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About NRICH
NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion. 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
- Offer challenging, inspiring and engaging activities
- Show rich mathematics in meaningful contexts
- Work in partnership with teachers, schools and other educational settings to share expertise
Developing confident, resilient problem-solvers
Supporting teachers, putting research into practice.
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
Interactive Tasks and Games
Interactive tasks and games.
Not a Member?
Read more about the Member Benefits of MAV and find out how to join MAV or renew your membership.
- Authentic tasks
- F - 10 Resources
Authentic tasks are designed to help students see mathematics as worthwhile and important. When students understand the purpose of a given problem in mathematics, they are more likely to persist when challenged. Authentic tasks generally have an ‘open middle’ which means that students can use different representations and solutions to communicate their knowledge and reasoning.
These curated links provide MAV members with access to nine authentic tasks from some of our primary consultants’ favourite resources. The 11 criteria provide MAV members with a research-informed context to consider each task’s potential impact on student thinking, ways of working, attitudes towards mathematics, their knowledge and understanding.
The following criteria was used to select the tasks based on their potential:
| Criteria | Elaboration |
|---|---|
| Intriguing contexts capture the students’ interests and curiosities | An opportunity for students to relate learning to their own lives and communities. High student motivation/enjoyment and sense of purpose can be anticipated or observed. |
| Problem solving is required to overcome obstacles | Exploring non-routine questions, real life challenges, posing problems and designing investigations. There are obstacles that students have to overcome in order to succeed. |
| Low entry/ high ceiling, and an open-middle encourages different strategies | Caters for a range of student abilities. Open-middle allows for different possibilities, strategies, materials and products to emerge. Task may adapt depending on student progress. |
| Opportunities for creative thinking and or visualising | Students invent, discover and imagine new ways to solve a problem. Students make connections and see relationships by visualising the problem or representing solutions visually. |
| Encourages reasoning and critical thinking | Logical, rational and critical thinking. eg: estimating, hypothesising, justifying, generalising, comparing, explaining, interpreting and looking back. |
| Opportunity to collaborate and see others working mathematically | Students challenge each other, the computer, the teacher etc and observe how they work mathematically. Make decisions in groups to communicate findings, engage with different ideas, monitor and regulate each other's thinking. |
| Opportunities for students to develop fluency | Estimating, collecting and interpreting data, using mathematical language, continuing patterns, choosing appropriate unit of measurement, recalling factual knowledge and concepts readily. |
| Promotes feedback and metacognition. | Self and peer reflection targeted at specific aspects of the work. eg: knowledge; how your thinking is changed as a result of lesson. Affective traits eg: problem solving attitude, collaborative skills. |
| Extends knowledge or applies knowledge in new contexts | Provides students with access to forms of knowledge beyond what they can pick up in everyday life or via the Internet. |
| Promotes an understanding of the ‘why’ and ‘how’ of mathematics | Seeing patterns, connecting related ideas based on previously constructed knowledge. Represent concepts (big Ideas) in different ways eg: developing number sense, place value. |
| Guides future learning | Provides data on student growth to guide future direction. eg: identifies patterns or errors, level of progress towards goal. Makes suggestions for future learning. |
Used with permission © Martin Holt Educational Consultant 2017
If you would like to learn more about this approach to assessing or using tasks contact [email protected]
Statistics and probability
| NRICH problem solving task: | Scootle lesson sequence: |
| Target Level: F - 2 | Target Level: 1 - 6 |
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Measurement and geometry
| Wildmaths interactive game: | Teach Engineering investigation: |
| Target Level: 2-4 | Target Level: F-2 |
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Number and algebra
| NZMaths lesson sequence: | MAV problem solving task: | ReSolve Maths by Inquiry lesson sequence: |
| Target Level: 5-6 | Target Level: 1-6 | Target Level: 5-6 |
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These support pages were produced using Strategic Partnership Program funding from the Department of Education and Training.
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South Australia
Department for education.
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
- Accessibility
- Acknowledgement of Country
The Joint Mathematical Council of the United Kingdom
Addressing the five ‘big questions’ in problem-solving with NRICH
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).
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
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
- Developing positive attitudes
- Cross-curricular contexts
- Physical and digital manipulatives
Advanced mathematics
- Decision Mathematics and Combinatorics
- Advanced Probability and Statistics
For younger learners
- Early Years Foundation Stage
Problem-Solving Schools
Problem-Solving Schools supports learners embed key problem-solving strategies as they progress through their schooling, backed by our Problem-Solving Schools' Charter .
Want to raise the profile of mathematical problem-solving in your school?
Looking for support to help your students become better problem-solvers?
Want to be connected to like-minded teachers?
Become a Problem-Solving School
What is the problem-solving schools initiative.
We aim to help you raise the profile of mathematical problem-solving in your school. Our Charter offers a framework intended to inform policy and practice.
Everything you need to know about joining this initiative.
Resources and professional development
Coming soon… Our support material and webinars will aim to help your school move forward on its problem-solving journey.
Welcoming our latest schools
Coming soon… Find out which schools in your area are raising the status of problem-solving in their mathematics classrooms.
IMAGES
VIDEO
COMMENTS
Developing Excellence in Problem Solving with Young Learners. Age 5 to 11. Becoming confident and competent as a problem solver is a complex process that requires a range of skills and experience. In this article, Jennie suggests that we can support this process in three principal ways. Using NRICH Tasks to Develop Key Problem-solving Skills.
Pattern spotting. Working backwards. Reasoning logically. Visualising. Conjecturing. The first two in this list are perhaps particularly helpful. As learners progress towards a solution, they may take the mathematics further (stage 3) and two more problem-solving skills become important: Generalising. Proving.
We have chosen these problems because they are ideal for consolidating and assessing subject knowledge, mathematical thinking and problem-solving skills. You may wish to use these as lesson starters, homework tasks, or as part of internal assessment exercises. Longer NRICH problems can be found on the Secondary Curriculum page.
A selection of rich tasks ideal for developing subject content knowledge, mathematical thinking, and problem-solving skills. The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.
The article Using NRICH Tasks to Develop Key Problem-solving Skills unpicks what we mean by these skills and draws attention to activities which will help learners develop them. Our youngest learners can start thinking about 'working systematically' in contexts such as choosing two toppings out of sprinkles, sugar stars or flakes to go on top ...
In summary, it is always helpful to bear in mind these problem solving tips. 1) Don't be afraid to experiment: try a few special case numbers to get a feel for the situation. 2) Don't be afraid to provide a partial solution to a problem. Many rich tasks are 'open': there is sometimes not necessarily a set, final answer.
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. ... Collections of NRICH tasks designed to develop learners' key problem-solving skills. Developing positive attitudes. Collections of tasks designed to encourage learners to be curious, resourceful, resilient and collaborative ...
A Guide to Problem Solving. When confronted with a problem, in which the solution is not clear, you need to be a skilled problem-solver to know how to proceed. When you look at STEP problems for the first time, it may seem like this problem-solving skill is out of your reach, but like any skill, you can improve your problem-solving with practice.
The focus is on the problem solving process, using NRICH problems to highlight the processes. Needless to say, this is not how problems should be taught to a class! ... including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
The Problem-solving Classroom By NRICH Primary Team and Jenny Earl This article forms part of our Problem-solving Classroom Feature, exploring how to create ... let's take a look at a sequence of two NRICH tasks: The Domino Sets investigation challenges learners to work out how they would check that a box of 0-6 dominoes they are given is a ...
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. ... Here you will find activities to develop your problem-solving skills and improve your understanding of mathematical topics. ... Post-16. These tasks are ideal for developing subject content knowledge together with problem ...
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. The NRICH four stage problem-solving process. This feature offers ideas on all of these aspects and also links different NRICH activities to each.
NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion. NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all ...
Explore these collections to develop your mathematical skills. Thinking Mathematically. Articles and books. STEP Support Programme. The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,children's solutions,interactivities,games,articles.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
NRICH problem solving task: Three Block Towers. Scootle lesson sequence: Dice Don't have Brains. Target Level: F - 2. Target Level: 1 - 6 . Why we love this task: Problem solving based; Low entry, open middle and high ceiling; Critical thinking and reasoning; Extends knowledge; Connects ideas to enhance understanding; Why we love this task ...
Nrich - a website with maths activities and games. Print this page. 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.
Addressing the five 'big questions' in problem-solving with NRICH . 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).
Secondary Curriculum-linked Problems. Secondary Curriculum-linked Problems. Our Secondary Curriculum Mapping Document offers our favourite NRICH tasks, organised by curriculum topic and age group. The tasks also appear in the collections below, which are organised using the same headings, but also offer short descriptions of each task.
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. It opens up a ...
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.