2nd 6-Weeks: Coordinate Graphing
Hook: “A cryptogram is text written with a code to keep the information secret. Math
is the best way to make these codes complex and difficult to crack. The NSA
has a site for kids all about cryptography http://www.nsa.gov/kids/home.shtml
The site includes games , activities, codes and ciphers.”
(Teacher note: Students should be given pages 183 and 185 from RIV
Engaging Mathematics.)
Spy Games
Goal:
An encrypted message has been intercepted by your agency and you must decode
the password to read the message.
Role:
You are a spy chief for a clandestine government agency.
Audience:
The agency you work for protects the country’s security and you report directly to the
President.
Situation:
An encrypted message has been intercepted. The message was sent by a known
double-agent so there is reason to believe that it contains government secrets. You
have been charged with decoding the message. The first line of the message is a
sequence of seemingly random numbers. Experience tells you that these numbers
are not as random as they seem. You have seen a similar method used years ago.
The numbers are ordered pairs! By plotting these ordered pairs you may be able to
determine the file’s password and decrypt the document.
Product Performance and Purpose:
1. The first line of the message looks like this:
4.5 3 3 4.5 3 6.5 4.5 8 6 8 7.5 6.5 7.5 4.5 6 3 4.5 3
On your worksheet titled “What Shape Am I?”, parentheses have been
inserted to turn these numbers into ordered pairs. Plot these points on your
worksheet and then determine the shape of the figure. You enter the name of
this shape as the password the document is decrypted!
2. You are not impressed with the double-agent’s work. He didn’t even think to
use any negative numbers to make the code a little tougher to crack. Answer
the question at the bottom of the worksheet titled “What Shape Am I?” to
explain how to plot an ordered pair like (-2, -1).
3. You are the mentor of a newly hired junior spy. You are in charge of her
training and she has been amazed by your method of cracking the coded
password. To help with her training, you have created the worksheet titled
“What Letter Am I”. She will learn the vocabulary of the coordinate plane by
completing this worksheet. Unfortunately, you must catch a plane for your next
secret mission and you will not be there to check her work. Create a key by
completing this worksheet so she may check her own work when she is done.
Extension: On a sheet of graph paper, draw a closed figure that forms a
recognizable picture or shape using all four quadrants. List the ordered pairs for your
picture in a manner similar to the table on the worksheet titled “What Shape Am I?”
Standards and Criteria for Success:
You will:
1. Plot the ordered pairs from the table on the worksheet titled “What Shape Am
I?” to determine the shape of the figure.
2. Answer the question at the bottom of the worksheet titled “What Shape Am I?”
to describe how the axes should be changed to plat a point like (-2, -1).
3. Complete the worksheet titled “What Letter Am I?”. Place each math
vocabulary word in the correct box and then answer all questions on the
worksheet.
4. Extension: On a sheet of graph paper, draw a picture or shape using all four
quadrants and then list the ordered pairs for all vertices in a table.