Mathematics for Halloween

A selection of Mathematical Halloween themed resources:

Perton Pumpkin 1
I do appreciate the dynamic Perton Maths Department, I have mentioned their various puzzle collections before – they are busy again, this time with Halloween puzzles!


Halloween Relay
Halloween relay – Chris Smith

From Chris Smith, try his great Halloween relay and note the whole set. I have used many of these very successfully – have fun whilst doing plenty of Maths!


From OCR Maths who are rather good at providing us with puzzles, try their fiendish number grid puzzle. OCR Maths regularly publish excellent puzzles many of which I have successfully used in class.

OCR Maths Puzzles
OCR Maths Puzzles

Nrich Halloween

From Nrich, thinking about systematic listing strategies with younger students, check this Halloween Investigation, just how many possible Halloween costumes are there?

Or a good starter for Thursday perhaps, try Halloween Day on Nrich, a problem taken from the UKMT Maths Challenges.

I like the way Nrich suggest related problems and strayed into Helen’s Conjecture here, one of many Nrich problems on Factors and Multiples similar to Helen’s Conjecture.



ghost curve

And to finish, a ghost from WolframAlpha!

Checking popular curve examples on WolframAlha, a discovery – I had not realised that it was possible to, for example, create a randomly colored ghost curveRefresh the page for different color ghosts!

Linking Curriculum Learning to Careers

The July 2021 Careers guidance and access for education and training providers document details the Statutory guidance for governing bodies, school leaders and school staff.

The aim is to make sure that all young people in secondary school get a programme of advice and guidance. It is recommended that schools should use the Gatsby Charitable Foundation’s Benchmarks to develop and improve their careers provision.

See the Gatsby site and also the very helpful Gatsby Benchmark Toolkit from The Careers and Enterprise Company, note in particular, benchmark 4, 

4. Linking curriculum learning to careers All teachers should link curriculum learning with careers. For example, STEM subject teachers should highlight the relevance of STEM subjects for a wide range of future career paths.

Pages 23 to 29 of the toolkit for school offers clear guidance on benchmark 4, or see this separate document, with just the pages on Benchmark 4. Page 18 includes examples including Tomorrow’s Engineers, an organisation I have mentioned previously as part of my Posters collection. Tomorrow’s Engineers have a variety of careers resources.
stem jobs
MEI (thank you) alerted me to this poster – 100 jobs in STEM!

Further resources:
We are fortunate in Mathematics to have the wonderful Maths Careers site with its extensive collection of resources for students from age 11 to adult. Read – The Gatsby Career Benchmarks – A Maths Perspective.

From amsp, Where maths meets the world of work. The AMSP is working on videos, which showcase the maths in different careers; each video is paired with a resource for the classroom or for use online, so students can get a real taste of what the job may entail. Looking at the first video ‘Try being a Data Detective’ there are versions of each resource available for students of different ages. Desmos Classroom activities are available for each version.

Plus Magazine has a whole series of Career interview articles.

Check the BBC Bitesize Careers page, the information available here includes Where could your favourite subject take you? Check out the Jobs that use Maths.

With UCAS you can explore jobs in a variety of ways, by job family, by subject or by skill; look at Science, Engineering and Mathematics for example.

Good Career Guidance: Reaching the Gatsby Benchmarks,

From amsp, see Supporting your students’ transition to Advanced Maths, their Maths: Opening the door to your future leaflet explores the post-16 maths qualifications available to students, to help them decide which one is best. Note too the 30 minute presentation, Why Study Maths, for students and parents/carers which is about the importance of studying maths post-GCSE. It outlines the options available, and provides compelling reasons for choosing to take an advanced maths qualification. Slides and speaker notes are available to download.

A wealth of free resources are available on Integral, see The FMSP Legacy Resources Archive. Access is free via Guest Access. 

Forum Case Studies, FORUM has published many case studies about employer-linked curriculum projects.

Autograph – Free

Note the new series of pages on Autograph – including the new web version.

A major announcement at La Salle Education’s Maths Conference #21 today –

Autograph for graphing and geometry is now part of the La Salle Education family and with the backing of La Salle Complete Maths, Autograph (version 5) is now available free to everyone forever. Teachers and students can download the software.

The dynamic graphing software has 4 modes, Statistics, 2D Graphing, 3D Graphing, and, introduced in version 4, Complex Numbers.

Perfect timing for myself and my Further Maths students as we are just about to study Complex Numbers. It is very simple to enter complex numbers and menu options mean that various operations are easily and quickly demonstrated, including displaying the nth roots of a complex number. A comprehensive manual is available – see the Help menu. Manuals can also be found on the Autograph site including useful summaries.
Autograph Complex Numbers

More for the Further Mathematicians, we can easily show transformations in 2D and 3D, use pre-sets or enter a matrix for a transformation .

Autograph - shear

Or very simply show your chosen number of terms of the Maclaurin series for sin x (select the graph, right click, choose create and select Maclaurin series).
Maclaurin series

Newton RaphsonAutograph is also excellent for illustrating the Newton Raphson method – something which will be very useful in teaching Numerical Methods for A Level.

So many excellent features are available – this is a powerful and sophisticated program. Note that a web application version is coming too.

Time to get studying the manuals and tutorials!
If you are unfamiliar with Autograph, you may like this training material by Simon Woodhead, Alan Catley, Craig Barton and Douglas Butler to get started.

Mathematical Miscellany #33

PhET and OneNote Integration

PhET to OneNoteI have often mentioned the excellent PhET simulations; it is now possible to embed these in OneNote. Simply paste any public PhET link, such as that for Balancing Act (https://phet.colorado.edu/sims/html/balancing-act/latest/balancing-act_en.html) on to a OneNote page and it will render it as a live interactive embed.

Reading the Microsoft blog on this integration, I noted  Coggle.it with which one can create mind maps; the free model allows 3 Private Diagrams and Unlimited Public Diagrams with PDF & Image Download. This looks like a simple way to produce such diagrams and I lke the fact that they can be integrated with OneNote.


MEI – Ritangle.
Registration for MEI’s Ritangle opens on October 7th. Ritangle is a competition for teams of students of A level Mathematics, the International Baccalaureate and Scottish Highers requiring no knowledge of mathematics beyond A level Mathematics. Students can use Technology to help with some of the questions.

There have been some great questions to challenge your older stdents in these Ritangle competitions. note the links to the questions and answers to the 2016-2018 competitions.

MEI Ritangle 2018 q1

MEI Ritangle – 2018, Question 1

This competition has been added to the updated Competitions page. This page includes Puzzle of the Week, a free international puzzle competition for schools.


Long Division & Multiplication – Formal methods

Mathisfun Long DivisionNoting the popularity of Long Division & Multiplication – Formal Methods I have checked and updated this page. This includes Algebraic long division.

Mathisfun Algebraic Long Division

Mathisfun – Algebraic Long Division


I’ll end with some highly recommended reading, Tom Sherrington on The #1 problem/weakness in teaching and how to address it.

For more reading, note the reading series of pages, including  Research – Learning and Teaching and Research – Mathematics Learning and Teaching.