Skip to content # Introduction to Finite Systems: Z6 and Z7

## Activity Guide

# This guide looks at the session in detail and gives sample problems.

Reiter, Harold. (2020). Introduction to Finite Systems: Z6 and Z7. In S. Kohli (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/introduction-to-finite-systems-z6-and-z7

Contributor(s): Harold Reiter

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

You are no doubt familiar with solving linear and quadratic equations with real numbers. However, in much the same way as learning Latin, French, or Spanish gives the language learner a better appreciation of English, so the careful examination of solution techniques in finite number systems adds depth to the mathematics students’ understanding of equation solving.
Precision is key when solving linear and quadratic equations in finite number systems where the only available digits are the remainders after dividing by 6 or 7. Discover why in Z7, adding 3 and 4 results in 0, and why the product of 3 and 4 is 5?

MP1 - Make sense of problems and persevere in solving them.

MP3 - Construct viable arguments and critique others' reasoning.

MP4 - Model with mathematics.

MP5 - Use appropriate tools strategically.

MP6 - Attend to precision.

MP7 - Look for and make use of structure.

MP8 - Look for and express regularity in repeated reasoning.

MP3 - Construct viable arguments and critique others' reasoning.

MP4 - Model with mathematics.

MP5 - Use appropriate tools strategically.

MP6 - Attend to precision.

MP7 - Look for and make use of structure.

MP8 - Look for and express regularity in repeated reasoning.