Mathematical Miscellany #20

SSDD tweet Craig Barton

Last week,  I mentioned Craig Barton’s two latest websites; Maths Venns and SSDD Problems – Same Surface, Different Deep Structure maths problems. Read more on the website.

I was amused by Craig’s tweet to see that it’s not just himself, his wife and his Mum using his SSDD Problems website!  Take a look at the many problems now available.  The menu on the right is helpful for finding problems. I rather like f(x) and g(x). The topic menu offers the chance to find more problems on functions; try function notation.

f(x) and g(x)

f(x) and g(x) – SSDD Problems

For Chalkdust Magazine, Rob Eastaway thinking outside (and inside!) the box with the nine dot puzzle and extensions.
Don Steward has also featured this classic puzzle in his post, Dot Connecting.

9 dot puzzle

9 dot puzzle illustrated on Desmos

I often update posts, particularly very popular ones. As people bookmark the original I want the original address to be unchanged. I thought I would add a new indicator to show when a post has been updated. Here we have for example – Functions.

Maths Genie Functions

Maths Genie – Inverse and Composite Functions


SPrice Legacy questions mapped to Further Core Pure.
Stuart Price (right-click once you have followed the link and you will be able to save the image) has very helpfully mapped legacy A Level questions to the Further Mathematics Core specification. This has also added to Mapping Documents, part of the A Level Reform series.

On Saint Patrick’s Day, (check Wolfram Alpha anniversaries and more for March 17th) it seems appropriate to have a look at Project Maths, an Irish site supporting Mathematics teachers. Looking at the teacher area, many resources are available. The traditional Leaving Certificate examination is the terminal examination of post-primary education and is taken when students are typically 17 or 18 years of age. These  teacher resources are for this group of students. A site well worth exploring, looking at Algebra we see for example under expressions:

Project Maths Student Resources Index
The student resources include many activities with accompanying GeoGebra files.
Project Maths Student Resources
Modulus Inequalities Project Maths

Integration and area

These whiteboard templates caught my eye, simply download the file, project it onto your whiteboard, use the interactive menu to choose the background you need and start writing!

Project Maths - Whiteboard Templates
Project Maths Ireland – Whiteboard Templates

Mathematical Miscellany #19

A series of resource updates this week…

Edexcel Codebreaker

Edexcel Worksheets – Codebreaker from @Just_Maths

The Problems and Activites series of pages, still a work in progress in the never-ending quest to make things easier to find, has had several updates, including a new page dedicated to the many excellent teaching resources from the Examination Boards. All the examination boards have excellent teaching resources.

The Problems and Activities Links page is just that, a simple list with brief descriptions. Further detail of resources can be found on the Problems and Activities Resources page. Further resources will be added in the coming weeks.

A new addition to the Examination Board resources is the result of the collaboration between MEI and the Institution of Engineering and Technology (IET); a set of maths resources.  This set of 20 KS4 activities have been created, aiming to:

  • address a range of GCSE Mathematics content
  • promote the development of reasoning and problem solving skills
  • make connections with engineering contexts and/or settings
  • promote student discussion and communication

MEI – IET Project Resources


Updates are regularly made to the 16+ Resources series of pages where you can find excellent teaching resources for this age group.

AQA has recently published a particularly valuable document, a commentary on their specimen papers, in which Dan Rogan, Chair of Examiners, explains how the specimen papers were created and how mark schemes will be applied.

AQA AS example

Note the new and very clear mark schemes which include a typical solution on the right-hand side. These will be very helpful for students. The document all includes information on how the use of calculators will be assessed.

AQA Mark Scheme example

The AQA page on specifications has been updated accordingly.

Venn Activity Craig Barton

Maths Venns – Craig Barton

Checking the tweets from Maths Conference 14, held in Kettering, note that Craig Barton has created a website SSDD Problems – Same Surface, Different Deep Structure maths problems. Read more on the website and you could get involved. Craig has created another new website Maths Venns; I have mentioned his excellent Venn activities before, they now have a dedicated website.


Women in Mathematics

March 8th 2018 is International Women’s Day.
We’ll start with an image I first shared two years ago that I think still says it all! Thank you Steve Lomax who shared this wonderful response to the task ‘Describe a mathematician’ from Mansfield Green E-ACT Academy.


Some useful references on women in Mathematics:

And for some History

On the subject of Caroline Herschel, are you aware of all the amazing stories of women in space? I highly recommend Libby Jackson’s A Galaxy of Her Own.

Linear Programming

For any teachers teaching Discrete Mathematics, solving Linear Programming problems with technology as well as by hand allows answers to be checked and more problems to be explored. The new UK Advanced Level specifications quite rightly emphasise the use of technology to enhance learning. Teachers who are using the OCR (MEI) Further Mathematics specification, note that specific mention is made in that specification of technology such as Excel Solver. With my own students, we will be exploring the tools described here. Using an old MEI example, full instructions are given for setting up problems using Excel Solver.

Mathematics for Students

For Linear Programming there are some excellent ways of using technology to help your learning. This post will look at online utilities from zweigmedia and the use of the Excel Solver.

This example from MEI (MEI Decision 1 Legacy Specimen Paper) will be used to illustrate the use of these tools.

A vet is treating a farm animal. He must provide minimum daily requirements of an antibiotic, a vitamin and a nutrient. He has two types of medicine available, tablets and liquid. The table summarises what the medicines contain and the requirements.
Vet Problem - table
The tablets cost £0.38 each and liquid medicine costs £1 per dose.
The vet wants to find the cheapest way to treat the animal.
We have x as the number of tablets which the vet prescribes per day, and y is the number of doses of liquid medicine, giving us the linear programming problem:
Minimise    0.38x + y
Subject to

View original post 226 more words

World Book Day

Maths texts

Image – Klara Kim on flickr

It is World Book Day on Thursday, March 1st.

On the subject of books I have checked and updated the free books information; this includes new additions.

Colin Foster - Instant Maths Ideas

Colin Foster – Instant Maths Ideas

Note in particular Colin Foster’s KS3 Instant Maths Ideas (3 books) – a wealth of ideas you can try in the classroom and now freely available online. Colin Foster is Associate Professor of Education at the University of Leicester.

Here’s some very nice World Book Day Maths Problems from Laura Rees-Hughes.

World Bok Day Problems

World Book Day Problems – Laura Rees-Hughes


I think that’s 71 pages.

For younger students, this revision resource was created for Year 6 (age 10-11) to use on World Book Day.

We could bring books and Mathematics together with some Statistics. UK readers who remember Statistics coursework may remember AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability. Similarly, we have Edexcel’s Newspaper Comparisons. A search for these old coursework tasks returned this Edexel document which has numerous investigations with mark schemes; Newspaper comparisons is on page 171. The document is a very useful source of problems and data handling activities.



We could consider the reading age of a text; consider these 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.

Writing - word lengths

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!

I tried the text of this post for readability – college level!