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Teaching and learning similarity

  • Cambridge Mathematics
  • For teachers and practitioners
  • Espresso
  • Teaching and learning similarity
  • Espresso
  • 50: Covariational reasoning
  • 49: Teaching and learning equivalence
  • 48: Early development of functional thinking
  • 47: Developing concepts of pattern
  • 46: Building and breaking 2D and 3D shapes
  • 45: Teaching logical reasoning
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09 November 2021

An infographic displaying Four ways to approach finding missing values when working with similarity. The four methods are: Between ratio, Within ratio, Scale factor and Transformation-based

What does research suggest about the teaching and learning of similarity?

  • Similarity brings proportional reasoning and geometry together, offering a context through which to develop the idea of mathematical argument and proof and move from visual to logical reasoning
  • Early intuitions about similarity are developed when children play with and describe models and distorted 2D and 3D shapes
  • The everyday language and ideas of sameness compared to that of mathematical similarity can cause confusion for students
  • Static approaches to similarity involve identifying scale factors and “matching” lengths or angles, although identifying corresponding parts is often challenging for students
  • Similarity tasks can be considered as differentiating between similar and non-similar shapes or constructing similar shapes
  • Similarity can be explored through the additive process of tiling or the multiplicative idea of scaling; both give insights into the geometrical properties of the shapes or objects involved
  • Similar shapes or objects can be identified, and missing values calculated, by considering between ratios, within ratios and scale factors, or using more dynamic approaches involving technology
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