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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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Can you complete this jigsaw of the multiplication square?

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

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

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

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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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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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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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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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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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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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Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

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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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Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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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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Number problems at primary level that may require resilience.

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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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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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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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Number problems at primary level to work on with others.

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There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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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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In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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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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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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Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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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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48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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An investigation that gives you the opportunity to make and justify predictions.

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Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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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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Can you find different ways of creating paths using these paving slabs?

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What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

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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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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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Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

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Have a go at balancing this equation. Can you find different ways of doing it?

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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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Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?