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Pomegranate juice is strong, tasty and good for you but it needs to be diluted with water… Version 1: You start with a cask of Pomegranate juice and a barrel of water, of equal volumes of liquid, neither quite full. You take a bucket, fill it with juice from the cask and pour it into the barrel (assume there is room). Mix thoroughly. Now transfer a full bucket from the water barrel to the juice cask. Which concentration is the greater: the juice in the barrel or the water in the cask? Extension 1: What happens if you do the same action on the result? Which concentration is the greater now? Version 2: You start with a cask of Pomegranate juice and a barrel of water, neither are quite full. You take a bucket, fill it with juice and transfer to the barrel; then two buckets from the barrel go into the cask; then one bucket from the cask back into the barrel. Or you could start with the water, transfer a bucket to the cask, transfer two buckets from the cask back to the barrel, then one bucket from barrel to cask. Which approach yields the higher concentration of Water in the cask?

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Mathematics Research & Teaching Conference Linking Professional Development and Research for Mathematics Teaching The British Library Thursday 15 February 2007

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