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.

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

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?

Can you work out how many lengths I swim each day?

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?

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. . . .

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.

An environment which simulates working with Cuisenaire rods.

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

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

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

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

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

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}.

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...

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

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...

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?

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?

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

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?

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?

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

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

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

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

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

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

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

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

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

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

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?

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

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.

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 the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

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?"

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

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

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Can you make lines of Cuisenaire rods that differ by 1?

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. . . .

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.

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

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

Find the smallest positive integer N such that N/2 is a perfect cube, N/3 is a perfect fifth power and N/5 is a perfect seventh power.