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 explain the strategy for winning this game with any target?

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

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.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

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?

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

What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?

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?

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?

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?

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

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

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?

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

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.

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

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.

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

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.

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

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

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

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?

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

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.

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

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

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

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

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

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

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

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.

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

Given the products of diagonally opposite 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?

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 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?"

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

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

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?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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

An environment which simulates working with Cuisenaire rods.