Rumors Design

The Rumors activity asks students to compare the difference in rates of growth of rumors in a population between a controlled situation and a real-life situation. Given the controlled situation graph, the students are asked to predict how the real-life situation will look in a graph.

This activity could be used to introduce and/or reinforce concepts of linear, step, and exponential functions. Often students don't understand the importance that the constant of time plays in a linear function. This exercise could also be used to compare controlled results vs. real-life results.

Problem Description
Shanika has learned from a phone call that William has dyed his hair green. She can't wait to share this rumor with all the people at school. She stands at the door to the cafeteria, where people are entering every ten seconds, and tells every person who enters. In real life, Shanika would probably not stand at the door of the cafeteria and tell the rumor to everyone who walks in. Here is a more realistic scenario: Shanika has just learned that William has dyed his hair green. Shanika is very excited and runs around telling the rumor to everybody she meets. She makes a point of telling people not to tell anyone else.

What will the shape of the graph be?

1. 2.  3.

Run the simulation to find the shape of the new graph. Use what you learn from the simulation to answer the questions.

Questions / Explorations

 * Describe the shape of the new graph in terms of the x and y axes. (Hint: How is it different from the first graph?)
 * What happened differently in how Shanika spread the rumor at the cafeteria door from how she spread it by running around during lunch that changed the way the graph looked?
 * What else is spread in the real world, similar to the way that rumors are spread?
 * Bonus: What if each person Shanika tells just can't keep the promise not to tell anyone else, and tells the rumor to other people? How will this change the shape of the graph?

Standards
NCTM Math Standards
 * Algebra
 * understand patterns, relations, and functions
 * Geometry
 * use visualization, spatial reasoning, and geometric modeling to solve problems
 * Problem Solving
 * solve problems that arise in mathematics and in other contexts
 * Communication
 * communicate mathematical thinking coherently and clearly to peers, teachers, and others
 * use the language of mathematics to express mathematical ideas precisely
 * Connections
 * recognize and apply mathematics in contexts outside of mathematics

Lesson Plans

 * ePOW (electronic Problem of the Week) activity hosted on the MathForum
 * Teacher Support
 * Lesson plans created by participants of the 2010 Summer Institute