Watch this animation. What do you see? Can you explain why this happens?

What do you think is going to happen in this video clip? Are you surprised?

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?

This task focuses on distances travelled by the asteroid Florence. It's an opportunity to work with very large numbers.

This task offers opportunities to subtract fractions using A4 paper.

Try out some calculations. Are you surprised by the results?

This task combines spatial awareness with addition and multiplication.

This challenge combines addition, multiplication, perseverance and even proof.

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

Have a go at balancing this equation. Can you find different ways of doing it?

What happens when you round these numbers to the nearest whole number?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Take turns to place a decimal number on the spiral. Can you get three consecutive numbers?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

How much do you have to turn these dials by in order to unlock the safes?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

A game in which players take it in turns to choose a number. Can you block your opponent?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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?

Can you replace the letters with numbers? Is there only one solution in each case?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

How would you move the bands on the pegboard to alter these shapes?

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you make square numbers by adding two prime numbers together?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?