Problems
Why not send us your solutions?
Even and Odd
Stage: 1 Challenge Level: 
This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?
Jig Shapes
Stage: 1 Challenge Level:
Can you each work out what shape you have part of on your card? What will the rest of it look like?
Sort Them Out (1)
Stage: 1 Challenge Level:
Can you each work out the number on your card? What do you notice? How could you sort the cards?
How Do You Do It?
Stage: 2 Challenge Level:
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Sort Them Out (2)
Stage: 2 Challenge Level:
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Fingers and Hands
Stage: 2 Challenge Level:
How would you count the number of fingers in these pictures?
Cyclic Quadrilaterals
Stage: 3 Challenge Level:
What can you say about the angles on opposite vertices of any cyclic quadrilateral? Working on the building blocks will give you insights that may help you to explain what is special about them.
Cinema Problem
Stage: 3 Challenge Level:
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Legs Eleven
Stage: 3 Challenge Level:
Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?
Tower of Hanoi
Stage: 4 Challenge Level:
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Why 24?
Stage: 4 Challenge Level:
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
Areas and Ratios
Stage: 4 Challenge Level:
What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.
Prime Sequences
Stage: 5 Challenge Level:
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
The Clue Is in the Question
Stage: 5 Challenge Level:
This problem is a sequence of linked mini-challenges leading up to the proof of a difficult final challenge, encouraging you to think mathematically. Starting with one of the mini-challenges, how. . . .
Transformations for 10
Stage: 5 Challenge Level:
Explore the properties of matrix transformations with these 10 stimulating questions.
Elsewhere...
Featured Solutions
Once Upon a Time
Marcus, Kathryn, Philippa and Ellie all used fantastic proportional reasoning as they worked on this problem.
Fair Shares?
Spreadsheets, trial and improvement, and simultaneous equations were just some of the approaches used to solve this problem.
Curve Match
We really liked the way Alex approached the solution to this problem, using a mixture of numerical and pure methods.
Articles & Games
Children’s Mathematical Graphics: Understanding the Key Concept
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Blog It
Members of the NRICH team are beginning to write blogs and this very short article is designed to put the reasoning behind this move in context.
Rich Mathematics Rich CPD
NRICH website full of rich tasks and guidance. We want teachers to use what we have to offer having a real sense of what we mean by rich tasks and what that might imply about classroom practice.
Factors and Multiples Puzzle
A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?
