Understanding a Billion
How Much is a Billion?
Everyone is talking about spending billions of dollars to save the economy but how much is a billion?
We all know how to count to 100. We count by 10's, 5's and 2's but when the numbers get higher it becomes more and more difficult to comprehend just how much that number means.
Here you will find books, games, activities and ideas for exploring large numbers. Hundreds, thousands, millions and even a billion. The numbers keep adding up. How much is a billion?
Photo Credit: $20 Dollars in Plant pot by Images_of_Money
Used under creative commons.
One Grain Of Rice: A Mathematical Folktale - A billion Grains of Rice
Gluing Rice to the Calendar
After reading the story, One Grain of Rice, take out a large page from a calendar. Tell the children that together you are going to glue grains of rice onto the days of the calendar to represent the rice that Rami received from the Raja.
At first it seems like an easy job but soon the numbers get just too high to count. This is a project that will never be completed but this realization is what it is all about.
Measuring a Billion Grains of Rice
A Billion Questions - Contemplating a Billion
Measuring a Billion Grains of Rice with Cups and Spoons
Now it's time to start talking about estimating. Somewhere between the 7th and the 10th days it will become too tedious to count individual grains. This is why people estimate or use measuring devices to determine amounts.
Count how many grains of rice fit in a teaspoon. How many teaspoons fit in a tablespoon? How many in a cup?
Going through the exercise of actually counting the rice to discover that you can measure the number of rice fairly accurately by spoonful or cupful is an important life skill and one that won't be forgotten when children are given the time to do the actual counting and measuring.
A Galaxy Billions of Light Years Away
This is a close-Up of a dusty and bright galaxy located billions of light-years away in infrared light. What is a light-year and how can we understand the distances involved in billions of light years?
When you talk about light taking billions of light years to reach us can you see why scientists say that we are looking at the past when we look at stars? The light that reaches us today left that star billions of light years ago.
- Math Forum - Ask Dr. Math
How long does it take to count to one billion counting one number per second?
- Counting to A Billion...
... Trivia: Most mammals live for about a billion heartbeats. At that rate, I'd just be reaching my warranty now but domesticated humans now live for more than two billion heartbeats. But I can count to sixty in under a minute...or would it just ta
- Counting by powers of ten
One, ten, hundred, thousand, ten thousand, hundred thousand, million, ten million, hundred million, billion, ... How many zeros are there in each of these numbers? One billion is 10 to the 14th power!
The National Debt Clock
The Debt Clock and Large Numbers
The National Debt Clock just had to add another digit in the 10 trillions place in order to record the amount of debt the US Government owes in comparison to the amount of assets that we have. They did this by replacing the dollar sign.
There are plans to replace the sign in order to add more place values.
Is it possible for anyone to understand numbers so high? Who will have to pay this money back?
Here is a lesson plan developed for 9th grade students to help them understand big numbers. Using estimation and understanding of relative sizes it helps students begin to visualize just how large these numbers are.
I'm Changing My Name To Fannie Mae - When they hand seven hundred million grand out....
Congress is handing out seven hundred million grand out. How many billion dollars is that? If the average salary of the parents in your classroom is $50,000 per year and each person paid all of the money they earned for 20 years, how many people would it take to pay that seven hundred million grand?
The MegaPenny Project - Using Pennies to Understand Large Numbers
The MegaPenny Project aims to help people understand these huge numbers by showing on a computer screen drawings of the quantities involved. It may very well be the best way to deal with the largest numbers but as much as possible it is important to experience these numbers with your hands.
Pile up as many pennies as you can. Ask to visit a vault at a bank to see more pennies and see if it is still possible to pick up a bag of pennies. Ask how much it weighs and how many pennies are in the bag.
How Much Is a Million? - Maybe it's easier to understand a million.
Now that we have experimented with gluing a billion grains of rice and thought about various ways of counting to a billion, maybe a million will seem a more reasonable amount to contemplate.
Children are often intrigued by or confused about (sometimes both) very large numbers. Here Schwartz uses concepts that are simple to help readers conceptualize astronomical numbers like a million, billion, and trillion.
Examples: If a million children climbed on each other's shoulders, they would reach higher into the sky than airplanes can fly; if a billion of them made a human tower, it would reach past the moon.
Some of the concepts can best be understood if there is previous knowledge (like the distance to the moon) but this is on the whole a successful effort. Extensive notes in small print seem addressed to adults.
Kellogg's bouncy, vibrant pictures, however, are colorful and funny and indubitably addressed to children.
Millions of Cats
Millions of Cats Bulletin Board
Children can relate easily to this story. From all the kittens available it's so hard to choose.
Start a bulletin board of cats. Children can draw them, cut them out, use stamps and stamp pads. Ask them to post the most beautiful cat. Each cat will be more beautiful than the last.
How many cats do you have? Hundreds of cats, thousands of cats, millions and billions and trillions of cats.
How to draw cats
Share with each other how each of you draws cats. Cut out your cats and start putting them up on the bulletin board. Look at pictures of cats in books, online and in art museums. Which one is the most beautiful?
Look for different artistic techniques and styles in the way that cats are drawn. Experiment with various styles and continue to cut out your cats and put them up on the bulletin board.
Now start counting the number of cats that you have drawn. Have you drawn ...hundreds of cats, thousands of cats, millions and billions and trillions of cats...? as mentioned in the story by Wanda Gag?
Maybe you need some help? Now ask the other classes in your school to join you. Ask your parents and the parents of the other children in the school. Would it be possible to draw a million cats? How many cats would each person in your school have to draw to make one million cats? How about a billion cats?
How long does it take you to draw a cat? Take out a stop-watch and find out the fastest or the average time it takes the children in your class to draw cats. How long would it take to draw one million or one billion cats at your average speed?
FreeRice - Donate rice to the United Nations World Food Program.
"What if just knowing what a word meant could help feed hungry people around the world? Well, at FreeRice it does . . . the totals have grown exponentially."
- Washington Post