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

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

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

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?

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

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.

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

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

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

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

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

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?

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?

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

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

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.

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?

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.

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

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

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

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?

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.

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?

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

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.

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?

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?

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?

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?

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

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

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 numbers to the nearest whole number?

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

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

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?

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?

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

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.

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.

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?