Mathematical Miscellany #59


Today is not only Halloween, it is Magic Day!

MathsPad Number Tricks

My post on Proof includes Magic or Number tricks which can be an ideal way into algebraic proof, try MathsPad – Number Tricks, one of the very generous collection of free resources on MathsPad (search on free), or be dramatic with Number Jumbler from Nrich! I have used this successfully with students from Year 7 to Year 12. Also try the suggested task, Double-Digit.

For a collection of mathemagical activities, try Transum Mathematics.

Transum Perfect Magic Square

You can find many activities on Transum, including Perfect Magic Square, which has 9 such puzzles, by the time we get to Puzzle 9 only two clues are given.

Wayne Chadburn – A little bit of maths each day

Tomorrow sees the start of November, so a good time to remind readers of Wayne Chadburn’s monthly calendars. He writes these calendars to provide regular, varied practice – a little bit of maths each day. In this academic year, he is producing calendars for year 11 students each month from September to April; the calendars for November 2021 are available. Note the three versions including crossover questions, Foundation, Foundation plus and Higher.

For November we have Barvember, from White Rose Maths, which was created to encourage the use of the bar model. Bar models can really help children visualise and then solve maths problems. See Bar Modelling.

Barvember – White Rose Maths

Nathan Day – factor Tree Puzzles

Back in July, Nathan Day published his very valuable CIMT Complete PDF. He now has a new website: Mr Day Maths where he is adding all the brilliant tasks, displays, resources, and thoughts he has shared on Twitter over the past few years to one place – a new treasure trove to explore! Try Factor Trees, for example, a set of (rather tricky) factor tree completion problems, that’s another lovely resource added to this Fill in the blanks collection.

For some quadratic questions to really get your students thinking, try these non-routine questions from @boss-maths. Follow the thread to the end for the answers!

Recovery Resources

Matt Woodfine continues to add to his brilliant site, a new addition is Level Up. a programme that targets basic numeracy.

From MEI, for KS3 have a look at these free GeoGebra interactive online classroom activities to support maths recovery at Key Stage 3. You can try the first three of five Algebra resources. Each lesson not only has a GeoGebra activity for use in the lesson, but also one for student independent learning. Full lesson plans and comprehensive notes for teachers are provided.

The collection will be expanded over the coming months to include similar sets of lessons for Number, Geometry and Measure, Ratio, and Statistics and Probability.

On the subject of GeoGebra, for the other end of the school, you will find on the Maths Emporium, a GeoGebra guide for A level Further Maths available to download or it is available with no login needed from the Edexcel website here. These activities have been produced to support teaching or could be used by students for independent study.

I have included many GeoGebra Resources on the GeoGebra series of pages. An extensive library of GeoGebra resources is available from Edexcel for GCSE (with many of these helpful for younger students also) and A Level.

Edexcel GeoGebra Resources

Edexcel GCSE GeoGebra Resources


Perton Maths Department is so good at providing us with problems for various events, check @PertonMaths for daily half-term challenges.

For more Halloween problems try the windows on Transum Mathematics Halloween.

Transum – Halloween starters

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!

Mathematical Miscellany #58


Following last week’s post on Mathematics for Psychology, note also these Desmos activities for Biology by Sarah Denison from AMSP/ASE Biology. My Mathematics for Science page has been updated with these Biology Resources.

Desmos Activities – Surface area to volume ratio, Sarah Desnison

As with the Psychology resources the Advanced Mathematics Support Programme [AMSP] are supporting Biology teachers of Psychology in their teaching of the maths and statistics requirements of the psychology specifications and provide free CPD and resources. Maths for Teachers of A Level Biology is an event starting on 30th November. The course is free to attend, priority is given to teachers from state-funded schools and colleges in England and trainee biology teachers. Full eligibility details as well as a detailed study schedule can be found on the AMSP site.

Seeing Jonathan Hall’s latest Mathsbot resource, Place Value and counting to 100, reminded me of a task that has been on my list for some time – an update to a resource list for Primary Mathematics, which now has its own page on the top level menu. This is still work in progress; more resources will be added in the coming weeks.

In case you missed this post – Compare & Discuss/Multiple Strategies

A new feature on Desmos – lists.

Seeing OCR’s latest puzzle, it struck me how ideal Autograph is for exploring this as plotting points and joining them with line segments is very straightforward. See the Autograph pages for more on Autograph.

On UK Exams and Assessments 2022, you can find updates from the exam boards including the formula sheets for GCSE Maths. For example, from AQA

Formula Sheets

Formula Sheets: Students will be given a formulae sheet in GCSE Maths and a revised equations sheet in GCSE Physics and GCSE Combined Science covering all the equations required in the subject content.
We will make these sheets available to schools for use in teaching and so students can familiarise themselves with them. They will also be provided in the exams. AQA

AQA have stated that everything in sections 1 and 2 of the appendix on pages 43-44 of the specification will be provided for the examination in 2022; anything required from section 3 will be given in the question as normal. You can view sections 1, 2 and 3 here.


For GCSE Maths, the exam support will be a separate formula sheet which gives students the formulae they may need to refer to in their assessment, appropriate to their tier of entry. This will be available as an additional insert on the day of the examination. The formulae sheet will shortly be accessible via the website and learners should then familiarise themselves with the formulae sheet ahead of the summer 2022 examinations. Edexcel

OCR Update on the formulae sheet for GCSE (9-1) Maths assessments in 2022.

What impact will Ofqual’s chosen grading system in 2022 have

fft education datalab – 30 September 2021:
What impact will Ofqual’s chosen grading system in 2022 have?

Mathematics in Psychology

You can also find these skills on the exam board websites, see AQA for example who state that “overall, at least 10% of the marks in assessments for Psychology will require the use of mathematical skills. These skills will be applied in the context of A-level Psychology and will be at least the standard of higher tier GCSE mathematics.”

Exam Board Teaching Resources

OCR student workbook
OCR Teaching Activities

The Association for the Teaching of Psychology has collaborated with the Advanced Mathematics Support Programme [AMSP] to support teachers of Psychology in their teaching of the maths and statistics requirements of the psychology specifications and provide free CPD and resources.

Catherine Van Saarloos – Desmos Activities for Psychology

Catherine Van Saarloos has created online resources for lessons on data collection and for the delivery of the mathematical requirements of Psychology courses. Here you will find a collection of Desmos activities.

Deb Gajic has created How to guides for non-parametric inferential statistical tests.

This information has been added to the UK Assessment series of pages where you can also find Mathematics for Science.

Compare & Discuss/Multiple Strategies

Have you seen…this important resource for our teaching?

From researchers at Harvard University and Vanderbilt University, the Compare and Discuss Multiple Strategies (CDMS) routine, and the curriculum materials for algebra courses?

Explore the curriculum materials and learn how to use the resources. See the About page for a summary of the Create & Discuss/Multiple Strategies routine which it is suggested should take about 20 minutes.

See also “One way is the wrong way to do math. Here’s the right way.” from The Harvard Gazette

Within each resource, you will find questions that could be used for discussion of the example, a “think-pair-share” routine and a “Big Idea” page that summarises the lesson objective for the example.

The teacher’s guide also explains each of the four strategies.

Compare & Discuss/Multiple Strategies – from researchers at Harvard University and Vanderbilt University

As you can see from the image here you can filter the resources by Type, Lesson Use and Topic, within each topic you will find several subtopics.