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At the start of this unit students learn about the difference between congruent and similar shapes. They use this knowledge to both perform and describe reflections, rotations, translations and enlargements on a grid. As learning progress they are challenged to describe a combination of transformations using the correct terminology.

This topics follows on from Properties of 2D Shapes and takes place in Year 10 Term 6.

**Prerequisite Knowledge**

- use conventional terms and notations: points, lines, vertices, edges, planes, parallel lines, perpendicular lines, right angles, polygons, regular polygons and polygons with reflection and/or rotation symmetries;
- identify an order of rotational and reflective symmetry for two dimensional shapes
- use the standard conventions for labelling and referring to the sides and angles of triangles; draw diagrams from written description
- Recognise linear functions in the form y = ± a and x = ± a

**Success Criteria**

- identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional scale factors)
- apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors

**Key Concepts**

- An object is transformed to create an image.
- Rotation, Translation and Reflections involve congruent objects and images whereas enlargement leads to the object being similar to the image.
- Translation vectors are used to describe movements along Cartesian axes.
- When reflecting objects the image is always the same distance from the line of reflection as the object.
- Rotations and enlargements are constructed from a centre.
- A scalar has direction only whereas a vector has direction and magnitude.
- A vector has a magnitude and direction but its starting point is variable.
- Parallel lines have vectors that are multiples of each other.
- To add and subtract vectors is similar to collecting like terms.

**Common Misconceptions**

- Translation vectors can incorrectly be written using the name notation as coordinate pairs.
- Translations, Rotations, Enlargement and Reflections all come under the umbrella term of transformation. Students often confuse the term translation for transformation.
- Students often have more difficulty describing single transformations rather than performing them.
- Writing vectors in their simplest form by collecting like terms is often a problem in examinations.

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