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GM5-3: Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms.

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Elaboration on this Achievement Objective

Students should create formulae for perimeters and areas of polygons by attending to features of those polygons. For perimeters they should recognise when side lengths are equal and use multiplicative strategies rather than additive ones. For example to calculate the perimeter of a parallelogram the student should double the length of two adjacent sides, for a regular pentagon they should multiply the length of one side by five.

Students should connect the formulae for finding areas of parallelograms, triangles, and trapeziums to the formula for the area of a rectangle using partitioning and reassembling the shapes. Students should be able to find perimeters and areas of shapes where the side lengths are simple decimals in order to understand that area, in particular, is not restricted to discrete situations where the units of measure can be counted individually.

 

Teaching resources for this Achievement Objective
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Area of a regular pentagon

Level Five
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in a task that requires them to apply geometric properties of polygons and right angles triangle techniques in solving for the area of a polygon.
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How High? and Other Problems

Level Five
Geometry and Measurement
Units of Work
In this collection of activities we use ruler and compass constructions to draw a variety of shapes and to construct angles such as 90°, 60°, 45° and 15°.
  • Apply Pythagoras' theorem.
  • Use their knowledge of the sum of interior angles of a polygon.
  • Construct angles based on halving and combining 90° and other straightforward angles.
  • Apply knowledge of length and area.
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Packing chocolates

Level Five
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in applying their knowledge of three dimensional solids to solve a package and packing problem.
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Penny's box

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Find the volume and surface area of rectangular prisms.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).
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Playdough balls

Level Five
Integrated
Problem solving activities
This problem solving activity has a measurement focus.
  • Compare the volume of a sphere and a cylinder by measuring or applying a formula.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, make a model).
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Square pegs in round holes

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a measurement focus.
  • Draw a diagram to represent a physical situation for a general case.
  • Apply Pythagoras’ theorem to a general situation.
  • Devise and use problem solving strategies to explore situations mathematically.