Play this game and see if you can figure out the computer's chosen number.

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

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

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.

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 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.

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

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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

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?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

Can you find any two-digit numbers that satisfy all of these statements?

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

What is the smallest number of answers you need to reveal in order to work out the missing headers?

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?"

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.

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

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

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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.

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.

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Find the highest power of 11 that will divide into 1000! exactly.

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

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

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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

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

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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

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?

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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?

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

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

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.

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

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

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

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?

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?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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

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?