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The Most Impactful GCSE Maths Topics Your Year 10 And Year 11 Should Revise For Their Foundation Exam In 2022

The past two years have been very challenging for the education sector, particularly in the domain of examinations (or lack thereof) and assessments. With the difficulties of teacher-assessed grades hopefully behind us, it is time to address the implications for GCSE maths topics and exam groups from 2022 onwards.

What is the current picture for GCSE maths?

GCSEs in 2022 are being adapted to help students who have been affected by the pandemic. Ofqual has consulted on proposed changes to exams; this consultation closed on 1st August 2021 and decisions were announced on 30th September. There were a variety of proposals, such as advance notice of topics and allowing the use of supporting materials in the exam.

For 2022, the only planned adaptation to Mathematics is the provision of a formula sheet. The release from Ofqual states that “exam boards will provide copies of the formulae sheet for use in teaching and to ensure that students are familiar with it prior to the exams”. It is unclear at the time of writing whether this is the formulae sheet that exam boards already provide for use during teaching, or whether there will be a new formulae sheet released.

With the announcement of this adaptation, it appears that our best strategy is to expect exam papers to look broadly similar to those from 2017-2019, and to continue preparing students as we usually would.

Further reading: Proposed changes to the assessment of GCSEs, AS and A levels in 2022

Building maths skills for the future

There is also a balance to be struck between preparing students for exams and providing them with skills for onward life and study. We must be mindful that the sole purpose of education is not to enable students to pass exams.

At GCSE level, a school-wide approach may be necessary, collaborating with colleagues to work out what skills are fundamental to success for post-16 study – this will depend on the school’s individual setting and demographic.

For example, it might be important to ensure that statistical content necessary for the study of AS/A Level Psychology is covered, or that students have sufficient algebra and graphing skills to be able to access A Level Sciences.

This blog focuses on strategies for exam preparation for Foundation and draws upon research and analysis conducted on the six series of Edexcel maths exam papers available (June 2017 – November 2019), so please bear this in mind if you use AQA or OCR. This companion piece gives more detail and is my rationale for the suggestions below.

What are the GCSE maths topics?

The GCSE maths topics are:

  • Number including fractions, decimals and percentages
  • Algebra including equations, nth term etc.
  • Geometry and measure including trigonometry
  • Ratio and proportion including exchange rates
  • Probability including frequency
  • Statistics including pie chart

Personalised online lessons to prepare your KS4 students for maths GCSEs

Weekly online one to one maths revision lessons delivered by specialist tutors and designed for the students who need it most.


The GCSE maths topics we think you should be learning

Number and proportion

Key topics
  • Context-rich work on four operations and calculation skills, including fractions, decimals and negative numbers, order of operations.
  • Proportional reasoning; using fraction, decimal, percentage and ratio skills flexibly and applying to a range of contexts.
  • Procedural work on factors, multiples, primes, HCF and LCM, standard form, power and root calculations.
Content to skim or skip
  • Problem-solving or rich problems using HCF, LCM, product of primes, standard form.

What do we know from the GCSE paper analysis?

One thing highlighted by the GCSE paper analysis is that numeracy skills and proportional reasoning are the backbones of the current GCSE Foundation programme of study, and a significant amount of this is assessed in a non-standard manner or using ‘real-life’ contexts.

Decimals and percentages GCSE maths topics lesson slide
Converting between decimals and percentages in Third Space Learning’s online interventions

It was clear from the Sample Assessment Materials, and the messaging from exam boards, that one of the goals for GCSE 2015 was to increase the demand in problem-solving, and also to ask more questions requiring connections to be made between topics. In conjunction with the need for these skills beyond school in many circumstances, I cannot see any considerable change in this regard to exams from 2022 and beyond.

What should you be teaching for 2022?

As such, in preparing the 2022 cohort, students need plenty of practice on number skills (four operations including fractions and decimals, calculations, percentages etc) so these are not limiting their ability to access the context-based problems. Ample time and opportunity should also be spent working with number and proportion skills in a wide variety of contexts.

Some number topics are typically assessed in a fairly procedural or context-free way; these include HCF, LCM, product of primes, standard form, power and root calculations. While there is some lovely rich content in these topics, it is less likely to be assessed on GCSE Foundation. That said, there is very little content in the number and proportion strand that could be considered non-essential.


Algebra

Key topics
  • The ‘algebra toolkit’ of simplifying, expanding, factorising, laws of indices, ensuring students can reliably apply methods to standard problems.
  • Applying mathematical formulae to a variety of real-life and unfamiliar contexts.
  • Sequences, functions and graphs, with focus on procedural ‘easy wins’ in graph work and sequences.
Content to skim or skip
  • Quadratic equations, particularly factorising and solving the form x2 + bx + c = 0; limited work on quadratic expressions.
  • Simultaneous equations, particularly context-based problems.

What do we know from the GCSE paper analysis?

In the Foundation tier, a significant amount of algebra is assessed in procedural, context-free ways; this suggests there is less value in spending a lot of vital exam preparation time on rich problems for these topics. It is worth remembering that, while the complexity and degree of problem-solving expected for algebra at Foundation is relatively low, students find the topics themselves more challenging, and so these are not necessarily easier marks.

Furthermore, we need to consider the frequency at which high-end algebra topics, such as simultaneous equations, quadratic expressions and equations, appear on Foundation papers, and think critically about the amount of teaching time spent on these for borderline grade 4/5 candidates.

What should you be teaching for 2022?

In the current climate, I would consider spending less time on these topics, in favour of more time on graphs, sequences and functions, particularly as these are traditionally tackled poorly by candidates. The 2018 Chief Examiner’s report states that “beyond drawing a simple graph of an equation, there appears to be little understanding of the relationship between equation[s] and graph[s], between graphs of parallel lines, or finding an equation from a straight-line graph.”

As the situation with exam changes unfolds, this may impact the accessibility of some of these topics – for example, the provision of a formula sheet might make coordinate geometry slightly more accessible. However, at Foundation, I cannot see this adaptation having a considerable impact on algebra topics.

Read more: Algebra Questions And Practice Problems (KS3 & KS4)


Shape

Key topics
  • Perimeter, area and volume, particularly context-based problems.
  • Speed, distance and time, and general time calculations.
  • Scale drawing work and bearings.
  • Procedural work on 2D shape (such as polygons) and angle properties (particularly angles on a line, around a point, in a triangle) and vectors.
Content to skim or skip
  • Trigonometry, particularly exact values.
  • 3D shape and angle properties.
  • Surface area and volume of spheres, cones and pyramids.

What do we know from the GCSE paper analysis?

One thing I noted from the paper analysis is a large amount of problem-solving based around perimeter, area and volume; there were relatively few procedural problems, in favour instead of real-life contexts and unfamiliar abstract situations. As well as ensuring students can reliably apply standard methods, they must be able to flexibly apply these skills to other problems. 

What should you be teaching for 2022?

Due to the crossover with proportional reasoning, speed, distance and time featured significantly more heavily than other compound units work, such as pressure or density. Students may benefit from additional practise here, and also addressing misconceptions around fractions of an hour, and use of a calculator for time problems.

Average speed GCSE maths topics revision lesson slide
Calculating average speed in a Third Space Learning online intervention lesson

I would also recommend plenty of coverage on the correct use of mathematical equipment, such as scale drawing work and bearings, as these come up frequently for a fair number of marks, and students may have had varying degrees of success working on these remotely.

For some students or classes, it might be appropriate to skim some of the top-end content, rather than spend a lot of teaching time on topics worth proportionally fewer marks. For example, while either Pythagoras or trigonometry comes up on most series, this is usually only once and for relatively few marks. 

3D shape properties can represent easy wins, but come up relatively infrequently.

The traditionally ‘higher’ surface area and volume work, such as spheres, cones and pyramids, also comes up infrequently, so it might be advisable to skim this in favour of spending more time on, for example, problem-solving using circumference and area of a circle.

Provision of a formulae sheet, the route chosen by Ofqual and exam boards, could change strategies; for example, provision of the trigonometric ratios and a table of exact values would make this content much more accessible.


Probability and statistics

Key topics
  • Procedural work on listing outcomes, Venn diagrams, frequency trees.
  • Application of fraction, decimal and ratio skills to problems about mutually exclusive events.
  • Presenting data; drawing and interpreting a wide variety of graphs.
  • Estimating the mean.
Content to skim or skip
  • Data collection and sampling.
  • Tree diagrams.

What do we know from the GCSE paper analysis?

Like algebra, a significant amount of probability and statistics is assessed at Foundation in procedural, context-free ways; again, there is less value in terms of exam preparation in spending lots of time on rich problems.

What should you be teaching for 2022?

In the probability strand, one topic that does attract a fair amount of non-standard problems is mutually exclusive events, which often embed skills using fractions or ratios, so it is worth focusing on problem-solving skills there. Procedural work on ‘newer’ topics such as Venns, listing outcomes and frequency trees would be valuable, as these topics seem to appear frequently. In fact, frequency trees were heavily favoured over standard tree diagrams, so I would be tempted to skim the latter…

In statistics, the emphasis is more heavily on presenting data rather than processing data, with equal focus on drawing or completing charts and graphs, and interpreting or critiquing existing representations. Pictograms and pie charts feature frequently, with fewer bar charts; scatter graphs usually include a drawing and interpreting component. Estimating the mean comes up on quite a few papers. Data collection and sampling does not appear on every series, and questions can usually be answered in a fairly intuitive way.

Read more: Probability Questions And Practice Problems (KS3 & KS4)

GCSE maths topics teaching strategies

Planning the content for a scheme of work for Year 11 will depend on how your particular setting and students have been impacted so far. For example, it might be prudent to begin by re-covering topics that many students may have missed or had patchy coverage of due to emergency closures. Beyond this, and in light of the proposed exam adaptations having no effect on the content examined, I do not think anything significantly different needs to be done for this cohort of students in terms of exam preparation.

Based on my Foundation analysis, it is clear that there needs to be a continued strong emphasis on number and proportion work, particularly in applying these in other contexts. Basic numeracy work needs to be continually revised and practised, as do standard procedures, such as expanding, factorising, simplifying and using formulae.

An ideal opportunity to do this is in the settler/starter portion of the lesson, focusing on five or ten key topics for a few weeks at a time – there are excellent resources online to support this.

Looking to build arithmetic skills and mathematical fluency through regular daily practice? Download our Fluent in Five packs!

1) GCSE Fluent in Five Arithmetic Pack (Half Term 1)
2) GCSE Fluent in Five Arithmetic Pack (Half Term 2)

We need to ensure that students are familiar with connections within the Foundation content – for example, using linear equations to solve 2D shape and angle problems, or using fractions and ratios in probability calculations.

However, in the context of severely reduced teaching time, and in the interests of giving these students the best possible chance of success with their exams, I would advocate spending less time on rich content and problem-solving within select topics in number, algebra, and most of statistics. For a more in-depth picture, see my Foundation analysis linked in the introduction!

A careful balance needs to be struck in terms of assessment; students may not be ready to sit a formal mock exam in the early Autumn term, as was standard practice in some schools pre-pandemic. However, continual, low-stakes formative assessment (regular mini-quizzes, or using the starting portion of the lesson for a Top 5/10) is more crucial than ever for identifying gaps in learning.

Intervention strategies need to be in place from the start of the school year to pick up those students who are already struggling.

Have you got a group of students who need more targeted GCSE revision support? We are here to help! The best way to plug individual gaps is to give each student personalised and targeted one to one support, but this might not be straightforward in a class of 30.

Third Space Learning’s weekly online interventions feature an initial diagnostic assessment to identify the most impactful lessons from our GCSE maths revision programme for that particular student.

Read more: How We Developed Our GCSE Maths Revision Programme

Finally, the decisions about Foundation vs Higher for borderline grade 4-5 candidates may need to be made for a larger group of students. It is likely that there will be some students who, with the normal, pre-pandemic amount of teaching time and support from Years 9-11, we would make the decision to chance the Higher paper to see if they got a 6, with a fallback of a grade 5.

These students within the 2022 cohort may have considerable gaps in their learning, and it may be more appropriate to enter them for an exam paper where they can securely achieve a 5. It is worth bearing in mind that, with the newer papers, exam boards encouraged more Foundation entries, particularly those who would have previously been considered ‘weak grade Cs’.

If you are looking for examples, practice questions and worksheets, head over to our GCSE maths revision pages covering a variety of topics, such as:

Do you have students who need extra support in maths?
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Christine Norledge
Christine Norledge
Secondary Maths Teacher and Author
Christine is a former secondary Maths teacher, currently working as a freelance author. Her resource-sharing website, Twitter and YouTube channel also keep her busy!
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Personalised online lessons to prepare your KS4 students for maths GCSEs

Weekly online one to one maths revision lessons delivered by specialist tutors and designed for the students who need it most.

Find Out More!

Personalised online lessons to prepare your KS4 students for maths GCSEs

Downloadable resource

Weekly online one to one maths revision lessons delivered by specialist tutors and designed for the students who need it most.

Find Out More!