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

**Classifications**

Author(s): Harold Reiter

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 studentsâ€™ 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?

Topics covered: Algebra / Arithmetic, Number Theory

Session styles: Problem Posing, Work Backwards

Mathematical practices: 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.

Supporting materials: Facilitator Guides

Associated Math Circles: MTC Network