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• 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

• VCMMG345

  Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes

  Elaborations

  • distinguishing between a practical demonstration and a proof (for example demonstrating triangles are congruent by placing them on top of each other, as compared to using congruence tests to establish that triangles are congruent)
  • performing a sequence of steps to determine an unknown angle giving a justification in moving from one step to the next.
  • communicating a proof using a sequence of logically connected statements

  VCMMG345 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning

• VCMMG320

  Apply trigonometry to solve right-angled triangle problems

  Elaborations

  • understanding the terms 'adjacent' and 'opposite' sides in a right-angled triangle
  • selecting and accurately using the correct trigonometric ratio to find unknown sides (adjacent, opposite and hypotenuse) and angles in right-angled triangles

  VCMMG320 | Mathematics | Level 9 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG344

  Formulate proofs involving congruent triangles and angle properties

  Elaborations

  • applying an understanding of relationships to deduce properties of geometric figures (for example the base angles of an isosceles triangle are equal)

  VCMMG344 | Mathematics | Level 10 | Measurement and Geometry | Geometric reasoning

• VCMMG319

  Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles

  Elaborations

  • developing understanding of the relationship between the corresponding sides of similar right-angled triangles

  VCMMG319 | Mathematics | Level 9 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG318

  Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles

  Elaborations

  • understanding that Pythagoras' Theorem is a useful tool in determining unknown lengths in right-angled triangles and has widespread applications
  • recognising that right-angled triangle calculations may generate results that can be integers, fractions or irrational numbers

  VCMMG318 | Mathematics | Level 9 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG346

  Solve right-angled triangle problems including those involving direction and angles of elevation and depression

  Elaborations

  • applying Pythagoras's Theorem and trigonometry to problems in surveying and design

  VCMMG346 | Mathematics | Level 10 | Measurement and Geometry | Pythagoras and trigonometry

• VCMMG343

  Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids

  Elaborations

  • investigating and determining the volumes and surface areas of composite solids by considering the individual solids from which they are constructed

  VCMMG343 | Mathematics | Level 10 | Measurement and Geometry | Using units of measurement

• VCMMG288

  Investigate the relationship between features of circles such as circumference, area, radius and diameter. Use formulas to solve problems involving determining radius, diameter, circumference and area from each other

  Elaborations

  • investigating the circumference and area of circles with materials or by measuring, to establish an understanding of formulas
  • investigating the area of circles using a square grid or by rearranging a circle divided into sectors
  • solving problems given one of radius, diameter, circumference or area of a circle, then the other quantities are determined from this

  VCMMG288 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG286

  Choose appropriate units of measurement for area and volume and convert from one unit to another

  Elaborations

  • choosing units for area including mm², cm², m², hectares, km², and units for volume including mm³, cm³, m³
  • recognising that the conversion factors for area units are the squares of those for the corresponding linear units
  • recognising that the conversion factors for volume units are the cubes of those for the corresponding linear units

  VCMMG286 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG290

  Solve problems involving duration, including using 12- and 24-hour time within a single time zone

  Elaborations

  • identifying regions in Australia and countries in Asia that are in the same time zone

  VCMMG290 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG287

  Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites

  Elaborations

  • establishing and using formulas for areas such as trapeziums, rhombuses and kites

  VCMMG287 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG293

  Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning

  Elaborations

  • establishing the properties of squares, rectangles, parallelograms, rhombuses, trapeziums and kites
  • identifying properties related to side lengths, parallel sides, angles, diagonals and symmetry

  VCMMG293 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VCMMG291

  Define congruence of plane shapes using transformations and use transformations of congruent shapes to produce regular patterns in the plane including tessellations with and without the use of digital technology

  Elaborations

  • understanding the properties that determine congruence of triangles and recognising which transformations create congruent figures
  • establishing that two figures are congruent if one shape lies exactly on top of the other after one or more transformations (translation, reflection, rotation), and recognising that the matching sides and the matching angles are equal
  • exploring tiling patterns in art and design

  VCMMG291 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• VCMMG289

  Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume

  Elaborations

  • investigating the relationship between volumes of rectangular and triangular prisms

  VCMMG289 | Mathematics | Level 8 | Measurement and Geometry | Using units of measurement

• VCMMG292

  Develop the conditions for congruence of triangles

  Elaborations

  • investigating the minimal conditions needed for the unique construction of triangles, leading to the establishment of the conditions for congruence (SSS, SAS, ASA and RHS)
  • solving problems using the properties of congruent figures
  • constructing triangles using the conditions for congruence

  VCMMG292 | Mathematics | Level 8 | Measurement and Geometry | Geometric reasoning

• 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