# Transformations

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.

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.

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

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

SSDD Triangle Transformations

Maths4Everyone Transformations Workbook

# Mathematical Miscellany #49

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.

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).

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.

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!

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.

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.

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:

# Mathematical Miscellany #48

From the BBC see this article on Learning at Home, including their latest schedules for Primary and Secondary Lockdown Learning.

On television programmes for primary pupils are on CBBC between 09:00 and 12:00 each weekday and for secondary school pupils on BBC Two, between 13:00 and 15:00.

Additionally programmes are available to catch-up, on-demand on iPlayer.

This coming week, commencing 18th January features Mathematics strongly, with three of the 13:00 slots including Maths and every afternoon at 14:00 we have Dr Hannah Fry.

This post can also be found on the Featured Posts Menu on the right hand side of this blog.

Chris McGrane’s Starting Points Maths is highly recommended, note this announcement regarding these wonderful curriculum booklets. Several are already available, including the first Algebra booklet which looks excellent.

Looking at the Algebra booklet Order of Operations exercises it struck me that Graspable Math would work well for checking such exercises.

I have mentioned Tim Brzezinski’s brilliant GeoGebra book of Open Middle themed problems before, this collection continues to grow. Many problems in the GeoGebra book are exact digital analogues of those found on Open Middle’s site, with other problems characteristic of the Open Middle theme. This collection is included in the GeoGebra series of pages under Investigations and Problems.

I always keep an eye on Tim’s collection of GeoGebra resources and particularly like his recent Angle Sketching by Estimation and also this Open Middle Definite Integral Problem.

I then found his recent extension, Open Middle: Definite Integral Problem (2) which should certainly keep everybody busy!

There is much to think about here, to investigate this what should we keep the same, what should we vary? I started playing around with Desmos to investigate further.

A recent happy discovery, thanks to Jane Hart’s Top Tools for Learning 2020 is featured on the Ed100 list, the digital tools voted for by educators and students in colleges and universities, ilovepdf. ilovepdf is a free PDF convertor and editor, many tools are all in one place. I have not tried many of the tools yet but certainly have successfully and easily used the Merge and Compress functions several times and have been very impressed.

I note from the analysis that the tools predominately reflect the situation in higher and adult education, only a small proportion of votes came from schools. The lists certainly seem to reflect the unprecedented times we are currently living in.

Seeing PowerPoint right up there on the list, I have noted from my blog statistics that still popular downloads, years after I uploaded them are David Millward’s PowerPoint collection. In fact I can see from the comments that it was 2012 when I uploaded these!

# Excel Resources

On the new Updates page, you will find featured posts as well as any which have been updated. A featured post currently is 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.

Also on the Updates page I have featured Maths at Home which 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.

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

# Oxford Online Maths Club

Have you seen the details for Oxford University’s Oxford Online Maths Club? This is a new weekly maths livestream from the Mathematical Institute of Oxford University providing free super-curricular maths for ages 16-18.

The sessions start on 7th January at 16:30 UK time.

The content will include maths problems, puzzles, mini-lectures, and Q&A. The sessions are all free and require no sign-up. The livestreams will be available on YouTube indefinitely.

The sessions will be of particular interest to students who are about to start an undergraduate Mathematics (or joint honours) degree later this year, also for those who are thinking of applying later this year to start a Maths degree next year.

Full details are available here, and you can see what the session on 7th January will include on the YouTube channel.