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• 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

• 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

• 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

• VCMNA311

  Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

  Elaborations

  • graphing parabolas, and circles connecting x-intercepts of a graph to a related equation

  VCMNA311 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA309

  Find the midpoint and gradient of a line segment (interval) on the Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding midpoint and gradient
  • recognising that the gradient of a line is the same as the gradient of any line segment on that line

  VCMNA309 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA310

  Sketch linear graphs using the coordinates of two points and solve linear equations

  Elaborations

  • determining linear rules from suitable diagrams, tables of values and graphs and describing them using both words and algebra

  VCMNA310 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA308

  Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software

  Elaborations

  • investigating graphical and algebraic techniques for finding distance between two points
  • using Pythagoras' theorem to calculate distance between two points

  VCMNA308 | Mathematics | Level 9 | Number and Algebra | Linear and non-linear relationships

• VCMNA306

  Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate

  Elaborations

  • understanding that the distributive law can be applied to algebraic expressions as well as numbers
  • understanding the relationship between expansion and factorisation and identifying algebraic factors in algebraic expressions

  VCMNA306 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra

• VCMNA303

  Express numbers in scientific notation

  Elaborations

  • representing extremely large and small numbers in scientific notation, and numbers expressed in scientific notation as whole numbers or decimals

  VCMNA303 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCMNA304

  Solve problems involving simple interest

  Elaborations

  • understanding that financial decisions can be assisted by mathematical calculations

  VCMNA304 | Mathematics | Level 9 | Number and Algebra | Money and financial mathematics

• VCMNA305

  Extend and apply the index laws to variables, using positive integer indices and the zero index

  Elaborations

  • understanding that index laws apply to variables as well as numbers

  VCMNA305 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra

• VCMNA301

  Solve problems involving direct proportion. Explore the relationship between graphs and equations corresponding to simple rate problems

  Elaborations

  • identifying direct proportion in real-life contexts

  VCMNA301 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCMNA302

  Apply index laws to numerical expressions with integer indices

  Elaborations

  • simplifying and evaluating numerical expressions, using involving both positive and negative integer indices

  VCMNA302 | Mathematics | Level 9 | Number and Algebra | Real numbers

• VCMNA307

  Apply set structures to solve real-world problems

  Elaborations

  • using a sort algorithm to determine the median of a set of numbers
  • exploring variation in proportion and means of random samples, drawn from a population

  VCMNA307 | Mathematics | Level 9 | Number and Algebra | Patterns and algebra