Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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.

Can you complete this jigsaw of the multiplication square?

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.

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?

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?

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.

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?

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?

Use the interactivities to complete these Venn diagrams.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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

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

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

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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?

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?

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!

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

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

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...

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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

A game that tests your understanding of remainders.

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

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

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.

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.

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

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

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

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?

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

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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

Can you find any perfect numbers? Read this article to find out more...

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?