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

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?

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

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

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

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

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

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?

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

Ben’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?

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

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.

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

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

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

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

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?

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?

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 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?

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

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?

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

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

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

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

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?

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

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.

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

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.

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?

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

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

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?

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

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

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

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Find the sum of all three-digit numbers each of whose digits is odd.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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

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

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

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