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

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

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

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?

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

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

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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

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

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?

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?

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

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

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 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?

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

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

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

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

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.

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

Can you explain the strategy for winning this game with any target?

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

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

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?

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

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

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

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?

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?

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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

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?

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?

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.

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?

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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.

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

It would be nice to have a strategy for disentangling any tangled ropes...

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.