Linear and Exponential Patterns Investigation
Mathematics Big Idea and Major Topic: Patterns—Linear and/or Exponential
Title: Rumor Control
More specific statement of the topic: Develop an intuitive notion of linear and exponential
growth
What the students already know: Write a linear equation in slope intercept form, make a table,
graph a linear equation, concept of exponent, use a calculator
and find intersection
What part will the students have to figure out on their own? Be able to recognize the pattern of
linear and exponential equations
through tables and graphs.
Context: Technology can help information spread very quickly.
Statement of the task: Each day a publicist sends an e-mail containing a rumor to 100 people.
These one hundred people are asked not to spread the rumor. In order to
stop the rumor, you send a text message with the truth to two people who
text two people the next day and those two people each text two new
people the following day and so on. Is it possible for more people to
receive the truth than the number of people who have received the rumor?
If so, on what day?
Where might they get stuck? Organizing their idea and visualizing their data
What questions can I use to prompt them without giving away answers?
Have you tried making a table? Can you identify the variables? Have you made a graph?
What have you tried? Show me what you did. Is there another way? Have you seen
anything like this before? What do you need to know? How can you find it? How many
new people will know the truth after one day? Two days? Three days? How many total
people will know the rumor after one day? Two days? Three days?
Improving Student Achievement in Algebra, Grades 7-12. The Dupage1 Mathematics Network.
DuPage Regional Office of Education. May 2007
1
Rumor Control
Student Worksheet
Each day a publicist sends an e-mail containing a rumor to 100 people. These people are asked
not to spread the rumor. In order to stop the rumor, you send a text message with the truth to two
people who text two people the next day and those two people each text two new people the
following day and so on. You need to know if it is possible for more new people to receive the
truth in one day than the total number of people who have received the rumor? If so, on what
day?
1. Complete each table.
Number of days
1
2
3
4
5
6
7
8
9
10
11
12
Number of people
who received the
e-mail containing
the rumor
100
200
Number of days
1
2
3
4
5
6
7
8
9
10
11
12
Number of people
who received the
text message with
the truth
2
4
A. Is it possible for more new people to receive the truth in one day than the total
number of people who have received the rumor? If so, on what day?
B. How is your answer shown in the table?
2. Write an equation for each table. Identify your variables.
Improving Student Achievement in Algebra, Grades 7-12. The Dupage1 Mathematics Network.
DuPage Regional Office of Education. May 2007
2
3. Create a graph of each table on the same coordinate grid.
Improving Student Achievement in Algebra, Grades 7-12. The Dupage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
3
How is your answer shown in the graph?
Improving Student Achievement in Algebra, Grades 7-12. The Dupage1 Mathematics
Network. DuPage Regional Office of Education. May 2007
4