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 names on 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, let's 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 on ...
As those who are told begin to tell others, the exponent grows.
The total number of people who know your secret (plus you!) is::
| Day | New People Told | Total People Who Know |
|---|---|---|
| 1 | 3 | 1 + 3 = 4 |
| 2 | 9 | 4 + 9 = 13 |
| 3 | 27 | 13 + 27 = 40 |
| 4 | 81 | 40 + 81 = 121 |
Moral of the story? Keep your secrets with you, or those you really trust.
Questions For You ...
- How long till your school or neighborhood knows your secret?
- How long till the whole country knows your secret?
- How long till the whole world knows your secret?
Activity courtesy of Hands On Math