Activity: Is Your Secret Safe? Think Exponentially
What you'll need:
- pen and paper
- a secret
1st: Think of a secret that you don't want anyone to know (aside from a couple of dear close friends).
2nd: Think of those close friends, draw them and write their name under each picture:
3rd: So, on the first day you tell each of your friends your secret, how many total people (aside from you) now know your secret? (Answer is 3, right?)
______ total people in ___ day
4th: Now, if the next day each of your friends tell three of their friends, how many people now know your secret (aside from you)? Draw them underneath each of their friends
______ total people in ___days
5th: Now, lets say the following day each of these friends tell three friends. Now how many people know your secret? Draw them
______ total people in ___ days
6th: We can see how fast your rumor can spread right? There's got to be a better way of calculating who will know your secret.
In Walks Exponents ...
Exponents will quickly allow us to calculate how many people know your rumor
Day 1: 31 (=3) know your secret
Day 2: 32 (= 3×3 = 9) plus the original 3 know your secret
Day 3: 33 (= 3×3×3 = 27) plus those on day 1 and day 2) know your secret
Day 4: 34 (= 3×3×3×3 = 81) plus those on day 1,2 and 3) know your secret, and so forth...
As those who are told begin to tell others, the exponent grows.
Moral of the story? Keep your secrets with you, or those you really trust.
Questions For You ...
- How long till you school or neighborhood knows your secret?
- How long till the country know your secret?
- How long till the world knows your secret?
Activity courtesy of Hands On Math