A compilation of mathematical goodies!
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.
Another recent resource from Andy is Solving Quadratics in Different Guises.
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.
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!
(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
Andrew Staccy has categorised Catriona Agg’s puzzles by the techniques used to solve them. Wonderful!
Looking ahead to 2027, note the changes in Admissions arrangements for the University of Cambridge.
Admissions 2027
