I have been updating the GCSE Maths revision resources page; this collection is available via the menu on the right-hand side for easy access. I will keep this updated as new resources become available.
It is so important that students check answers for reasonableness, yet they frequently don’t. Examiners frequently report that students lose “easy” marks by providing answers that are physically or mathematically impossible. Checking answers can make a difference in students’ grades.
For example, always sanity-check real-world results. I once had a student calculate an individual’s height as 4 cm. It wasn’t until I asked her to check that distance on a physical ruler that she realised her ‘maths’ failed the common-sense check.
Examiners frequently recommend estimation to verify the reasonableness of an answer, yet I find many students fail to do this as a matter of course. Instead, there is a tendency to rely solely on their calculators, trusting whatever figure appears on the screen without a second thought.
Visualising the maths is just as vital as the calculation itself. For instance, when finding the gradient of a straight line, students only need to look at the graph—or produce a quick sketch of two known points—to confirm whether the gradient should be positive or negative. This simple ‘directional check’ prevents a very common sign error in coordinate geometry.
We need to talk about checking answers, something I do a lot. I was delighted to find a recent resource from a favourite resource author, Andy Lutwyche, titled Checking Techniques, available on TES Resources. This is a set of over 50 questions that have been answered incorrectly. Students can discuss why the given answer cannot be correct. Such a useful collection, it covers topics from Number, Algebra, Geometry and Statistics. A detailed menu helps to navigate the questions.
Andy Lutwyche – Checking TechniquesAndy Lutwyche – Checking Techniques
Written while teaching the Year 12 A Level course, Andy devised the resource to pinpoint any gaps in GCSE knowledge. The examples are in various sections and include solving quadratic equations by factorisation, completing the square, and using the quadratic formula. The final section is on hidden quadratics.
For more on Hidden quadratic equations, refer to this post, which includes several resources.
Dr Austin Maths – A Level, Hidden QuadraticsDr Austin Maths
Using the example from Dr Austin Maths, leads to the next item. Note what’s new, including A Level Revision. I have often used Dr Austin’s GCSE Revision Grids (use the Revision tab), happily, she has now started a set for A Level.
On the subject of new resources, take a look at some great new resources on MathsBot. Try, for example, this Keyword Starter, or your choice of topic for a GCSE Maths Workout.
The GCSE Workouts cover Number, Algebra, Geometry and Statistics. I can see a total of 149 choices!
Currency Conversions
(The exchange rate is given on the workout)
I like the latest organisation of Craig Barton’s website,with so many brilliant resources, including his latest Plenty in Twenty numeracy practice questions, available from Primary through to Year 11 and providing unlimited practice on Numeracy basics. These can be used online, and/or a worksheet can be created.
I have written on Oak Academy Lessons before. Did you know there is a unit on using calculators available? Lessons include the use of the fx-83/85GT CW, fx-991CW, and fx-CG50 aimed at Year 9. Oak Academy – Calculator Functionality – Year 9
❤️ Love this ❤️@mathforge.org has done what I’ve never been organised enough to do myself, and catalogued every #geometrypuzzle I’ve ever posted on social media. It looks amazing!
Checked and updated annually, ideas and resources for Valentine’s Day … (Whilst some of these resources were created some time ago, they are still ideal for Valentine’s Day.)
Desmos – math-o-grams
From Desmos, send one of their great math-o-grams to your mathematical friends!
For an alternative source of Valentine’s cards, we can turn to NASA!
From Sarah Hart, on M+a+t+h=Love, we have a whole collection of Valentine’s Day activities. (Note that you will find further details on the Mobius strip activity below.)
The excellentMaths Careerssite 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?
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 (embedded further down this page), 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.
I printed the document to create my strips 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.
This Valentine Relay from Chris Smithis excellent as are all the other relays in this excellent set of resources. You can find more excellent resources from Chris on TES and follow him on Twitter here.
From Clarissa Grandi on Artful Maths, a selection of creative Valentine’s Day maths activities, including an origami neat little paper heart, drawing cardioids and plotting parametric hearts, and a slotted paper heart globe
From Plus Magazine, see their review of Strange Attractors: Poems of love and mathematics which includes the poem, “Where the Kissing Never Stops” by Ann Calandro which the reviewer points out very effectively use mathematical imagery, for tangential curves (“kissing curves”).
A song which has always made me smile from The Klein 4…
It’s that time of year again, and we can play the 2026 NCTM Year Game in our January lessons. Use the digits in the year 2025 and the operations +, −, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), along with grouping symbols to write expressions for the counting numbers 1 through 100. Full rules are here.
We see that the title Happy 2026 is most appropriate, as 2026 is a happy number! Happy Numbers – one of my favourite investigations!
We can also check WolframAlpha for number properties of 2026.
2026 is a semiprime (semiprimes are used in Cryptography), meaning it is the product of exactly two prime numbers: 2×1013. Consulting the Online Encyclopedia of Integer Sequences, we can search for sequences in which 2026 appears as a term, and we see that 2026 occurs in numerous sequences, including sequences connected with semiprimes.
Sarah Carter has several lovely New Year 2026 activities, including a challenge and several puzzles on her excellent M + A + T + H = love blog. You can find all the activities here.
Returning to WolframAlpha we can see what 2026 looks like in historical numeral forms. We could use the various historical numerals examples to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.
The Babylonian system was a positional base 60 system, though it interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.
We could look back and use the excellent MacTutor History of Mathematics from the University of St Andrews, Scotland. We could check today or any day for Mathematicians who were born or died on that day.
The site is searchable in several ways, including the comprehensive index of History Topics.
From Quanta Magazine, The Year in Math (2025); the features of Quanta’s video are described as follows:
Video: 2025 marked a historic year in mathematics. Researchers solved a major case of Hilbert’s ambitious sixth problem, proved a sweeping new theorem about hyperbolic surfaces, and settled the longstanding three-dimensional Kakeya conjecture.
Wishing educators and students everywhere a Happy New Year!
