Tuesday, December 12

Fractions, Spreadsheets, And Bonding

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“Bill, how do you do fractions?”  Don Phillip asked in his medium plaintive voice.  

“I cheat.”  I told him flippantly then added “I convert the fraction to a decimal, and then do the math operations.”  “Star Trek Voyager” would be on soon and I was just settling down to some chips with my special cracked pepper — bleu cheese dip.    

He grinned at me because he could see that would make it all very easy, but then he explained, “I got all these math problems with fractions … ” he was starting to get plaintive again.

“Lets see what you got…”  I looked in the big (written in 1994) math book and sure enough, these weren’t the fun, little, mental exercise fractions like 2/6 plus a 1/3, these were serious, hard work, fractions like 7/9s divided by 9/7s.  “Well, it has been a long time … “, I was getting a little plaintive myself.  Its always hard to explain to a sixth grader that while being able to divide fractions is very important … you’ve pretty much forgotten how to do it yourself.  

“Look, I can’t do your homework for you … you have to do it.”  I’ve used this line so many times over the last year that I’m surprised he hasn’t figured out that what I mean is “I have no idea how to solve Peter and Mary both have bicycles … “

“I just need some help … can I have some dip?” Don Phillip was getting more plaintive all the time.  When it comes to plaintive … 11 year old boys doing homework always win over 45 year old men trying to watch “Star Trek Voyager”.  So, while 7 of  9 was calculating how to disrupt the energy beam from the Borg’s cube I was busy trying to make sense of why 7/9s …

After looking at the book for a few minutes … and remembering back over 30 plus years to Mr. Becker’s class … it struck me that where I was taught to cross multiply, Don Phillip was having to invert the fraction.  So he understood what reciprocal meant while I would have just had the numbers after the equal sign.  “This is good dip … why is blue cheese sometimes spelled B-L-U-E and sometimes spelled B-L-E-U … and sometimes its even spelled B-L-U?”  Don Phillip has one serious weakness — food.  If you can get him to eat then he will forget about almost any other problem and he becomes much less plaintive.

“Its French … has to do with patent laws and copyright — say don’t you have some math to do?”  He wasn’t plaintive anymore.  So now I could be stern and demanding … “No more dip until the math is finished.”  That’s the way 7 of  9 would handle it.

Of course the damage was already done.  By the time 7 of  9 had taught Naomi Wilder to erect a level ten force field in the isometrics lab, I had MS Excel running.  I was considering what a sixth grader should have in a fractions program.  My first idea was to have places where he could look up the lowest common denominators.  When I was a kid, lowest common denominators were pretty important.  I settled on using a set of tables that sequentially multiplied the numerator and denominator by numbers 1- 16 (later expanded to 1-33).   This system allows the user to look up common denominators.  Don Phillip mentioned that if you just multiplied the denominators together you could create large fractions, then after the math operations were done all you had to do was reduce down the result.  This seemed like a very simple solution … so I used it.  (Mr. Becker … I would have thought of it myself … Really I would have).   

That led to the importance of having a good way to reduce the fraction.  Of course with some creative math and the use the Modula function I could have just calculated and displayed the fraction.  The thing is that the program should be teaching something, so again I created at table.  This time dividing the numerator and denominator of the fraction by a series of numbers (1-33).  This table shows that a ratio of 7/9s is proper, and it can be expressed as 14/18, but the user can get very esoteric and see the fraction also evaluates to 5/6.43.  I’m actually very proud of this feature.  

Okay, so after all the math is done then comes the bells and whistles … Don Phillip hates to type … so numbers can be entered using spin buttons and scroll bars as well as typing them in.  Once a number is selected … it can be moved to other operations using a command button.  Perhaps the cleverest/simplest/most useful thing I included was a graph … its easier to grasp fractions when you can see them graphically.  The little bar graph shows exactly what 7/9s looks like.  In the adult version I might include a .JPG of 7 of 9.

After the spin buttons, graphs, scroll bars, and interesting tables of numbers what would be left?  Well, as I told Don Phillip in the first place — I cheat, thus every fraction entered or calculated is displayed as a decimal … so if you really want to know … 7/9s is displayed as 0.77777778.

A day passed and there was just one last thing to add — one more table … down at the end of the spreadsheet.  I was starting to make a list of prime numbers when Don Phillip’s medium plaintive voice sounded in the doorway … “Bill, I have this report to make about Germany…”



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