For Valentine’s Day

From Perton Maths Department, try their Valentine puzzles.

Desmos – math-o-grams

From Desmos, send one of their great math-o-grams to your mathematical friends!

NASA Valentines
For an alternative source of Valentine’s cards, we can turn to NASA! Take your pick from this post or these fabulous NASA images. (And don’t forget that NASA provides us with many Mathematics resources.)

From @OCR_Maths, we could try this puzzle.
OCR Valentine Puzzle
OCR often share some great maths puzzles, look out for them.

Transum Valentine Puzzle
Here’s a Valentine logic starter from Transum.

The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?  


For Valentine’s day we have an appropriate article from Maths Careers, did you know that 6 is a kissing number?! And for your Further Mathematicians, What is the equation for a heart?


Also from Maths Careers, see this post with instructions on how to make this wonderful pair of linked Möbius hearts.


If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
Note the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper.

To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white space at the end – the picture here has been made using strips 10 cells long.

Think Maths Parametric Heart

From the MEI Archives, the February 2015 edition of the MEI Monthly Maths Magazine includes some connections between maths and Valentine’s Day. On page 7 note the article “A Happy Ending” which includes references to some Numberphile videos, Professor Ron Graham discusses the Happy Ending Problem and from Dr Emily Riehl, The Stable Marriage Problem. We also have a great Parametric Heart spreadsheet from Think Maths.

This edition of the magazine includes some lovely activities which link paper folding and proof.…………………………………………………..

Remaining with the loving theme you can express your feelings for WolframAlpha!

I Love YOU

and from the WolframAlpha archives, Computing Valentine’s Day.


How well do you know some basic derivatives and integrals?

Can you answer these questions? Write down the answer then compare yours to the answer on the next slide.
You need to be really fluent with these.

Oxford Online Maths Club

Are any of you thinking about applying for Maths at university? Or perhaps you have applied for this year. The Oxford Online Maths club should be of interest – all free and available indefinitely on YouTube – no sign up required.

Mathematics, Learning and Technology

Have you seen the details for Oxford University’s Oxford Online Maths Club? This is a new weekly maths livestream from the Mathematical Institute of Oxford University providing free super-curricular maths for ages 16-18.

The sessions start on 7th January at 16:30 UK time.

The content will include maths problems, puzzles, mini-lectures, and Q&A. The sessions are all free and require no sign-up. The livestreams will be available on YouTube indefinitely.

The sessions will be of particular interest to students who are about to start an undergraduate Mathematics (or joint honours) degree later this year, also for those who are thinking of applying later this year to start a Maths degree next year.

Full details are available here, and you can see what the session on 7th January will include on the YouTube channel.

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University Admissions Tests

An annual update on preparation for UK University Entrance Examinations for Mathematics; note that these resources provide challenging questions for any students anywhere studying Mathematics beyond age 16.

From Nrich, Prepare for University.

Nrich University prep
Nrich – Prepare for University


To further challenge yourself, MAT, STEP and AEA questions provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.

For mark schemes see:

  • MAT (Maths Admissions Test), scroll down the page for past papers, solutions and additionally video solutions. For superb resources for these questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.
  • STEP mark schemes can also be found on the Cambridge Assessment Preparing for STEP page. Note that STEP 1 will no longer exist from Summer 2021.
  • The AEA questions are legacy questions, extended solutions are currently available for the papers which have been used from the University of Warwick. Legacy papers and mark schemes are available on Colmanweb.

Underground Mathematics Review Menu

The Underground Mathematics Review Questions include Oxford Mathematics Admissions Test questions and full solutions

TMUA is a newer admissions test only one question is available on the Underground Maths site, however, there is much overlap between the specifications for the TMUA and other tests such as the Oxford MAT, so these questions should provide useful resources for students taking this examination. Interestingly, Durham University states that “Those students already registered for MAT may substitute those results in place of our own test, if they do not wish to take both.”
Warwick University advise taking one of MAT, TMUA or STEP.

Oxford Admissions Test

TUMA papers and mark schemes are available from Cambridge Assessment and I would highly recommend the presentation introducing the test, from Julian Gilbey. As suggested – try the questions first (pdf file) before watching the presentation.

Talking to Julian Gilbey, he recommends for the TMUA, the importance of working through the Extended specification notes on the website, to learn about the logic side. (See Test Specifications for the specification and enhanced specification with its notes on logic and proof.) He also stresses that the more Maths you can do, the more you work on stretching problems and think hard about maths the better you will get at maths. Examples he mentions for resources are any questions on the Underground Maths website, (not just the review questions already mentioned here), UKMT and olympiad problems, STEP problems.

“And essentially your ability to ‘think mathematically’ and to solve mathematical problems is all that these tests are testing”

For further resources try UKMT Senior Maths Challenge Questions.


…and also see MadAsMaths with its many papers and solutions increasing in difficulty.

You can download a free copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core Mathematics. Whilst written to support students taking STEP examination papers, Advanced Problems in Mathematics is excellent preparation for any undergraduate Mathematics course.

Advanced Problems in Mathematics
Advanced Problems in Mathematics Problem Index

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 75 problems.

STEP (Sixth Term Examination Paper) Mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics.

STEP Database


You will find free STEP soluions on MEI’s site. The STEP question papers are all available on the Cambridge Assessment website; note the STEP resources include a searchable database.  The AEA qualification from Pearson is based on the A Level specification and designed for the top 10% of students to help differentiate between the most able candidates. The Sample Assessment Materials provides a valuable source of challenging questions (with mark schemes) for A Level mathematicians.

STEP papers here. Underground Mathematics has STEP questions within their Review Questions. Each question comes with a fully worked solution.

Underground Maths STEP example

See also, from Cambridge University, their STEP Support Programme. From the home page, access the resources, you will see STEP Support Programme Foundation modules, STEP 2 modules and STEP 3 modules.

Factorisation of Quadratic Expressions

When factorising quadratic expressions do you check coefficients first? If the coefficient of x2 and the constant are prime for example you should be able to just write down the factorisation without needing an elaborate method.

However, when that is not the case then try these handy techniques.

Lyszkowski’s Method

Full details of the ‘box’ method and Lyszlowski’s method are provided in this post:
Factorisation of Quadratic Expressions.

Summer 2020

A little Maths through the Summer.
See also: Transition Time.

Mathematics, Learning and Technology

AMSP Transition AMSP Transition to A level Mathematics

For Year 11 students, AMSP (Advanced Mathematics Support Programme have announced that their Transition to A level Mathematics free online course has now launched.

(See also Maths At Home which includes further links to transition resources, including AMSP’s resources for Year 10(no registration or log in required for Year 10 resources), also note Colin Hegarty’s collection of online lessons.

Arithmagons posterFrom Nrich for Primary and Secondary, a challenge each weekday from 20 July to 28 August.

Noted in Mathematical Miscellany #42, remember we have from Wayne Chadburn Keeping Year 10 going over the summer

Mr Chadburn Summer Boost Calendars

Wayne Chadburn has produced calendars for July and August which can be given to Year 10 students for daily practice of key mathematical skills over the summer break.

July 2020 Transum Starters

On Transum, the starters for every day include of course, July and August.

Every day…

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HELM Notes

For a very comprehensive library of Notes and Examples – see the HELM Project.

Mathematics, Learning and Technology

I have referred to the HELM (Helping Engineers Learn Mathematics) notes many times over the years on this blog. They are referred to on the Notes and Examples page for Further Mathematics as well as in many individual blog posts, for example Mechanics – Dimensional Analysis, Differential Equations, and Further Calculus.

HELM Notes - Basic Algebra HELM (2008): Workbook 1: Basic Algebra

If you have not come across the HELM Project before, the project was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include very clear worked examples. Whilst the workbooks cover the basic engineering mathematics and statistics teaching for first and second year students in a typical UK undergraduate engineering degree many of the workbooks include content appropriate for A Level Mathematics and particularly, Further Mathematics. For easy access to these resources, the HELM Project Workbooks are hosted by Loughborough University’s Mathematics…

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Learning Mathematics at Home

Are you studying Mathematics at home?

Several posts and pages here may be useful. See:

Back in 2014 I was using free samples from Bring on the Maths resources with my students. A whole series of activities where you must pick out the correct answers is provided. Activities are available for young children right through to Advanced Level.

I must recommend the free samples from Bring On the Maths, the Core 3 activity – Logarithmic equations worked really well with my Year 13 class and next week I’ll use the C4 Binomial Expansion resource when we are talking about the validity of a given expansion. I have used the Trigonometric Ratios resource before – and will again; there are several other great resources in that list of samples – explore!

Kangaroo Maths
Bring on the Maths Logarithmic Equations
Free access is available to the complete set of these resources on the old Kangaroo Maths site. Log in with the user and password as above to access all the resources. This will give access to all the activities for students from Key Stage 2 right through to A Level – note that this being the old site, the resources are aligned to earlier schemes of learning but still so useful.

Looking at the old level 5 and 6 Algebra resources for example, we could try Simplifying Expressions  or Constructing and solving equations.

Distance Learning will be demanding, it’s certainly a chance to read more or perhaps get away from screens and listen to a story. For as long as schools are closed, Audible are providing stories which are free to stream on a desktop, laptop, phone or tablet. An extensive collection of stories, including titles across different languages is available. No accounts or passwords are needed. See Audible’s ‘How to Use Stories‘ and start listening; note the menu where children can select by age.

White Rose
White Rose Maths has so many free high quality resources, see for example Secondary Schemes of Learning and Assessments for End of Block or End of Term. Check their Home Learning, the White Rose Maths Team has prepared a series of five maths lessons for each year group from Year 1-8. More will be added each week for the next few weeks. Every lesson comes with a short video showing  clearly and simply how to help children to complete the activity successfully.


The summer term includes work on consolidation for the year, see this collection from Nicola Whiston who has started a collection of Knowledge Organisers which followAlgebra KO extract Nicola Whiston

the White Rose Schemes of Learning, she is sharing the collection here, via Dropbox. These are really attractive.

CK-12 Foundation has created a resource page with hand-picked lessons in math and science popular during the month of March.

From Bobby Seagull, “The Magic of Numbers: Why Everyone Should Love Maths”.

And of course you will need a break, maybe a puzzle? Try Futoshiki and other puzzles.
It’s certainly a chance to read more or perhaps get away from screens and listen to a story. For as long as schools are closed, Audible are providing stories which are free to stream on a desktop, laptop, phone or tablet. An extensive collection of stories, including titles across different languages is available. No accounts or passwords are needed. See Audible’s ‘How to Use Stories‘ and start listening; note the menu where you can select by age.

Stay safe everyone.

Futoshiki and other puzzles

Mathematics, Learning and Technology

FutoshikiI first came across and enjoyed a Futoshiki puzzle in the Guardian puzzles section.

Work out the digit that goes in each cell. In this 4×4 example, the digits from 1 to 4 must appear exactly once in each row and column.

Initially, some digits might be revealed and additionally, the board might also contain some inequalities between the board cells; these inequalities must be respected and following them will help you find the missing digits.

Futoshiki2In the above puzzle, difficulty level, easy, we see that the fourth column already has a 1 and a 3, the remaining digits 2 and 4 can only be placed one way as we have to follow the inequality sign.

On from Vlad Daskalu, you can generate puzzles of sizes from 4×4 to 9×9 and choose one of 4 difficulty levels.

Other sites offering these puzzles include Brain Bashers where you can play…

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