Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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?

Here are two kinds of spirals for you to explore. What do you notice?

An investigation that gives you the opportunity to make and justify predictions.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn 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?

This challenge is about finding the difference between numbers which have the same tens digit.

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Are these statements always true, sometimes true or never true?

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.

How many centimetres of rope will I need to make another mat just like the one I have here?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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?

This challenge focuses on finding the sum and difference of pairs of two-digit 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 encourages you to investigate the number of edging pieces and panes in different sized windows.

Try out this number trick. What happens with different starting numbers? What do you notice?

It starts quite simple but great opportunities for number discoveries and patterns!

This challenge asks you to imagine a snake coiling on itself.

This activity involves rounding four-digit numbers to the nearest thousand.

What happens when you round these three-digit numbers to the nearest 100?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Find the sum of all three-digit numbers each of whose digits is odd.

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?

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 is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Watch this animation. What do you see? Can you explain why this happens?