In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
What happens when you round these three-digit numbers to the nearest 100?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
What happens when you round these numbers to the nearest whole number?
This challenge is about finding the difference between numbers which have the same tens digit.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
This activity focuses on rounding to the nearest 10.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
This activity involves rounding four-digit numbers to the nearest thousand.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
An investigation that gives you the opportunity to make and justify predictions.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Try out this number trick. What happens with different starting numbers? What do you notice?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
Find the sum of all three-digit numbers each of whose digits is odd.
This task follows on from Build it Up and takes the ideas into three dimensions!
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.
These tasks give learners chance to generalise, which involves identifying an underlying structure.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
It starts quite simple but great opportunities for number discoveries and patterns!
This challenge asks you to imagine a snake coiling on itself.
Got It game for an adult and child. How can you play so that you know you will always win?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.