Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

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

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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?

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

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

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

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

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

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

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

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 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.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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

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?

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 three-digit numbers to the nearest 100?

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

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

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

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

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?

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

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.

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?

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

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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?

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?

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

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

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

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?

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?

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

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?

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

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

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

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?

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

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?

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

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?

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?

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