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Q&A #830


Teaching bases to middle school children

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From: Marielouise (for Teacher2Teacher Service)
Date: Nov 22, 1998 at 11:26:21
Subject: Re: Teaching bases to middle school children

Hi, Jennifer, The important part of learning different bases is what the place value represents. You could do this with any type of manipulative. See if you have access to chips or objects of different types. If need be purchase different types of dried beans: white navy beans, pinto beans, peas. Suppose you were to work in base five. Five peas might equal 1 pinto bean and 5 pinto beans would equal 1 navy bean. Therefore 8 peas, 6 pinto beans and 2 navy beans could be expressed in the following way: 1. Exchange 5 of the 8 peas for 1 pinto bean. You now have 3 peas, 7 pinto beans and 2 navy beans. 2. Exchange 5 of the 7 pinto beans for 1 navy bean. You now have 3 peas, 2 pinto beans and 3 navy beans. 3. Your expression of 3(navy) + 2(pinto) + 3(peas) = 323 in base five. To evaluate this in base 10, convert: 3(5^2) + 2(5^1) + 3(5^0) = 75 + 10 + 3 = 88 in base 10. To convert the 88 in base 10 to base 5, divide by the largest power of 5. In this case it is 25 or 5^2. 25 divides into 88 = 3 (25) + remainder of 13. The next highest power of 5 which divides into 13 is 5. 13 = 2(5^1) + 3. Since the quotient when divided further by 5 is zero, the last digit of 3(5^ 0) = 3. What is beneficial in working with the beans is that each day you can change the base. 88 in base 10 becomes 323 in base 5. What is 88 in base 10 when converted to base 3? Look for the largest power of 3 that divides into 88. Since it is 3^4 = 81, you will end up with a five "digit" number. Mix the beans into a jar, choose a scoop of them. Convert the beans into a base "anything" number." Happy converting. -Marielouise, for the Teacher2Teacher service

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