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Maths Problem Solving At KS2: Strategies and Resources For Primary School Teachers

John Dabell

Maths problem solving KS2 is crucial to succeeding in national assessments. If your Key Stage 2 pupils are still struggling with reasoning and problem solving in Maths, here are some problem solving strategies to try with your classes; all aligned to Ofsted’s suggested primary school teaching strategies.

Reasoning and problem solving are widely understood to be one of the most important activities in school mathematics. As far back as 1982,  The Cockcroft Report , stated:

‘The ability to solve problems is at the heart of mathematics. Mathematics is only “useful” to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name “problem solving”. […] At each stage […] the teacher needs to help pupils to understand how to apply the concepts and skills which are being learned and how to make use of them to solve problems. These problems should relate both to the application of mathematics to everyday situations within the pupils’ experience, and also to situations which are unfamiliar.’

Thirty plus years later and problem solving is still the beating heart of the Maths curriculum and – along with fluency and reasoning – completes the triad of aims in the 2014 New National Curriculum.

Ofsted’s view on problem solving in the Maths curriculum

Despite its centrality, Ofsted report that ‘ problem solving is not emphasised enough in the Maths curriculum ’. Not surprisingly, problem solving isn’t taught that well either because teachers can lack confidence, or they tend to rely on a smaller range of tried and tested strategies they feel comfortable with but which may not always ‘hit home’. If you’re looking to provide further support to those learners who haven’t yet mastered problem solving, you probably need a range of different strategies, depending on both the problem being attempted and the aptitude of the pupil.

We’ve therefore created a free KS2 resource aimed at Maths Coordinators and KS2 teachers that teaches you when and how to use 9 key problem solving techniques:  The Ultimate Guide to Problem Solving Techniques

The context around KS2 problem solving

According to Jane Jones, former HMI and National Lead for Mathematics, in her presentation at the Jurassic Maths Hub:

• Problems do not have to be set in real-life contexts, beware pseudo contexts.
• Providing a range of puzzles and other problems helps pupils to reason strategically to approach problems, sequence unfolding solutions, and use recording to help their mathematical thinking for next steps.
• It is particularly important that teachers and TAs stress reasoning, rather than just checking whether the final answer is correct.
• Pupils of all ability need to learn how to solve problems – not just the high attainers or fastest workers.

The Ultimate Guide to Problem Solving Techniques

9 ready-to-go problem solving techniques with accompanying tasks to get KS2 reasoning independently

How to approach KS2 maths problems

So what do we do? Well Ofsted advice is pretty clear on what to do when teaching problem solving. Jane Jones says we should:

• Set problems as part of learning in all topics for all pupils.
• Vary the ways in which you pose problems.
• Try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.
• Make sure you discuss alternative approaches with pupils to help develop their reasoning.
• Ensure that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

Perhaps more than most topics in Maths, teaching pupils how to approach problem solving questions effectively requires a systematic approach. Pupils can face any number of multi-step word problems throughout their SATs and they will face them without our help. To truly give pupils the tools they need to approach problem solving in Maths we must ingrain techniques for  approaching  problems.

With this in mind, below are some methods and techniques for you to consider when teaching problem solving in your KS2 Maths lessons. For greater detail and details on how to teach this methods, download the  Ultimate Guide to Problem Solving Techniques

Models for approaching KS2 problem solving

Becoming self-assured and capable as a problem solver is an intricate business that requires a range of skills and experience. Children need something to follow. They can’t just pluck a plan of attack out of thin air which is why models of problem solving are important especially when made memorable. They help establish a pattern within pupils so that, when they see a problem, they feel confident in taking the steps towards solving it.

Find out how we encourage children to approach problem solving independently in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils.

The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely:

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

Many models have followed the Polya model and use acronyms to make the stages stick. Which model you use can depend on the age of the children you are teaching and sometimes the types of word problems they are trying to solve. Below are several examples of Polya model acronyms:

C – Circle the question words U – Underline key words B – Box any key numbers E – Evaluate (what steps do I take?) S – Solve and check (does my answer make sense and how can I double check?)

R – Read the problem correctly. I – Identify the relevant information. D – Determine the operation and unit for expressing the answer. E – Enter the correct numbers and calculate

I – Identify the problem D – Define the problem E – Examine the options A – Act on a plan L – Look at the consequences

R – Read and record the problem I – Illustrate your thinking with pictures, models, number lines etc C – Compute, calculate and check E – Explain your thinking

R – Read the question and underline the important bits U – Understand: think about what to do and write the number sentences you will need C –  Choose how you will work it out S – Solve the problem A – Answer C – Check

Q – Question – read it carefully U – Understand – underline or circle key elements A – Approximate – think about the size of your answer C – Calculate K – Know if the answer is sensible or not

T – Think about the problem and ponder E – Explore and get to the root of the problem A – Act by selecting a strategy R – Reassess and scrutinise and evaluate the efficiency of the method

The idea behind these problem solving models is the same: to give children a structure and to build an internal monitor so they have a business-like way of working through a problem. You can choose which is most appropriate for the age group and ability of the children you are teaching.

The model you choose is less important than knowing that pupils can draw upon a model to follow, ensuring they approach problems in a systematic and meaningful way. A far simpler model – that we use in the   Ultimate Guide to KS2 Problem Solving Techniques  – is UCR: Understand the problem, Communicate and Reflect.

You then need to give pupils lots of opportunities to practice this! You can find lots of FREE White Rose Maths aligned maths resources, problem solving activities and printable worksheets for KS1 and KS2 pupils in the Third Space Learning Maths Hub .

You might also be interested in:

• 25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)
• 30 Problem Solving Maths Questions And Answers For GCSE
• Why SSDD Problems Are Such An Effective Tool To Teach Problem Solving At KS3 & KS4

What’s included in the guide?

After reading the  Ultimate Guide to KS2 Problem Solving Techniques , we guarantee you will have a new problem solving technique to test out in class tomorrow. It provides question prompts and activities to try out, and shows you step by step how to teach these 9 techniques

• Open ended problem solving
• Using logical reasoning

Working backwards

Drawing a diagram

Drawing a table

Creating an organised list

Looking for a pattern

Acting it out

Guessing and checking

Cognitive Activation: getting KS2 pupils in the lightbulb zone

If you need more persuasion, pupils who use strategies that inspire them to think more deeply about maths problems are linked with higher Maths achievement. In 2015 The  National Education Research Foundation  (NFER) published ‘ PISA in Practice: Cognitive Activation in Maths ’. This shrewd report has largely slipped under the Maths radar but it offers considerable food for thought regarding what we can do as teachers to help mathematical literacy and boost higher mathematical achievement.

Cognitive Activation isn’t anything mysterious; just teaching problem solving strategies that pupils can think about and call upon when confronted by a Maths problem they are trying to solve. Cognitive It encourages us as teachers to develop problems that can be solved in more than one way and ‘may require different solutions in different contexts’. For this to work, exposing children to challenging content and encouraging a culture of exploratory talk is key. As is:

• Giving pupils maths problem solving questions that require them to think for an extended time.
• Asking pupils to use their own procedures for solving complex problems.
• Creating a learning community where pupils are able to make mistakes.
• Asking pupils to explain how they solved a problem and why they choose that method.
• Presenting pupils with problems in different contexts and ask them to apply what they have learned to new contexts.
• Giving pupils problems with no immediately obvious method of solution or multiple solutions.
• Encouraging pupils to reflect on problems.

Sparking cognitive activation is the same as sparking a fire – once it is lit it can burn on its own. It does, however, require time, structure, and the use of several techniques for approaching problem solving. Techniques, such as open-ended problem solving, are usually learned by example so we advise you create several models to go through with pupils, as well as challenge questions for independent work. Many examples exist and we encourage you to explore more (e.g. analysing and investigating, creating a tree diagram, and using simpler numbers).

Read these:

• How to develop maths reasoning skills in KS2 pupils
• FREE CPD PowerPoint: Reasoning Problem Solving & Planning for Depth
• KS3 Maths Problem Solving

That time, effort, and planning will – however – be well spent. Equipping pupils with the tools to solve problems they have never seen before is more akin to teaching for life than teaching for Maths. The skills they gain from being taught problem solving successfully will be skills they use and hone for the rest of their life – not just for their SATs.

For a range of problem solving techniques, complete with explanations, contextual uses, example problems and challenge questions – don’t forget to download our free  Ultimate Guide to KS2 problem solving and reasoning techniques  resource here.

KS2 problem Solving FAQs

Here are some techniques to teach problem solving to primary school pupils: Open ended problem solving Using logical reasoning Working backwards Drawing a diagram Drawing a table Creating an organised list Looking for a pattern Acting it out Guessing and checking

Ofsted say that teachers can encourage problem-solving by: Setting problems as part of learning in all topics for all pupils. Varying the ways in which you pose problems. Trying to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations. Making sure you discuss alternative approaches with pupils to help develop their reasoning. Ensuring that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

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TES Maths Investigations Collection

Engaging investigation ideas to inspire creative thinking in your classroom

Since the abolition of maths coursework, there is no formal requirement to carry out investigations with your students. However, it is only through investigative work that students of all ages and abilities can start to appreciate the true beauty of the subject. They can hypothesise, be creative, challenge themselves, work with other students and potentially discover things that have never been discovered before.

At our school, we do an investigation with each year group every half term. They may last 20 minutes or five lessons. Here is a selection of the best investigations that the TES Maths community has to offer.

I really hope you and your students find them useful, enjoyable and stimulating.

Craig Barton, TES Maths adviser

• Creativity in maths This useful guide is worth reading before embarking upon any maths investigation. What does it mean to be creative and how can you provide opportunities for creativity in your classroom? It comes complete with five puzzles in a ready-to-print format.
• Maths investigations A collection of over 20 maths problems, puzzles, games and investigations that are designed for KS2, but which could easily be used to extend the learning and problem solving skills of younger KS3 students.
• More maths investigations This resource contains lots of ideas for real-life maths investigations, covering number, algebra, shape, space and measure. Again, while they are aimed at KS2 pupils, they could be adapted for use with KS3 students as well.
• Even more maths investigations! These starter sheets introduce a topic for investigation and come with levelled guidance to help students to self- and peer-assess as they progress through it. Although they are targeted at Year 7, these are suitable for year groups at both KS2 and KS3.
• Investigative lesson presentations A collection of classic maths investigations, including chessboards and tetrahedron towers, presented as PowerPoint presentations with learning objectives and level expectations.
• Challenging ideas for KS4 and Post-16 This was one of my TES Maths Resources of 2014 and it’s easy to see why. These investigations are ideal for gifted and talented GCSE and sixth form students and include everything from code-breaking and Goldbach’s conjecture to the Riemann hypothesis and game theory.
• Diagonals of rectangles This may be one of my own resources, but it is one of my all-time favourites as it’s so versatile. It can be accessed by Year 6 students, while still challenging the most able Year 11s. The concept is so simple, but the potential depth is great.
• Investigating circle theorems Some of the best investigations are topic-specific and this activity is no exception. It uses the free dynamic geometry package, GeoGebra, to help students derive, identify and better understand all of the key circle theorems.
• Prison cells investigation The famous investigation about the numbers on prison cell doors is well-presented, has a really clear structure and some fantastic ideas for differentiation.
• Pentominoes Pentominoes are a superb, versatile teaching resource that can be used for investigating many aspects of shape. This resource takes you through lots of ideas for making the most of them.
• Mathemagic These maths magic tricks are engaging way of presenting a problem to your KS3 pupils, before challenging them to investigate how and why they work. Better still, can they go on to design their own?
• Noughts and crosses investigation Who would have thought you could get so much maths goodness from a game of noughts and crosses?  This game will appeal to secondary students of all ages.

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Area and Perimeter KS2

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Numerically Equal

Can you draw a square in which the perimeter is numerically equal to the area?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Brush Loads

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Torn Shapes

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Twice as Big?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Area and Perimeter

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

Ribbon Squares

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Through the Window

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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Solving Problems (Year 5)

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In KS2 Maths, we learn to solve problems using addition, subtraction, multiplication, and division. Year Five kids tackle bigger numbers and explore measures like distance, weight, capacity, and time.

Real-life problems mean using addition, subtraction, multiplication, or division. Imagine taking a train from Sheffield to London, changing at Peterborough. The first train is 2 hours, the second is 1 hour. But don't forget the time to change trains and when the second train leaves - your journey might be 4 hours or even more!

Test your skills in this quiz. Can you solve problems with addition, subtraction, multiplication, and division?

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Problem Solving

 A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and problem solving in primary mathematics.

Problem Solving in Primary Maths - the Session

Quality Assured Category: Mathematics Publisher: Teachers TV

In this programme shows a group of four upper Key Stage Two children working on a challenging problem; looking at the interior and exterior angles of polygons and how they relate to the number of sides. The problem requires the children to listen to each other and to work together co-operatively. The two boys and two girls are closely observed as they consider how to tackle the problem, make mistakes, get stuck and arrive at the "eureka" moment. They organise the data they collect and are then able to spot patterns and relate them to the original problem to find a formula to work out the exterior angle of any polygon. At the end of the session the children report back to Mark, explaining how they arrived at the solution, an important part of the problem solving process.

In a  second video  two maths experts discuss some of the challenges of teaching problem solving. This includes how and at what stage to introduce problem solving strategies and the appropriate moment to intervene when children find tasks difficult. They also discuss how problem solving in the curriculum also helps to develop life skills.

Cards for Cubes: Problem Solving Activities for Young Children

Quality Assured Category: Mathematics Publisher: Claire Publications

This book provides a series of problem solving activities involving cubes. The tasks start simply and progress to more complicated activities so could be used for different ages within Key Stages One and Two depending on ability. The first task is a challenge to create a camel with 50 cubes that doesn't fall over. Different characters are introduced throughout the book and challenges set to create various animals, monsters and structures using different numbers of cubes. Problems are set to incorporate different areas of mathematical problem solving they are: using maths, number, algebra and measure.

Problem solving with EYFS, Key Stage One and Key Stage Two children

Quality Assured Category: Computing Publisher: Department for Education

These three resources, from the National Strategies, focus on solving problems.

  Logic problems and puzzles  identifies the strategies children may use and the learning approaches teachers can plan to teach problem solving. There are two lessons for each age group.

Finding all possibilities focuses on one particular strategy, finding all possibilities. Other resources that would enhance the problem solving process are listed, these include practical apparatus, the use of ICT and in particular Interactive Teaching Programs .

Finding rules and describing patterns focuses on problems that fall into the category 'patterns and relationships'. There are seven activities across the year groups. Each activity includes objectives, learning outcomes, resources, vocabulary and prior knowledge required. Each lesson is structured with a main teaching activity, drawing together and a plenary, including probing questions.

Primary mathematics classroom resources

Quality Assured Collection Category: Mathematics Publisher: Association of Teachers of Mathematics

This selection of 5 resources is a mixture of problem-solving tasks, open-ended tasks, games and puzzles designed to develop students' understanding and application of mathematics.

Thinking for Ourselves: These activities, from the Association of Teachers of Mathematics (ATM) publication 'Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves. Activity 1: In the bag – More or less requires students to record how many more or less cubes in total...

8 Days a Week: The resource consists of eight questions, one for each day of the week and one extra. The questions explore odd numbers, sequences, prime numbers, fractions, multiplication and division.

Number Picnic: The problems make ideal starter activities

Matchstick Problems: Contains two activities concentrating upon the process of counting and spotting patterns. Uses id eas about the properties of number and the use of knowledge and reasoning to work out the rules.

Colours: Use logic, thinking skills and organisational skills to decide which information is useful and which is irrelevant in order to find the solution.

GAIM Activities: Practical Problems

Quality Assured Category: Mathematics Publisher: Nelson Thornes

Designed for secondary learners, but could also be used to enrich the learning of upper primary children, looking for a challenge. These are open-ended tasks encourage children to apply and develop mathematical knowledge, skills and understanding and to integrate these in order to make decisions and draw conclusions.

Examples include:

*Every Second Counts - Using transport timetables, maps and knowledge of speeds to plan a route leading as far away from school as possible in one hour.

*Beach Guest House - Booking guests into appropriate rooms in a hotel.

*Cemetery Maths - Collecting relevant data from a visit to a local graveyard or a cemetery for testing a hypothesis.

*Design a Table - Involving diagrams, measurements, scale.

Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.

Starting Investigations

The forty student investigations in this book are non-sequential and focus mainly on the mathematical topics of addition, subtraction, number, shape and colour patterns, and money.

The apparatus required for each investigation is given on the student sheets and generally include items such as dice, counters, number cards and rods. The sheets are written using as few words as possible in order to enable students to begin working with the minimum of reading.

NRICH Primary Activities

Explore the NRICH primary tasks which aim to enrich the mathematical experiences of all learners. Lots of whole class open ended investigations and problem solving tasks. These tasks really get children thinking!

Mathematical reasoning: activities for developing thinking skills

Quality Assured Category: Mathematics Publisher: SMILE

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

Real Life Graphs

Four lessons in this section:

Conversion graphs is a complete lesson with a discussion starter and three visual explanations. Includes a differentiated main task and problem-solving questions.

Real life graphs features distance-time graphs and capacity-time graphs. Pair-work and differentiated main task, with literacy story-telling plenary.

Using gradients of line segments to calculate speed from distance-time graphs.

Area under graphs is a complete lesson on area under graphs and gradient, velocity-time graphs and acceleration/deceleration. Clear explanation, Bloom's Taxonomy questions and a differentiated main task.

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Maths Problem Solving Booklets

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

23 August 2022

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Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability.

Designed to be printed as A5 booklets.

Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten. I am a maths problem magpie and collect maths problems wherever I find them. All I have done is bundled these ones up to make it convienent.

If you find a problem that is yours and you don’t want it used please comment and I’ll remove it - cheers.

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• Ks2 Maths Polya Problem Solving

KS2 maths – Polya’s problem-solving

From groans and panic to calm and curiosity – how Claire Coolin made systematic maths lessons less scary…

Are you met with groans when you utter the term ‘problem-solving’ to your class?

We all agree that it’s is an important aspect of the curriculum and indeed a life skill, but yet remains a divisive topic of conversation with pupils, parents and colleagues.

So, what is the problem with problem-solving? 

My Year 5 class were high-achieving. In general, they enjoyed maths but when it came to problem-solving many of them froze.

They showed disinterest, nervousness and confusion, saying things like, “The information is hard to process,” and “I couldn’t understand the information as it was just a block of words”.

Interestingly, pupils found the lessons boring when the problems that they solved followed the same routine and pattern, and didn’t provide a level of challenge, interest or excitement.

These routine problems ‘took the fun’ out of maths for them, and while using skills such as addition, subtraction , and so on are all part and parcel of problem-solving, is this what we are trying to achieve here? 

Routine and non-routine problems

Problem-solving can show an in-depth understanding of mathematical concepts where pupils are required to manipulate numbers in order to get to an answer.

However, while routine problems might be easier for the children to solve, they are not aligned to maths in real life .

We don’t live our adult lives practising budgeting for the weekly supermarket shop from Monday to Thursday, with the real deal happening on Friday. Rather, real-life problems can often be spontaneous, unexpected and at first have no obvious solution.

Should we therefore be teaching pupils what to do with the unexpected? Should we be equipping them with the skills to solve non-routine problems? I think the answer is, yes, most definitely. 

Polya’s problem-solving

So what can be done? Is it enough to tell the children in your class to highlight the important words in the problem ?

While this might have helped a few of my pupils to see a way forward, for many this just became a colouring exercise with an impressive array of fancy highlighters on show.

And so I began an action research project to find answers. After poring over many academic articles, I came across Polya’s problem-solving cycle : a cyclical four-step process that could be used to solve any problem, in maths or otherwise. The steps are:  

• Understanding the problem 
• Devising a plan 
• Carrying out the plan 
• Looking back and reflecting 

Polya’s process was something I wanted to introduce to my class, and so I taught this way of thinking about a problem over a term. The results were surprising and long-lasting, with four key takeaway points. 

I found that the cycle: 

Developed time management skills and enhanced focus 

Polya’s cycle automatically forced students to work through each phase in turn, slowing them down and therefore helping them explore the problem with a more thoughtful and connected approach.

Instead of jumping straight into the doing, the children took time to think about their understanding of what was being asked, and would often get out a dictionary to look up a word they didn’t know the meaning of, or on one occasion, a child even dusted off the ‘never-really-used-before-but-every-class-has-one’ maths dictionary to look up the meaning of a mathematical term.  

Equipped all students with a strategy for tackling any maths problem 

When talking to a group of pupils in my class about problem-solving, I recall them saying, “I can’t work out if I should multiply or add or subtract or whatever.”

This is true for many students and can lead to them freezing, or in some cases, frantically adding and subtracting numbers – essentially jumping straight into phase three.

They needed a strategy. Using the problem-solving steps gave my class a framework, allowing them to think in a logical way.

Straight away, students unfroze, the manic scribbling stopped, and they started from a phase one and worked through the problem more systematically.  

Allowed pupils to see the link between maths and the real world  

When I asked my class why they thought we were learning about problem-solving, I was met with answers about becoming better at maths.

But after using Polya’s steps, the children began to see how the skills in solving maths problems are the same ones used in solving real-world problems.

For example, they realised that if a maths problem can be divided into chunks, then so could any problem.

One sunny afternoon, a couple of students came to me to help solve their playground argument. You can imagine my utter surprise when one of the students said, “I think first we need to understand why we have fallen out then we can come up with a plan to put it right.” Real life problem-solving in action! 

Equipped students with the necessary tools to engage with challenge 

Having challenge in any subject is important, but having the right level of challenge is even more so.

Routine problems can remove that challenge for many, and one of my pupils commented that, “You shouldn’t do lots of the same as it gets too easy. You don’t want to spoil it by knowing all the answers.”

Using Polya’s problem-solving steps with non-routine problems gives the more able pupils enhanced scope and freedom to try out and manipulate numbers in different ways, while giving that scaffolding to support the less able in the class. 

So, what now?

What have I learned from this experience? Well, with more than 10 years teaching under my belt, this action research brought me back to my roots.

I started from scratch with something and didn’t rely on my tried-and-tested resources. I had a chance to listen to my pupils and in doing so stumbled onto a way of thinking that works not just for a maths problem, but for all problems.

The steps have since become a classroom philosophy, and I use the vocabulary of the process daily. Trying something new can pay off!  

How to introduce Polya’s process 

• Talk about the cycle and what each phase means. Take note that it’s like a roundabout, which means you can get off at any stop and go back if necessary.  E.g. If you’re carrying out your plan (phase three) but it’s not working, you can go back to phase one: understanding the problem.  
• Use subheadings. I wanted the students to really spend time thinking about each phase, so I made a very simple Performa with each phase sub-headed. The students were required to write within each subheading. 
• Model how to do it. Using different non-routine problems, I modelled how I would use the problem-solving phases. I then built up to working on problems as a class, and finally asked pupils to work in pairs to solve problems using the steps.  
• Make it part of your classroom vocabulary. To embed the process in my class, the language didn’t just come out when doing maths problems, but was used in other subjects and day-to-day school life.   

Claire Coolin conducted this research project while teaching Year 5 at Oxford High Prep School, GDST with the Global Action Research Collaborative, ICGS. From September 2022 she will be a maths specialist teacher and PSHE head of department at Summer Fields School, Oxford.

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