Front End Estimation with Adjustment

Date: 02/17/2004 at 15:38:21
From: Marci
Subject: Front End Estimation with adjustment

I have been asked to teach front end estimation with adjustment.  My
students are confused and I can see why.  It seems that when following
this procedure the actual numbers in the problem are not being
recognized.  Students are only thinking about the individual digits.

For example:

 1,876
+3,940

Estimate using front end  1000 + 3000 = 4000.  Adjust 876 to 900 and
940 to 900.  Add them together to get 1800 and then 1800 + 4000 = 5800
which is close to 6000.  It makes more sense to just estimate by
rounding and not to use front end estimation.

Any thoughts you might have on teaching front end estimation so that 
it makes sense would be greatly appreciated.

Date: 02/17/2004 at 16:29:20
From: Doctor Peterson
Subject: Re: Front End Estimation with adjustment

Hi, Marci.

I agree with you wholeheartedly, but I think I can see why they don't 
just teach estimation by rounding, and I see a way to turn the front-
end idea into something meaningful that is worth teaching.

You can read some of my opinions, and evidence I've found about the 
variability of the concept, here:

  Front End Estimation (FEE)
    http://mathforum.org/library/drmath/view/59027.html 

As I point out there, if the skill of estimation is tested in a valid 
way, it shouldn't matter what method you actually teach, since there 
is no one "right" estimate of any particular problem, and no standard 
test ought to require a particular method.  I don't know whether that 
is true in practice, though.

What I would want to teach is, first, what estimation is (any way you 
can get a reasonably accurate approximation to an answer without 
having to do all the calculation); second, a sense of what features 
of a sum make the most difference, and therefore should be used as an 
estimate (which is what the "front-end" idea is all about); and, 
finally, an awareness of when estimation makes sense, and how much 
accuracy is needed in any given situation.  Rounding is one technique 
that works well, but the foundational concepts come first.

So I would approach front-end estimation in terms of concepts rather 
than a specific method.  The "front-end" digits contain most of the 
value, so if you start with them you will get close to the real 
answer immediately (and be able to get closer by continuing to work 
from left to right until you feel you've done enough work).  So
"front-end" is just an awareness of the importance of place value, and 
"adjustment" is either rounding, or continuing to work left to right. 
If you understand why it works, you will not make the mistake I have 
seen in some presentations, where they use the thousands digit from 
one number and the hundreds digit from the other, which makes no 
sense at all.

Here are more thoughts on estimation that may help:

  Estimating Quotients
    http://mathforum.org/library/drmath/view/57198.html 

  Estimation vs. Rounding
    http://mathforum.org/library/drmath/view/57214.html 

  Exploring Estimation
    http://mathforum.org/library/drmath/view/63979.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/