From: Gail (for Teacher2Teacher Service)
Date: Apr 18, 2008 at 20:44:03
Subject: Re: Rounding of numbers

Hi Neil,
    
What I have always tried to help my students understand is that rounding
numbers is like trying to figure out where the number is on the number line,
and then deciding which of two benchmarks it is closer to.

If you are looking to round to a whole number sort of benchmark, you might 
be looking at the nearest thousand (like, 3000 or 4000), the nearest hundred
(like 600 or 700, or 2300 or 2400), the nearest ten (like 70 or 80, or 150 or
160).  You are just looking at the span between the two benchmarks, and
figuring out which one your number is closer to.

The same thing applies if you are trying to round to a place value less 
than zero, like tenths, or hundredths, or thousandths.  The important thing 
is to select two CONSECUTIVE benchmarks.  Choosing between 0.70 and 0.90, 
or 120 and 140, won't work.

Think about the number 0.37, rounding to the nearest tenth.  The choices 
(benchmarks) are 0.30 and 0.40.  0.37 is farther than halfway, so it is 
closer to the 0.40 choice.

When we have a number that is exactly halfway between two consecutive 
benchmarks, we just choose the higher of the two.  I used to tell my 
students (elementary) a story about when I was trying to cross a busy 
street that didn't have a middle area to wait at if traffic was coming.  If 
I started out, and was just a few feet from the curb, and big trucks came, 
I would go back to where I started.  If I was just a few steps away from 
the opposite curb, I would hurry to that side.  And if I was right in the 
middle, I would go ahead and finish crossing, since it was the same 
distance either way, and I wanted to get across the street.

Of course, if it is a word problem you are trying to answer, you have to 
consider the context, also.  If you are looking for the number of buses 
needed for a field trip, and the exact answer is 2.3 buses, you had better 
order 3 buses, even if 2.3 really rounds to 2, or you are going to have 
some very unhappy students.

I hope this answers your question, and gives you something to think about 
as you consider lessons.  :-)

 -Gail, for the T2T service

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