problem solving skills maths gcse

The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

Resources for GCSE Mathematics students

Home > Students > GCSE Mathematics > Resources for GCSE Mathematics students

Here are some resources to help you in working towards taking your GCSE Mathematics. We’ll add further resources to these in the future.

If your school has registered with the AMSP your teachers should be able to access additional resources that they can share with you. These include resources for the AQA Level 2 Certificate in Further Mathematics and for the OCR Level 3 FSMQ in Additional Mathematics, as well as for GCSE Mathematics.

Develop your problem-solving skills

Maths feast.

Practice and competition materials produced for the Maths Feast enrichment competition for Year 10 students

Revising for your GCSE

Here are some suggestions to help you prepare for your exams:

• check you’ve covered all of the content
• make a plan of how you will use your revision time – it’s better to set yourself realistic targets and achieve them, than to be too ambitious and end up feeling negative about not achieving it
• in the early stage of your revision use your notes to help you; nearer the exams aim to complete past exam papers in timed conditions and without your notes
• practise answering as many past exam papers as possible
• after you’ve completed a past paper, read the mark scheme, taking particular note of what the marks are awarded for
• read the examiner’s reports for the papers you try – these usually give useful comments on common mistakes candidates made
• if you’re stuck seek help from a teacher or a friend
• if you’re struggling with a particular topic, practise some additional questions on this from your textbook

Planning to study Core Maths?

Core maths skills course.

This self-study online course helps you to get ready to study Core Maths.

You can register for this course between May and October.

Planning to study A level Mathematics?

Transition to a level mathematics resources: essential skills.

Many students say that they find the initial transition from GCSE challenging. These resources focus on developing key skills that will be used across the whole spectrum of AS and A level Mathematics.

Transition to A level Mathematics course

This free online interactive course aims to give you the confidence that you’re ready to start A level Mathematics. It covers the topics that are of most value at the beginning of the A level course and aims to improve your understanding – not just your fluency with skills – by delving deeper into GCSE content.

• Primary Hub
• Art & Design
• Design & Technology
• Health & Wellbeing
• Secondary Hub
• Citizenship
• Primary CPD
• Secondary CPD
• Book Awards
• All Products
• Primary Products
• Secondary Products
• School Trips
• Trip Directory
• Trips by Subject
• Trips by Type
• Trips by Region
• Submit a Trip Venue

Trending stories

Top results

Structural Support – How To Teach Problem Solving Strategies at Maths GCSE

A greater emphasis on problem solving for maths GCSE may provide new challenges for teachers and students alike – but Michael McGarvey has some solutions The reform of GCSE content and assessment criteria is underway, with mathematics amongst the first subjects to change. The introduction of new specifications, content and methods of assessment brings new […]

A greater emphasis on problem solving for maths GCSE may provide new challenges for teachers and students alike – but Michael McGarvey has some solutions

The reform of GCSE content and assessment criteria is underway, with mathematics amongst the first subjects to change. The introduction of new specifications, content and methods of assessment brings new challenges for teachers to navigate in this phase of first teaching ahead of the first exams under the new curriculum, which will take place in Summer 2017.

In maths, one of the core changes is the greater emphasis on problem solving, which now accounts for 30% of the Higher Tier assessment and 25% of Foundation. This means students will need to be made comfortable with problem-solving strategies, as well as the key skills of reasoning, interpreting and communicating. These will now also make up 30% and 25% of assessment at Higher and Foundation tier respectively.

So what is the best way for problem solving strategies to be taught, in order for students to get the maximum impact out of their learning?

Step by step

One way to tackle the increased weighting given to problem solving is to begin with a scaffolded approach, equipping students with a set of steps that they can use as a supportive framework to apply to any new mathematical problem. For example:

Step 1 may simply be ‘Work out what you have to do by reading the question carefully’.

Step 2 could then be ‘Assess what information is needed and check that you have it all.’

Step 3 may be to ask, ‘Is there any information given that you don’t need?’, followed by…

Step 4 , which can be ‘Decide what maths you can do.’

The final steps will be to set out the working clearly, and to check that you’ve answered the question.

When Professor Malcolm Swan, whom some may know as the driving force behind the Standard Units, developed his Eight Core Principles of Teaching Mathematics , one idea he stressed was the need to emphasise methods, rather than answers. This is exactly what a scaffolding approach aims to do.

Strategy sweep

Alongside the scaffolded framework, you can help students to build a mental ’toolkit’ of different problem-solving strategies that they can select from when they reach the step ‘Decide what maths you can do.’

For instance, one problem-solving strategy that could be taught is ‘Draw a diagram’. This involves making sure students learn and understand different diagram types – line diagrams, tables, frequency graphs and polygons – and their functions. Students can then choose an appropriate one to apply to their question, depending on what is being asked. This can turn the problem into something more visual, and enable pupils to work through the question in a way that may feel more logical.

Often we find that learners are more focused on getting the answer right than they are on learning the method, and that they see completion as more important than comprehension. Encouraging students to build a base of different problem-solving strategies will help them focus on learning how to start tackling new questions. If students don’t know where to start, there is a risk that they will feel too overwhelmed by new problems and tasks, and that they won’t be confident enough to try. Using different strategies to think around the problem can help these pupils figure out the best way to make the first approach.

Conversely, building different strategic skills can help more advanced students to whom the solution to a task is obvious – because they will still be able to apply the different skills to other, more challenging problems in the future. Emphasising method in this way may mean learners work on fewer problems overall, but pupils should develop a deeper understanding of them by tackling them using more than one strategy.

Growing confidence

Having a scaffolding system and a range of different strategies in place means students can gain confidence in a varied framework of techniques. Over the course of the academic year, the scaffolding supporting them can be removed as students become more fluent problem-solvers. Theoretically, this will leave candidates with a range of learned techniques to employ confidently in their final exams.

Combining these new approaches with all the additional content now included in the GCSE may seem like a lot to be faced with at once. However, with a reasoned, supportive approach, teachers can help students build the structures they need to tackle problem solving head on.

Michael McGarvey has over 20 years of experience in the global education sector, and currently works as the Director of UK Education at Cambridge University Press

Sign up to our newsletter

You'll also receive regular updates from Teachwire with free lesson plans, great new teaching ideas, offers and more. (You can unsubscribe at any time.)

Which sectors are you interested in?

Early Years

Thank you for signing up to our emails!

You might also be interested in...

Why join Teachwire?

Get what you need to become a better teacher with unlimited access to exclusive free classroom resources and expert CPD downloads.

Exclusive classroom resource downloads

Free worksheets and lesson plans

CPD downloads, written by experts

Resource packs to supercharge your planning

Special web-only magazine editions

Educational podcasts & resources

Access to free literacy webinars

Newsletters and offers

Create free account

I would like to receive regular updates from Teachwire with free lesson plans, great new teaching ideas, offers and more. (You can unsubscribe at any time.)

By signing up you agree to our terms and conditions and privacy policy .

Already have an account? Log in here

Thanks, you're almost there

To help us show you teaching resources, downloads and more you’ll love, complete your profile below.

Welcome to Teachwire!

Set up your account.

Lorem ipsum dolor sit amet consectetur adipisicing elit. Commodi nulla quos inventore beatae tenetur.

Log in to Teachwire

Not registered with Teachwire? Sign up for free

Reset Password

Remembered your password? Login here

To read this content please select one of the options below:

Please note you do not have access to teaching notes, developing problem-solving skills in mathematics: a lesson study.

International Journal for Lesson and Learning Studies

ISSN : 2046-8253

Article publication date: 3 January 2017

Problem solving is a skill in mathematics which although always relevant has heightened priority due to the changes in the new mathematics GCSE (Department for Education, 2013). It has previously been a skill which is deemed underdeveloped within mathematics and therefore is a theme which teachers are seeking to improve and nurture in order to align with the new changes. The GCSE is the formal qualification that students take at the end of Key Stage 4 (KS4) in the UK. The paper aims to discuss these issues.

Design/methodology/approach

The focus of the enquiry was to explore, using lesson studies, the differences in students’ approaches to problem solving. Consequently, key themes relating to the mediation of gender, ability, and academic motivation surfaced. Considering these themes, the paper subsequently reflects upon pedagogical practices which might effectively develop students’ ability to problem solve. The study took part in a mixed gender comprehensive secondary school with students taking part in the observation lesson ranging in age from 11 to 12 years old. The authors are the teachers who took part in the lesson study. The teachers implemented observation techniques in the form of video and peer observation with the accompanying teacher. In addition, students provided feedback on how they approached the problem-solving tasks through a form of semi-structured interviews, conducted via the use of video diaries where no teachers were present to prevent power bias. Following this, a thematic analysis of both the observations and student video diaries generated conclusions regarding how said key themes shaped the students’ approaches to problem solving.

Students’ frustration and competitive need to find a specific answer inhibited their ability to thoroughly explore the problem posed thus overseeing vital aspects needed to solve the problem set. Many students expressed a passion for problem solving due to its freedom and un-rigid nature, which is something teachers should nurture.

Originality/value

Generally, teachers are led by a culture in which attainment is the key. However, an atmosphere should be developed where the answer is not the key and students can explore the vibrant diversity mathematics and problem solving can offer.

• Lesson study
• Mathematics
• Problem-solving skills
• Video diaries

Bradshaw, Z. and Hazell, A. (2017), "Developing problem-solving skills in mathematics: a lesson study", International Journal for Lesson and Learning Studies , Vol. 6 No. 1, pp. 32-44. https://doi.org/10.1108/IJLLS-09-2016-0032

Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited

Related articles

We’re listening — tell us what you think, something didn’t work….

Report bugs here

All feedback is valuable

Please share your general feedback

Join us on our journey

Platform update page.

Visit emeraldpublishing.com/platformupdate to discover the latest news and updates

Questions & More Information

Answers to the most commonly asked questions here

Resourceaholic

Ideas and resources for teaching secondary school mathematics

• Blog Archive

Problem Solving

• Problem Solving Booklet - Complete Mathematics
• GCSE Mathematics - 90 Problem Solving Questions - AQA (and PowerPoint collated by @EJMaths)
• Additional Mathematics Problem Solving Questions (& Teacher Guide ) - AQA
• GCSE Problem Solving  - MEI
• 55 Problems - MathsBox
• Maths problems, puzzles and ideas - Cubed Maths
• UKMT Problems PowerPoint - collated by Dan Walker
• San Gaku Problems - Dan Walker
• Support for Problem Solving  - OCR
• Badger Maths Problem Solving Samples (Years 1 - 6) - via National Stem Centre
• Daily Maths Puzzles (Key Stage 2) - Sarah Farrell
• Mathematical challenges for able pupils in Key Stages 1 and 2 - DfE
• Problem solving with EYFS, Key Stage 1 and Key Stage 2 children - DfE
• Solve My Maths
• Catriona Agg
• Maths Problem Solving
• MathsChallenge.net
• Brilliant.org
• Underground Mathematics
• Openmiddle.com
• United Kingdom Mathematics Trust
• 1001 Math Problems

Teaching support from the UK’s largest provider of in-school maths tuition

resources downloaded

one to one lessons

schools supported

Built by teachers for teachers

In-school online one to one maths tuition developed by maths teachers and pedagogy experts

Hundreds of FREE online maths resources!

Daily activities, ready-to-go lesson slides, SATs revision packs, video CPD and more!

Maths Problem Solving: Engaging Your Students And Strengthening Their Mathematical Skills

Meriel willatt.

Maths problem solving can be challenging for pupils. There’s no ‘one size fits all’ approach or strategy and questions often combine different topic areas. Pupils often don’t know where to start. It’s no surprise that problem solving is a common topic teachers struggle to teach effectively to their pupils.

In this blog, we consider the importance of problem solving and share with you some ideas and resources for you to tackle problem solving in your maths classroom, from KS2 up to GCSE.

What is maths problem solving?

Why is maths problem solving so difficult, how to develop problem solving skills in maths, maths problem solving ks2, maths problem solving ks3, maths problem solving gcse.

Maths problem solving is when a mathematical task challenges pupils to apply their knowledge, logic and reasoning in unfamiliar contexts. Problem solving questions often combine several elements of maths.

We know from talking to the hundreds of school leaders and maths teachers that we work with as one to one online maths tutoring providers that this is one of their biggest challenges: equipping pupils with the skills and confidence necessary to approach problem solving questions.

The Ultimate Guide to Problem Solving Techniques

Download these 9 ready-to-go problem solving techniques that every pupil should know

The challenge with problem solving in maths is that there is no generic problem solving skill that can be taught in an isolated maths lesson. It’s a skill that teachers must explicitly teach to pupils, embed into their learning and revisit often.

When pupils are first introduced to a topic, they cannot start problem solving straight away using it. Problem solving relies on deep knowledge of concepts. Pupils need to become familiar with it and practice using it in different contexts before they can make connections, reason and problem solve with it. In fact, some researchers suggest that it could take up to two years to do this (Burkhardt, 2017). 

At Third Space Learning, we specialise in online one to one maths tutoring for schools, from KS1 all the way up to GCSE. Our lessons are designed by maths teachers and pedagogy experts to break down complex problems into their constituent parts. Our specialist tutors then carefully scaffold learning to build students’ confidence in key skills before combining them to tackle problem solving questions.

In order to develop problem solving skills in maths, pupils need lots of different contexts and word problems in which to practise them and the opportunity to engage in mathematical talk that draws on their metacognitive skills. 

The EEF suggests that to develop problem solving skills in maths, teachers need to teach pupils:

• To use different approaches to problem solving
• Use worked examples
• To use metacognition to plan, monitor and reflect on their approaches to problem solving

Below, we take a closer look at problem solving at each stage, from primary school all the way to GCSEs. We’ve also included links to maths resources and CPD to support you and your team’s classroom teaching.

At lower KS2, the National Curriculum states that pupils should develop their ability to solve a range of problems. However, these will involve simple calculations as pupils develop their numeracy skills. As pupils progress to upper KS2, the demand for problem solving skills increases. 

“At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems.” National curriculum in England: mathematics programmes of study (Upper key stage 2 – years 5 and 6)

KS2 problem solving can often fall into the trap of relying on acronyms, such as RICE, RIDE or even QUACK. The most popular is RUCSAC (Read, Underline, Calculate, Solve, Answer, Check). While these do aim to simplify the process for young minds, it encourages a superficial, formulaic approach to problem solving, rather than deep mathematical thinking. Also, consider how much is wrapped up within the word ‘solve’ – is this helpful?

We teach thousands of pupils KS2 maths problem solving skills every week through our one to one online tutoring programme for maths. In our interventions, we encourage deep mathematical thinking by using a simplified version of George Polya’s four stages of problem solving. Here are the four stages:

Understand the problem

• Devise a strategy for solving it
• Carry out the problem solving strategy
• Check the result

We use UCR as a simplified model: Understand, Communicate & Reflect. You may choose to adapt this depending on the age and ability of your class.

For example:

Maisy, Heidi and Freddie are children in the same family. The product of their ages is a score. How old might they be?

There are three people.

There are three numbers that multiply together to make twenty (a score is equal to 20). There will be lots of answers, but no ‘right’ answer.

Communicate

To solve the word problem we need to find the numbers that will go into 20 without a remainder (the factors).

The factors of 20 are 1, 2, 4, 5, 10 and 20.

Combinations of numbers that could work are: 1, 1, 20 1, 2, 10 1, 4, 5 2, 2, 5.

The question says children, which means ‘under 18 years’, so that would mean we could remove 1, 1, 20 from our list of possibilities. 

In our sessions, we create a nurturing learning environment where pupils feel safe to make mistakes. This is so important in the context of problem solving as the best problem solvers will be resilient and able to overcome challenges in the ‘Reflect’ stage. Read more: What is a growth mindset

Looking for more support teaching KS2 problem solving? We’ve developed a powerpoint on problem solving, reasoning and planning for depth that is designed to be used as CPD by primary school teachers, maths leads and SLT. 

The resource reflects on how metacognition can enhance reasoning and problem solving abilities, the ‘curse’ of real life maths (think ‘Carl buys 60 watermelons…) and how teachers can practically implement and teach strategies in the classroom.

You may also be interested in: 

• Developing Thinking Skills At KS2
• KS2 Maths Investigations
• Word problems for Year 6

At KS3, the importance of seeing mathematical concepts as interconnected with other skills, including problem solving, is foregrounded. The National Curriculum also stresses the importance of a strong foundation in maths before moving on to complex problem solving.

“Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems” National curriculum in England: mathematics programmes of study (Key stage 3)

“Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4.” National curriculum in England: mathematics programmes of study (Key stage 3)

For many students, the transition from primary to secondary school can be a huge challenge.

Especially in the aftermath of the Covid-19 pandemic and the resultant school closures, students may arrive into Year 7 with various learning gaps and misconceptions that will hold them. Some students may need focused support to plug these gaps and grow in confidence.

You can give pupils a smoother transition from KS2 to KS3 with personalised one to one online tuition with specialist tutors with Third Space Learning. Our lessons cover content from Years 5-7 and build a solid foundation for pupils to develop their problem solving skills. Pupils are supported towards independent practice through worked examples, questioning and support slides.

The challenge for KS3 maths problem solving activities is that learners may struggle to get invested unless you start with a convincing hook. Engage your young mathematicians on topics you know well or you know they’ll be invested in and try your hand at designing your own mathematical problems. Alternatively, get some inspiration from our crossover ability and fun maths problems .

Since the new GCSE specification began in 2015, there has been an increased focus on non-routine problem solving questions. These questions demand students to make sense of lots of new information at once before they even move on to selecting the strategies they’ll use to find the correct answer. This is where many learners get stuck.

In recent years, teachers and researchers in pedagogy (including Ofsted) have recognised that open ended problem solving tasks do not in fact lead to improved student understanding. While they may be enjoyable and engage learners, they may not lead to improved results.

SSDD problems (Same Surface Different Depth) can offer a solution that develops students’ critical thinking skills, while ensuring they engage fully with the information they’re provided. The idea behind them is to provide a set of questions that look the same and use the same mathematical hook but each question requires a different mathematical process to be solved.

Read more about SSDD problems , tips on writing your own questions and download free printable examples. There are also plenty of more examples on the NRICH website.

Worked examples, careful questioning and constructing visual representations can help students to convert the information embedded in a maths challenge into mathematical notations. Read our blog on problem solving maths questions for Foundation, Crossover & Higher examples, worked solutions and strategies.

Remember that students can only move on to mathematics problem solving once they have secure knowledge in a topic. If you know there are areas your students need extra support, check our Secondary Maths Resources library for revision guides, teaching resources and worksheets for KS3 and GCSE topics.

Do you have students who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils 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 150,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Subsidised one to one maths tutoring from the UK’s most affordable DfE-approved one to one tutoring provider.

Related Articles

FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

Ideal for running staff meetings on mastery or sense checking your own approach to mastery.

Privacy Overview

• International
• Schools directory
• Resources Jobs Schools directory News Search

Gcse problem solving

Subject: Mathematics

Age range: 14-16

Resource type: Assessment and revision

Last updated

22 February 2018

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

MathsBelongsToAll

Empty reply does not make any sense for the end user

mbdownlands

Londonsecondary, donnadaly75.

Excellent variety of problem solving questions, thank you!

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource: