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?

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

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?

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?

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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?

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

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

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

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 asks you to imagine a snake coiling on itself.

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?

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.

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

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

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?

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

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.

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?

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

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?

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

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?

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

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

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

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