# 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.

The planned exam adaptations to Mathematics in 2022 are:

- Provision of a formula sheet;
- Advance information on what exams will cover.

The release from Ofqual in October stated 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” (see Proposed changes to the assessment of GCSEs, AS and A levels in 2022). Edexcel, AQA and OCR have now provided these formula sheets, which are available on their websites. The formula sheets are identical in content and differ only slightly in presentation.

Advance information on what exams will cover is due to be released on 7th February 2022, or sooner if the situation with the pandemic worsens. It is not clear at the moment what form this advance information is likely to take; the JCQ has further general information available, but note that there are no maths-specific examples.

With the announcement of these adaptations, it appears that our best strategy is to expect exam papers to look broadly similar to those from 2017-2019, and to continue to prepare students as we usually would. The release of advance notice information in February is intended to inform areas to focus revision, rather than to omit sections of content to be taught.

**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 their GCSE maths 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
- Structure and calculation
- Fractions, decimals and percentages
- Measures and accuracy

- Algebra
- Notation, vocabulary and manipulation
- Graphs
- Solving equations and inequalities
- Sequences

- Ratio, proportion and rates of change
- Geometry and measure
- Properties and constructions
- Mensuration and calculation
- Vectors

- Probability
- Statistics

In addition, there are three assessment objectives that will be tested:

- AO1: Use and apply standard techniques
- AO2 Reason, interpreet and communicate mathematically
- AO3: Solve problems within mathematics and in other contexts

These are all taken from The DfE’s subject content and assessment objectives for GCSE mathematics.

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### How does Third Space Learning tackle GCSE maths topics?

GCSE maths is interconnected, and that’s how we approach our online GCSE revision programme. When designing the programme, we focus on each individual high-value lesson as part of an interconnected web, rather than teaching each main topic differently. This allows our tutors to adjust their teaching depending on the student and their level.

Within these individual lessons, our GCSE tutor slides follow a similar structure to support the revision of a topic. We move from a warm-up question to the actual lesson split into three learning objectives, which cover the topic.

In response to the student’s understanding, each learning objective moves through an exam-style question, a ‘support’ slide and an ‘assess’ slide. The lesson ends with the option of a ‘challenge’ slide to build on the previous learning objectives.

### The GCSE maths topics we think you should be learning

It is our view, as a result of the research we’ve undertaken, (the results of which can be seen in our previous article) that to make the most of the time you have available with your students you can focus on a few specific topics and approaches.

#### 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.

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.

In terms of exam adaptations, the formula sheet includes the algebraic formula for compound interest, but this is stated in formal terms, using “principal amount”, “interest rate” and the word “accrued” – it may be worth ensuring students are familiar with these terms if they intend to rely on the given formula in the exam.

#### 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 x
^{2}+ 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.”

Advance notice of topics may be particularly helpful with algebra at the Foundation stage, as this tends to be assessed in a fairly procedural manner, allowing revision to focus on cherry-picked grade 4/5 topics. However, there is nothing relating to algebra topics on the formula sheet at the Foundation level.

**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 practice here, and also addressing misconceptions around fractions of an hour, and the use of a calculator for time problems.

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.

Both Pythagoras’ theorem and the trigonometric ratios are provided on the formula sheet at Foundation, along with area of a trapezium, volume of a prism, and circumference and area formulae – which, along with advance information when available, may allow for careful selection of more difficult topics to focus on.

#### 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, plugging gaps once advance information has been released if necessary.

The formula sheet gives candidates the addition rule for “or” probabilities – however, this is given in the full form *P(A or B = P(A) + P(B) – P(A and B)*, and this notation may confuse some students…

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.

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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.

GCSE 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

How We Developed Our Free GCSE Maths Revision Lesson Library

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’.

**Read more:** GCSE Grade Boundaries

### GCSE maths topics FAQs

**How many topics are in GCSE maths?**

There are 6 main GCSE maths topics: Number, Algebra, Ratio, proportion and rates of change, Geometry and measure, Probability, Statistics.

**What are the hardest GCSE maths topics?**

The hardest GCSE maths topics vary from person to person but from our research the most complex questions are to be found in proportional reasoning, perimeter, area and volume, and substitution and formulae. Although students traditionally struggle with probability and statistics the questions asked in GCSE Mathematics are sometimes easier than in other topics.

**What are the 3 GCSE maths papers?**

The 3 GCSE maths papers are:

Paper 1: Non-Calculator

Paper 2: Calculator

Paper 3: Calculator

If you have followed the foundation syllabus these will all be foundation papers. If you’ve followed the higher tier syllabus the three papers will all be higher papers.

**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:**

- Gradient of a line
- Nth term
- Solving equations
- Percentage change
- Pythagoras’ theorem
- Recurring decimals to fractions
- Algebraic expressions
- Cosine rule
- Quadratic sequences
- Circle theorems
- Area of a quadrilateral
- Sine rule

**Do you have students who need extra support in maths?**

Every week Third Space Learning’s maths specialist tutors support thousands of students across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress.

Since 2013 we’ve helped over 90,000 primary and secondary students become more confident, able mathematicians. Find out more about our GCSE Maths Revision Programme or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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