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

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.

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...

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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

A game that tests your understanding of remainders.

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?

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

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?

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?"

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

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

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

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

Can you find a way to identify times tables after they have been shifted up?

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

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?

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!

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.

Is there an efficient way to work out how many factors a large number has?

Can you complete this jigsaw of the multiplication square?

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?

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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?

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

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

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.

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

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

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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

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?

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

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

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

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

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?

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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

Are these statements always true, sometimes true or never true?

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

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

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?

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

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

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?