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

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 ...?

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?

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?

Delight your friends with this cunning trick! Can you explain how it works?

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

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

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

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

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

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

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

Can you find a way of counting the spheres in these arrangements?

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

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?

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

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

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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

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

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?

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

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

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

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

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

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

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?

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?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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?

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.

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

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

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

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

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.

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

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

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

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

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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

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

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?

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