Sometimes estimation involves making your "best guess," but whenever possible, your "best guess" should be an educated guess based on information you know. Extrapolating is taking information you do know, and using it to make a reasonable "guess."

For example, if I showed you a picture which had 54 dots on it, and asked you to quickly tell me approximately how many dots there are, your reasoning might go something like this: "Well, I know roughly what a group of ten dots would look like, and it looks like I could divide those dots into about 5 groups like that, so there's probably about 50 dots."

Or maybe you're at a carnival, and there's a giant jar of candy corn, and whoever guesses the closest the amount of candy in the jar will get to take the jar home with them.  Your reasoning might go something like this: "I can see about 50 candies visible on the top, and the jar is tall enough that there are about 20 layers of candy from top to bottom. So that makes 50 times 20 = 1,000 candies."

If you've ever heard a survey result that sounded like this: "23% of all Americans think that the president is doing a good job," you're listening to some extrapolation. The people who conducted that survey did NOT contact every American to ask their opinion. They contacted a very small group of Americans (maybe 1000 or so) and found that of that 1000 Americans, 230 of them think the president is doing a good job. From that they extrapolated that the same was true of all of Americans..

Suppose you want to know how many pumpkins are in a pumpkin patch.  You can see that there are 2 pumpkins in one square meter, and you guess that the pumpkin patch is 10 meters by 20 meters in size. Therefore you say, "There's about 2 pumpkins in every square meter, and the pumpkin patch is 200 square meters, so there must be about 400 pumpkins."

In the first page of this unit I wrote about the amount of time it would take for a pencil to fall from the roof of a three story building. That was also an example of extrapolation. I knew how long it would take the pencil to drop from my shoulder height, and I used that information to build a reasonable guess for the drop from the top of the building.

1.

You count about 120 beans in a row of beans. The rows are about a yard apart, and the bean patch is about 30 feet wide. How many beans do you think there are?

2.

A ream of paper (500 sheets) is about 3 inches tall. A room is about 8 feet tall, and has 10 stacks that reach to the ceiling. How many sheets of paper are there?

3.

500 Americans are polled, and 200 of them think that the president should give everyone gummy bears for their birthday. If 2,000,000 Americans were asked this question, about how many of them would say the same thing?

4.

If you have 833 hairs per square inch on your head, about how many hairs do you have in all on your head?

5.

If you stack quarters one foot high, how much will it be worth?