Transformations & Vectors

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.


Transformations & Vectors Lessons

Revision Lessons

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.

Mr Mathematics Blog

Trigonometric Identities Sin, Cos and Tan

How to introduce the sin, cos and tan trigonometric identities.

Calculating a Reverse Percentage

How to teach calculating the original amount after a percentage change.

Comparing Datasets using the Mean and Range

The importance of the range when comparing comparing datasets.