The Benefit of Estimation

     I have always loved and excelled in the area of estimation. I learned the rules of rounding numbers quickly and applied them to many aspects of my life. I was taught one simple strategy and was able to apply it to every situation I encountered. If the number following the number to be rounded was 4 or less, the number stayed the same. If that same number was 5 or more, the number being considered for rounding went up by 1. A simple strategy that works every time....or does it? I have recently been introduced to clustering, front-end estimation with or without adjustment, and substitution of compatible numbers. While clustering and the substitution of compatible numbers are similar to my rounding technique, front-end estimation without adjustment made me pause. How does this form of estimation work and how does it benefit the student?
     As I began my search for the answer, I found that even Dr. Math questions the technique. However,I also found that having a good sense of estimation and the use of different techniques leads to better estimation in school and in life. So how does front-end estimation benefit students? It gives students another method to use and builds the foundation for adding the adjustment later. Here is an example of front-end estimation:

This technique then leads to front-end estimation with adjustment.

    1560
+    821
________

To solve, first apply the rules of front-end adjustment to add 1,000 plus 800 to get 1,800. This leaves about 600 (560) and 20 (21), or 620 left to add. The total amount is about 2,420. With rounding the first number, the answer would be about 2800. The actual answer is 2381, making our front-end estimation with adjustment the closer estimate in this case.
    The lesson learned in the exploration of estimation is that each math problem is unique and one technique may not fit every problem. Also, students benefit from using different estimation techniques to find which method makes the most sense to them and fits the problem they are trying to estimate . This skill is beneficial as we need to be able to estimate in order to double check the totals on our calculators and computers. I may still use my rounding technique, but now I know that there are alternate estimation techniques that may arrive at a closer answer. Here are some fun sites with estimation activities:

http://www.mathsisfun.com/numbers/estimation-game.php

http://www.gamequarium.com/estimation.html