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

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

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...

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.

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?

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?

An environment which simulates working with Cuisenaire rods.

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

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?

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

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

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?

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?

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 a cuboid 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?

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?

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.

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

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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

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

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

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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

How many noughts are at the end of these giant numbers?

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

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.

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

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.

The nth term of a sequence is given by the formula n^3 + 11n . Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. . . .

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.

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

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?"

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. . . .

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.

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

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

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

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

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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

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

Can you work out what size grid you need to read our secret message?

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