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• 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

• VCMMG222

  Connect decimal representations to the metric system

  Elaborations

  • recognising the equivalence of measurements such as 1.25 metres and 125 centimetres

  VCMMG222 | Mathematics | Level 6 | Measurement and Geometry | Using units of measurement

• VCMMG226

  Interpret and use timetables

  Elaborations

  • planning a trip involving one or more modes of public transport
  • developing a timetable of daily activities

  VCMMG226 | Mathematics | Level 6 | Measurement and Geometry | Using units of measurement

• VCMMG230

  Introduce the Cartesian coordinate system using all four quadrants

  Elaborations

  • understanding that the Cartesian plane provides a graphical or visual way of describing location

  VCMMG230 | Mathematics | Level 6 | Measurement and Geometry | Location and transformation

• VCMMG228

  Construct simple prisms and pyramids

  Elaborations

  • considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia
  • constructing prisms and pyramids from nets, and skeletal models

  VCMMG228 | Mathematics | Level 6 | Measurement and Geometry | Shape

• VCMMG229

  Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies

  Elaborations

  • understanding which attributes of a shape remain the same or change under the effects of transformations such as size, shape or orientation
  • creating tessellations with simple shapes or simple composite shapes

  VCMMG229 | Mathematics | Level 6 | Measurement and Geometry | Location and transformation

• VCMMG225

  Connect volume and capacity and their units of measurement

  Elaborations

  • recognising that 1ml is equivalent to 1cm³

  VCMMG225 | Mathematics | Level 6 | Measurement and Geometry | Using units of measurement

• VCMMG223

  Convert between common metric units of length, mass and capacity

  Elaborations

  • identifying and using the correct operations when converting units including millimetres, centimetres, metres, kilometres, milligrams, grams, kilograms, tonnes, millilitres, litres, kilolitres and megalitres
  • recognising the significance of the prefixes in units of measurement

  VCMMG223 | Mathematics | Level 6 | Measurement and Geometry | Using units of measurement

• VCMMG231

  Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles

  Elaborations

  • identifying the size of a right angle as 90° and defining acute, obtuse, straight and reflex angles
  • measuring, estimating and comparing angles in degrees and classifying angles according to their sizes
  • investigating the use of rotation and symmetry in the diagrammatic representations of kinship relationships of Central and Western Desert people
  • recognising and using the two alternate conventions for naming angles

  VCMMG231 | Mathematics | Level 6 | Measurement and Geometry | Geometric reasoning

• VCMMG224

  Solve problems involving the comparison of lengths and areas using appropriate units

  Elaborations

  • recognising and investigating familiar objects using concrete materials and digital technologies

  VCMMG224 | Mathematics | Level 6 | Measurement and Geometry | Using units of measurement

• VCMMG227

  Measure, calculate and compare elapsed time

  Elaborations

  • recognising that some units of time are better suited for some tasks than others, for example, seconds rather than minutes to measure the duration of a short event
  • using a stopwatch to measure and compare the duration of a series of events, for example, how long does it take to jump a skipping rope 100 times
  • using the starting and finishing times to calculate and compare elapsed time, for example, the time taken to walk to school compared to the time taken to ride to school

  VCMMG227 | Mathematics | Level 6 | Measurement and Geometry | Using units of 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