Transformations and Symmetry

 



Prerequisite Knowledge
  • Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies.
  • Use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D.

Key Concepts
  • A mirror line or tracing paper can be used to check if a shape has a line of reflective symmetry.    A mirror line is called a line of reflective symmetry.
  • Students tend to find reflections in a diagonal line of symmetry more difficult than those in horizontal or vertical.
  • A plane of symmetry bisects a shape into halves that are mirror images of each other.
  • A 2D shape has rotational symmetry if it can be rotated so that it fits perfectly on itself in a new position.
  • The order of rotational is the number of positions the shape looks the same when it is rotated 360°.
  • A translation vector is used to describe a translation.
  • To rotate a shape a centre, direction and amount of turn is needed.  Students should use tracing paper when rotating shapes.
  • A positive scale factor greater than 1 increases the size of a shape.  A postive scale factor less than one decreases the size.  More advanced students should enlarge a shape from a centre.
  • Rotations, reflections and translations result in congruent shapes.  Enlargements result in similar shapes.


Working mathematically

Develop fluency

  • Use language and properties precisely to analyse 2-D and 3-D shapes.

Reason mathematically

  • Make and test conjectures about patterns and relationships; look for proofs or counter-examples
    Begin to reason deductively in geometry including using geometrical constructions

Solve problems

  • Begin to model situations mathematically and express the results using a range of formal mathematical representations
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

Geometry and measures

  • Describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric
  • Identify properties of, and describe the results of, translations, rotations and reflections applied to given figures
  • Identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids
  • Interpret mathematical relationships both algebraically and geometrically.

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