Transformations and Symmetry

Scheme of work: Key Stage 3: Year 7: Term 6: 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.

Transformations and Symmetry Resources

Mr Mathematics Blog

Planes of Symmetry in 3D Shapes

Planes of Symmetry in 3D Shapes for Key Stage 3/GCSE students.

Use isometric paper for hands-on learning and enhanced understanding.

GCSE Trigonometry Skills & SOH CAH TOA Techniques

Master GCSE Math: Get key SOH-CAH-TOA tips, solve triangles accurately, and tackle area tasks. Ideal for students targeting grades 4-5.

Regions in the Complex Plane

Explore Regions in the Complex Plane with A-Level Further Maths: inequalities, Argand diagrams, and geometric interpretations.