Mathematical Miscellany #9

Now on the outstanding Diagnostic Quesions site – United Kingdom Mathematics Trust Quizzes – choose a theme or a quiz with random topics. To use the resources will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.” (See this post for Diagnostic Examination Questions).

aqa-ao3From AQA, on their ‘All About Maths‘ site see their Further Guidance and Practice Questions for the AO2 and AO3 requirements of the new 8300 GCSE. The 120 questions in this resource have been selected from legacy specifications which, to quote AQA “exemplify each of the strands of these Assessment Objectives and would therefore be suitable questions for the new GCSE as well.” AQA have arranged the questions in approximate order of difficulty andhave also divided them into those suitable for Foundation tier only, common to both tiers, and those suitable for Higher tier only, as well as by Assessment Objective. To

Remember fAQA 90 Problemsrom AQA we also have the excellent, GCSE Mathsematics: 90 maths problem  solving questions. These problems have been designed for use in supporting the teaching and learning of mathematics. There is a helpful intruductory section for teachers and note also the helpful Classification Tables by Strategy and by Content Area. Em,  has a brilliant PowerPoint with all the questions and answers – see it here.


Staying with problem solving, on TES Resources cchristian’s Multi-Stage Problem Solving is an excellent resource. These problems could make great starter activities.

Also, remember the GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team, @WRMathsHub available on TES Resources.

White Rose Maths Hub problems

The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning now includes Year 7 material (UK age 11-12); an assessment is also available.

scooby-mysteryFrom author Captain Loui a TES resource, BIDMAS – Solve a Scooby Doo Mystery! Note that answers are provided in the author’s description of the resource. The theme is engaging but doesn’t get in the way of doing plenty of Mathematics!  Captain Loui’s resources are all free to use and as you can see have very favourable reviews.

Splat - Steve Wyborney

Splat – Steve Wyborney

A resource that caught my eye recently is Steve Wyborney’s Splat! Definitely a resource I wnt to explore further; you can read Steve’s blog post and download the lessons here.

Thursday 2nd March is World Book Day; we could bring books and Mathematics together with some Statistics (at any time); have a look at this resource from TES, World Book Day Maths Data Investigation where students analyse word length and sentence length in some book extracts. UK readers who remember Statistics coursework, this brings back memories of AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability. Note too the launch of a new website, is an international research-based initiative which sets out to explore various aspects of integrating stories reading and writing in mathematics instruction.

AQA - Read All About It

AQA – Read All About It

The extension task for the TES resource above considers the reading age of a text, you may wish to consider further readability formulae; if you paste some text to this site, Readability Formulas you can easily check statistics for your chosen text and generate a reading age according to the various tests.

WolframAlpha can be used for Words and Linguistics, note the various examples given, including number names.and document length.

Analyze My Writing

Alternatively, try Analyze My Writing. Simply paste in some text for a comprehensive analysis including basic statistics, word and sentence length and readability. It is also possible to create Cloze tests.  You can read more about this resource on Richard Byrne’s always impressive “Free Technology for Teachers”.

It seems appropriate to check some world records on books!

On the subject of books see the free books information and note in particular Colin Foster’s Instant Maths Ideas – lots of ideas you can try in the classroom.

View more posts in the Mathematical Miscellany Category.


Functions – an update


I have updated a post on functions with the excellent PhET simulation, Function Builder

The post includes several excellent resources for teaching functions. See also this further post aimed at older students.

PhET Simulations look excellent, I will be exploring more of these. I have used the Projectiles Simulation with Mechanics A Level students and have posted on this for students on Mathematics for Students. There are numerous PhET simulations covering Physics, Biology, Chemistry, Earth Science and Mathematics. Note the growing collection of HTML5 versions which will work across all platforms and devices. The Projectiles simulation here is currently a Flash resource.

You can download an app for iOS also for Android.

PhET Balancing Act working nicely on my phone!


Learning & Teaching GCSE Mathematics

Following my post, Learning Mathematicsthe following is the slide set used for the Learning & Teaching GCSE Mathematics session at the  excellent Somerset Professional Development Proramme February 2017.

Lots of pages, but if you are interested then the best way to view is via these files:
Learning & Teaching GCSE Mathematics PowerPoint and Learning & Teaching GCSE Mathematics for the pdf file. The pdf version seems much faster to operate if you wish to use all the embedded hyperlinks to the various resources. Note the table of contents which allows for navigation through the various pages.

On Slideshare – you can see the slides – hyperlinks will lead you to all the resources but for slide to slide navgation use the files above.

There have been several updates since this was first published, including:

  • Easier navigation via the Contents page
  • Additional resources, note the oustanding Diagnostic Questions with all its examination questions also the ability to assign your students to one of the streams so they will receive just two questions a day in the run up to the exams. The Insights provided are so valuable. Edexcel have like AQA provided some great Topic Tests. For further very helpful Edexcel Resources see the Edexcel GCSE page.
  • A reminder of some of the many very useful revision resources including this post for students. (Something I will update further over shortly).

Mathsbot – Revision Grid


For Valentine’s Day…Make Linked Möbius Hearts

The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  We even have 9 Maths skills you need to win the Great British Bake Off!

careers-heartsFor Valentine’s Day, have a look at this post from Maths Careers with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked  as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
use-to-create-mobius-heartsNote the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper. See Valentine’s Day for the Desmos details.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white spce at the end – the picture here has been made using strips 10 cells long.

Learning Mathematics


I was delighted to be part of the excellent Somerset Professional Development Progamme February 2017.

I can confirm that Simon Singh was inspirational. His presentation slides are available for teachers to use – all that wonderful Mathematics in both The Simpsons and Futurama. In an earlier post here where Simon Singh spoke on Mathematics Teaching, you will find the link to his presentation.

My own sessions were (1) on all the wonderful resources availabe for Mathematics but with an eye on the learning first and (2) on the new GCSE Mathematics Specifcation.

Firstly, Learning Mathematics – lots of pages, but if you are interested then the best way to view is via these files:
learning-mathematics PowerPoint and learning-mathematics-pdf. The pdf version seems much faster to operate if you wish to use all the embedded hyperlinks to the various resources. Note the table of contents which allows for navigation through the various pages.

My GCSE Mathematics presentation will follow in the next few days.

On Slideshare – you can see the slides – hyperlinks will lead you to all the resources but for slide to slide navgation use the files above.

Valentine’s Day …

It’s that time of year again – save your money and send your loved ones (or anybody!) a math-o-gram!

..and see also “Make Linked Möbius  Hearts“.

Click on the image and move that slider!

Click on the image and move that slider!

Desmos have provided you with the means to send a math-o-gram to the mathematicians in your life!

Valentine’s Day seems an appropriate time to express love for Desmos!
Geeky people you could even use the Desmos API …

Remining with the loving theme you can also express your feelings for WolframAlpha!

I Love YOU


Valentine Relay – Chris Smith

For some Valentine class activities, try the Valentine Relay from Chris Smith and note all the other relays in this excellent set of resources. You can find more excellent resources from Chris on TES and follow him on Twitter here.

Transum Valentine Puzzle
and here’s a Valentine logic starter from Transum.


Mathematics – Have an Espresso!

For really easy to digest research on Mathematics education from Cambridge Mathematics, see their Espresso page where in their words, “Each month we bring you an Espresso – a small but intense draught of filtered research on mathematics education, expressly designed with teachers in mind. Each Espresso considers one particular issue in mathematics education, and how the latest good-quality research can provide helpful guidance or further reading.”

Note the Research page which includes the link to this excellent site and more references whilst not specific to Mathematics I believe are important to teachers of any subject. Note the resources from Chris Moyse who understands that teachers are busy people!