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## FABLE

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**FABLE**THE ORIGINS OF NUMERATION AND ARITHMETIC Pamela Leutwyler**Once upon a time, in ancient Greece, there was a**USED CAMEL DEALER.**Each day, he counted his camels.**This was difficult. They would not stand still. They all looked alike. And sometimes…**So one day, the used camel dealer got a good idea.**Having just counted, he knew exactly How many camels were on the lot. used camels He went into his showroom**Where he built a shallow box on the floor**In which he placed ONE pebble to represent each camel on his lot.**If 2 camels are born**If he bought 2 camels If 1 camel dies If he sold 3 camels**This system was an improvement over running around in all**kinds Of weather to chase and count the actual camels. But as he Prospered, the huge pile of pebbles became awkward to count.**This system was an improvement over running around in all**kinds Of weather to chase and count the actual camels. But as he Prospered, the huge pile of pebbles became awkward to count. Then he got a really good idea!**The pebbles are temporarily removed**Then partitions are built The first pile will function just as the original pebble board One pebble represents one camel**In this pile 1 pebble represents 1 camel**Let’s view the pebble board from the top 3 camels are born 1 camel dies he sells 1 camel he buys 5 camels**Instead of allowing the pebbles to pile up, the dealer makes**this rule: In this pile 1 pebble represents 1 camel When 10 pebbles accumulate in a pile, they are replaced with 1 pebble in the next pile**Instead of allowing the pebbles to pile up, the dealer makes**this rule: In this pile 1 pebble represents 10 camels When 10 pebbles accumulate in a pile, they are replaced with 1 pebble in the next pile**Instead of allowing the pebbles to pile up, the dealer makes**this rule: When 10 pebbles accumulate in a pile, they are replaced with 1 pebble in the next pile Ten tens become 1 hundred**This is beginning to look familiar. Representing a camel**with a Pebble was the first level of abstraction. Next, piles of pebbles will Be replaced with symbols. Then, we do not need pebbles and boards. 5 2 3**The laws of arithmetic**arise from this pebble board**6**5 + 4 8**3**Put down 3 6 5 + 4 8**3**1 Put down 3 6 5 Carry 1 + 4 8**1**3 1 1 Put down 3 6 5 Carry 1 + 4 8 Put down 1 1 Carry 1**2**5 - 8**1**Borrow 1 1 2 5 - 8**1**Borrow 1 1 2 5 - 8 1 7**Why did the used camel dealer choose the number 10 ?**Probably it was because he had 10 fingers. Our numeration system is called base ten. If we choose another number – lets say 7 - when we Make the rule about when to move pebbles, we generate a BASE SEVEN NUMERATION SYSTEM