Transformations and Symmetry

Scheme of work: Key Stage 3: Year 7: Term 6: Transformations and Symmetry

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.

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 360Â°.
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.

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.

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.