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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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 adjacent cells, can you complete this Sudoku?

This article for primary teachers outlines why developing an intuitive 'feel' for numbers matters, and how our activities focusing on factors and multiples can help.

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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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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.

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

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How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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

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How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?