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The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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

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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.

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A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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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?

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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.

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

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Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

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

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

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

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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

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

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

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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...

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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...

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Can you work out what step size to take to ensure you visit all the dots on the circle?

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Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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

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Explore the relationship between simple linear functions and their graphs.

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

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

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

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

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You'll need to know your number properties to win a game of Statement Snap...

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

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A collection of resources to support work on Factors and Multiples at Secondary level.

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Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

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

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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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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.

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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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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?"

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Data is sent in chunks of two different sizes - a yellow chunk has 5 characters and a blue chunk has 9 characters. A data slot of size 31 cannot be exactly filled with a combination of yellow and. . . .

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Here is a chance to create some Celtic knots and explore the mathematics behind them.

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

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Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

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Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?

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

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Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.