Teaching Large Number Concepts

Date: 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/