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Secondary Magazine - Issue 125: Building Bridges

Created on 10 September 2015 by ncetm_administrator
Updated on 01 October 2015 by ncetm_administrator


Secondary Magazine Issue 125'Under the Bridge' by Alan Levine (adapted), some rights resered

Building Bridges

There’s been much in the media over the summer and the last few weeks about GCSE Maths in FE colleges, and the challenges of teaching FE students who now are supposed to re-sit Maths and English if they haven’t achieved a grade C. With this in mind, this month’s article considers how to build a bridge from pre- to post-16 study of GCSE Maths.

When winter’s shadowy fingers first pursue you down the street and your boots no longer lie about the cold around your feet, do you spare a thought for your Scheme of Work, and does it reflect what we know to be true in relation to GCSE maths resits? (with huge apologies to Lindisfarne!)

A GCSE maths resit 16-year old student is a wily beast. He will have a plethora of reasons as to why he didn’t get the Willy Wonka golden ticket of a C grade that will pave the way to a great future full of fame and fortune. Not one will be the fact that he didn’t work hard enough. It’s always someone else’s fault: you will hear a multitude of excuses - supply teachers, rubbish teachers, no teachers, hadn’t covered the topics, gave us the wrong coloured post-its - you will hear it all. Recognising – and overcoming – the distancing and disengaging defence mechanisms of the species is crucial if he is to avoid exam-tinction next June.

There are thousands of these students, and to be honest, we let most of them down at present: look at the pitiful success rates in resit GCSE. As Jonathan Simons from the Policy Exchange tells us, over five times as many students retake GCSE in an FE setting rather than remaining at school: 110 811 students in fact.

graph showing English/maths retake students

With pass rates at an average of 36% in FE that means we haven’t got this right for a mind-numbing 75 000 students, though it’s not much better in schools either. Note the comment below that this is not the full cohort of D grade students - but from this year they are mandated to resit, so the number of students re-taking will increase enormously.

There is a multitude of reasons why the pass rates are so low, but one of them is definitely the Scheme of Work, and that’s one that is under our control. It has to look, feel and sound different to the regime that these students have followed (have endured, they feel) before. There is no new content that will surprise them – they’ve seen it, they can do some of it, they can’t do the rest of it – so we have to think about the presentation and the teaching: old wine in new bottles.

graph showing retake results

A resit student has seen all the maths needed for GCSE: she cannot do all of it, but she can do some of it, that’s why she has a D grade already. The skill in teaching resit students is uncovering what they can’t do fully and tackle that, while sustaining everything else so that they don’t forget what they do know – and remember that they will not have done any maths since June, so what they did know then is already fading. The clock’s ticking.

Preparing for a resit can be split into the following “Five R’s” (inflation from the three when I was at school…), each feature being an element of your SoW:


There are 48 “killer” facts for a C grade and 80 “killer” facts for an A*: well, so says the Mathematical Association with their revision postcard sets. Use these as the basis of your fast and furious, fluent, regular recall with questions such as:

  • name the first 20 prime numbers
  • what are the six types of quadrilateral? And sketch them
  • how do you calculate mean, median and mode?
  • draw and name the parts of a circle.


The effort of practice, practice, practice is imperative if students are to be successful in a resit. Elements such as Corbettmaths 5-a-day and JustMaths Bread & Butter are good routines to set up from day one. If you can encourage students to keep up their 5-a-day through half term and over Christmas (six, then, if you include the sprouts), then even better. Routinely going over misconceptions such as those presented as Challenge 2 in the C/D borderline page on m4ths.com will bring rewards. studymaths.co.uk and Form Time Ideas are further favourites for practice opportunities. The 30 second challenges in the Daily Mail are good, and there are some of these types of activities at mathematicshed.com. A fun regular element is playing “You can’t do simple maths under pressure”. Doing maths makes people more successful at maths; routine hard work and practice translates into success.


There are key topics that straddle the D/C borderline and always present difficulties to students. Topics such as finding an expression for the value of the nth term of a sequence, manipulating fractions, index laws and Pythagoras’ Theorem always raise a painted eyebrow, and so these are the topics that are worth teaching in full and in depth with all students. Just Maths lists its Top 40 topics, m4ths.com has a really good Help Guide Sheet highlighting all of the C grade topics, while Hegarty Maths and Corbett Maths provide some excellent self-study videos too. With around 40 revision topics to focus upon on the borderline, that is roughly one per week in an FE timetable, which is manageable. Using an Entrance/Exit ticket to ascertain prior knowledge and progress made would be an informative and worthwhile addition to your lesson.


Once revised, each topic has to be repeated: that means exam questions. Corbett Maths provides sets of exam questions and textbook questions. Combined with the use of a maths passport such as the ones from Miss B’s Resources, you now have a mechanism by which you can check knowledge and understanding of the key C grade topics in a measured way. Pret homeworks is another excellent source of repeat and challenge questions, as is Miss B’s Quick Wits.


Exam-ready and prepared. A good strategy for final preparations is to mark a past paper as it is and award the actual marks and grade it would get; then mark it again as though no avoidable errors had been made, but instead award these marks back to the student. This really highlights the impact on grading, and these are the easiest pitfalls to avoid in exam technique: simple notes-to-self such as “remember units” and “check results by estimating” have a big impact.

Some colleges routinely set a past paper per week from February, and this is generally a higher paper. Past paper “walkthroughs” are effective, as are “group papers” where everyone contributes and peer marking occurs with the mark scheme. Another successful technique is to offer exam questions with no grading attached. Students are not really interested in the grade F and E type questions: they want to know what they need to do to get a C grade. Some teachers are clever and can present questions up to a B grade without mentioning it until completed, which hugely raises confidence.

If you can include these five elements of recall, routine, revise, repeat, ready within every session, then you have the basis of a SoW which should lead to more successful outcomes. The finer detail on this suggested FE GCSE Maths Resit SoW is at Making the grade D to C, which has a number of elements of exemplary practices from FE Colleges that seem to have addressed at least some of the challenges this group of students presents.

Further reading

  • the NCETM's Developing a Scheme of Work is well worth a read. It was written in response to the Ofsted report, Mathematics: Understanding the Score, which stated that a good SoW is rare in secondary schools. There are few if any bespoke FE GCSE resit SoWs out there: everything focuses upon GCSE in Year 11, but the FE SoW needs to be slightly different as we have discussed
  • Kangaroo Maths is favoured by many and links to numerous NRICH resources as well as their own. It covers the full range of key stages including AS and A2
  • each awarding body produces a SoW that runs alongside its syllabus. These tend to be specific to the exam board style, although they are written by experts and informed by practising teachers. Cambridge University Press has been über-generous with their free editable new curriculum SoWs for AQA, OCR and Edexcel, with one-year, two-year and three-year schemes combining to form a five-year scheme through KS3 into KS4
  • the inimitable Craig Barton has a great series on his blog, with 19 articles and a hand-holding guide through the production of a tailored SoW
  • We Teach Maths has posted a variety of SoWs on the TES, written for the new specification and designed for two- or three-year delivery.

But what if you’re looking for a tried and tested and been-round-the-block-a-few-times Scheme of Work for a GCSE maths resit or a fast-track GCSE? Well, apart from a few commercially available (i.e. hand-in-your-pocket time) items, there’s not much out there. We can change that: let’s all share @NCETMsecondary the SoW we’re following at the moment.

Image credits
Page header by Alan Levine (adapted), some rights reserved



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01 October 2015 12:33
And don't forget to explore the NCETM 'Essentials' package Resources and CPD for those working with students resitting GCSE Mathematics www.ncetm.org.uk/resourced/38830
By Fiona_Allan
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