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

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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 complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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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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Can you work out some different ways to balance this equation?

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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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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?

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

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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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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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When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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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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Number problems at primary level that may require resilience.

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On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

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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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Can you make square numbers by adding two prime numbers together?

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How many different sets of numbers with at least four members can you find in the numbers in this box?

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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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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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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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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 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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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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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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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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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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Number problems at primary level to work on with others.

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There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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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.

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

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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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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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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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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...

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

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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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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.

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

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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?

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

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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Are these statements always true, sometimes true or never true?

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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?