Take One Example
Stage: 1 and 2
This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.
School Fair Necklaces
Stage: 1 and 2 Challenge Level: 
How many possible necklaces can you find? And how do you know you've found them all?
Division Rules
Stage: 2 Challenge Level:
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Follow the Numbers
Stage: 2 Challenge Level:
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Exploring Wild & Wonderful Number Patterns
Stage: 2 Challenge Level:
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Take Three Numbers
Stage: 2 Challenge Level:
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Always, Sometimes or Never? Numberlive
Stage: 2 Challenge Level:
Are these statements always true, sometimes true or never true?
Always, Sometimes or Never? Shape
Stage: 2 Challenge Level:
Are these statements always true, sometimes true or never true?
Six Ten Total
Stage: 2 Challenge Level:
This challenge combines addition, multiplication, perseverance and even proof.
Money Bags
Stage: 2 Challenge Level:
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Six Numbered Cubes
Stage: 2 Challenge Level:
This task combines spatial awareness with addition and multiplication.
Three Neighbours
Stage: 2 Challenge Level:
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
This Pied Piper of Hamelin
Stage: 2 Challenge Level:
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Magic Vs
Stage: 2 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Got It
Stage: 2 and 3 Challenge Level:
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Make 37
Stage: 2 and 3 Challenge Level:
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Factors and Multiples Game
Stage: 2, 3 and 4 Challenge Level:
This game can replace standard practice exercises on finding factors and multiples.
NRICH is part of the family of activities in the Millennium Mathematics Project.