Year Two Maths Problem Solving Activities Linked to NRICH

Early Years Resources

There are 22 maths problems which cover all of the maths objectives in the Year 2 curriculum for children to do independently. These are linked to the NRICH website .

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Early Years Staffroom

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

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For younger learners

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The Problem-Solving Schools' Charter

The NRICH team has developed this Charter to help you reflect on how you currently promote mathematical problem-solving in your school

Values and ethos

We have a shared belief that:

  • Mathematical ability is not fixed: everyone can learn and make progress
  • Problem-solving often involves taking wrong turns and making mistakes: every learner has the right to struggle and the right to enjoy success
  • Everyone should have the opportunity to develop the skills and attitudes necessary to become confident problem-solvers
  • Problem-solving can motivate learners to learn new mathematics, apply previous learning and make mathematical connections

Leadership and professional development

In our setting:

  • Our staff promote positive attitudes towards problem-solving
  • Time is set aside to discuss problem-solving in our meetings
  • Our displays, newsletters, website, and social media content celebrate problem-solving for all
  • Our monitoring system ensures that priority is given to problem-solving and mathematical thinking
  • We engage with printed, online and face-to-face professional development opportunities offered by subject organisations

Curriculum, pedagogy and assessment

We are committed to:

  • Regularly embedding non-standard problem-solving opportunities in our maths curriculum for all
  • Ensuring that problems, and classroom support, offer opportunities for all to experience both struggle and success
  • Allocating time to developing key problem-solving skills and positive attitudes
  • Including non-standard problems in our internal/formative assessments
  • Liaising with other subjects so that meaningful cross-curricular links can be made

Classroom culture

  • Create a safe environment in which learners explore, take risks, and appreciate the value of learning from their mistakes
  • Celebrate multiple approaches to solving problems and discuss the merits of the different strategies offered
  • Provide frequent opportunities for individual and collaborative problem-solving, where learners are given both thinking time, and opportunities to share ideas and insights
  • Celebrate the mathematical thinking of every learner

Problem-solving beyond the classroom/school

We encourage:

  • Learners to engage with school Maths Club(s) and high quality maths books, ideally stocked by the school library
  • Learners to take advantage of printed, online and off-site mathematical enrichment opportunities
  • Parents and carers to engage with problem-solving through family homeworks and in-school events, while recognising that not every adult has had a positive experience of maths
  • Our learners to appreciate, and learn more about, the achievements of a diverse range of mathematicians

Become a Problem-Solving School

South Australia

Department for education.

Home

Nrich - a website with maths activities and games

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Resources to develop mathematical reasoning and problem solving. Nrich aims to enrich the mathematical experiences of all learners and embeds rich mathematical tasks into everyday classroom practice.

Structure and features

Activities and games can be explored independently or together with families.

The website covers topic such as:

  • measurement
  • problem solving

The 'Thinking Mathematically' sections provide additional educational activities.

Links and files

Teacher notes.

The resources are grouped into levels. Level 1 aligns with early years, while level 4 aligns with lower secondary. Teachers can use the search functionality to find tasks that match the topic that they are teaching.

The tasks are not mapped to the Australian Curriculum but align well with the mathematical concepts.

Page last updated: 12 Oct 2022

learningathome [at] sa.gov.au

Careative commons attribution

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Cambridge University Faculty of Mathematics

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  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
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  • Coordinates, Functions and Graphs

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  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

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  • Handling, Processing and Representing Data
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Working mathematically

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For younger learners

  • Early Years Foundation Stage

Advanced mathematics

  • Decision Mathematics and Combinatorics
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Published 2008 Revised 2019

Getting Started with Solving Rich Tasks

Don't panic and it is ok to be stuck.

  • Factors and multiples game
  • Consecutive sums
  • Peaches today, peaches tomorrow
  • Isosceles triangles
  • Fibonacci factors
  • Data matching

Cambridge University Faculty of Mathematics

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Mathematical mindsets
  • Cross-curricular contexts
  • Physical and digital manipulatives

For younger learners

  • Early Years Foundation Stage

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics

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nrich problem solving year 2

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nrich problem solving year 2

Sign up to NRICH’s Problem-solving Schools programme

nrich problem solving year 2

NRICH, a trusted provider of free problem-solving resources and teacher support, is launching the Problem-solving Schools programme.

Register for free to enhance problem-solving provision across your school and sign up to the Problem-solving Schools Charter.

Why is problem-solving so important?

With the rise of AI, problem-solving skills are more important than ever for students.

To thrive both inside and outside of the classroom, they need to develop resilience, be able to work collaboratively, and think creatively and flexibly. And, perhaps most importantly, they will need to be able to solve problems.

Problem solving opens up a world of possibilities. Students have to apply their knowledge, think laterally, and use their creativity to solve challenges.

Not only does problem solving serve a longer-term purpose of empowering students for the future, it is also a crucial part of helping them to discover the joy of mathematics.

Imagine only engaging with football through practice drills and never seeing Messi score, or learning music through scales and never hearing an orchestra play…

Problem solving is the light bulb moment for students when it comes to maths. They start to see the value in what they are doing.

Once they really understand its value, that’s when they become engaged and motivated to learn!

Highlighted by Ofsted

A new Ofsted report, published in July 2023, said that the teaching of mathematical problem solving remains an area “of weakness across many schools”, and emphasised the importance of teaching skills that “equip [pupils] for the next stage of education, work and life”.

As well as asking schools to teach specific problem-solving strategies, they want students to have plenty of opportunities to put these strategies into practice and choose the best one for each situation.

What is NRICH doing to support schools?

NRICH’s core mission is to develop confident, resilient problem-solvers who value and enjoy working mathematically. With that mission in mind, we are launching the Problem-solving Schools programme.

The aim of this new initiative is to help embed problem-solving in classrooms by providing:

  • Targeted problem-solving resources
  • Dedicated teacher CPD on how best to use them
  • Advice on engaging parents so they can support their children at home
  • A dedicated schools Charter to sign up for, demonstrating your school’s commitment to put problem solving at the heart of maths learning.

The programme is open to all schools with resources and CPD available for key stages 2–4.

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Cambridge logo

NRICH launches new Problem-Solving Schools initiative

Our NRICH programme has launched a new initiative to help schools prioritise problem-solving in maths. The NRICH Problem-Solving Schools programme will offer free resources, advice and teacher professional development training. 

Problem-solving is a critical skill when it comes to empowering students for the future. It opens up a world of possibilities as students have to apply their knowledge, think laterally and use their creativity to solve challenges. Problem-solving is also a crucial part of helping students to discover the joy of mathematics. "Imagine only engaging with football through practice drills and never seeing Messi score, or learning music through scales and never hearing an orchestra play," say the NRICH team.

For over 25 years NRICH has been at the forefront of developing mathematical problem-solving resources, reaching millions of users each year through the free NRICH website. The Problem-Solving Schools programme builds on this expertise and experience in supporting schools, teachers and students to help schools embed problem-solving in the curriculum.

Along with fluency and reasoning, problem-solving is central to the National Curriculum for maths, and the launch of NRICH's Problem-Solving Schools programme offers timely additional support for schools. A new report published by Ofsted in July 2023 encourages schools to focus more consistently on teaching problem-solving, and ensure that all students have opportunities to practise applying their knowledge in a range of problem-solving contexts.

To find out more about the programme, and how to register your school, see the NRICH Problem-Solving Schools information.

You can read more about the Problem-Solving Schools initiative in this University of Cambridge news story .

© 2023 University of Cambridge Privacy notice

The Joint Mathematical Council of the United Kingdom

Addressing the five ‘big questions’ in problem-solving with NRICH

nrich problem solving year 2

The importance of ensuring learners acquire the problem-solving skills which will enable them to thrive both socially and economically in their increasingly automated world is widely recognised (Luckin et al., 2017). Nevertheless, government inspectors have reported serious concerns about the quality and quantity of problem-solving in our schools (Ofsted, 2015). This summer schools were challenged to reflect on ‘Five big questions for problem-solving’ (EEF, 2021). In this blog, we will consider each of those five questions and explore the ways that the NRICH team is supporting schools to address them.

Question one: Do teachers in your school select genuine problem-solving tasks for which pupils do not already have a ready-made method available?

Too often, learners are presented with routine word problems which merely require the application of a known algorithm. ‘Genuine’ problems enable them to make their own problem-solving decisions by choosing their own strategies and enabling them to compare their approach with those of other learners, thus developing their problem-solving efficiency and flexibility. At NRICH , our award-winning activities allow learners to develop these key skills alongside the confidence to tackle genuine problems. Moreover, our ‘ low threshold, high ceiling ‘ approach enables everyone to get started on the problem while ensuring a suitable level of challenge too, making them ideal for whole-class teaching.

Question two: Are pupils given the opportunity to see – through multiple worked examples – to use, and to compare different approaches to solving a problem?

Many problems can be explored in more than one way. Working flexibly, making connections between different areas of the curriculum and reflecting on various problem-solving approaches are key steps towards becoming a more fluent mathematician. NRICH encourages learners to develop these skills in these two ways:

Our primary , secondary and post-16 Live Problems invite learners to explore and submit their ideas to the team. We review each submission that we receive and publish a selection on our website showcasing different approaches and the reasoning behind them.

Our NRIC H online activities sometimes feature ‘hide and reveal’ buttons showcasing different starting points towards a solution for learners to explore further for themselves. This approach enables learners to widen their range of strategies for solving unfamiliar problems and develop alternative approaches to explore when they get stuck using their first-choice strategy.

Question three: Are pupils encouraged to use visual representations to support them to solve a problem?

One of the most important approaches towards solving an unfamiliar problem is drawing a good diagram. Learning to draw diagrams is a skill which we encourage learners of all ages to develop alongside their other mathematical skills and knowledge. From sketching graphs to drawing a bar model, good diagrams can help learners clarify their understanding and identify possible ways forward.

Our four steps towards problem-solving feature highlights the importance of drawing a diagram to enable young learners to get started on a problem. We often highlight a useful diagram, table or sketch graph in the solutions chosen for publication. As learners progress through their learning, the team model more specific drawing skills, such as sketching a graph to help solve a STEP problem.

Question four: Are pupils supported to monitor, reflect on, and communicate their reasoning and choice of strategies, possibly through the use of prompt questions?

NRICH  encourages learners to reflect on their learning using this approach inspired by the Strands of Mathematical Proficiency model introduced by Kilpatrick et al. (2001).

nrich problem solving year 2

Our approach uses child-friendly language that teachers and parents can share with students five key ingredients that characterise successful mathematicians. At NRICH , we believe that learning mathematics is about much more than just learning topics and routines. Successful mathematicians understand the curriculum content and are fluent in mathematical skills and procedures, but they can also solve problems, explain their thinking and have a positive attitude about themselves as learners of mathematics.

With this in mind, we have created  this self assessment tool  to help learners recognise where their mathematical strengths and weaknesses lie. We hope learners will explore NRICH activities and then take time to reflect on their own mathematical capabilities using our model.

Question 5: Is professional development time allocated to develop teachers’ pedagogical understanding of problem-solving, with particular support for early career teachers?

NRICH supports teachers to maximise the potential of our activities by offering free, regular professional development for teachers .  Each session is delivered online, enabling teachers to access the support wherever they are based, reducing teacher travel and cover costs for schools. We also record the sessions and upload them to our website so that schools can access them for future professional development days or staff/department meetings in their settings.

The live sessions are led by NRICH team members and they link directly to our latest primary , secondary and post-16 Live Problems. This approach enables teachers to consider the possibilities of the activities with the NRICH team before exploring them the next day with their own classes. Later, they are invited to share their classwork with our team for possible publication on the NRICH website.

The five ‘big questions’ provide excellent starting points for evaluating the teaching and learning of problem-solving in different settings. I hope that this blog shares an insight into the different ways that NRICH can support schools to address the five questions for themselves by engaging with our activities, Live Problems and teacher webinars.

Dr Ems Lord FCCT

Director of NRICH

Centre for Mathematical Sciences

University of Cambridge

Selected references

EEF. (2021). EEF Blog: Integrating evidence into maths teaching – guiding problem-solving. Accessed from https://educationendowmentfoundation.org.uk/news/eef-blog-integrating-evidence-into-mathematics-guiding-problem-solving /

Kilpatrick, J. Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (Vol. 2101). J. Kilpatrick, & National research council (Eds.). Washington, DC: National Academy Press.

Luckin, R., Baines, E., Cukurova, M., Holmes, W., & Mann, M. (2017). Solved! Making the case for collaborative problem-solving. Accessed from http://oro.open.ac.uk/50105/1/solved-making-case-collaborative-problem-solving.pdf

Ofsted. (2015). Better Maths Conference Spring Keynote 2015. Accessed here https://www.slideshare.net/Ofstednews/better-mathematics-keynote-spring-2015

IMAGES

  1. Year Two Maths Problem Solving Activities Linked to NRICH

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  2. Nrich Place Value Problem Solving Ks2

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  3. year 2 problem solving nrich

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  4. Nrich Addition And Subtraction Problems Ks2

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  5. Nrich Place Value Problem Solving Ks2

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  6. problem solving nrich

    nrich problem solving year 2

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COMMENTS

  1. NRICH topics: NC NC Yr 2

    There are 28 NRICH Mathematical resources connected to NC Yr 2, you may find related items under NC. Broad Topics > NC > NC Yr 2 Problem Primary curriculum How Many? Have a look at these photos of different fruit. How many do you see? How did you count? Age 5 to 11 Challenge Level Problem Primary curriculum Digit Addition Try out this number trick.

  2. Problem Solving

    Using NRICH Tasks to Develop Key Problem-solving Skills Age 5 to 11 This article, written for primary teachers, discusses what we mean by 'problem-solving skills' and draws attention to NRICH tasks which can help develop specific skills. Trial and Improvement at KS1 Age 5 to 7

  3. NRICH

    The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

  4. What's the Problem with Problem Solving?

    What's the Problem with Problem Solving? The focus of this feature is to show that every lesson can be a problem solving lesson. In planning for problem solving there are several areas to consider: 1. The type of problem you want to focus on 2. The problem-solving strategy or skill you wish the children to develop 3.

  5. Your Solutions

    The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

  6. Year Two Maths Problem Solving Activities Linked to NRICH

    Year Two Maths Problem Solving Activities Linked to NRICH There are 22 maths problems which cover all of the maths objectives in the Year 2 curriculum for children to do independently. These are linked to the NRICH website.

  7. Primary Interactive Resources

    These general interactive resources can be used in a variety of contexts in the primary classroom to support learners working on mathematics. Dice & Spinners Interactive. Geoboards. Red or Black Spinner. Dominoes Environment. Interactive Balance. Cuisenaire Environment. Tangram Browser. Tessellation Interactivity.

  8. Millennium Mathematics Project

    In the 2021/22 school year our web-based mathematical resources attracted over 9.5 million visits from users worldwide and around 30 million page views, while over 13,000 school students and more than 2,900 teachers were involved in our face-to-face activities and online webinars and events. ... NRICH resources focus on problem-solving and take ...

  9. The Problem-Solving Schools' Charter

    Curriculum, pedagogy and assessment. We are committed to: Regularly embedding non-standard problem-solving opportunities in our maths curriculum for all. Ensuring that problems, and classroom support, offer opportunities for all to experience both struggle and success. Allocating time to developing key problem-solving skills and positive attitudes.

  10. Developing Mathematical Thinking

    Working Backwards at KS2 The upper primary tasks in this collection could each be solved by working backwards. Age 5 to 7 Visualising at KS1 These lower primary tasks all specifically draw on the use of visualising. Age 7 to 11 Visualising at KS2 These upper primary tasks all specifically draw on the use of visualising. Age 5 to 7

  11. About NRICH

    NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education - completely free and available to all. We aim to: Enrich and enhance the experience of the mathematics curriculum for all learners. Develop mathematical thinking and problem-solving skills.

  12. Nrich

    Resources to develop mathematical reasoning and problem solving. Nrich aims to enrich the mathematical experiences of all learners and embeds rich mathematical tasks into everyday classroom practice. ... Level 1 aligns with early years, while level 4 aligns with lower secondary. Teachers can use the search functionality to find tasks that match ...

  13. Getting Started with Solving Rich Tasks

    In fact, you might be wondering what, exactly, is a rich task, and how are the NRICH problems different from, say, standard textbook questions (as, indeed, they are). To answer this question, let us first look at a piece of school maths: quadratic equations. A standard question might be written as $$ \mbox{Solve } x^2 -4x +3 = 0 $$

  14. Games and Interactives

    The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.

  15. Part 1: Problem solving with NRICH

    Learners - 16-18 years Learners - 19+ years All Learner Resources Get Support. HE Contact for Students ... This first blog provides an introduction to problem solving with NRICH, and explores how important it is to choose appropriate tasks. The second will explore how you can structure the problem-solving process, and embed problem solving into ...

  16. Addition and Subtraction KS1

    Two Dice Age 5 to 7 Challenge Level Find all the numbers that can be made by adding the dots on two dice. Unit Differences Age 5 to 7 Challenge Level This challenge is about finding the difference between numbers which have the same tens digit. Cuisenaire Counting Age 5 to 7 Challenge Level Here are some rods that are different colours.

  17. Sign up to NRICH's Problem-solving Schools programme

    30 Second Briefing NRICH, a trusted provider of free problem-solving resources and teacher support, is launching the Problem-solving Schools programme. Register for free to enhance problem-solving provision across your school and sign up to the Problem-solving Schools Charter. Why is problem-solving so important?

  18. Part 2: Problem solving with NRICH

    April 6, 2016 Read the second of two guest posts from Liz Woodham, Primary Coordinator at NRICH, with more advice on how their mathematical tasks can be used in the classroom. In Abacus, we currently link out to a number of NRICH's enriching mathematical tasks.

  19. Working Systematically at KS2

    Working Systematically at KS2 Working Systematically at KS2 Scroll down to see our complete collection of KS2 problems that require children to work systematically, or explore the two sub-collections focusing on important aspects of systematic working. This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

  20. Maths at Home

    NRICH welcomes millions of users every year to share our free, online mathematical activities for learners aged 3-19. We have a huge bank of award-winning resources, ideal for children and students to work on independently while schools are closed, and for teachers to use when teaching remotely. We have created some collections of our best ...

  21. NRICH launches new Problem-Solving Schools initiative

    30 Nov 2023 Our NRICH programme has launched a new initiative to help schools prioritise problem-solving in maths. The NRICH Problem-Solving Schools programme will offer free resources, advice and teacher professional development training. Problem-solving is a critical skill when it comes to empowering students for the future.

  22. Addressing the five 'big questions' in problem-solving with NRICH

    This summer schools were challenged to reflect on 'Five big questions for problem-solving' (EEF, 2021). In this blog, we will consider each of those five questions and explore the ways that the NRICH team is supporting schools to address them.

  23. Addition and Subtraction

    Addition and Subtraction These activities are part of our Primary collections, which are problems grouped by topic. Addition and Subtraction Age 5 to 7 These lower primary tasks all involve addition, subtraction or both. Addition and Subtraction Age 7 to 11 Have a go at these upper primary activities which all involve addition, subtraction or both.