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

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?

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?

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

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

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.

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?

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

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

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

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

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?

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

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. . . .

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

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

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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...

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

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.

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

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?

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

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

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?

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...

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

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.

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?"

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

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

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

A number N is divisible by 10, 90, 98 and 882 but it is NOT divisible by 50 or 270 or 686 or 1764. It is also known that N is a factor of 9261000. What is N?

Find the highest power of 11 that will divide into 1000! exactly.

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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

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?

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

The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.

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?

Consider numbers of the form un = 1! + 2! + 3! +...+n!. How many such numbers are perfect squares?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.