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WORK PROGRAM

Chapter 12 Area, volume and capacity

Strand: Measurement

Substrands and outcomes:

AreaMS2.2 Estimates, measures, compares and records the areas of surfaces in square centimetres and square metres

AreaMS3.2 Selects and uses the appropriate unit to calculate area, including the area of squares, rectangles and triangles

Volume and capacityMS2.3 Estimates, measures, compares and records volume and capacities using litres, millilitres and cubic centimetres

Volume and capacityMS3.3 Selects and uses the appropriate unit to estimate and measure volume and capacity, including the volume of rectangular prisms

Perimeter and areaMS4.1 Uses formulae and Pythagoras’ theorem in calculating perimeter and area of circles and figures composed of rectangles and triangles

Surface area and volumeMS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders

Section / GC tips, Investigations, History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles / SkillSHEETS, WorkSHEETS, Interactive games,
Test yourself, Topic tests
(CD–ROM) / Technology applications
(CD–ROM) /

Learning outcomes

Are you ready? (page 428) / SkillSHEETS (page 428)
12.1: Area units
12.2: Area of figures drawn on centimetre grid paper
12.3: Area of rectangles
12.4: Area of triangles
12.5: Volume units
12.6: Volume of a solid constructed from cubic-centimetre blocks / MS2.2
  • using the abbreviations for square metre (m2) and square centimetre (cm2)
  • explaining where square metres are used for measuring in everyday situations
  • measuring a variety of surfaces using a square centimetre overlay
  • recording area in square centimetres
MS3.2
  • identifying situations where square kilometres are used for measuring area
  • using the abbreviations for square kilometre (km2) and hectare (ha)
  • explaining that the area of rectangles can be found by multiplying the length by the breadth (Communicating, Reasoning)
  • finding the relationship between the base, perpendicular height and area of triangles
MS2.3
  • using the abbreviation for litre (L)
  • using the abbreviation for cubic centimetre (cm3)
MS3.3
  • using the abbreviation for cubic metre
  • constructing rectangular prisms using cubic centimetre blocks and counting to determine volume

Area (page 429)
WE 1a-b, 2
Ex 12A Area (page 432) / Maths Quest challenge: Q1-5 (page 433)
Investigation: Investigating the area of a rectangle (page 434) / SkillSHEET 12.1: Area units (page 432)
SkillSHEET 12.2: Area of figures drawn on centimetre grid paper (page 432) / MS2.2
  • measuring a variety of surfaces using a square centimetre grid overlay
  • recording area in square centimetres
  • estimating, measuring and comparing areas in square centimetres
MS3.2
  • selecting the appropriate unit to calculate area

Finding the area of a rectangle (page 434)
WE 3a-b
Ex 12B Finding the area of a rectangle (page 435) / SkillSHEET 12.3: Area of rectangles (page 436) / Mathcad: Area of a rectangle (page 436)
Excel: Area of a rectangle (page 436)
Cabri geometry: Area of a rectangle (page 436) / MS3.2
  • finding the relationship between the length, breadth and area of squares and rectangles
  • explaining that the area of rectangles can be found by multiplying the length by the breadth (Communicating, Reasoning)
  • explaining that the area of squares can be found by squaring the side length (Communicating, Reasoning)
MS4.1
  • developing and using formulae for the area of a square and rectangle
  • finding the areas of simple composite figures that may be dissected into rectangles
  • solving problems relating to area (Applying strategies)

Converting units of area (page 439)
WE 4a-c
Ex 12C Converting units of area (page 440) / 10 Quick Questions 1 (page 442) / Mathcad: Converting units of area (page 440)
Excel: Area units converter (page 440)
Excel: Area units converter (DIY) (page440) / MS3.2
  • using the abbreviation for square kilometre and hectare
  • recognising that one hectare is equal to 10000 square metres
MS4.1
  • converting between metric units of area

Finding the area of a triangle (page 443)
WE 5a-b
Ex 12D Finding the area of a triangle (page 444) / Investigation: What area does your hand cover? (page 446)
Code puzzle (page 447) / SkillSHEET 12.4: Area of triangles (page 444)
Game time 001 (page446)
WorkSHEET 12.1 (page446) / Cabri geometry: Area of a triangle (page 444)
Mathcad: Area of a triangle (page 444) / MS3.2
  • finding the relationship between the base, perpendicular height and area of triangles
MS4.1
  • developing (by forming a rectangle) and using the formula for the area of a triangle
  • finding the areas of simple composite figures that may be dissected into rectangles and triangles
  • solving problems relating to area (Applying strategies)

Volume (page 448)
WE 6a-b
Ex 12E Volume (page449) / SkillSHEET 12.5: Volume units (page 449)
SkillSHEET 12.6: Volume of a solid constructed from cubic-centimetre blocks (page 449) / MS3.3
  • constructing rectangular prisms using cubic centimetre blocks and counting to determine volume

Finding the volume of a rectangular prism (page451)
WE 7
Ex 12F Finding the volume of a rectangular prism (page 452) / Investigation: Volume of a rectangular prism (page451)
10 Quick Questions 2 (page 455) / WorkSHEET 12.2 (page454) / Excel: Volume of a rectangular prism (page452)
Mathcad: Volume of a rectangular prism (page452) / MS3.3
  • explaining that the volume of rectangular prisms can be found by finding the number of cubes in one layer and multiplying by the number of layers (Applying strategies, Reflecting)
  • finding the relationship between the length, breadth, height and volume of rectangular prisms
  • calculating the volume of rectangular prisms
MS4.2
  • developing the formula for volume of prisms by considering the number and volume of layers of identical shapes
  • solving problems involving volume of right prisms (Applying strategies)

Finding the volume of other types of prisms (page 456)
WE 8, 9
Ex 12G Finding the volume of other types of prisms (page 457) / Game time 002 (page 460) / MS4.2
  • developing the formula for volume of prisms by considering the number and volume of layers of identical shapes
  • calculating the volume of a prism given its perpendicular height and the area of its cross-section
  • calculating the volume of prisms with cross-sections that are rectangular and triangular
  • solving problems involving volume of right prisms (Applying strategies)

Capacity (page 460)
WE 10a-c
Ex 12H Capacity (page461) / Maths Quest challenge: Q1-3 (page 464)
Investigation: Around the house (page 465) / WorkSHEET 12.3 (page464) / Excel: Capacity unit conversions (page 461)
Mathcad: Capacity unit conversions (page 461) / MS3.3
  • selecting the appropriate unit to measure volume and capacity
  • calculating the volume of rectangular prisms
  • equating 1 cubic centimetre to 1 millilitre and 1000 cubic centimetres to 1 litre
MS4.2
  • using the kilolitre as a unit in measuring large volumes
  • converting between m3 and kL

Summary (page 466)
Chapter review (page 467) / ‘Test yourself’ multiple choice questions
(page 470)
Topic tests (2)