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?

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.

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

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?

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

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?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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

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?

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

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?

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

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.

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

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

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

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

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

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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

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

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?

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?

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

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

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

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

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

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

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.

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?

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

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

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

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.

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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?