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.
article
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.
article
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.
article
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.
article
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.
list
Curriculum
project
TSA NRICH Day October 31st 2018
article
Early number sense
This article explores the basic foundations of number sense and outlines relevant research in this area.
article
Subitising
In this article for EY practitioners, Dr Sue Gifford outlines what we mean by subitising and how we can teach it.
list
Features
article
Place value: the ten-ness of ten
This article develops the idea of 'ten-ness' as an important element of place value.
article
Rich mathematics
In this very brief article, the NRICH Team outlines what they understand by the term 'rich mathematics'.
article
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.
list
Recent solutions
article
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.
article
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.
article
Models in mind
This article looks at how models support mathematical thinking about numbers and the number system
article
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.
list
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.
list
Related teacher playing with shape
More activities with 2-d shape for younger and older children
article
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.
list
Maths at home
article
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.
list
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.
list
Geometric thinking - teacher articles
This series of three articles discusses the development of geometric thinking.
article
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.
article
Encouraging primary children to work systematically
This article for primary teachers suggests ways in which to help children become better at working systematically.
article
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.
article
Primary children's mathematical recording
This article for teachers outlines different types of recording, depending on the purpose and audience.
list
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.
article
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.
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.
problem
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?
list
Tasks for an adult and child
Age
3 to 11
Challenge level
This collection of tasks are for an adult and child working together.
list
Can you play strategically?
These games will encourage you to play strategically. Can you think ahead and modify your tactics as you go along?
list
Compare to pair
This feature offers interactive 'matching pairs' games which will help learners understand equivalence in a variety of contexts.
article
Developing logical thinking: the place of strategy games
This article outlines how strategy games can help children develop logical thinking, using examples from the NRICH website.
list
Starting the term with rich tasks
These tasks, chosen from our 2022 summer challenges, are particularly suitable for the start of term, when you are getting to know your learners.
article
Integrating rich tasks - activity 3
The aim of this professional development activity is to
successfully integrate some rich tasks into your curriculum
planning.
article
Creating a low threshold high ceiling classroom
This article explores the key features of a Low Threshold High Ceiling classroom.
article
The development of spatial and geometric thinking: the importance of instruction
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
article
Mechanics in the primary years
This article for teachers sets out some ideas for introducing
children to some of the concepts at the root of mechanics.
list
Hidden gems
This feature brings together hidden gems from the NRICH site to celebrate NRICH's 20th birthday.
game
Two stones
This game is known as Pong hau k'i in China and Ou-moul-ko-no in Korea. Why not challenge a friend to play it with you?
list
Being resilient - lower primary geometry
Are you resilient enough to solve these geometry problems?
list
Exploring problem solving, reasoning and fluency in a geometrical context
These tasks offer geometrical contexts in which to explore the three aims of the primary National Curriculum for mathematics.
list
Play to win
list
More lower primary number pattern tasks
Here are some more lower primary number pattern tasks for you to try.
list
Understanding information
These lower primary challenges focus on different types of information.
article
Supporting students to work collaboratively
This page, and the accompanying webinar recording, suggests ways in which teachers can help students to work more collaboratively.
list
Becoming a better mathematician
In this feature we have brought together groups of linked tasks, which will help you develop the five key ingredients that make successful mathematicians.
list
What is the question?
The tasks in this feature encourage learners to become fluent with times tables, but with a difference...
list
Matching
article
Place your counters...
An article for teachers which first appeared in the MA's Equals journal, featuring activities which use counters.
list
Always, sometimes or never tasks
Here you can find all our primary 'always, sometimes or never?' tasks.
article
Integrating rich tasks - activity 4.1
This professional development activity is designed to help you
assess your embedding of rich tasks into the curriculum through
peer observation
article
Placing our trust in learners
In this article Liz Woodham reflects on just how much we really listen to learners’ own questions to determine the mathematical path of lessons.
list
I'm stuck but ....!
article
On what day did it happen?
Read this article to find out the mathematical method for working out what day of the week each particular date fell on back as far as 1700.
article
Creative approaches to mathematics across the curriculum
Suggestions for teachers about exploring maths in different
contexts: art, history and so on
game
Sz'kwa
This Chinese game for two players is a simple version of Wei ch'i or Go. Each player has 20 distinctive pieces - try coins, pebbles, shells. You could try marking the board out in wet sand.
list
Being resilient - lower primary statistics
Are you resilient enough to solve these statistics problems?
game
Celebrate 25 years of NRICH
To celebrate NRICH's 25th birthday, why not play this special version of our classic game, Got It? Can you devise a strategy so that you will always win?
list
Exploring the geometrical strands of the National Curriculum in a problem-solving context
This group of tasks will help you support the geometry curriculum using a problem-solving approach.
list
Reasoning
These activities will give you chance to use mathematical reasoning in different ways.
list
Number sense and place value
This lower primary feature focuses on number sense and place value.
article
Developing mathematical thinking - Exploring and noticing
This page, and the accompanying webinar recordings, draw attention to the value of offering learners opportunities to explore and build on their discoveries.
list
More playing with number lower primary
Some additional activities to develop children's understanding of addition and subtraction of number through playing with number.
problem
Scissors, paper, rock Chinese style
Try the Chinese version of this well-known game with a friend. Great to play in the garden or in the park.