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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?

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

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

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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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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?

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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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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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Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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

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

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

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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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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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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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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.

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Can you complete this jigsaw of the multiplication square?

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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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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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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?

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

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Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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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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Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

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

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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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56 406 is the product of two consecutive numbers. What are these two numbers?

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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...

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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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How many different rectangles can you make using this set of rods?

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

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

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There are eight clues to help you find the mystery number on the grid. Four of them are helpful but the other four aren't! Can you sort out the clues and find the number?

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Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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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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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.

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

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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.