The Magic in Wondering about a Million, Billion, and Trillion

The title of this week’s book poses the question:  How much is a million?  While last week’s book How many Jelly Beans? provides an answer, as with most mathematical questions, there is much more to explore!

The Book

First published in 1985 by Lothrop, Lee & Shepherd books, and rereleased by Collins in 2004 for its 20th anniversary edition,  How much is a million? was written by the prolific STEM picture book author David M. Schwartz.

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In the book, Marvelossissimo the Mathematical Magician leads the way through a sequence of “If, then” statements about three quantities: One million (1,000,000), One billion (1,000,000,000) and One trillion (1,000,000,000,000).  The book offers answers to these questions:

  1. How high would one million/one billion/one trillion kids reach if they climbed on each other’s shoulders?
  2. How big a goldfish bowl would you need to hold one million/one billion/one trillion goldfish?
  3. How long would it take to count to one million/one billion/one trillion?
  4. How many pages would one million/one billion/one trillion stars fill?

Steven Kellogg’s illustrations are lovely. Their whimsy and detail engage earning him a Boston Globe/Horn Book Honor Book for Illustration in 1985.

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This book is recommended to ages 4-8, however I’m certain older children will enjoy it.

The Math

It is easy to throw around words like million, billion and trillion with no concept of how large these quantities are. For example, how much is the U.S. National Debt? (Here it is in real time: http://www.usdebtclock.org)

Being able to conceptualize large quantities like these is an important part of mathematical literacy.  “… knowing that it takes only about eleven and a half days for a million seconds to tick away, whereas almost thirty-two years are required for a billion seconds to pass, gives one a better grasp of the relative magnitudes of these two common numbers.” [ John Allen Paulos, Innumeracy: Mathematical Illiteracy and Its Consequences]

In the image below, each stack is made from $100 bills.
1_million,_100_million,_1_billion,_1_trillion.
SOURCE: http://googology.wikia.com/wiki/Googology_Wiki

While we often associate the quantities of one million, billion and trillion with money, How much is a million? provides images for these quantities without using money.

In addition to providing images, the book is an invitation for children to calculate these quantities for themselves (e.g.,  How long does it take to count to 1 billion? Remember, it takes a lot longer to say “14,358,126” than it does to say “one” ).  Children can compare their calculations with each other’s and the author’s ( given at the end of the book).

The Magic

First, the main character is a wizard and there’s a unicorn on every spread. But there’s more!

This book had my children WOWing, OMGing, and wondering from start. After reading that one trillion children stacked up won’t quite reach Saturn’s rings,  my 7 year proceeded to use the illustration to estimate how many more children are needed to reach the rings.

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In addition to answering the questions: How much is a million/billion/trillion?, the book ends with the question  How much is a zillion?

Now a zillion isn’t really a name for an actual number,*  but this prompted a discussion in my house about the names for numbers larger than a trillion. Here’s a list from Wikipedia. 

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And here are a couple more.

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Notice that many names in the list stand for two different quantities. Here’s is a note from Wikipedia about why: “The long and short scales are two of several large-number naming systems for integer powers of ten that use the same words with different meanings. The long scale is based on powers of one million, whereas the short scale is based on powers of one thousand.”

Luckily we don’t have much need for numbers beyond a trillion. Here’s an article about the largest number with any real world application. The article includes a story about how the number googol was named by a 9 year old boy named Milton Sirotta. How cool is that?!

Children like to name and think about big numbers, so if you haven’t already, I encourage you to join Marvelossissimo the Mathematical Magician on this magical trip towards a million and beyond.

*Schwarz mentions in his book  G is for Googol, that a zillion isn’t the name of an actual number. As mentioned here, Siena and I are following along with G is for Googol. We’ve had conversations about Möbius Strips, Diamonds, Abacuses,  Symmetry and more. If you have a child/student with Letter of the week, get the book and join us at any time!

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Thanks and see you next Monday! #mathbookmagic

 

 

 

 

 

 

 

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