SUBJECT: Algebra
GRADE: Ninth
TECHNOLOGY: Spreadsheet
BY: Kristin Ramey

THE RUMOR PROBLEM

Audience: Basic Algebra / High School, 9th grade

Objectives:

Students will identify the exponential equation based on the spread of the rumor. They will investigate the attributes of the function using a spreadsheet and will predict the growth of the equation. They will experiment with the rate of expansion by manipulating the base unit. Students will apply this data to a real life problem and be able to address questions based on the rumor scenario.

Materials: A computer lab with a spreadsheet software (Microsoft Excel is the model used, an overhead or chalk board).

Procedure:

Rumor Problem:

Tara, a high school junior, wants to ask Billy to the prom. Tara tells her two best friends her plans. Unbeknownst to Tara, her two friends each tell two of their friends, who in turn tell two of their friends. So, on the first day, two students know the rumor; on the second day four more students will know the rumor; on the third day eight more students will know the rumor, and so on. How many new students will be told the rumor on day 10? Supposing that Billy is the last student to know, and there are 16,000 students at Jamestown, on what day will Billy hear about Tara's intentions?

Note: This problem is similar to the rumor problem posed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, p.99).

Pose the problem to the students. Physically draw out the first three days on the chalkboard to make sure students see how the rumor is spreading.
Ask students to make a chart of the rumor. Assist the students to come up with the three different headings:

1) Day
2) The number of new people who hear the rumor on a given day
3) Total number of people who have heard the rumor on a given day, including Tara.

Have students fill in the first four days. Ask them if they see a pattern. Work students through the formula.

n --- for Day
2^n ---- for The number of new people...
2^(n+1) - 1 ---- for Total number of people...

Now, have students open Microsoft Excel on their computers. Ask them to label the table so that it will concur with the previous chart.
Pose the problem of going from one column to the next, to the students. Students will type in the equations for each column.
In the cell under "Days" : =A2+1
In the cell under "NewÖ" : =2^(A2)
In the cell under "TotalÖ": =2^(A2 +1) - 1

Using the Cut and Paste options, they will continue the chart.
They will then answer questions based on the data.

Evaluation:

Students will print out their charts. This will serve as evidence of the functional properties. A handout will also assist in rating their level of meeting the objectives (following page). The questions on the worksheet range from testing simple comprehension to actual analysis.

Worksheet: The Rumor Problem

1) What equation did you use in the "Day" column?

2) What equation did you use in the "The number of new people who hear the rumor on a given day" column?

3) What equation did you use in the "Total number of people who have heard the rumor on a given day, including Tara" column?

4) What is the total amount of people who will know the rumor in two weeks?

5) How many new people will find out on the 10th day?

6) On what day will Billy find out?

What if each person told 5 new people instead of only two?

Create a new spreadsheet and compare the data between the two cases.