Lesson 9 Framed tiles

Framed tiles

   
Overview Resources
The concepts of area and perimeter are used in the context of rectangles with ‘whole number’ sides. The aim is to encourage a deeper conceptual appreciation of perimeter and area beyond the application of memorised algorithms. The emphasis, therefore, is on using the concrete image and activities to encourage mental operations which build the ways of working out the perimeter and area, then verbalising them before moving to symbolisation. Worksheets 1 - 3
Squared paper (1/2 cm is sufficient)
Aims Curriculum links
  • Highlight differences between perimeter and area for the same rectangle, and how they are related or unrelated.
  • Revisit the formulae for area and perimeter through experience.
  • Meanings of area and perimeter in standard and uniform non-standard units.
    EPISODE 1
    Two meanings for the 'biggest rectangle'
    The pupils consider the size of a rectangular array of square tiles. They will need to distinguish perimeter and area through practical experience and without using formal measurements. Perimeter and area are handled together to emphasise their differences and so help pupils avoid confusing the two, as can happen when they are met separately.
    EPISODE 2
    Working it out with numbers
    This episode moves to investigating the longest and shortest border strip needed to surround given numbers of tiles.
    EPISODE 3
    Quicker ways of working out
    The specific cases of the square array of tiles and the 2:1 rectangular array of tiles are considered. Formulae are developed for both situations.

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    Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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