When is Three a Half of Eight?

I spent the past two days at a meeting at the Vermont Agency of Education discussing the new Elementary Education Licensure requirements that are due out in a couple of years. The two days of meetings went by quickly and although I don't think we achieved all our goals there was some great discussion and some meeting up with old friends. It was particularly good to see Casey Murrow again after so many years and to know that he is still publishing his wonderful Connect magazine at Synergy Learning. 

It was also good to meet up with some folks from the Vermont Math Institute as we always have really good mathematical discussions. One interesting question that caught my ear that I hadn't  heard before was "When is three half of eight?". Always up to the challenge I thought about the question from every angle I could. I thought about different bases and how the 8-ball is significant in pool. I tried fractions and finally realized that I was getting nowhere. If using 8 as a cardinal number doesn't work is there something else about it that I could use? Perhaps the answer lay in the physical quality of the numeral 8. Bingo! If you slice the numeral 8 in half vertically the half on the right side is 3 and the half on the left side is a backward 3.

This is quite e neat mathematical problem because a fraction only really has value when you know what the one is to which it refers. As long as I kept thinking about 8 as a cardinal number, the identification of a group of eight, I was getting nowhere in solving the problem. If, however, I found a different 'one' to which the 'half' referred perhaps my problem would be solved. Once I had selected the numeral 8 itself it was then only a short step to see the 3 as the right side of the 8.

Now would you rather have half the money in my left hand or a quarter of the money in my right hand?