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An environment which simulates working with Cuisenaire rods.

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

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

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Can you complete this jigsaw of the multiplication square?

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

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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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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. . . .

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

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Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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

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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?

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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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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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 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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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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

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

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

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

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

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Number problems at primary level that may require resilience.

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These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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Number problems at primary level to work on with others.

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

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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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Can you work out what step size to take to ensure you visit all the dots on the circle?

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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?