Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

FREE daily maths challenges

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

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.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

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

Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Related articles

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

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

Free Year 7 Maths Test With Answers And Mark Scheme: Mixed Topic Questions

Free Year 7 Maths Test With Answers And Mark Scheme: Mixed Topic Questions

What Is A Number Square? Explained For Primary School Teachers, Parents & Pupils

What Is A Number Square? Explained For Primary School Teachers, Parents & Pupils

What Is Numicon? Explained For Primary School Teachers, Parents And Pupils

What Is Numicon? Explained For Primary School Teachers, Parents And Pupils

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

Your browser's Javascript functionality is turned off. Please turn it on so that you can experience the full capabilities of this site.

TTS School Resources Online Shop

  • FREE Catalogue
  • Customer Services
  • Contact Your Local Supplier

ks2 reasoning and problem solving white rose

White Rose Maths Reasoning & Problem Solving Kit

Product code: 708-ma10155, product actions.

  • Send to a Friend

Why you'll love this product

Collaborative Design

White Rose Maths partnered in the development of this kit, enhancing the teaching of reasoning and problem solving across multiple key stages.

Versatile Teaching Tool

This kit is designed to enhance reasoning and problem-solving skills across Key Stage 1 and Key Stage 2, making it a practical addition to enhance mathematical learning.

Comprehensive Resource Set

Ensures comprehensive support for children's mathematical development through a variety of resources including Dip n Pick and Graded Problem Solving Cards.

Practical Storage Solution

The kit includes a Gratnell Storage Tray with a lid, ensuring that all resources stay organised and secure, aiding quick setup and safe storage.

Key Stage 1 and 2 Focus

Specifically supports 'Number - addition and subtraction' in Key Stages 1 and 2, helping children solve multi-step problems effectively.

White Rose Maths Reasoning & Problem Solving Kit

Enhance reasoning and problem-solving skills with collaborative resources from White Rose Maths.

This kit enriches the mathematical experience for children across Key Stages 1 and 2, by offering targeted support in critical areas such as number processing, geometrical reasoning, and algebraic operations.

Each resource within the kit, including Problem Solving Cards and Bar Model Teacher Version, is meticulously selected to promote an in-depth understanding and application of mathematical concepts. These resources assist children in working through complex, multi-step problems using strategic, thought-provoking approaches.

Integrating these resources into daily maths lessons can significantly enhance children's analytical and reasoning capabilities, thereby supporting structured learning and assessment alignment with educational standards across various key stages.

Read more about our fantastic White Rose Maths Kits here.

Supports the National Curriculum

Mathematics, Key Stage 2, Number - Addition & Subtraction

Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Mathematics, Lower Key Stage 2, Number - Number & Place Value

Identify, represent and estimate numbers using different representations.

Mathematics, Year 3, Number - Addition & Subtraction

Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

Technical Summary

Product includes

1 x Dip n Pick Problem Solving Cards Group Set,1 x Graded Problem Solving Cards Group Set,1 x Making Maths Connections Activity Cards Group Set,1 x Bar Model Teacher Version,1 x Tray Lid,1 x Gratnell Storage Tray

Your TTS photos

ks2 reasoning and problem solving white rose

This website uses cookies

This website uses cookies to improve user experience. The cookies relate to performance, analytics, personalisation and advertising. You can choose to Accept or change your browser preferences

Cookie Consent

We use cookies to help provide a better website experience for you, and help us to understand how people use our website. Our partners will also collect data and use cookies for ad personalisation and measurement.

Clicking "Accept" will allow us and our partners to use cookies, learn more in our cookie policy or to change your cookie preferences, click "Manage".

To find out more about cookies and the types of cookies we are setting please visit our cookie policy .

If you'd prefer that certain types of cookie are not saved on your browser when visiting our website, use the toggles below to adjust those preferences and click "Save choices".

Strictly Necessary

These cookies are necessary for the website to function and without them you would not be able to reliably use the website. For example, logging into your account or completing forms.

Analytics Cookies

A series of cookies that collect anonymised data on how users interact with our website. This anonymous data helps us improve the website with a focus on its users, for example, ensuring the most popular content is easier to access.

View associated providers +

Marketing Cookies

These cookies track your online activity to help advertisers deliver more relevant and personalised advertising or to limit how many times you see an ad. These cookies can share that information with other organisations or advertisers.

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

White Rose Maths - KS2 - Problems of the Day 2018

White Rose Maths - KS2 - Problems of the Day 2018

Subject: Mathematics

Age range: 7-11

Resource type: Other

White Rose Education's Shop

Last updated

10 March 2023

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

ks2 reasoning and problem solving white rose

It’s back! White Rose Maths Problem of the Day.

Along with the usual PDFs we have added a powerpoint that will be updated each day. The calendar is hyperlinked to take you straight to the new problems and answers are provided. Full worked solutions will be provided at the end of the month.

For the month of March, each day we will publish some reasoning and problem solving questions for use with your classes. Practice is crucial to maths success, and our questions are designed to support your daily routines. A new question will be posted each evening for the next day, and cover topics and areas that your pupils can expect to see as part of their SATs. If you tweet a picture of your classes hard at work solving a problem to @WRMaths, you will be entered into our special weekly prize draw during March 2018! Please ensure that any photos you tweet have relevant permissions, as we will be retweeting a selection of these.

Thank you for your continued support.

Enjoy - The White Rose Maths Team

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.

adnan_katesh

Empty reply does not make any sense for the end user

Great stuff. Would be even better if all the days were in one single PDF as well as separate, but we can't have everything!<br /> <br />

abiye_manuel

Precisely what I needed. 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:

IMAGES

  1. White Rose Maths

    ks2 reasoning and problem solving white rose

  2. Year 3 place value White Rose Problem solving strips

    ks2 reasoning and problem solving white rose

  3. White Rose Maths

    ks2 reasoning and problem solving white rose

  4. Year 2

    ks2 reasoning and problem solving white rose

  5. White Rose Maths

    ks2 reasoning and problem solving white rose

  6. KS2 Reasoning and Problem Solving Questions White Rose Maths Hub

    ks2 reasoning and problem solving white rose

VIDEO

  1. PROBLEM SOLVING AND REASONING

COMMENTS

  1. Maths problem of the Day

    Practice is crucial to maths success, and our questions are designed to support your daily routines. These problems can be used across Y1 and Y2 throughout the year. Download. Our maths problems of the day provide four problems across KS1, KS2 and Lower KS3 for pupils to solve. View our Maths resources from White Rose Maths.

  2. PDF KS2 Reasoning & Problem Solving Questions

    KS2 Reasoning and Problem Solving Questions ... .org course of As always we welcome any feedback on the work we are Information This booklet contains over 40 reasoning and problem solving questions suitable for KS2 and KS3 classes. These are the questions that we have been putting out ... The White Rose Maths Hub Team . KS2

  3. White Rose Maths: Free Resources For Years 1-6

    A new KS2 maths challenge every day. Perfect as lesson starters - no prep required! ... consolidation and problem solving; Year 6 White Rose scheme of learning Find out more. White Rose Maths Year 6, ... reasoning and problem solving questions to ensure that all pupils are exposed to all elements of the national curriculum.

  4. PDF KS2 Reasoning & Problem Solving Questions

    Here are 3 identical rectangles. Part of each shape has been shaded. 1 4 3 5 What fraction of the middle shape is shaded? 7 10 11 Here are 3 identical rectangles.

  5. PDF KS 2 Reasoning & Problem Solving Questions 2017

    This booklet contains over 40 reasoning and problem solving questions suitable for KS2 classes. These are the questions that we have been putting out each day in March 2017 on Twitter in the run up to SATS. The answers are provided with some simple notes at the questions and variation has been provided.

  6. WRM

    Age range: 7-11. Resource type: Worksheet/Activity. File previews. pdf, 744.4 KB. pdf, 551.38 KB. pdf, 733.58 KB. pdf, 539.77 KB. For the month of March, each day we publish some reasoning and problem solving questions for use with your classes. Practice is crucial to maths success, and our questions are designed to support your daily routines.

  7. KS2

    KS2 - WRMH Problems of the Day Compilation - 2017. This booklet contains over 40 reasoning and problem solving questions suitable for KS2 classes. These are the questions that we have been putting out each day in March 2017 on Twitter in the run up to SATS. The answers are provided with some simple notes at the back of the booklet and for some ...

  8. White Rose Maths Year 6: What Students Learn & Free Resources

    About White Rose Maths . The White Rose Maths scheme of learning follows the national curriculum with a mastery approach to maths with a range of fluency, reasoning and problem solving elements. They also encourage concrete, pictorial and abstract representations to develop deep understanding of mathematical concepts. Read more: White Rose Maths

  9. Year 2

    This problem solving pack contains resources that challenge children's reasoning, investigative and problem solving skills. They include problems involving number, money, shape, position and direction, statistics and fractions. All resources have answers provided. The pack contains: Children can use concrete resources to help investigate and ...

  10. Maths resources for teachers

    Happy teachers. We use the White Rose Education schemes and lesson-by-lesson overviews throughout the school, and the printed workbooks add yet another top quality layer of time- and stress-saving benefits on top of those! We no longer spend precious time printing and sorting worksheets: the new booklets fit perfectly with the video content and ...

  11. PDF Year 5 Mathematics 2022 Spring White Rose Reasoning Problem Solving Paper 2

    Paper 2: reasoning and problem solving First name Middle name Last name Date of birth Day Month Year Teacher This progress check has been designed by White Rose Maths. For more information, please visit whiterosemaths.com Spring progress check Year 5 9 781804 780237 ISBN 978-1-80478-023-7

  12. Maths Problem Solving KS2: Strategies & Resources

    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.

  13. Fast Finishers: White Rose Maths Problem-solving: Ages 9-10

    Product description. Help students to achieve mastery a variety of maths topics with this box of maths problem-solving cards designed for fast finishers. Matches to the White Rose Maths new scheme of work for 2022. Contains 13 problem solving cards per half term (78 in total) and 2 content cards. Two problems per card covering a variety of ...

  14. Workbook answers

    Spring Workbook Answers. Spring Block 1. Spring Block 2. Spring Block 3. Spring Block 4. Spring Block 5. Spring Block 6. Answers. Block 1 - Year 1.

  15. We have collated all our reasoning and problem solving ...

    We have collated all our reasoning and problem solving questions from our free schemes of learning into a handy editable PowerPoint! We hope this is...

  16. White Rose Maths Reasoning & Problem Solving Kit

    The Reasoning and Problem Solving Kit has been developed in collaboration with White Rose Maths, and supports their programme. The Kit is suitable to teach and strengthen reasoning and problem solving skills in KS1 and KS2. This kit is a whole-school solution, with resources for each year.

  17. PDF Autumn progress check Year 4

    Paper 2: reasoning and problem solving First name Middle name Last name Date of birth Day Month Year Teacher This progress check has been designed by White Rose Maths. For more information, please visit whiterosemaths.com Autumn progress check Year 4 9 781804 780169 ISBN 978-1-80478-016-9

  18. Reasoning and Problem Solving Questions Collection

    pptx, 2.35 MB. pdf, 3.51 MB. These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS. The answers are provided with some simple notes at the back of the booklet and for some ...

  19. KS2 Reasoning and Problem Solving Questions White Rose Maths ...

    KS2 Reasoning and Problem Solving Questions White Rose Maths Hub Twitter March 2016 - Free download as PDF File (.pdf), Text File (.txt) or view presentation slides online. Maths

  20. Professional development

    View our Maths resources from White Rose Education. Cookie Consent. We use cookies to help provide a better website experience for you, and help us to understand how people use our website. Our partners will also collect data and use cookies for ad personalisation and measurement.

  21. White Rose Maths

    pptx, 9.98 MB. pdf, 5.59 MB. It's back! White Rose Maths Problem of the Day. Along with the usual PDFs we have added a powerpoint that will be updated each day. The calendar is hyperlinked to take you straight to the new problems and answers are provided. Full worked solutions will be provided at the end of the month.