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• 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

• VCMMG315

  Investigate very small and very large time scales and intervals

  Elaborations

  • investigating the usefulness of scientific notation in representing very large and very small numbers

  VCMMG315 | Mathematics | Level 9 | Measurement and Geometry | Using units of measurement

• VCMMG313

  Calculate the surface area and volume of cylinders and solve related problems

  Elaborations

  • analysing nets of cylinders to establish formulas for surface area
  • connecting the volume and capacity of a cylinder to solve authentic problems

  VCMMG313 | Mathematics | Level 9 | Measurement and Geometry | Using units of measurement

• VCMMG317

  Solve problems using ratio and scale factors in similar figures

  Elaborations

  • establishing the relationship between areas of similar figures and the ratio of corresponding sides (scale factor)

  VCMMG317 | Mathematics | Level 9 | Measurement and Geometry | Geometric reasoning

• VCMMG314

  Solve problems involving the surface area and volume of right prisms

  Elaborations

  • solving practical problems involving surface area and volume of right prisms

  VCMMG314 | Mathematics | Level 9 | Measurement and Geometry | Using units of measurement

• VCMMG316

  Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar

  Elaborations

  • establishing the conditions for similarity of two triangles and comparing this to the conditions for congruence
  • using the properties of similarity and ratio, and correct mathematical notation and language, to solve problems involving enlargement. For example, scale diagrams
  • using the enlargement transformation to establish similarityunderstanding that similarity and congruence help describe relationships between geometrical shapes and are important elements of reasoning and proof

  VCMMG316 | Mathematics | Level 9 | Measurement and Geometry | Geometric reasoning

• VCMMG312

  Calculate the areas of composite shapes

  Elaborations

  • understanding that partitioning composite shapes into rectangles and triangles is a strategy for solving problems involving area

  VCMMG312 | Mathematics | Level 9 | Measurement and Geometry | Using units of measurement

• VCMMG367

  Establish the sine, cosine and area rules for any triangle and solve related problems

  Elaborations

  • applying knowledge of sine, cosine and area rules to authentic problems such as those involving surveying and design

  VCMMG367 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG368

  Use the unit circle to define trigonometric functions as functions of a real variable, and graph them with and without the use of digital technologies

  Elaborations

  • establishing the symmetrical properties of trigonometric functions
  • investigating angles of any magnitude
  • understanding that trigonometric functions are periodic and that this can be used to describe motion
  • identifying points on the unit circle via arc lengths in radians, which correspond to specified values of the circular functions sine, cosine and tangent

  VCMMG368 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG369

  Solve simple trigonometric equations

  Elaborations

  • using periodicity and symmetry to solve equations

  VCMMG369 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG370

  Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles

  Elaborations

  • investigating the applications of Pythagoras's theorem in authentic problems

  VCMMG370 | Mathematics | Level 10A | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG365

  Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids

  Elaborations

  • using formulas to solve problems
  • using authentic situations to apply knowledge and understanding of surface area and volume

  VCMMG365 | Mathematics | Level 10A | Measurement and Geometry | Using units of measurement

• VCMMG366

  Prove and apply angle and chord properties of circles

  Elaborations

  • performing a sequence of steps to determine an unknown angle or length in a diagram involving a circle, or circles, giving a justification in moving from one step to the next
  • communicating a proof using a logical sequence of statements
  • proving results involving chords of circles

  VCMMG366 | Mathematics | Level 10A | Measurement and Geometry | Geometric reasoning