TES Maths: Inspect the spec - transformations
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:
- Transformations lessons
TES Author, Pixi_17, has created well-designed, differentiated lessons for each of the transformation types, including reflection, rotation, translation and enlargement.
- Transformations worksheets
Consolidate students' learning of transformations with these detailed worksheets, including worked examples.
- Combinations of transformations investigation
Ideal as an introduction to the concept of invariance, this investigation gives studentss the chance to explore combinations of transformations.
- Invariance of co-ordinates
Explore invariance with this well-structured presentation and accompanying worksheet, focusing on reflections and rotations.
- Invariance activity sheet
Test students' understanding of identifying invariant points with this differentiated worksheet, incorporating cloze, matching and Venn diagram activities.
Craig Barton, TES Maths adviser
Craig is a secondary maths teacher in the North of England.
Find more resources to support the changes to the GCSE maths specification by taking a look at the rest of the series.