We begin this unit by asking the question, "What is estimation?" Here are a few answers:

Estimation is the process of obtaining reasonably accurate answers through making educated guesses.

Estimation is the process of using approximations to get a "close enough" answer.

Estimation is the process of extrapolating from known information to unknown, in order to get close to the correct answer.

Do you notice something that all of these definitions have in common?  I mean, besides the fact that they have the word "estimation" in them? They all center around the idea of an answer that is close enough, but not necessarily 100% accurate.

This is important to remember; estimation is valuable when you don't need an exact answer. If you need to have a perfectly precise answer, it's probably not a good idea to try estimation techniques.

Why is estimation important? There are a few reasons why you might want to estimate.

If a Perfect Answer isn't Feasible to Obtain

Suppose you've been approached by someone who wants you to mow the lawns at a golf course. They ask you how much you're going to charge to do the job. Since you've never done it before, you don't know how long it's going to take you. So you're going to have to make an estimate. You think to yourself, "Well, it takes me x hours to mow my lawn, and theirs is about 10 times as big as mine," and you use that information to come up with a price. You've just estimated. Until you've actually done the job, there's no way to know how long it's going to take to do it, so you had to make your best guess.

Self-employed people who do contract work do this kind of estimating all the time.

Sometimes answers aren't feasible to obtain because you don't have a calculator available, and you're dealing with nasty numbers. Suppose for some strange reason you had to multiply 18.9563 times 25.1158, but you didn't have either a calculator or pen and paper available. If you don't need a perfect answer, you can say, "Well, 18.9563 is pretty close to 20, and 25.1158 is pretty close to 25. Twenty times twenty-five is 500, and that's close enough." (The actual answer is about 476.1, so the estimate is fairly close).

Testing an Answer

Maybe the problem you're trying to solve really does have a solvable answer, but you're unsure that you've solved it correctly.  One of my favorite examples is this: Suppose I'm calculating the amount of time it will take for a pencil to hit the ground if it's dropped from the top of your three-story school building. I use my kinematics equations to solve the problem, and determine that it's going to take 45 seconds. I'm skeptical of this answer, so I try some estimating. Here's what I think to myself: "If I'm holding a pencil at shoulder height, it's going to take about a half a second to hit the ground.  The school building is - at most - ten times as tall as me, and since the pencil is picking up speed, there's no way it's going to take longer than 0.5 times 10 = 5 seconds. So my answer of 45 seconds is just silly!"

In the next pages we'll explore in more detail some of the methods of estimation.

1.

Can you think of a time when you used estimation? Describe the situation.

2.

Estimation often requires use of your senses. Give an example of using the sense of sight to make an estimation.

3.

Give an example of using your sense of touch/feeling to make an estimation.

4.

Give an example of estimating in a situation where a perfect answer is not possible.

5.

Give an example of estimating in order to test an answer.