Mars! Exclamation Explanation
Mars Factorial
Description:
This is a whole class, group, or partner activity.
In mathematics, 3! is a special number. It’s not excited. That’s not what the exclamation point is all about. The exclamation point tells you that 3! is equal to 6. Well, that’s what it tells mathematicians. Confused? Check this out:
The language first - How do you say "3!" out loud? You don't shout it. You say "three factorial." In mathematics the "!" stands for "factorial." That doesn't tell you much, but at least it's a start. Someone came along with a name for this funny creature, 3!, before you or I did, and we all go along with it.
The meaning second - Suppose you and two friends are going to Mars. "Who gets on the ship first?" the driver might ask. And when the first kid has gotten on, the driver would most likely ask, "Who's next?" Well, how many different possibilities are there for you and your friends to be first, second, and third? The answer to that is 6 —you can prove that by making a list:
Alan, Bob, Cindy
Alan, Cindy, Bob
Bob, Alan, Cindy
Bob, Cindy, Alan
Cindy, Alan, Bob
Cindy, Bob, Alan
Procedures:
Have students find out how many ways they could enter the spaceship (with 2 people going, with 3 people, with 4 people, with 5 people, 6 people…….)
Table of Factorials 1! - 10!
01! = 1 (1)
02! = 2 (1x2)
03! = 6 (1x2x3)
04! = 24 (1x2x3x4)
05! = 120 (1x2x3x4x5)
06! = 720 (1x2x3x4x5x6)
07! = 5040 etc….
08! = 40320
09! = 362,880
10! = 3,628,800