We sometimes have unsolved problems which require solutions. If there are any below, do consider having a go at them, and send us your solutions.
You may be interested in the article we have written, which explains what we are looking for when we decide which solutions to publish.
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Recent Solutions
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A good foundation for number learning for five year olds?
This article, written by Dr. Sue Gifford, evaluates the Early Learning Numbers Goal in England, in the light of research.
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Pattern and Structure
The tasks in this feature for Primary teachers will help you to develop learners' awareness of pattern and will serve as a springboard to exploring mathematical structures.
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The Value of Two
Ruth Trundley outlines her doctoral research and concludes that development of an understanding of cardinality is a crucial element of counting that can be overlooked.
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Developing Number Through Tidying Up
This article describes how one nursery setting focused on tidying up time as a context in which to explicitly target the development of number and calculation skills.
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Maths at Home
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Working with a grown-up?
Lower primary tasks designed for an adult and child to work on together, adapted from some of our activities for developing group-working skills.
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Mathematical problem solving in the early years: developing opportunities, strategies and confidence
In this article for Early Years practitioners, Dr Sue Gifford outlines ways to develop children's problem-solving strategies and confidence in problem solving.
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Maths at Home - Summer Challenges 2024
The tasks in this collection are ideal to work on at home over the summer, perhaps with friends and/or relatives.
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Young Children's Mathematical Recording
In this article, Janine Davenall reflects on children's personalised mathematical recordings as part of a small research project based in her Reception class.
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TSA NRICH Day October 31st 2018
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Early Number Sense
This article explores the basic foundations of number sense and outlines relevant research in this area.
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Subitising
In this article for EY practitioners, Dr Sue Gifford outlines what we mean by subitising and how we can teach it.
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Place Value: The Ten-ness of Ten
This article develops the idea of 'ten-ness' as an important element of place value.
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Rich mathematics
In this very brief article, the NRICH Team outlines what they understand by the term 'rich mathematics'.
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How Can I Support the Development of Early Number Sense and Place Value?
This article for primary teachers expands on the key ideas which underpin early number sense and place value, and suggests activities to support learners as they get to grips with these ideas.
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Dot Card Games
These games devised by Jenni Way use dot cards which will help children see the structure of numbers 1-6 and give them confidence as they begin to add and subtract these numbers.
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The importance of shape and space in the early years
In this article for EY practitioners, Dr Sue Gifford discusses children's early spatial thinking and how this predicts their mathematical understanding and achievement.
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Models in mind
This article looks at how models support mathematical thinking about numbers and the number system
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Maths at Home
This article for teachers, parents and carers offers guidance on how learners can get the most out of the activities in our Maths at Home features.
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Related teacher playing with shape
More activities with 2-d shape for younger and older children
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Using dice games in the classroom
This article outlines some of the benefits of using dice games in the classroom, especially as a tool for formative assessment.
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Welcoming Your New Class
What might your first lesson with a new class look like? In this article, Cherri Moseley makes some suggestions for primary teachers.
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Geometric thinking - teacher articles
This series of three articles discusses the development of geometric thinking.
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Getting the balance right
In this article for primary teachers, Ems shares some common misconceptions surrounding the equals sign, and suggests ways to help learners develop their understanding.
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Encouraging primary children to work systematically
This article for primary teachers suggests ways in which to help children become better at working systematically.
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Curriculum
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ACME Report: Developing able young mathematicians
Lynne McClure gives an overview of the ACME report 'Raising the bar: developing able young mathematicians', published in December 2012.
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Features
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Primary Children's Mathematical Recording
This article for teachers outlines different types of recording, depending on the purpose and audience.
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Tasks for an adult and child
Age
3 to 11
Challenge level
This collection of tasks are for an adult and child working together.
interactivity
Red or Black Spinner
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at least version 9.
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Favourite
Seesaw Shenanigans
Age
3 to 7
Challenge level
A group of animals has made a seesaw in the woods. How can you make the seesaw balance?
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Flexibility in Geometry
In this feature for Primary teachers, you will find tasks to help learners develop their flexibility in a geometrical context.
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Maths at Home
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Being Resilient
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Learning From Other People's Starting Points
In this feature, you can see how some children started each task, but this isn't because we want to give away the solutions!
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Puzzling with Paper
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Statistics
This collection of activities covers the areas of probability and collecting and analysing data.
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Reasoning: The Journey from Novice to Expert ( Selection of tasks )
These tasks particularly lend themselves to helping children along the journey from novice reasoner to expert reasoner.
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Developing Group-working Skills Related Content
Developing group-working skills related content.
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Shape, Position and Movement ( Geometry)
Have a go at these activities, which involve shapes and moving objects in different ways.
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Playing with Dice
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Handling Data
This collection of activities covers the areas of probability and collecting and analysing data.
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Working with Higher attaining mathematicians
In this article for teachers, Bernard describes ways to challenge higher-attaining children at primary level.
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Group-worthy tasks and their potential to support children to develop independent problem-solving skills
In this article for teachers, Jennie Pennant outlines how group-worthy tasks support the development of children's problem-solving skills.
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Natural Born Mathematicians
Helen Joyce interviews the neuropsychologist Brian Butterworth
whose research has shown that we are all born with a "built-in"
sense of cardinal number.
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Integrating rich tasks - Activity 2.1
This professional development activity looks at what teachers can
do to support learners engaging with rich tasks
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The development of spatial and geometric thinking: 5 to 18
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the work of Piaget and Inhelder.
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Shape Your Proof
In this feature for Primary students, we offer geometrical tasks which give you the chance to notice patterns, make conjectures and create convincing mathematical arguments.
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Primary Teachers
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Reasoning: Identifying Opportunities ( Selection of Tasks )
These tasks offer opportunities for learners to reason for different purposes and in different ways.
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Getting Better at Group Work
Have a go at these lower primary activities to improve your group-working skills.
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Handling data ( Statistics)
These challenges will test your understanding of information, as well as how likely different events are.
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Search for Structure: actions and objects
John Mason describes the thinking behind this month's tasks.
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Adding with the Abacus
Nowadays the calculator is very familiar to many of us. What did
people do to save time working out more difficult problems before
the calculator existed?
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From Playing to Explaining
The tasks in this feature encourage you to play and explore, then think deeply about the mathematical ideas underneath.
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Maths Explorers
Are you a maths detective? Choose a task and use your mathematical skills to solve the problem.
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Puzzling with Paper
These tasks offer opportunities for deepening learners' mathematical understanding and their positive learning dispositions.
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Maths Club and Roadshow Resources
Hands-on resources that might be useful for teachers planning to run maths events.
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Getting Better at Group Work Lower Primary
Three or four brains are usually better than one! Working on a problem in a group rather than on your own is often a good idea. These activities will help you get better at group work.
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Measurement
These activities are all about measuring different things, including time! Can you try and make a sensible guess about the size of something before you measure it?
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Reasoning: The Journey from Novice to Expert ( Article )
This article for primary teachers suggests ways in which we can help learners move from being novice reasoners to expert reasoners.
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I've submitted a solution - what next?
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
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Primary Proof?
Proof does have a place in Primary mathematics classrooms, we just need to be clear about what we mean by proof at this level.
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Shape your Thinking
These activities will encourage you to think flexibly about shape, position and movement (geometry).