Tuesday, June 14, 2016

Curious Question on Fractions

Fraction, Variables, Math, Division In math, we teach that a fraction represents an part of a whole. The part may be distance, part of a total, etc., but it is always an equal part.  I was walking over to the library today and realized that we sometimes divide distances into segments based on landmarks rather than actual distance.

This may be one reason some students have trouble with drawing pictures showing fractions.  I had a student several years ago who would draw a rectangle and divide it into three uneven sections.  She honestly did not know the segments were supposed to be even.

Think about the different ways we use fractions including estimation.  I did a search to find out why we estimate fractions and how estimation of fractions is used in real life but I could not find much on the topic.  Most of the material I found is on how to estimate, figuring out if a fraction is closer to 0, 1/2, or 1 but nothing on its real world uses.

So does that mean it is not something that is done in real life or is it not considered important?  I know that when I buy things by the pound I might say "I'd like a quarter pound of tea.  Please get as close as you can."  Or the sales person might say "You are just under 1/4 pound."  These are close but not exact. In fact, sometimes, places break the price down to a per ounce weight rather than deal with fractions of a pound.  Many tea shops price tea by the ounce since that is easier to use.  

After a bit more search, I found a few things on how to estimate fractions so you are actually founding the fraction to something a bit easier to use. An example would be 2 1/3 is rounded to 2 for estimating a total sum.  The example here was estimating so you'd know about how much ribbon to buy.  That does work but you'd never round down for ribbon because you want to make sure you get enough.

When you sew a dress or anything else, you tend to round the amount up so you have enough material for the outfit just in case you make a mistake.  But that does not always answer the question "Why do I need to round fractions?"

I would love it if people could answer the question "What are some real life examples for rounding fractions?"  In other words, why would we estimate fractions in real life?"  I could use some help.  Thanks in advance.