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.


The reading series of pages is devoted to various reading materials – many of which are free!

A post for students is on Mathematics for students; note this book is currently free on Kindle:

GMAT Foundations of Math – 900+ Practice problems (see also GMAT Math Practice).

For a limited edition bargain on Kindle, I see Thinking Better: The Art of the Shortcut from Marcus du Sautoy for 99p.

Looking at the Books (free) page, for puzzle fans perhaps try Henry Ernest Dudeney’s puzzle collection.

Mind Hurdles

Looking at the free Kindle offerings, these include Mind Hurdles: Mystery Number – a set of ‘number mysteries’, one or more of which would make a good lesson starter and Henry Ernest Dudeney’s – Amusements in Mathematics a puzzle collection (with solutions). The first set of puzzles will offer a trip down memory lane for those who remember money – pre-decimal! There are several categories of puzzles available.

And do make sure you have Colin Foster’s KS3 books in your collection.

Colin Foster - Instant Maths Ideas
Colin Foster – Instant Maths Ideas

Colin Foster’s KS3 Instant Maths Ideas (3 books) are now freely available online; these contain a wealth of ideas to try in the classroom. Colin Foster is a Reader in  Mathematics Education in the Mathematics Education Centre at Loughborough University. Read Colin’s blog here.

Summer Maths 2022

Nrich will again publish a challenge a day throughout the UK summer break. Every weekday from 18 July to 2 September, a new interactive game or puzzle will appear on this Primary page and this Secondary page. Once students have tried the day’s challenge, they will be able to compare their approach to previously published students’ solutions.

Nrich – What Numbers Can We Make Now?

Also, from Nrich, remember there are many interactive games and puzzles.

Transum Mathematics

Perhaps try some curve stitching on Transum. Also, on Transum, you will find School Holiday Maths Activities; this collection has many activities to encourage students to continue their learning during the holidays. These are categorised, and we have a lovely mixture of learning, puzzles, and games to make students think. There is a great deal of choice here. See also the full list of all fun maths activities.

Try these brilliant GeoGebra puzzles from Daniel Mentrard, also his 64 geometric puzzles.

Puzzles – Daniel Mentrard

Perhaps try Tangram on Mathigon.
How many of the different shapes can you make?

Nrich also have a Tangram activity for students age 7 – 11 or for 5-14 years olds try Tangram Pictures.

Nrich Tangram Browser

I do enjoy puzzles, and the summer break offers time for more! Try the series of pages, Puzzles & Games available from the top menu.


To highlight just a few resources from this large collection, Algebra includes the lovely SolveMe mobiles puzzles.

Or, for a rather different approach, try Shuttle Mission Workshop from Math Playground, here students build and solve their own visual math puzzles. Play Shuttle Mission Pro first to practise.

Nrich features on many pages, including reading; Nrich has many excellent articles on the use of games in the classroom; hence a Reading page.

Math Playground – PEMDAS Exhibit

On Number, Math Playground, PEMDAS Exhibit provides great practice for order of operations. Touch an operation to form that part of the operation.

On Geometry of course follow Catriona Agg who regularly posts new puzzles and has made her collection of screenshots freely available.

Catriona Agg

Following each puzzle, you can find a discussion on the puzzle. Have a look at this puzzle and discussion for example.

In response to this puzzle, you can see various solutions, including an Autograph file created by Rob Smith. Rob has this up to change both squares and you can move also move a point on the smaller square.

Another brilliant Geometry puzzle author is Ed Southall who made 40 puzzles available to celebrate his 40th birthday last year; he has also provided slides for teachers. Check his Geometry Cheat Sheet.

On Probability and Statistics try…

Guess the Correlation
Guess the Correlation – Omar Wagih

The collection includes from Cambridge PhD student Omar Wagih, ‘Guess the Correlation‘, a rather addictive game with a purpose – Omar Wagih is collecting the data on the guesses collected and using it to analyse how we perceive correlations in scatter plots. Select About to read the rules and further details.

The Underground Maths page includes several resources on puzzles and games.

Underground Maths – Equation Sudoku

From Underground Maths try Equation Sudoku for example.

We can write down equations:

f+g+a =19

m+k+c =16

and so on.

As always on Underground Maths, we have suggestions, a complete solution, and printable/supporting materials.

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