TOO BIG

or

TOO SMALL?

suitcase full of money
Does one million dollars in one dollar bills fit
in a suitcase?

man on the phone

The Story

Just as you decide to go to bed one night, the phone rings and a friend offers you a chance to be a millionaire. He tells you he won two million dollars in a contest. The money was sent to him in two suitcases, each containing one million dollars in one-dollar bills. He will give you one suitcase of money if your mom or dad will drive him to the airport to pick it up. Could your friend be telling you the truth? Can he make you a millionaire?


money in a suitcase

To put the question another way: 

Will one million one dollar bills fit in a suitcase?

This book will help you answer the question.  If you would like to try solving the problem on your own, don't go any farther in the book.  If you get stuck, come back to the book.

Our three tutors, Pedro, Hali and Monty, will help by reminding you about some math you will need  from earlier classes.

Click on each of them for an introduction



There are many places we could start on a problem like this. You can think of your own plan, or you can follow this path.

FIRST: HOW BIG IS A DOLLAR BILL?

1. We can measure a dollar bill.

2. We can look at a website that has the data.

http://www.factmonster.com/ipka/A0774850.html

SECOND: Record the dimensions and other facts about a one dollar bill on your group's worksheet. (Don't forget to check with Monty for a helpful hint.)


stack of bills

What are the dimensions of a stack of one dollar bills?

  • You can decide how big you want your stack to be.
  • HINT: Ask Monty if you need some help.

What is the total dollar value of the stack?

What is the volume of the stack? (Click on Pedro if you don't remember how to find the volume.)

Record your answers on your group's worksheet.

Think about: Do these numbers make sense to me?

 


many stacks of dollar bills

Now let's put the stacks together and calculate how much space is required.

  • Consider how many stacks you want to put on top of each other.
  • Consider how many stacks you want to put side by side.
Answer the following questions:
  • What are the dimensions of your group of stacks?
  • What is the volume of your group of stacks?
  • What is the value of your group of stacks?

Record your calculations and answers on your group's worksheet. 

Ask yourself:  Do these numbers make sense to me?

 


suitcase full of money
  • How many piles would you need to put together to make one million dollars?
  • What is the volume of the pile of one million dollar bills?

Ask yourself: Does this still make sense?


Record the answers to these questions on your group's worksheet.


suitcase selection

There are many ways to think about whether one million bills will fit into a suitcase. You may have a way you would like to use. That is just fine!

If you want to continue on with this approach you can:

  • Choose a suitcase size that makes sense to you. (pay careful attention to the units of measure) You can measure the suitcase sample in the classroom, image a suitcase and take its measurements, or negotiate with your group members to agree on a size that seems reasonable.
  • Calculate the volume of the suitcase. (Check with Pedro if you need help with your volume calculation.)
  • Compare the volume of the suitcase with the volume of the money you calculated on the last page. Which is bigger? By how much is it bigger? Would it make a difference if you used a bigger suitcase?

packing trunk

Are you ready to answer the question?

WILL ONE MILLION DOLLAR BILLS FIT IN A SINGLE SUITCASE?

Please share your answer and your evidence with the class. You may use any of the following methods to show us what you learned:

  • Prepare an oral presentation.
  • Describe your thinking on poster paper and hang it on the wall.
  • Use the white board to display your work.
  • Draw a picture or chart that shows your thinking.

I will be looking for the following in your presentation, whatever way you choose to communicate:

  • A clear statement of your answer to the question: Does one million dollars fit into a suitcase?
  • A justification for your answer that includes your calculations and your thinking.

If you have time before the end of class, please go on to the next page for additional challenges.



Other Interesting Questions to Explore:

  • If you found a suitcase big enough to fit one million dollar bills, how much would it weigh?
  • What is the smallest denomination of currency that would allow you to fit one million dollars into a suitcase?
  • How big would a suitcase need to be to fit one million dollars worth of hundred dollar bills? How much would the suitcase weigh?