Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

If you have only four weights, where could you place them in order to balance this equaliser?

Can you complete this jigsaw of the multiplication square?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Can you explain the strategy for winning this game with any target?

An environment which simulates working with Cuisenaire rods.

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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.

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Given the products of adjacent cells, can you complete this Sudoku?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Given the products of diagonally opposite cells - can you complete this Sudoku?

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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 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?

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

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

56 406 is the product of two consecutive numbers. What are these two numbers?

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

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.

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

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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?