Teaching Large Number ConceptsDate: 11/05/97 at 12:52:42 From: Dana Steffan Subject: Teaching the concept of millions, billions, and trillions I am an elementary education major and I have to do a project on how to teach the concept of millions, billions, and trillions to elementary school children. I have tried to search for books and articles on the subject but I can't seem to find any. I can't come up with any ideas of my own either other than bean sticks or base ten blocks. Any suggestions? Date: 11/05/97 at 18:24:17 From: Doctor Tom Subject: Re: Teaching the concept of millions, billions, and trillions Hi Dana, There's actually a book by David M. Schwartz and Steven Kellogg (the illustrator) called <i>How Much is a Million?</i> http://www.amazon.com/exec/obidos/ISBN=0688040500/9246-7743053-031600 and another by Hendrik Hertzberg called <i>One Million</i> which is out of print: http://www.amazon.com/exec/obidos/ISBN=0812920996/9246-7743053-031600 It has 5000 dots on each page, and there are 200 pages. It's a pretty concrete example! (There's actually more to the book - interesting numbers are flagged with references, so you can get an idea of the relative sizes of smaller numbers.) Even without a book, you can do something similar: make an estimate of the number of characters on a page of a book (count the characters on a few lines to get an average count, and multiply by the number of lines on a page), and figure out about how many pages are needed for a million characters. It'll be a fair-sized (but not huge) book. Look for other examples - there are about 31 million seconds in a year, for example. How long would it take to count to a million, if you count one number per second, 24 hours per day? Well, about 12 days. Figure out about how big a million grains of rice would be - 1 pound? 10 pounds? 100 pounds? After the kids have a solid idea for 1 million, point out that a billion is 1000 times that (you're talking about the American "billion," right? The European "billion" is a million million.) So it will be about the number of characters in 1000 books. If they were lined up on a shelf, how wide would the shelf have to be? There are about 270 million people in the United states, so a billion people is about 4 times the population of the U.S. The world's population is about 5.7 billion. Trillion is, of course, even tougher. Get them to understand how much bigger a billion is than a million, and then a trillion is that much bigger than a billion. Sometimes if you work with volumes, it's easier. For example, the "base 10 blocks" would be good to work with. I don't know how big each block is - perhaps 1/4 inch on a side? If so, a block of 10 by 10 by 10 is a cube about 2 1/2 inches on a side, and has 1000 blocks in it. Now, thinking in terms of those 1000-block cubes, 10 by 10 by 10 of those will be a million tiny blocks. This will be a cube 25 inches by 25 inches by 25 inches. To get a billion little cubes, it's 10 by 10 by 10 of these larger blocks - 250 inches or about 20 feet on a side. A billion blocks would thus pack a very large classroom, right? A trillion? Well, it's a block 10 classrooms by 10 classrooms by 10 classrooms, all filled with the tiny blocks! It would be a giant cube about 1/2 mile on a side. Think about filling football stadiums with ping-pong balls, counting leaves on trees, et cetera, and try to get the kids to estimate whether they're roughly a thousand, million, billion, or trillion. Bill Gates is worth roughly 40 billion dollars. If he puts his money in the bank at 5 percent interest, how much does he earn every day? Well, about 2 billion per year, so (roughly) a 5 million dollars per day, or (roughly) 200,000 dollars per hour (24 hour day), or 4000 dollars per minute, or about $63 per second. I hope some of these ideas are useful. Good luck. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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