Activity: Is Your Secret Safe? Think Exponentially

What you'll need:

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:

secret exponent 1


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

secret exponent 2


______ 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

secret exponent 3


______ 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 ...


Activity courtesy of Hands On Math