Big Numbers
Task
Are we becoming numb to large numbers? We hear them on the news. We see them in the newspaper. Do we really know what they mean?
According to a Burlington Free Press article dated 10/24/93, this large number was mentioned with others as amounts of money that are spent by the federal government.
"The granddaddy of all the unfilled schemes was President Ronald Reagan's Strategic Defense Initiative, dubbed 'Star Wars.' In 10 years, taxpayers poured $30 billion into that program with very little to show for it."
Please find a way of describing 30 billion that will help us understand what it means.
Alternate Versions of Task
| More Accessible Version:
Collect 100 of the same object. Display the objects in some way. For instance, you can put them in a jar, glue them onto paper or line them in a row. Take a photograph of them.
Now create a representation to show what 1,000 of your object would look like. For example, if your display of 100 objects were in a jar, how many jars would you need to show?
Can you represent 10,000 of your objects? 100,000 of your objects? What patterns do you notice?
More Challenging Version:
Are we becoming numb to large numbers? We hear them on the news. We see them in the newspaper. Do we really know what they mean?
According to a Burlington Free Press article dated 10/24/93, this large number was mentioned with others as amounts of money that are spent by the federal government.
"The granddaddy of all the unfilled schemes was President Ronald Reagan's Strategic Defense Initiative, dubbed 'Star Wars.' In 10 years, taxpayers poured $30 billion into that program with very little to show for it."
Please find a way of describing 30 billion that will help us understand what it means.
The money netted by the movie "Star Wars: Episode I – The Phantom Menace" was $925.5 million. How does this compare to the amount of money spent on the strategic defense initiative?
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Context
At the beginning of the year we study large numbers. Naming and writing numbers to the billions. I wanted students to get a better understanding of how large the numbers we were studying were. Putting the number in context allowed them to think of the number as a real quantity rather than just an abstract set of digits. The class brainstormed some areas that students could link the number to such as science and social studies. Most students were quite surprised by their findings.
What This Task Accomplishes
This task allows students to investigate and become more familiar with large numbers that they may hear on the radio, see on television or read in the newspapers. Since the number was too big for most calculators, the students had to find alternative ways of working with the large numbers.
What the Student Will Do
Most students brainstormed among themselves until they came up with an idea they liked. Many had to go to other sources for information.
Time Required for Task
50 minutes
Time can easily be extended to cover several days if you want to make this a larger project.
Interdisciplinary Links
Because they are comparing 30 billion to other things, there are many possibilities for interdisciplinary links such as science (molecules, the size of the universe) and social studies (circumference of earth, number of soldiers killed in all wars or any particular war or set of wars).
Teaching Tips
Many good ideas were a spin off of those presented in the short brainstorming session the class had. If you want to extend this project, you can encourage students or teams of students to do library research to develop their ideas.
Suggested Materials
Availability of reference materials (This makes a great library project.)
Possible Solutions
Solutions will vary, but the solution should give the reader an idea of how large 30 billion is.
| More Accessible Version Solution:
Solutions will vary. When assessing the student’s solution look for accuracy in counting, computation and reasoning.
More Challenging Version Solution:
Ronald Reagan's Strategic Defense Initiative was about 30 times more expensive than the money made from the "Star Wars" movie.
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Task Specific Assessment Notes
Novice:
The solution does not really address the task in a meaningful way. Just talking about the number of zeros after the number does not give the reader a feeling for how large 30 billion is.
Apprentice:
The student has the idea that they are to link 30 billion to some context, but the information is too vague. How many people are in Vermont? New England? There is an incomplete explanation of the student's reasoning.
Practitioner:
The solution shows a deep understanding of the task. The student shows how many times 30 billion will stretch end-to-end around the equator. The student's strategy is clearly explained and s/he uses mathematical notation effectively.
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Expert:
The student showed a deep understanding of the problem. Not only did s/he explain two ways to describe 30 billion, but s/he also showed some important relationships between place values and the use of exponents.
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