How many centimetres of rope will I need to make another mat just
like the one I have here?
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
An investigation that gives you the opportunity to make and justify
Find out what a "fault-free" rectangle is and try to make some of
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Here are two kinds of spirals for you to explore. What do you notice?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This challenge is about finding the difference between numbers which have the same tens digit.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
What happens when you round these three-digit numbers to the nearest 100?
What happens when you round these numbers to the nearest whole number?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
This challenge asks you to imagine a snake coiling on itself.
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
This activity involves rounding four-digit numbers to the nearest thousand.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Find the sum of all three-digit numbers each of whose digits is
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Think of a number, square it and subtract your starting number. Is
the number you’re left with odd or even? How do the images
help to explain this?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind