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?

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

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

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

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

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

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?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

What happens when you round these numbers to the nearest whole number?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

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

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

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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?

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?

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?

Can you work out how to win this game of Nim? Does it matter if you go first or second?

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?

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.

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.

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

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

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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.

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

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

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

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

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

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?

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?

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?

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