Monday, September 22, 2014

Base 7

Playing with arithmetic in different bases was an esoteric exercise in number theory until the invention of computers gave practical expression to binary, octal, and hexadecimal.  But the abstract exercise is still enjoyable. Driving in to work, I wondered what 121 would be in base seven.  I tried working it out in my head.  Finally, several weeks later, I resorted to paper and pencil.

I rediscovered the method I had been taught in the 7th grade at Lincoln High School in Cleveland, Ohio, in 1962.  But the rote method was not satisfactory.  I had to figure out why it worked.

To check my answers, I turned to Purple Math.  I knew Elizabeth Stapel’s website from my daughter’s years in high school.  Back then, I purchased two CD-ROMs, one for each of us.  On the Purple Math website, I found interactive exercises that let me practice what I had re-learned. 

Graphic shows repeated divisions to convert a number from one base to another
Interactive tutorial from Purple Math
4 times 7^4 = 9604
2 times 7^3 = 686
1 times 7^2 = 49
6 times 7^1 = 42
2 times 7^0 = 2
TOTAL =  10383

 I thought that it would be easy to find this in Common Core.  I assumed that the progressives would want children to practice useless number bases – and that conservatives would be outraged.  I was wrong.  In fact, Common Core is all about Base Ten.  If you want lesson plans in Base 7, you need Bob Jones University, the Christian fundamentalists who think that Earth is 10,000 years old.  Find BJU Press materials for homeschoolers here

Long ago, at a coin show, when my wife was proofreading for Bantam Doubleday, I found a lapel button from Encyclopedia Britannia home sales: “We never guess. We always look it up.”  Amen.


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