Untitled Document

A Mathematical Search for Santas

Created by:

Modified by:

Pat Roederer
STCIroquois High School
Louisville, KY
proeder1@jefferson.k12.ky.us

Dr. Joyce J. Valenza
Teacher's notes

The Question

You know, I've been thinking about all those Santas running around. I mean, they told us that they were just helpers. At least, that's what my mom always told me. She said there was only one true Santa. Well, I'm older now and I just don't believe all that stuff. How could one person (magical or not) manage to wiggle down all those chimneys in one night? Come with me on a quest to find out how many Santas there really are.

The Task

If we're going to figure out how many Santas there are, I guess we'd better start figuring out how many houses they have to visit. Using your SantaQuest worksheet, click on the resources shown below to start getting to the bottom of this mystery.

Resources

Go to the World Population Clock to see what the population of the world is. Wow! That's a lot of people. I wonder how many of them are kids?

The U.S. Census Bureau has some interesting information about the number of children in the United States. We'll use the United States information as an average for the rest of the world. Let's assume that there are two children in each household. Our task now leads us to wonder how far Santa has to travel.

We better start figuring out how many square miles of habitable space are on the planet. Go to Nasa to find out the radius of the earth and the percentage of the earth's surface that isn't covered by water. That radius is given in kilometers. We can use the conversion calculator to enter the number of kilometers and change them into miles. How many square miles are on the surface of the earth ? We'd better visit Dr. Math to find the formula for the surface area of a sphere.

Okay, let me think, we know the surface area of the earth. We know how many houses Santa has to visit. Let's just assume these houses are spread out over the earth's land surface. How many houses would be on each square mile?

I'm beginning to understand why no one has ever bothered to take a really scientific look at this problem before. We've already had to make a number of assumptions that may or may not be true. Write a paragraph each about 4 different factors that could influence your results. Discuss how each factor would affect your answer.

Okay, just for the sake of argument, let's agree that reindeer really can fly. Moving at the accepted rate of rmph (reindeer miles per hour), I still don't see how they could get to more than 8 houses every hour. How many hours would it take for Santa to get to all the houses?

Now, you tell me, how many Santa's do there have to be to get presents to all the kids houses in 24 hours?

Evaluation

You will be evaluated on your SantaQuest using the following criteria:

determining how many children (10 points)

calculating how many square miles could contain houses (10 points)

calculating how many hours it would take to visit all the houses (10 points)

calculating how many Santas it would take (10 points)

written paragraphs with 4 factors that affect results (60 points)

Conclusion

Aha! I knew there had to be more than one Santa! All those guys sitting in the malls are really, truly Santas!! Did you ever wonder about how many sacks of toys each Santa would have to carry? Or....how many reindeer would be needed to pull those sleighs...or...how many cookies it would take to feed all those Santas?...

Happy Holidays!

	Created by: Modified by:	Pat Roederer STCIroquois High School Louisville, KY proeder1@jefferson.k12.ky.us Dr. Joyce J. Valenza	Teacher's notes
The Question	You know, I've been thinking about all those Santas running around. I mean, they told us that they were just helpers. At least, that's what my mom always told me. She said there was only one true Santa. Well, I'm older now and I just don't believe all that stuff. How could one person (magical or not) manage to wiggle down all those chimneys in one night? Come with me on a quest to find out how many Santas there really are.
The Task	If we're going to figure out how many Santas there are, I guess we'd better start figuring out how many houses they have to visit. Using your SantaQuest worksheet, click on the resources shown below to start getting to the bottom of this mystery.
Resources	Go to the World Population Clock to see what the population of the world is. Wow! That's a lot of people. I wonder how many of them are kids? The U.S. Census Bureau has some interesting information about the number of children in the United States. We'll use the United States information as an average for the rest of the world. Let's assume that there are two children in each household. Our task now leads us to wonder how far Santa has to travel. We better start figuring out how many square miles of habitable space are on the planet. Go to Nasa to find out the radius of the earth and the percentage of the earth's surface that isn't covered by water. That radius is given in kilometers. We can use the conversion calculator to enter the number of kilometers and change them into miles. How many square miles are on the surface of the earth ? We'd better visit Dr. Math to find the formula for the surface area of a sphere. Okay, let me think, we know the surface area of the earth. We know how many houses Santa has to visit. Let's just assume these houses are spread out over the earth's land surface. How many houses would be on each square mile? I'm beginning to understand why no one has ever bothered to take a really scientific look at this problem before. We've already had to make a number of assumptions that may or may not be true. Write a paragraph each about 4 different factors that could influence your results. Discuss how each factor would affect your answer. Okay, just for the sake of argument, let's agree that reindeer really can fly. Moving at the accepted rate of rmph (reindeer miles per hour), I still don't see how they could get to more than 8 houses every hour. How many hours would it take for Santa to get to all the houses? Now, you tell me, how many Santa's do there have to be to get presents to all the kids houses in 24 hours?
Evaluation	You will be evaluated on your SantaQuest using the following criteria: determining how many children (10 points) calculating how many square miles could contain houses (10 points) calculating how many hours it would take to visit all the houses (10 points) calculating how many Santas it would take (10 points) written paragraphs with 4 factors that affect results (60 points)
Conclusion	Aha! I knew there had to be more than one Santa! All those guys sitting in the malls are really, truly Santas!! Did you ever wonder about how many sacks of toys each Santa would have to carry? Or....how many reindeer would be needed to pull those sleighs...or...how many cookies it would take to feed all those Santas?...
Happy Holidays!