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.

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.
Placeholder: several colourful numbers
article

Rich mathematics

In this very brief article, the NRICH Team outlines what they understand by the term 'rich mathematics'.
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
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.
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.
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.
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.
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.
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.
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.
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.
Seesaw Shenanigans
problem
Favourite

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

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.
Becoming a Better Mathematician
list

Becoming a Better Mathematician

Age
5 to 11
In this feature we have brought together groups of linked tasks, which will help you develop the five key ingredients that make successful mathematicians.
What is the Question?
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What is the Question?

Age
5 to 11
The tasks in this feature encourage learners to become fluent with times tables, but with a difference...
Reasoning
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Reasoning

Age
5 to 7
These activities will give you chance to use mathematical reasoning in different ways.
Primary Toughnuts
list

Primary Toughnuts

Age
5 to 11
These Primary problems haven't been solved yet. Why not take a look?
Shapes
list

Shapes

Age
5 to 7
These activities are all about shapes!
Exploring fractions
article

Exploring fractions

This article, written for primary teachers, links to rich tasks which will help develop the underlying concepts associated with fractions and offers some suggestions for models and images that help support ideas around fractions.
Going For Games
article

Going For Games

In this article for teachers, Liz Woodham describes the criteria she uses to choose mathematical games for the classroom and shares some examples from NRICH.
Placeholder: several colourful numbers
article

Group Roles

Here are description of the group roles used in our group worthy tasks, and others.
Stacks of Maths!
article

Stacks of Maths!

In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.
Mu Torere
game

Mu Torere

Try playing this game from New Zealand at the beach by drawing the board in the sand. Find an opponent and see if you can win by ending up with your shell in the centre space.
Multiple Representations
list

Multiple Representations

Age
5 to 11
This feature for primary teachers focuses on representing mathematical thinking in different ways.
Being Curious - Lower Primary Students
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Being Curious - Lower Primary Students

Age
5 to 7
Are you a curious mathematician? Would you like to get better at asking mathematical questions? If so, these lower primary tasks are for you!
Pedagogical approaches
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Pedagogical approaches

Age
5 to 11
These articles focus on pedagogical aspects of primary classroom practice, including links to relevant research.
Play to Win
list

Play to Win

Age
5 to 11
In this feature, we share some of the problems from the Play to Win pathway on Wild Maths.
Placeholder: several colourful numbers
list

Reasoning

Age
5 to 7
In our view, you can't do maths without reasoning! Why not have a go at these activities which will give you chances to reason in different ways? Can you explain your solution and convince someone else it is correct?
Number Sense and Place Value
list

Number Sense and Place Value

Age
5 to 7
Have a go at these activities which will help you get to grips with one of the main ideas about place value - that is knowing how important the position of a digit is in a number.
Moving around
list

Moving around

Age
5 to 7
What different ways of moving around can you think of? In these tasks, you can move different objects around in lots of different ways.
From WOW to WHY?
article

From WOW to WHY?

A surprising situation can grab our attention and make us curious to find out more...
Positive About Negative Numbers
article

Positive About Negative Numbers

In this article for teachers, Liz Woodham describes resources on NRICH that can help primary-aged children get to grips with negative numbers.
Building up to coding
article

Building up to coding

This article describes the underlying mathematical ideas and skills involved in the important mathematical application of coding.
Opening Out
article

Opening Out

Bernard Bagnall describes how to get more out of some favourite NRICH investigations.
Path of Discovery Series: 1. Uncertain Beginnings
article

Path of Discovery Series: 1. Uncertain Beginnings

Marion Bond suggests that we try to imagine mathematical knowledge as a broad crazy paving rather than a path of stepping stones. There is no one right place to start and there is no one right route to follow. This article looks at ways of offering children mathematical experiences throughout the day, not just in maths lessons.
Working Effectively with All Learners
article

Working Effectively with All Learners

Some questions and prompts to encourage discussion about what experiences you want to give your pupils to help them reach their full potential in mathematics.
Seega
game

Seega

An ancient game for two from Egypt. You'll need twelve distinctive 'stones' each to play. You could chalk out the board on the ground - do ask permission first.
Matching Pairs
list

Matching Pairs

Age
5 to 11
The matching pairs games in this feature give you the chance to compare amounts represented in different ways.