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

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.

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?"

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!

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?

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

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?

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

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

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

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.

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

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

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?

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?

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

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

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

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

A game that tests your understanding of remainders.

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?

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

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

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?

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?

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.

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.

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.

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?

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

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

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

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?

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...

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

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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

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

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.

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

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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

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?

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

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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

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?