UCMP Lessons  

How Much Is a Billion?

Author: Anne Monk

Overview: In these scenarios and this activity, students get a sense of how big a billion really is. This is necessary in order to understand deep time.

Lesson Concepts:

Grade Span: 3–8


Advance Preparation:

— Make copies of asterisk pages if using that part of the activity.

Time: A few minutes to one class period

Grouping: Whole class

Teacher Background:

Life has been on earth for a very long time. Most of us have trouble envisioning a million years and find the idea of a billion years incomprehensible. But, it is important for students to get a sense of deep time so that they may begin to understand that life has had plenty of time to do what it has done—evolve into innumerable forms again and again, resulting in what we see around us today and what we see in the fossil record.

Teacher Resources: Send students to Life Has a History at http://www.ucmp.berkeley.edu/education/explorations/tours/intro/.

Teaching Tips:

Use the little scenarios below to jog your students’ minds about deep time. Continue with the activity if you deem it is worth the investment in paper to get the point across.

Vocabulary: million, billion

Procedure: To set the stage for understanding what a billion is, select from the following scenarios to share with the students:

  1. Scenario #1
    One penny is 2 centimeters wide. 1 billion pennies = 2 billion centimeters = 20,000 kilometers. If you had a billion pennies and stretched them from end to end you would have a line of pennies extending almost 20,000 kilometers. This is nearly half the circumference of the Earth at the equator. Or you could line up your pennies and pave your way from San Francisco to Madrid, and back again!

    Or you could take a little cross-country trip. If you start your journey in Seattle, WA you could head for...
    San Diego, CA (1710 km),
    then on to San Antonio, TX (2100 km),
    next stop Orlando, FL (1890 km),
    continue to Portland, ME (2260 km),
    return to Seattle, WA (4980 km),
    head out for Nashville, TN (3610 km),
    drive to Denver, CO (1900 km)
    and have enough pennies left to go skiing in Aspen.

  2. Scenario #2
    Let’s say your friend decides to count to 1 billion. How long will it take her to get there?

    She will be able to say the small numbers like 4 or 31 fairly rapidly, but most of the numbers between one and a billion are long and difficult to pronounce. When she starts counting the larger numbers like 467,051,372 she is really going to slow down (how long does it take you to say four hundred and sixty-seven million, fifty-one thousand, and three hundred seventy-two?). If we allow your friend just 3 seconds to say each number and she takes no breaks at all, it will take her 3 billion seconds to finish counting.

    3 billion seconds = 50,000,000 minutes
    = 83,333.333 hours
    = 34,722.2 days
    = 95.1 years is how long it will take your friend to count to 1 billion

  3. Scenario #3
    You decide to take a “billion step” hike. If you took really big steps of about 1 meter in length, how far can you go in a straight line and what kind of special equipment will you need?

    A 1 meter step = 1 billion meters traveled
    1,000 meters = 1 kilometer so a billion meters = 1,000,000 kilometers

    If you walk in a straight line you will be forced to leave the Earth’s surface. Your hike will take you to the moon and back with enough distance left over to almost make it to the moon a second time. You will definitely want your spacesuit for this one, and as much trail mix as you can carry!

    Of course if the idea of space travel doesn’t appeal to you, you could simply circle the Earth at the equator (40,000 kilometers) 25,000 times!

  4. To give visual learners a first-hand experience with large numbers, conduct the following activity.
    • Download the page containing 4,000 asterisks. It would take 250 of these pages to total 1,000,000 asterisks. This can be used to help convey the enormity of the numbers used in talking about the history of Earth and life.
    • Try papering a wall with 1,000,000 asterisks, line the corridor to show a million or make a binder containing 250 asterisk pages (or 125 if double-sided).
    • Ask your students how many pages would be needed to show the number of years that have passed since the dinosaurs went extinct (the dinosaurs went extinct 65 million years ago so 65 X 250 = 16,250 pages) or other such problems.
    • It will take 250,000 of these pages to show 1 billion asterisks. This is too many to paper the walls or make a binder with. In fact if you were to make up a binder that contained 4 million asterisks (500 pages, double-sided), you would need 250 such binders to show 1 billion asterisks.
    • One ream of paper contains 500 sheets and typically stands 5 cm tall, so 250 sheets = 2.5 cm. Ask your students how tall the stack of paper would be to show the amount of time that has passed since the dinosaurs went extinct (65 X 2.5 cm= 162.5cm or 1.62 m) or other such problems.
    • How tall would the stack be to show 1 billion years? Remember, 1 million years = 2.5 cm. 1000 x 1 million = 1 billion; so you'd have a stack 2500 cm, or 25 meters, tall (that’s as tall as an 8-story building).
    • How tall would the stack be to show the entirety of the Earth’s history? The Earth is 4.6 billion years old so you would need a stack 117 m high to show that amount of time. That is higher than a football field is long!

Posted May 24, 2004

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