List

Primary toughnuts



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.

The Value of Two
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.

Developing Number Through Tidying Up
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.
Young Children's Mathematical Recording
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.
book
Ages
3-7

One Is a Snail, Ten Is a Crab

This 'counting by feet' book offers opportunities to focus on counting and introduce multiplication with its entertaining illustrations.

book
Ages
3-7

The Doorbell Rang

Ma has made plenty of cookies for her children, but then the doorbell rings. And rings... And rings... This book is perfect for discussing sharing equally.

book
Ages
3-7

The Shopping Basket

With Steven having to fend off various animals on his way back from the shops, he arrives home with fewer items than his mum requested. This book is a great context in which to count, and in particular to talk about 'one less'.

book
Ages
3-7

Five Minutes' Peace

Mrs Large the elephant wants five minutes' peace away from her three children... but they keep interrupting her!

book
Ages
3-7

The Bad-Tempered Ladybird

The bad-tempered ladybird tries to fight bigger and bigger animals throughout the day - but will it win a fight against the biggest animal of all?

Early Number Sense
article

Early number sense

This article explores the basic foundations of number sense and outlines relevant research in this area.
Subitising
article

Subitising

In this article for EY practitioners, Dr Sue Gifford outlines what we mean by subitising and how we can teach it.

book
Ages
3-7

The Great Pet Sale

This book tells the story of a pet shop where lots of animals are for sale at a variety of prices - but which will the boy choose?

Placeholder: several colourful numbers
article

Rich mathematics

In this very brief article, the NRICH Team outlines what they understand by the term 'rich mathematics'.
book
Ages
3-7

How Big is a Million?

Pipkin is a small penguin who asks big questions. He wants to know how big a million is! He finds ten fish, a hundred penguins in a huddle and a thousand snowflakes... but will he find a million of anything?

book
Ages
3-7

Walter's Wonderful Web

Walter the spider wants to spin a perfect web, so he tries making webs of different shapes and sizes. Will he end up with a wonderful web?

Dot Card Games
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.
Models in mind
article

Models in mind

This article looks at how models support mathematical thinking about numbers and the number system
book
Ages
3 to 7

Ten Apples Up On Top

In this captivating rhyming story, a dog, a lion and a tiger all try to balance ten apples on their heads while tightrope walking and roller skating!

Maths at Home
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.
book
Ages
3-7

Pete the Cat and His Four Groovy Buttons

Pete the cat wears his favourite shirt with four groovy buttons. But what happens when one of the buttons pops off and rolls away? This story introduces children to subtraction number sentences.

Pattern and Structure
list

Pattern and structure

Age
3 to 11
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.
Ten-frames Games
article

Ten-frames games

These games use ten-frames to develop children's 'sense of ten'.
Using dice games in the classroom
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.
book
Ages
3-7

The Secret Birthday Message

On the night before Tim's birthday, he finds a secret message under his pillow! Can you work out what the different shapes in the message mean to help Tim find his birthday present?

book
Ages
3-7

Color Zoo

When we turn the page to remove a layer, what animal will the picture show now? And what shape will be removed? Have a look at the colour zoo to find out!

Welcoming Your New Class
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.
book
Ages
3-11

Grandpa's Quilt

Grandpa is so long and thin that his quilt doesn't cover his toes. This story tells of his grandchildren's attempts to change the shape of the quilt so he is toasty from head to foot.

Placeholder: several colourful numbers
list

Working with a grown-up?

Age
3 to 7
Lower primary tasks designed for an adult and child to work on together, adapted from some of our activities for developing group-working skills.
Getting the balance right
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.
book
Ages
3-7

Lucy in the City

Lucy the raccoon is in the city one night looking for food with her family. But when they leave her behind by mistake, she has to find her way home with the help of a friendly owl who gives her directions.

book
Ages
3-7

Henry's Map

Henry the pig likes knowing exactly where everything is. But when he looks out of the window, the farm is a mess! Follow Henry's story as he draws a map to show where everything in the farm should be.

book
Ages
3-7

Balancing Act

This book builds on children's experience of seesaws and balancing. Join the two mice who make a seesaw (or teeter totter) and see what happens as their friends hop on too.

Seesaw Shenanigans
problem

Seesaw shenanigans

Age
3 to 7
Challenge level
filled star empty star empty star

A group of animals has made a seesaw in the woods. How can you make the seesaw balance?

Red or Black Spinner
interactivity

Red or black spinner

Age
3 to 16
Challenge level
filled star empty star empty star
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.
Play to Win
list

Play to win

Age
5 to 7
Can you find a winning strategy for each of the games in this feature? Do you notice anything that is the same about the games?
Being Collaborative - Primary Teachers
list

Being collaborative - Primary teachers

Age
5 to 11
These problems are ideal for children to work on with others. Encourage your learners to share ideas, and recognise that two heads can be better than one.
Number Sense and Place Value Current Feature
list

Number sense and place value current feature

Age
5 to 11
This feature aims to support you in developing children's number sense and their understanding of place value. The first three articles unpick the ideas associated with these important areas of mathematics and outline relevant research. The fourth article links to a range of tasks and our rationale for choosing them. You can see the tasks themselves, which we have grouped into five categories, by scrolling down further.
Why's ten important?
list

Why's ten important?

Age
5 to 7
In these tasks you can explore tens and ones, and learn about the place value of numbers.
Placeholder: several colourful numbers
list

Playing with numbers

Age
5 to 7
All these activities use adding and taking away. Can you spot the connections?
A Random Rambling Rant
article

A random rambling rant

A random ramble for teachers through some resources that might add a little life to a statistics class.
MEI 2005
article

MEI 2005

Presentation given at the MEI conference in Reading 2005

Playing Strategically
list

Playing strategically

Age
5 to 11
This feature offers a variety of playful contexts in which pupils will be challenged to think ahead and modify their tactics as they become more expert at each of the games.
Starting the term with rich tasks
list

Starting the term with rich tasks

Age
5 to 11
These tasks, chosen from our 2022 summer challenges, are particularly suitable for the start of term, when you are getting to know your learners.
Placeholder: several colourful numbers
list

I'm stuck but ....!

Age
5 to 7
These tasks are tough! Can you keep going and find a solution?
Hidden Gems
list

Hidden gems

Age
5 to 11
This feature brings together hidden gems from the NRICH site to celebrate NRICH's 20th birthday.
Number
list

Number

Age
5 to 11
This collection of resources will support understanding of Number.
Mechanics in the Primary Years
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.
Can you play strategically?
list

Can you play strategically?

Age
5 to 11
These games will encourage you to play strategically. Can you think ahead and modify your tactics as you go along?