Tes Maths: Inspect the spec - transformations

Craig Barton
05th September 2016
Tes Maths, inspect the spec, GCSE, new specification

Lesson ideas to help you teach transformations according to the new GCSE specification

Everyone is talking about functions and frequency trees, but what else has changed with the advent of the new specification? And what resources are available to help? Throughout this series, TES Maths aims to find out.

What does the specification say?

The expectation is that:

  • All students will develop confidence and competence with the content identified by standard type
  • All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
  • Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

G7: Identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors)

G8: Describe the changes and invariance achieved by combinations of rotations, reflections and translations

G24: Describe translations as 2D vectors

What's the same?

The part of the specification that relates to transformations remains largely unchanged. All students will need to be comfortable reflecting, rotating, translating and enlarging, as well as recognising and describing each of these transformations.

However, it is worth pointing out that students across both tiers will need to be able to use vector notation to describe translations and enlarge shapes with fractional scale factors. The delights of negative scale factors, as well as combinations of transformations, are reserved for those students sitting the higher tier.

What has changed?

Higher tier students will now have to get their heads around the concept of invariance. When carrying out and describing combinations of transformations, they need to be on the lookout for points that change and those that remain invariant. This is not a huge addition, and does not require a massive rethink of how you approach the teaching of transformations, but it is vital to ensure students are comfortable with this new terminology.

It is also worth considering the context in which invariance could be tested. It could be a one-mark throw-away question, such as:

The shape above is reflected in the line y=x. How many of its vertices remain invariant? 

Or something more challenging, like:

A square is reflected in the line y = 2 and then rotated 90 degrees clockwise about the point (3, 4). What is the greatest number of invariant points? 

We shall have to wait and see!

How can TES Maths can help?

As ever, the wonderfully talented authors of the TES Maths community have stepped up to the mark to lend a hand. Here is a selection of my favourite resources to help support the teaching of this topic:

  1. Transformations worksheets
    Consolidate students' learning of transformations with these detailed worksheets, including worked examples.
  2. Combinations of transformations investigation
    Ideal as an introduction to the concept of invariance, this investigation gives studentss the chance to explore combinations of transformations.
  3. Invariance of co-ordinates
    Explore invariance with this well-structured presentation and accompanying worksheet, focusing on reflections and rotations.
  4. Invariance activity sheet
    Test students' understanding of identifying invariant points with this differentiated worksheet, incorporating cloze, matching and Venn diagram activities

Transformations package

A collection of all my transformations worksheets. They are available elsewhere on TES and the ones where shapes move about to create words have PPTs to go with them (search transformations jigsaw) These are some of the most popular worksheets I do with the students so I thought it might be useful to group them altogether. PLEASE REVIEW
By Tristanjones

Combinations of transformations investigation

An investigation activity where pupils explore combinations of transformations. Plenary activity involves pupils summarising their comprehension in a fill in the blanks activity based around equivalent transformations. Rotation, reflection, translation.
By ben-ncfc

Invariance of co-ordinates

An introduction to the concept of points being invariant after a transformation.
The worksheet is based upon reflections and rotations.
By alisongilroy

Invariance Activity Sheet

A RAG (Red, Amber, Green) worksheet around identifying invariant points on different transformations, incorporating a CLOZE activity (fill in the blanks), a matching activity, and a Venn Diagram activity
By Peter Mattock

Craig Barton, Tes Maths adviser

Craig is a secondary maths teacher in the north of England.

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