure, calculate and compare elapsed time; interpret and use timetables and itineraries to plan activities and determine the duration of events and journeys

  Elaborations

  • planning a trip involving one or more modes of public transport
  • developing a timetable of daily activities for a planned event, for example, a sports carnival
  • investigating different ways duration is represented in timetables and using different timetables to plan a journey

  VC2M6M03 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• VC2M6M04

  identify the relationships between angles on a straight line, angles at a point and vertically opposite angles; use these to determine unknown angles, communicating reasoning

  Elaborations

  • using protractors or dynamic geometry software to measure and generalise about the size of angles formed when lines are crossed, and combinations of angles that meet at a point, including combinations that form right or straight angles
  • demonstrating the meaning of language associated with properties of angles, including right, complementary, complement, straight, supplement, vertically opposite, and angles at a point
  • using the properties of supplementary and complementary angles to represent spatial situations with number sentences and solving to find the size of unknown angles

  VC2M6M04 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• VC2M6M02

  establish the formula for the area of a rectangle and use it to solve practical problems

  Elaborations

  • using the relationship between the length and area of square units and the array structure to derive a formula for calculating the area of a rectangle from the lengths of its sides
  • using one-centimetre grid paper to construct a variety of rectangles, recording the side lengths and the related areas of the rectangles in a table to establish the formula for the area of a rectangle by recognising the relationship between the length of the sides and its calculated area
  • solving problems involving the comparison of lengths and areas using appropriate units
  • investigating the connection between the perimeters of different rectangles with the same area and between the areas of rectangles with the same perimeter

  VC2M6M02 | Mathematics | Mathematics Version 2.0 | Level 6 | Measurement

• VC2M6N07

  solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies with and without digital tools

  Elaborations

  • explaining how 13 of a quantity can be achieved by dividing by 3, and how knowledge of 13 of a quantity can be used to find 23 or 43 of the same quantity, using situations involving money, length, duration, mass or capacity
  • investigating percentage discounts of 10%, 25% and 50% in an online toy sale, using their equivalent decimal representations of 0.10, 0.25 and 0.50 to calculate the amount of discount on sale items, with and without digital tools
  • linking percentages to their decimal equivalent of tenths and hundredths and using these to determine percentage discounts; for example, finding a 30% discount by using its equivalence to 0.3, dividing by 10 and multiplying the result by 3 to give 30%
  • explaining the equivalence between percentages and fractions, for example, 3313 % and 13 , keeping to percentages that are equivalent to fractions with small denominators such as 6623 % and 12.5%
  • representing a situation with a mathematical expression, for example, numbers and symbols such as 14 × 24, that involves finding a familiar fraction or percentage of a quantity; and using mental strategies or a calculator and explaining the result in terms of the situation in question

  VC2M6N07 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6N06

  multiply and divide decimals by multiples of powers of 10 without a calculator, applying knowledge of place value and proficiency with multiplication facts, using estimation and rounding to check the reasonableness of answers

  Elaborations

  • applying place value knowledge, including that the value of the digit is 10 times smaller each time a place is moved to the right, and known multiplication facts, to multiply and divide a decimal by powers of 10
  • applying and explaining estimation strategies in multiplicative situations involving a decimal greater than one that is multiplied by a two- or three-digit number, using a multiple of 10 or 100 when the situation requires just an estimation
  • explaining the effect of multiplying or dividing a decimal by 10, 100, 1000 … in terms of place value and not the decimal point shifting

  VC2M6N06 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6N05

  solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions

  Elaborations

  • representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes
  • determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems
  • calculating the addition or subtraction of fractions in the context of real-world problems (for example, using part cups or spoons in a recipe), using the understanding of equivalent fractions
  • understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators

  VC2M6N05 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6N01

  recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane

  Elaborations

  • extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (−2) and (+2) and their relationship to zero as −2 < 0 < 2
  • using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event
  • using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero (for example, elevators, above and below sea level) and distinguishing a location by referencing the 4 quadrants of the Cartesian plane
  • recognising that the sign (positive or negative) indicates a direction in relation to zero – for example, 30 metres left of the admin block is (−30) and 20 metres right of the admin block is (+20) – and programming robots to move along a number line that is either horizontal or vertical but not both at the same time
  • representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line

  VC2M6N01 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• 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

• VC2M6N04

  apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers

  Elaborations

  • applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
  • applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
  • working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic Games in the women’s long jump or shot-put and comparing school records to the Olympic records
  • deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 − 0.0035 or 2.345 + 1.4999

  VC2M6N04 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6N03

  apply knowledge of equivalence to compare, order and represent common fractions, including halves, thirds and quarters, on the same number line and justify their order

  Elaborations

  • applying factors and multiples to fraction denominators (such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths) to determine equivalent representations of fractions in order to make comparisons
  • representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators
  • explaining equivalence and order between fractions using number lines, drawings and models
  • comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, 58 is greater than 12 can be written as 58 > 12 , because half of 8 is 4; 16 is less than 14 , because 6 > 4 and can be written as 16 < 14

  VC2M6N03 | Mathematics | Mathematics Version 2.0 | Level 6 | 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 13 of 180, or 52% is about 12
  • 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

• VC2M6N02

  identify and describe the properties of prime, composite, square and triangular numbers and use these properties to solve problems and simplify calculations

  Elaborations

  • using the definition of a prime number to explain why one is not a prime number
  • testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns
  • representing composite numbers as a product of their factors, including prime factors when necessary and using this form to simplify calculations involving multiplication, such as 15 × 16 as 5 × 3 × 4 × 4, which can be rearranged to simplify calculation to 5 × 4 × 3 × 4 = 20 × 12
  • identifying and describing the product of a number with itself as square; for example, 3 × 3 is the same as 3²
  • using spreadsheets to list all the numbers that have up to 3 factors, using combinations of only the first 3 prime numbers, recognising any emerging patterns, making conjectures and experimenting with other combinations

  VC2M6N02 | Mathematics | Mathematics Version 2.0 | Level 6 | Number

• VC2M6P02

  conduct repeated chance experiments and run simulations with an increasing number of trials using digital tools; compare observations with expected results and discuss the effect on variation of increasing the number of trials

  Elaborations

  • using digital tools to simulate multiple tosses of a coin or dice and comparing the relative frequency of an outcome as the number of trials increases; and identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials
  • using online simulations of repeated random events to recognise emerging patterns, discussing and comparing expected results to the actual results
  • investigating the relative frequencies of all outcomes for a chance experiment and verifying that their sum equals one
  • systematically recording the outcome of large numbers of spins on a spinner and analysing the relative frequencies of outcomes, representing these as percentages

  VC2M6P02 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability

• VC2M6P01

  describe probabilities using fractions, decimals and percentages; recognise that probabilities lie on numerical scales of 0–‍1 or 0%–100%; use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals

  Elaborations

  • recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it will not happen and one or 100% means it is certain to happen
  • using a scale of zero to one or 0% to 100% to estimate chances of events
  • listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more than or less than for each possible event, for example, the probability of getting a number greater than 4
  • recognising the language used to describe situations involving uncertainty, such as what it means to be ‘lucky’, a ‘75% chance’ of rain or a ‘1-in-100 years’ flood
  • exploring Aboriginal and/or Torres Strait Islander children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

  VC2M6P01 | Mathematics | Mathematics Version 2.0 | Level 6 | Probability