Search results

Result list

• VC2M7A06

  manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables

  Elaborations

  • experimenting with different sets of tables of values from formulas; for example, using volume of a rectangular prism = length × width × height, and specifying a fixed width and equal length and varying the height
  • using spreadsheets and the formula function to recognise the effect of changing parameters on the entries in cells
  • analysing distance travelled for different combinations of average speed and time of travel using a table of values and the distance formula

  VC2M7A06 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7A05

  generate tables of values from visually changing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane

  Elaborations

  • plotting points from a table of values generated using simple linear functions and recognising patterns, such as the points lie on a straight line
  • discussing and using variables to create a general rule and using the rule to determine the value of the dependent variable for any given value of the independent variable; for example, plotting the value of the circumference of a circle for varying values of radius
  • using function machines to generate a table of ordered pairs using input and output values, plotting the relationships on a Cartesian plane and describing the graph in terms of shape
  • using diagrams and manipulatives to form linear growth patterns, representing these patterns in tables and describing the relationship in terms of the way the pattern is growing and in the context of the situation

  VC2M7A05 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7A01

  recognise and use variables to represent everyday formulas algebraically and substitute values into formulas to determine an unknown

  Elaborations

  • linking variables to attributes and measures being modelled when using formulas, such as the area of a rectangle is equal to the length × width as
    A=l×w; or using p=6g+b to describe a total of points expressed as goals (worth 6 points) and behinds (worth one point)
  • interpreting and using formulas obtained from other sources, for example, maximum heart rates and target heart rates for moderate exercise
  • substituting numerical values for variables when using formulas and calculating the value of an unknown in practical situations; for example, calculating weekly wage W given base wage b and overtime hours h at 1.5 times rate r, W=b+1.5 ×h ×r, using values for mass m and volume v to determine density d of a substance where d=mv
  • using everyday formulas and their application to contexts on Country/Place, investigating the relationships between variables

  VC2M7A01 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7A03

  solve one-variable linear equations of increasing complexity with natural number solutions; verify equation solutions by substitution

  Elaborations

  • recognising that solving an equation is a process of determining a value that makes the equation true; and using substitution to determine whether a given number is a solution to an equation or not
  • solving equations using concrete materials, the balance model and backtracking, explaining the process
  • solving linear equations such as 3x+7=19 algebraically, and verifying the solution by substitution

  VC2M7A03 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7A02

  apply the associative, commutative and distributive laws to aid mental and written computation, and formulate algebraic expressions using constants, variables, operations and brackets

  Elaborations

  • simplifying calculations
  • forming simple estimates for calculations involving multiple and/or combined operations
  • generalising arithmetic expressions to algebraic expressions involving constants, variables, operations and brackets; for example, 7+7+7=3×7, x+x+x=3×x noting that 3x includes implied multiplication and recognising the difference between 3x+4 and 3x+4
  • formulating algebraic expressions that represent mathematical relationships; for example, translating from words to symbols in ‘think of a number’ type activities
  • recognising and applying the concept of variable as something that can change in value, investigating the relationships between variables, and the application to processes on Country/Place, including how cultural expressions of Aboriginal and Torres Strait Islander Peoples, such as storytelling, communicate mathematical relationships that can be represented as mathematical expressions

  VC2M7A02 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2M7M02

  solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units

  Elaborations

  • building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length
  • developing the connection between the area of the parallel cross-section (base), the height and the volume of a rectangular or triangular prism to other prisms
  • connecting the area of the floor space and the number of floors of a high-rise building to calculate the volume of a building
  • using dynamic geometry software, spatial reasoning and prediction to derive the formula for the volume of prisms

  VC2M7M02 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2M7M03

  describe the relationship between π and the circumference, radius and diameter of a circle

  Elaborations

  • recognising the features of circles and their relationships to one another; for example, labelling the parts of a circle including centre, radius, diameter and circumference and using one of radius, diameter or circumference to determine the measure of the other 2; and understanding that the diameter of a circle is twice the radius, or that the radius is the circumference divided by 2π
  • comparing the circumference of circles in relation to their radius and diameter with materials and measuring, to establish measurement formulas; for example, using a compass to draw several circles, then using string to approximate the circumference, comparing the length of string to the diameter of the circle
  • investigating π as the constant in the proportional relationship between the circumference of a circle and its diameter, and historical approximations from different civilisations, including Egypt, Babylon, Greece, India and China
  • investigating the applications and significance of circles in everyday life of Aboriginal and Torres Strait Islander Peoples, such as in basketry, symbols and architecture, recognising the relationships between the centre, radius, diameter and circumference

  VC2M7M03 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• 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