This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

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Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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How many possible symmetrical necklaces can you find? How do you know you've found them all?

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Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out?

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EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

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Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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This challenge combines addition, multiplication, perseverance and even proof.

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This task combines spatial awareness with addition and multiplication.

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I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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Take three consecutive numbers and add them together. What do you notice?

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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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This game can replace standard practice exercises on finding factors and multiples.