Rumors
Numbers and Number Relations
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Objective
Students will explore an exponential growth pattern using problem solving, reasoning,
communications and connections.
Overview of the Lesson
The teacher shares the following scenario with the students:
Two students who were both born on December 21st, the date of the winter
solstice, decide that it would be great not to have to attend school on that day.
Therefore, they start a rumor that schools will be closed to celebrate the winter
solstice. So, on December 1st, one of the students told two of her friends that
school would be closed. On the next day, each of these students tells 2 students
and on consecutive days, each of the new students tells 2 more students and so
on. If there are 8,000 students in the school district, the question arises as to
whether the rumor was started early enough for everyone to have heard it?
Students act out the problem to understand how the rumor is being spread. Next, students
work in groups to determine strategies and solutions for solving this and related problems.
Materials
- Calculators
Procedure
Begin the class by having the students focus on how rumors are spread. In the video, the
teacher whispers something in the ear of one of the students who, in turn, whispers it to
her neighbor, and so on.
Next, set up a similar scenario as described below for your class:
Justin Miller and Agnes Malika share the same birthday on December 21st. One
day at the lunch table, they were discussing how great it would be not to have to
attend school on that day. Agnes figured that the winter solstice is a day of
celebration somewhere in the world, so it should be in New Briton, Connecticut.
She decided to start a rumor that all schools in the city will be closed on
December 21st. On December 1st, Agnes tells her friends Melissa and Tina. She
tells each of them to tell two more students and that each of the new students
should tell two more on the following day. There are 8,000 students in the
school district.
Allow students to act out this scenario by having students form a human triangle where
Agnes is first, then Melissa and Tina, then four student representing the two that Melissa
told and the two Tina told, etc. This will help students visualize the problem, understand
how this rumor is being spread, and an idea of the growth pattern.
Have students create mathematics questions about this situation. For example: Was the
rumor started early enough for all of the students to have heard that school will be closed
on December 21st? On which day would all of the students have heard that school will be
closed on the 21st? How many students would have heard the rumor by the 10th day of
December?
Encourage students to apply some of their problem solving strategies (make a diagram,
make an organized list, create a rule, etc.) to assist in their construction of solutions to the
problems. Tell students that as they work, try to create an algebraic representation or rule
which can be used to calculate the number of students who should have heard the rumor
on any given day.
Place students in groups. Encourage the groups to intuitively arrive at a prediction based
on the information obtained from the enactment. Have students devise strategies and
make predictions on: How many students they think should have heard the rumor by the
10th day? On which day could at least half of the students heard the rumor? Allow an
appropriate amount of time for groups to discuss their predictions.
In their groups, allow students to continue their investigation of whether the rumor was
started early enough for all of the students in the district to have heard it. They must be
able to support their answers. Some students may be able to construct a mathematical rule
to symbolize their findings.
Engage students in a class discussion to review their solutions and reasoning. Again, pose
questions designed to have students justify their conclusions. These conclusions might be
similar to those illustrated in Mathematically Speaking . . .
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