In this unit, students apply the concepts and processes related to real numbers to the study of other operational systems. By relating everyday situations to abstract concepts, students build reasoning skills. Students use their knowledge of mathematics as a language of carefully defined terms and symbols to make sense of modular arithmetic and operations in bases other than base 10. Modular arithmetic is one of the foundations of number theory and, along with number systems in other bases, provides the foundation for abstract algebra.
In previous math courses, students learned operations and properties of numbers in infinite number systems. In this unit, students combine the set theory they have learned in IM with their knowledge of number operations and properties to consider finite sets in modular arithmetic. Their analysis of systems for group properties provides an introduction to group theory. Students learn that modular arithmetic and finite operational systems have real-life applications; including computer programming, chemistry, music, and visual arts.
Computers and computer graphics are applications of number systems with bases other than base 10. As students consider other number bases, they apply their foundational knowledge of place value. Throughout this unit, students make connections to the mathematics concepts and processes they have learned; and have the opportunity to strengthen their mathematical foundations as they strengthen their abstract reasoning skills.
Instructional flow (PDF)
Unit 6 Standards for Investigations into Mathematics (IM)(PDF)
Explanation of what your child should understand by the end of each unit (enduring understandings), how he/she will get to that understanding (essential questions), and how he/she will be evaluated (indicators).
Content map for IM Unit 6 (PDF)
| Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7 |