# 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 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.

#### 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.