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• VC2M7M06

  use mathematical modelling to solve practical problems involving ratios of lengths, areas and volumes; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation

  Elaborations

  • using fractions to model and solve ratio problems involving comparison of quantities, and considering part-part and part-whole relations
  • modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, or food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing
  • modelling the situation using manipulatives, diagrams and/or mathematical discussion; for example, mixing primary colours in a variety of ratios to investigate how new colours are created and the strength of those colours
  • investigating commercialised substances founded on Aboriginal and/or Torres Strait Islander Peoples’ knowledges of substances, including pharmaceuticals and toxins, understanding how ratios are used in their development

  VC2M7M06 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M7M05

  demonstrate that the interior angle sum of a triangle in the plane is 180° and apply this to determine the interior angle sum of other shapes and the size of unknown angles

  Elaborations

  • using concrete materials to demonstrate that the sum of the interior angles of a triangle is 180°; for example, using paper triangles and tearing to demonstrate that the interior angles when combined form 180°
  • using decomposition and the angle sum of a triangle to generalise the interior angle sum of an n-sided polygon, as 180n-2=180n-360

  VC2M7M05 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M7M01

  establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem-solving

  Elaborations

  • building on the understanding of the area of rectangles to develop formulas for the area of triangles
  • establishing that the area of a triangle is half the area of an appropriate rectangle
  • using area formulas for rectangles and triangles to solve problems involving areas of surfaces

  VC2M7M01 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M7M04

  identify corresponding, alternate and co-interior relationships between angles formed when parallel lines are crossed by a transversal; use them to solve problems and explain reasons

  Elaborations

  • constructing a pair of parallel lines and a pair of perpendicular lines using their properties, a pair of compasses and a ruler and set squares, or using dynamic geometry software
  • using dynamic geometry software to identify relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal
  • using dynamic geometry software to demonstrate how angles and their properties are involved in the design and construction of scissor lifts, folding umbrellas, toolboxes and cherry pickers
  • using geometric reasoning of angle properties to generalise the angle relationships of parallel lines and transversals, and related properties, such as the size of an exterior angle of a triangle is equal to the sum of the sizes of opposite and non-adjacent interior angles, and the sum of the sizes of interior angles in a triangle in the plane is equal to the size of 2 right angles or 180°

  VC2M7M04 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VCMMG264

  Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal

  Elaborations

  • defining and classifying pairs of angles as complementary, supplementary, adjacent and vertically opposite

  VCMMG264 | Mathematics | Level 7 | Measurement and Geometry | Geometric reasoning

• VCMMG265

  Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning

  Elaborations

  • constructing parallel and perpendicular lines using their properties, a pair of compasses and a ruler, and dynamic geometry software
  • defining and identifying the relationships between alternate, corresponding and co-interior angles for a pair of parallel lines cut by a transversal

  VCMMG265 | Mathematics | Level 7 | Measurement and Geometry | Geometric reasoning

• VCMMG261

  Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries

  Elaborations

  • describing patterns and investigating different ways to produce the same transformation such as using two successive reflections to provide the same result as a translation
  • creating and re-creating patterns using combinations of reflections and rotations, using digital technologies

  VCMMG261 | Mathematics | Level 7 | Measurement and Geometry | Location and transformation

• VCMMG260

  Draw different views of prisms and solids formed from combinations of prisms

  Elaborations

  • using aerial views of buildings and other 3-D structures to visualise the structure of the building or prism

  VCMMG260 | Mathematics | Level 7 | Measurement and Geometry | Shape

• VCMMG259

  Calculate volumes of rectangular prisms

  Elaborations

  • investigating volumes of cubes and rectangular prisms and establishing and using the formula V = l × b × h
  • understanding and using cubic units when interpreting and finding volumes of cubes and rectangular prisms

  VCMMG259 | Mathematics | Level 7 | Measurement and Geometry | Using units of measurement

• VCMMG263

  Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral

  Elaborations

  • using concrete materials and digital technologies to investigate the angle sum of a triangle and quadrilateral

  VCMMG263 | Mathematics | Level 7 | Measurement and Geometry | Geometric reasoning

• VCMMG258

  Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving

  Elaborations

  • building on the understanding of the area of rectangles to develop formulas for the area of triangles
  • establishing that the area of a triangle is half the area of an appropriate rectangle
  • using area formulas for rectangles and triangles to solve problems involving areas of surfaces

  VCMMG258 | Mathematics | Level 7 | Measurement and Geometry | Using units of measurement

• VCMMG262

  Classify triangles according to their side and angle properties and describe quadrilaterals

  Elaborations

  • identifying side and angle properties of scalene, isosceles, right-angled and obtuse-angled triangles
  • describing squares, rectangles, rhombuses, parallelograms, kites and trapeziums

  VCMMG262 | Mathematics | Level 7 | Measurement and Geometry | Geometric reasoning

• VC2M7N02

  represent natural numbers in expanded notation using powers of 10, and as products of powers of prime numbers using exponent notation

  Elaborations

  • relating the sequences 10, 100, 1000, 10 000 … and 10¹, 10², 10³, 10⁴ …
  • applying and explaining the connections between place value and expanded notations, for example, 7000=7×103 and 3750=3×103+7×102+5×101
  • applying knowledge of factors to strategies for expressing natural numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees, for example, 48=6×8=2×3×2×2×2=31×24=3×24
  • developing familiarity with the sequence 1, 2, 4, 8, 16, 32, 64, 128, 256, 512 and powers of 2; the sequence 1, 3, 9, 27, 81, 243, 729 and powers of 3; and the sequence 1, 5, 25, 125, 625 and powers of 5
  • solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of natural numbers by comparing their prime factorisation

  VC2M7N02 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N09

  recognise, represent and solve problems involving ratios

  Elaborations

  • using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios 1:4 and 1:1:2
  • using fractions to solve ratio problems involving comparison of quantities and considering part-part and part-whole relations; for example, dividing a set into the ratio 1:2 by determining the number of parts as 3
  • sharing quantities in a given ratio; for example, sharing an amount of money in a given ratio, such as sharing $20 in the ratio 2:3
  • applying ratios to realistic and meaningful contexts – for example, mixing 500 millilitres of a liquid with a concentration of 1:4 means 15 concentrate and 45 water so, 0.2 of 500 millilitres is concentrate and 0.8 of 500 millilitres is water – and interpreting results in context

  VC2M7N09 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N06

  use the 4 operations with positive rational numbers, including fractions and decimals, to solve problems using efficient mental and written calculation strategies

  Elaborations

  • solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
  • choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as 12.5%, 18, 0.125 or 1251000
  • developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate 23 of 12 , giving 12 of 23=13
  • solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
  • developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
  • carrying out calculations to solve problems using the representation that makes computations efficient, such as 12.5% of 96 is more efficiently calculated as 18 of 96, including contexts such as comparing land use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases or decreases in energy accounts each account cycle

  VC2M7N06 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N04

  round decimals to a given accuracy appropriate to the context and use appropriate rounding and estimation to check the reasonableness of computations

  Elaborations

  • identifying the interval between a pair of consecutive integers that includes a given rational number
  • choosing and applying conventions for rounding correct to a specified number of decimal places based upon the context
  • checking that the accuracy of rounding is suitable for context and purpose; for example, for the amount of paint required or the cost estimate for renovating a house, purchasing 2 litres of paint to paint the bedroom even though 1.89 litres is the exact answer or estimating a renovation budget to the nearest $100

  VC2M7N04 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N03

  find equivalent representations of rational numbers and represent positive and negative rational numbers and mixed numbers on a number line

  Elaborations

  • investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as 23 is equivalent to 46 and 69 and therefore 23 < 56
  • expressing a fraction in simplest form using common divisors
  • applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers, for example, 16%, 0.16, 16100 and 425, using manipulatives, number lines or diagrams
  • representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero

  VC2M7N03 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N08

  compare, order and solve problems involving addition and subtraction of integers

  Elaborations

  • using less-than and greater-than notation in expressions when comparing and ordering integers; for example, negative 5 is less than positive 2 and can be represented as -5<+2; -3>-6
  • discussing language such as ‘addition’, ‘subtraction’, ‘magnitude’, ‘difference’ and ‘sign’ and synonyms of these terms
  • ordering, adding and subtracting integers using a number line

  VC2M7N08 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N07

  find percentages of quantities and express one quantity as a percentage of another, with and without digital tools

  Elaborations

  • using authentic problems to express quantities as percentages of other amounts

  VC2M7N07 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M7N10

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts such as ‘best buys’; formulate problems, choosing representations and efficient calculation strategies, designing algorithms and using digital tools as appropriate; interpret...

  Elaborations

  • modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero, or in geography when determining altitude above and below sea level
  • modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of the bottle cost to the recycling refund, proportion of the school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted ‘yes’ to a change of school uniform; and interpreting and communicating answers in terms of the context of the situation
  • modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
  • finding the sum of a set of consecutive numbers using a loop structure
  • constructing geometric patterns such as a honeycomb, using dynamic geometry functionality
  • using mathematical modelling to investigate the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt

  VC2M7N10 | Mathematics | Mathematics Version 2.0 | Level 7 | Number