Front End Estimation with AdjustmentDate: 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/ |
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