Mathematical Miscellany #70

Thinking about November exams – in the Summer, 1st Class Maths created excellent resources based on the Advance information, watch for foundation papers for Edexcel/AQA.

Mr Chadburn – calendars

Whether or not students are taking November examinations, Short questions can make ideal starters – see this Revision post for many suggestions including collections of 1 mark questions, recently updated with Wayne Chadburn’s great monthly calendars which provide regular, varied practice – a little bit of maths each day. Calendars for the 2022-23 academic year (so far up to December) are available here. Note the three versions including crossover questions (these appear on both Foundation and Higher papers so great practice for the more challenging Foundation questions), Foundation, Foundation plus and Higher; answers are provided.

Unlimited Edexcel GCSE 1 mark questions

Show that….
A reminder of this post with resources to encourage students to show their working.


My post on Transition includes the excellent free Transition resources from Sparx Maths, also available free from Sparx Maths is a free formative baseline assessment for Year 7 with a supporting Question level analysis resource (QLA) providing student, class and year group performance on individual questions. The QLA also provides a topic-level analysis of students’ performance in the topics they will need to be fluent in to access the Key Stage 3 curriculum.

Sparx Maths – Fluency Quiz

Not only have Sparx Maths provided the test and accompanying documents but fluency quizzes with answers provided.


Ben Sparks – Circle Theorems

From Ben Sparks on GeoGebra – interactives for all 8 circle theorems discussed at GCSE maths.

Tim Devereux

On the subject of Circle Theorems, see also Tim Devereux’s GeoGebra appletsYou can access each theorem from the menu on the left which includes a useful summary of all the theorems. From the menu, we can see that proofs are also available.


Transum Yohaku Puzzles

To finish with a puzzle, try Transum’s Yohaku Puzzles. For numerous Puzzles and Games – see this collection.


Mathematical Miscellany #69

A compilation this week:


From Julia Smith (@TessMaths), have a look at this wonderful collection of Mathematical Hooks.


In Mathematical Miscellany #68 I included From Complete Maths (@LaSalleEd) this brilliant 128-page Task Booklet from Jonathan Hall (@StudyMaths). The tasks which aim to promote mathematical thinking and behaviour in the classroom have been designed to be used with an appropriate model or manipulative. (See also NCETM’s Using Mathematical Representations at KS3.)

Note the playlist, Tasks on the Complete Maths YouTube CPD channel where Jonathan Hall is sharing his thoughts on some of these tasks. He recently shared this on Negative Combinations:


From Sparx Maths, have a look at their Transition Booklets, one for Year 6 to 7 and one for GCSE to A Level; these booklets are free whether you have Sparx Maths or not. The Year 6 to 7 booklet with over 130 questions is based on the Year 6 DFE/NCETM ‘ready to progress’ guidance from June 2020. The GCSE to A Level booklet uses over 120 questions taken from 11 key topics on Sparx Maths. Answers can be obtained by completing a form with your school details.


In my post on Proof I included some Geometrical proofs. We could treat this diagram as a goal free problem; what is the diagram showing you? This idea came from Colin Foster’s article –Trapezium Artist: Some thoughts on the formula for the area of a trapezium where he discusses a Year 8 lesson on area. Colin Foster states “The formula for the trapezium stood out as being the only one that wasn’t immediately ‘see-able’. With thought, those for the triangle, rectangle, parallelogram and kite could all be seen to be correct at a glance. That got us thinking about different ways of proving the formula. We were seeking something not only believable but striking enough as an image to stick in our minds. All our methods involved converting to simpler shapes”

“I have ended up quite keen on Method 6”

For an animation to illustrate this, see Trapezoid Area (2) from Tim Brzezinski.

…and in case you are wondering about Trapezid Area (1)


George Stone (@DrStoneMaths) is producing one slide summaries of interesting educational research papers.

For research summaries – see also the reading pages Research – Mathematics Learning & Teaching including easy to digest research on Mathematics education from Cambridge Mathematics (see their Espresso page), and Research – Learning & Teaching which includes Research in 100 Words from Chris Moyse and summaries of educational research from Tom Sherrington.


Mathematical Miscellany #68

From Mark Dawes (@mdawesmdawes) for Core Maths comes a brilliant new site, What the Graph. This is a new website for Core Maths critical analysis. ‘What the graph’ is a collection of graphs from the media for students to analyse. Read how to use the tasks and check the very comprehensive Teachers’ notes for each resource. There are already several resources available and the collection will grow over the summer and beyond. What the Graph has been added to this page on Core Maths Resources.


From Complete Maths (@LaSalleEd) download this brilliant 128-page Task Booklet from Jonathan Hall (@StudyMaths). The tasks which aim to promote mathematical thinking and behaviour in the classroom have been designed to be used with an appropriate model or manipulative. (See also NCETM’s Using Mathematical Representations at KS3.)


Added to the GeoGebra tutorials page is Mr Rowlandson’s (@Mr_Rowlandson) booklet of training activities for teachers learning to use GeoGebra. Remember we have numerous activities written for GeoGebra, see for example this page of Edexcel resources.

Edexcel GeoGebra Resources

My page on November Examinations 2022 has been updated recently; Mr Watts on ExamQ has already added the advance GCSE information for November.

ExamQ – Mr Watts

On ExamQ from Mr Watts you can quickly search for Edexcel Maths GCSE and A-Level exam questions. You can choose from GCSE Foundation or Higher, AS or A level, you can also select by exam series, paper, area and topic. Selecting November 2022 Advanced Information displays a menu of questions by paper based on the Advance Information.

The interface is very clear indeed, easily display the questions or mark schemes.


For the last few days of term if you are still at school, these ideas for End of Term Activities may be useful.

Mathematical Miscellany #67

Taking a break this week, some popular posts from recent weeks…

Note that with the recent publication of advance information for the November examinations a new page, Examinations – Mathematics November 2022 has been created which will be updated as more information becomes available.

Workers of Zen, End of Term Activities

Mathematical Miscellany #66

Still in the examination season – I have updated GCSE Revision Papers 2 & 3.

Jess Prior Breakfast Warm-Up, Edexcel

See also A Level Summer 2022.


Parallel from Simon Singh is written to challenge your student mathematicians; all materials and resources are completely free and teachers will have access to all the student scores from the Parallelograms which are automatically marked.

Some exciting news currently:


Complete Maths CPD

From Complete Maths, try some Bitesize CPD, CPD Shorts.


Free for students who are intending to study Mathematics at university, an online event from the Institute of Mathematics and its applications, ‘What it’s like to study Mathematics at University?’ Conference 2022. Find out what it’s like to study Mathematics at University, hear from some current students and guest speakers on topics such as university applications, interviews, tips for entering the field of mathematics at an early career stage, and postgraduate research. Full details are available on the IMA site.


From MEI, it’s nearly Calculator Crunch time! Have a look at these excellent free resources from previous Calculator Crunch competitions.

Calculator Crunch 2021