Daniella Bak (dbak@dimacs.rutgers.edu)
Joanie Funderburk (funderbu@dimacs.rutgers.edu)
Bill Metzler (wmetzler@dimacs.rutgers.edu)
Lora Monfils (lmonfils@dimacs.rutgers.edu)
Category
Modular Arithmetic
The Problem
We have crash-landed on a planet where the creatures have 8 fingers. The numerical systems are all based on the number 8. The activity will be to compute some calculations within this different type of system. An extension will be done using similar creatures with 14 fingers. (Others could be done as well).
Grade Levels
The lesson is appropriate for grades 7-12.
Suggested Materials
Some students may wish to use calculators.
Prerequisites
Simple arithmetic is all that is needed.
Activity Description
As an introduction to the activity, the teacher poses the following questions:
A. 9+6=3. What am I talking about if that makes sense?
B. A lightbulb package says it has a life of 1000 hours. If the light we turned on right now, at what time will it burn out?
C. What day of the week will it be 97 days from now?
(Below is an activity for students to complete in small groups. The teachers will circulate and guide the students to work modular 8.)
You have crash-landed on the planet of the Eights. This planet is a carbon copy of Earth, with one noticeable exception: the creatures on this planet have four fingers on each hand. The society functions around the number 8 (for example, the clock goes from 1 to 8).
The teacher poses the following questions:
1. Explain how the following areas of life will operate: time(clock, calendars), measurement, etc. Be specific, and justify your explanations.
2. Use your explanations above to answer the following questions. Justify your answers.
3. On a neighboring planet, the creatures have 14 fingers (seven on each hand). Complete questions 1 and 2 above for this new planet.
4. (If you finish:); Write a few questions about the Planet of the Eights (or another planet) for your classmates to answer.