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NSW Syllabuses

Mathematics K–10 - Stage 5.1 - Measurement and Geometry Area and Surface Area

Outcomes

A student:

  • MA5.1-1WM

    uses appropriate terminology, diagrams and symbols in mathematical contexts

  • MA5.1-2WM

    selects and uses appropriate strategies to solve problems

  • MA5.1-8MG

    calculates the areas of composite shapes, and the surface areas of rectangular and triangular prisms

Related Life Skills outcome: MALS-29MG

 

Content

  • Students:
  • Calculate the areas of composite shapes (ACMMG216)
  • calculate the areas of composite figures by dissection into triangles, special quadrilaterals, quadrants, semicircles and sectors
  • identify different possible dissections for a given composite figure and select an appropriate dissection to facilitate calculation of the area (Problem Solving) CCT
  • solve a variety of practical problems involving the areas of quadrilaterals and composite shapes
  • apply properties of geometrical shapes to assist in finding areas, eg symmetry (Problem Solving, Reasoning) CCT
  • calculate the area of an annulus (Problem Solving)
  • Solve problems involving the surface areas of right prisms (ACMMG218)
  • identify the edge lengths and the areas making up the 'surface area' of rectangular and triangular prisms LCCT
  • visualise and name a right prism, given its net LCCT
  • recognise whether a diagram represents a net of a right prism (Reasoning) CCT
  • visualise and sketch the nets of right prisms CCT
  • find the surface areas of rectangular and triangular prisms, given their net
  • calculate the surface areas of rectangular and triangular prisms
  • apply Pythagoras' theorem to assist with finding the surface areas of triangular prisms (Problem Solving)
  • solve a variety of practical problems involving the surface areas of rectangular and triangular prisms

Background Information

It is important that students can visualise rectangular and triangular prisms in different orientations before they find their surface areas. Properties of solids are treated in Stage 3. Students should be able to sketch different views of an object.

Language

When calculating the surface areas of solids, many students may benefit from writing words to describe each of the faces as they record their calculations. Using words such as 'top', 'front', 'sides' and 'bottom' should also assist students in ensuring that they include all the faces required.

The abbreviation m2 is read as 'square metre(s)' and not 'metre(s) squared' or 'metre(s) square'. The abbreviation cm2 is read as 'square centimetre(s)' and not 'centimetre(s) squared' or 'centimetre(s) square'.

When units are not provided in an area question, students should record the area in 'square units'.