To start, we can look at some really useful GeoGebra resources to demonstrate Transformations. Looking at this page on Edexcel GeoGebra resources in the Use of Technology series, we can check the GCSE collection. The Transformations and constructions section includes transformations which covers all four transformation types and enlargement centre and scale factor. Many other GeoGebra resources are available on Transformations, Reflection in the line y=x, illustrated below allows students to experiment by moving the points, the resource also includes questions. See also Reflections of an object, Transformations – Rotation, Enlargement and Translations. From Tim Brzezinski see his GeoGebra book, Transformations! Geometry.

We could learn about Transformations with Desmos, we could also use Autograph. I am very much looking forward to all-device web version of Autograph. I find Autograph very intuitive for illustrating transformations. It is very simple to enter a shape and transform it. The shape can be a user defined so it is very easy to set up illustrations. It is also very simple to add labels. With Autograph when you select objects then right click you get a menu of appropriate choices, selecting an object and equation offers the option to reflect.

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I have written on Transum many times, with its very clear Topic Index for Teachers also, for students a Maths Map with numerous activities to support their learning the site is very easy to navigate. The resources are very clear and attractively presented, they display well for demonstration in class as well as being very good for self-study for students.

Transum has activities for Transformations. I have found this activity which allows students to draw transformations online and have them checked particularly useful.

Level 1 covers reflections, including reflecting in the lines y=x and y=-x, level 2, Translations, Level 3, rotations about the origin, and Level 4 Enlargement. For students studying Matrices and Transformations, Level 5 illustrates examples. Level 6 has some questions, we could easily illustrate the answers with Autograph.

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There are of course many more resources available for Transformations, a selection…

What for me looks like a very happy new discovery, Blutik. This includes resources on Transformations (Section 8). As well as clearly explained videos, a worked example is displayed for each level and there are interactive questions to try, can you drag the shape to the correct place? Step by step help is given. The interactive questions appear at the bottom of the screen. If you check your diagram at any stage you will be told the number of points you have correct.

I will return to Blutik again. We see from the pricing information that the extensive library of interactive questions, easy-to-follow teacher videos, and AI teachers guiding students as they enter each line of working will always be free. See the Frequently Asked Questions also the Getting Started Guides.

London Grid for Learning is increasing their use of the Blutick system as you can hear about in this video. The video is of interest to a wider audience also as it describes the resources.

Don Steward’s resources include Duncan Keith’s lovely Excel Transformation Golf.

Andy Lutwuche TES resources on Transformations including Clumsy Clive, can you find the mistakes in Clive’s homework? Transformation Codebreakers, Andy’s SSDD Questions, Building Blocks – Transformations.

My favourite way of teaching Enlargement is to use Vectors, this technique is clearly illustrated in this free TES resource which has questions as well as a very clear PowerPoint.

Also on TES – Find Them All.

Colin Foster’s Geometry Etudes include resources on Enlargement and Rotations.

Corbett Maths includes videos and worksheets on Enlargements, Reflections, Rotations and Translations.

From Nrich Decoding Transformations, Transformations – Short Problems, Growing Rectangles, Robotic Rotations, Surprising Transformations.

Open Middle Transformations Problems.

Quizzes from Diagnostic Questions, we could use Transformations quizzes from White Rose or the Exam Boards

Dr Frost this example is from his Year 7 scheme of work. Search DrFrostMaths for many more, including several videos.

Maths Genie

Transformations Videos

Rotations Reflections Enlargements Translations Mixed Transformations

Rotations Solutions Reflections Solutions Enlargements Solutions Translations Solutions Mixed Transformations Solutions

Teachitmaths Transformations resources includes many practice questions in this KS4 resource with 5 worksheets and an answer sheet.

SSDD Triangle Transformations

Maths4Everyone Transformations Workbook

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In January 2013 I published a first compilation type post on this blog, showing a collection of resources. The title of such posts changed over the course of some posts and it was in 2016 that I wrote Mathematical Miscellany #1, looking back I see over these early collections sites that no longer exist, or use Flash, or perhaps refer to earlier specifications. Correcting / updating material is an ongoing job and I’ll work on a good index for the resources which are still useful. I thought it would be interesting here to look at a small sample of resources which are still useful now.

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In the very first Mathematical Miscellany post in 2016, I included OCR’s Check In tests. Full details of the Check in tests with suggestions for use can be found in the Teachers’ Guide. Each test is of a similar format in that Questions 1-5 cover procedural calculations (AO1), questions 6-8 require the ability to reason and communicate mathematically (AO2) and questions 9-10 relate to problem solving tasks (AO3). There is also an extension task.

These test are still excellent and just recently new tests have been added for GCSE and for Further Maths A Level. For GCSE we have Analysing data and Interpreting graphs. (Choose a qualification, then Planning and Teaching under Resource materials).

NEW #GCSE (9-1) #MATHS RESOURCES!

We've just published 2 new Check In tests! Download them now…

Foundation – 12.03a & 12.03b Analysing data: Summary statistics https://t.co/X4TIrasEk6

Higher – 7.04 Interpreting graphs https://t.co/Rh9MkiVzfc

There's more on the way too… pic.twitter.com/DLuhn3U3e5

— OCR Maths (@OCR_Maths) January 17, 2021

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A site I have used for many years: Mudd Math Fun Facts. Try for example Squares Ending in 5 and Multiplication by 11 both make excellent starters, we looked at proofs as well as enjoying the mental Maths tricks! You will find more mental arithmetic suggestions on the site. You can search by difficulty and subject.

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In 2017 a resource that caught my eye was Steve Wyborney’s Splat! Definitely a resource to explore further; you can read Steve’s blog post and download the lessons here.

Steve is clearly still very busy! Have a look at his recent resources. He is posting a new math resource every school day for the rest of the school year.  You can read his plan. Also see this post on The 12 Most Popular Math Strategies and Downloads. I see the first is Splat!

New Esti-Mysteries and Number Sense Resources Every Day for the Rest of the School Year https://t.co/ydAGQWAWrw

— Steve Wyborney (@SteveWyborney) November 2, 2020

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Back in 2016, I first mentioned Gareth Westwater’s great resources (@westiesworkshop) and again some years later in Mathematical Miscellany #45 with a very welcome addition for Further Mathematics. All the past paper by topic PowerPoints are also now up on Westie’s Workshop; note that you can download the full PowerPoints as well as accessing individual sections. The PowerPoints are very clearly structured and use questions from past papers also from the sample assessment material. The resource can be used by pupils for self-study or worked through in class. For GCSE you can select AQA, Edexcel or OCR.

More updates are on the way. The video explains the very comprehensive Course Support section. This is really useful with so much in one handy place. Look at Integration for example discussed in the video and you will see that we have Dr Frost resources, Berwick Maths, Owen’s PowerPoints and much more.

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Problem Solving is an open access (free) book which looks at research on Mathematical Problem Solving.

This has been added to the Free Books page.

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I read an article from Science Alert back in 2016 stating that Australian researchers have discovered that school children fare better at solving maths problems when they trace their fingers over practice examples, outperforming students who simply read the questions without touching them.

Well that’s certainly easy to try and in fact reminded me of my love of dot to dot as a child. Some years ago I created some polar curves for my students. Work out the correct order to join the dots and trace out those curves! (Join the dots 4 curves for the file in case anyone wants it).

You can easily create some graphs in dots on Desmos – here’s an example:

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Do check Excel Resources – Mike Hadden. There are some excellent demonstrations here for GCSE and A Level Maths and Further Maths.

If we look at the A/AS Statistics files we see BinHyp.xls, the notes clearly describe this resource.

We can illustrate this with a question from Edexcel’s sample Statistics paper (Paper 2 question 5):

The resources include several illustrations for the Further Mathematicians also, including resources on Complex Numbers and Matrices.

Further recent updates:

Maths at Home is being regularly updated and checked. I have included Jack Brown’s extensive library of videos which is available on his website, TLMaths.com; these are excellent for independent study. Also added to this post is Oxford University’s Oxford Online Maths Club; the session from Thursday’s livestream is available on their YouTube channel.

A new page is Investigations and Problems for the GeoGebra series and John Tranter’s lovely  Algebragons and Fractionagons on Transum Mathematics have been added to this post on Arithmagons which has a large collection of resources on Arithmagons, including a lesson plan from Colin Foster.