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

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

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

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?

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

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

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?

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

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

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.

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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

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

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

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

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?

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?

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

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?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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

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

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

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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

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

These tasks give learners chance to generalise, which involves identifying an underlying structure.

Got It game for an adult and child. How can you play so that you know you will always win?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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

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.