Front End EstimationDate: 08/08/2005 at 21:33:50 From: nikki Subject: I don't know how to do front end estimation My math class is working on front end estimation, and I just don't get it. Can you explain it to me? Date: 08/08/2005 at 23:13:55 From: Doctor Peterson Subject: Re: I don't know how to do front end estimation Hi, Nikki. I've seen different ways to present front-end estimation (some of which are much better than others!), so I'm not sure exactly how you're being taught to do it. You'd have to check your book or ask your teacher, or show me what your book says so I can help you understand it. But I can tell you the main idea, which I think is better than following a detailed procedure anyway. Look at a number like this: 123 Which digit has the most effect on the value of the number? The one on the left, the 1. Why? Because that tells how many hundreds there are, while the 2 only tells how many tens you have. (If you wanted to quickly count the money in your wallet, it would be more important to count the hundred dollar bills than the ones, since it would take a lot of ones to be worth as much as a single hundred.) So if you want to make a quick estimate of a calculation without actually doing all the work, you would want to focus on the "front end digits"--the digits on the left. As an example, to add the numbers 12345 and 56789, you could ignore all the digits except the first digit in each, and pretend that the problem was 10000 + 50000 ------- 60000 That's pretty easy! You've ignored a lot of stuff, so the answer isn't very accurate, but it's a start, and it's certainly a lot closer than if you used only the LAST digit in each number and added 00005 + 00009 ------- 14 Now, you can do a lot to improve the estimate. Some of these things you can invent for yourself, just by thinking about how addition (or whatever operation you are doing) works. For example, you might look at the next digit in each number, and think about what would happen if you included those. Would the result be different enough from our simple answer to be worth the trouble? This sort of thinking can lead you to use "rounding" to get a better estimate, and also to using the sizes of the next digits to decide whether to add 1 to the "front-end" result, or in some cases to round one number up and the other down. Another direction to think is, what happens if the numbers don't have the same number of digits? If we added 12345 and 5678, would we still want to use the 1 and the 5, or is that not really helpful for making a good estimate? One thing to keep in mind when you do estimation problems is that THERE IS NO REALLY WRONG ANSWER. Well, there are some really stupid estimates (like my 14 above), but there is no one RIGHT answer. Estimation means deliberately getting a wrong answer, when you know that you don't NEED an exact answer, and you do need a FAST or EASY answer. For example, if you are estimating the total of your purchases in a store to make sure you don't exceed the amount you have in your wallet, you don't need to know the sum right down to the penny, but you do need to know how many dollars (or tens of dollars) you've spent, and you want to be able to do it in your head. So the kind of thinking we've been talking about will be appropriate there. But you might get a slightly different answer than I get, and it doesn't matter as long as both of us agree on whether we have enough money. For example, if your estimate is 60,000 and mine is 70,000, when the actual answer is 69,134, both are reasonable estimates obtained by slightly different methods. (The 60,000 is what we got above, and the 70,000 is what I would get by rounding appropriately, which is closer with hardly any more work. So mine is better, but yours is still okay.) So get to it, try it out, and see what you can do, without worrying about doing it wrong. I recommend always doing the exact calculation after making an estimate, then thinking not only about how accurate your estimate was, but about what you might have done to get closer, and whether your work was as easy as an estimate ought to be. You'll be developing some important skills. 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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