What a great puzzle! Jonny Griffiths is aiming these puzzles (which always have a unique solution) at late GCSE/early A level Maths students. As Jonny says, this type of puzzle seems to engage students fast, making a great starter that revises important theory quickly; the aim of a Digitiser puzzle is to both practice and teach (or reteach) a piece of mathematics,
The image shows a simple sample task, you can find the solution on his website. The Digitisers pdf file is free. Clear instructions explaining the puzzles and notation used are given, we then have all the tasks by topic to help you pick your task – brilliant! Each task has a difficulty rating from 1 to 3 stars. Full solutions are provided.
This is a wonderful resource – puzzles like this go down well with students, but to have them all clearly by topic is perfect – thank you Jonny, for yet another amazing resource!
Choose Completing the Square for example and we have:
Staying with starters for A level, for linear A Level courses Retrieval Practice is essential. From crashMaths, these AS Maths Key Skills Check worksheets are very valuable for Year 13 in the second year of their A Level course. The Skills Checks are all on Pure Mathematics and make ideal lesson starters.
When working through solutions, take every opportunity to illustrate with technology.
Andy Lutwyche’s collection of Erica’s Errors where students must identify errors in solutions can be an ideal starter for either retrieval practice for an earlier topic or to consolidate learning for a current topic.
Stoke Maths MEP Starters are very attractively presented high-quality resources. Looking at the Spot the Mistake PowerPoints for example, as you can see in the image below there are a great collection of questions that include full answers. It’s great to see Mechanics and Statistics collections. The revision question starters provide very useful question sets.
From Ben Bently, comes a collection of low stakes quizzes using questions from Diagnostic questions.
On Transum try Advanced Starters, some of which I think could be useful for students aiming at the highest GCSE grades as well as for Advanced Level students. The problem, Find the Radius, illustrated in the tweet is very neat!
Looking at the Main Transum Starters page I see at the foot of the page we have various categories of starters including the Advanced Starters. I see many starters here I like, looking at Coordinate Distance, I can never resist a Desmos page to illustrate a problem! This starter could be also be used to review some coordinate geometry – find the midpoint? Find the equation of the line?
On Jethwa Maths you will find starters for Mathematics and Further Mathematics A Level.
From OCR (MEI) their Foundations of Advanced Mathematics level 2 qualification covers arithmetic, algebra, graphs, trigonometry and statistics. Assessment is by a two-hour examination that consists of 40 multiple-choice questions. As OCR suggest these questions could be used for diagnostic tests.
Choose Past Papers, mark schemes and reports. Papers and mark schemes from June 2007 are freely available.
We could of course illustrate the solution well with the use of a little use of technology!
For superb resources for the Oxford Admissions test multiple choice questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.
A trip down memory lane! (Edexcel’s Emporium has some papers from this era.)
University of London June 1986 Mathematics 1
At the start of my teaching career I really liked the first paper of the Mathematics A level from the University of London School Examinations Board – thirty multiple choice questions to complete in one hour, 15 minutes.
For questions 1 to 20, candidates had to select one answer from 5 and for questions 21-30 the instructions were as follows.
The pdf file here has the paper, followed by the exam board answers followed by notes from the 1986 version of me! These days I would illustrate with Desmos and/or WolframAlpha for example as well where appropriate.
Note the comment from Graham Cummings below, there are further papers available in the Edexcel’s Emporium:
The Emporium has some 17 multiple-choice question papers from the period 1988-1992 – by no means a complete set, but they range across the Mathematics, Further Mathematics, Pure Mathematics and Applied Mathematics syllabuses. You can find them in the “Pre-C2000” cabinet within GCE AS/A Level.
Signing up to Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you use. Register for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number.