Lesson 1a Algebra: Exploring area on a grid

Algebra: Exploring area on a grid

Exploring area on a grid  
Overview Resources
Pupils explore the areas of shapes drawn on the isometric grid in terms of triangular units. They relate the area and perimeter of shapes to the lengths of their sides. As in lesson 1-roofs, challenges range from recognition of one-step and multi-step relationships to algebraic symbolisation and proof. But the greatest benefit for pupils at each step is not in the algebra, rather in generating ideas, verbalising and sifting through them and testing patterns. Isometric dotty grid on board or OHT.
Aims Curriculum links
  • Explore the areas of shapes using triangles, and express the relationship measures between area and sides in language and algebra.
  • See complex shapes as composites of simple ones and express their algebra areas in words and algebraically accordingly.
  • Area in non-standard measures
    General number and algebra
    Reasoning and justification
    EPISODE 1
    Focus on parallelograms
    Pupils discuss the smallest shapes that can be drawn on the isometric grid: the triangle, rhombus and trapezium, with the rhombus as a special case of the parallelogram. They find areas of these shapes in terms of the unit triangle. They investigate parallelograms and attempt to formulate a rule for the relationship between the lengths of the sides and the area.

    In the sharing phase pupils sift through the rules generated, recognise similar and partial rules, and attempt to symbolise them in algebra.
    EPISODE 2
    Focus on triangles
    Pupils handle triangles and recognise the advantage of seeing them as half of a rhombus. They explore the relationship between the lengths of the sides and the area, and approach symbolisation.
    EPISODE 3
    Focus on trapezia
    Pupils now move on to investigate the trapezium and advantages of seeing it as a composite shape of a parallelogram and a
    triangle, or two different triangles. They look at how the parts of the formula for the trapezium reflect the composition of the
    shapes.

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

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