Additive Numeration Systems
1.2 Tally Numeration System…3
1.3 Egyptian Numeration System…5
1.4 Roman Numeration System…7
1.5 Creating an Additive Numeration System of Your Own…12
1.6 Monetary Numeration System…13
1.7 Practice Exercises for Chapter 1…15
As a teacher or student of mathematics, you need to have a strong conceptual understanding of math. Looking at different numeration systems will give you a deeper understanding as to what a numeration system is, how different systems work, and how they are connected to our present day system. What is a numeration system? A numeration system is a collection of properties and symbols agreed upon to represent numbers systematically. Our present day numeration system is the Hindu-Arabic numeration system and we will compare symbols used in other systems to equivalent symbols in our present day system. We will discuss the Hindu-Arabic system in more detail in the next section.
In this chapter, you will examine three different additive systems, Tally, Egyptian, and Roman Numeration Systems. You will also be given the knowledge as to how you could build your own unique additive numeration system. You will also see how a common task performed on a daily basis could be thought of as a special numeration system.
The Tally Numeration System introduced in this chapter is probably the best known and used by many individuals in their life without calling it a numeration system. This system could be introduced early to give students an interesting way of counting by fives and ones. Later on, it could be used as an abstract way to practice finding the sum of repeated addition by five’s and one’s.
The Egyptian Numeration System introduced in this chapter is probably the least known and is seldom introduced to individuals. This system could be introduced to your students as a means of introducing the concept behind a numeration system, develop a visual connection between objects and numerals, and practice addition.
The Roman Numeration System introduced in this chapter was part of the math curriculum up until somewhere in the 90’s and is now seldom discussed in the classroom. Roman numerals are used today in several places such as, page numbers in the beginning of a book, corner stone of old buildings, and the Super Bowl. This system could be introduced to your students as a means of introducing the concept behind a numeration system, develop a visual connection between objects and numerals, and practice addition.
Do not make students memorize the symbols and their values. This will more than likely create math anxiety in some of your students and turn them off to math. We want students to enjoy and be interested in math. The goal is for the student to understand what an additive numeration system is and be introduced to the existence of other numeration systems. Therefore, tables and values should always be available and used on assignments and quizzes.
You could also use the Babylonian Numeration System or Mayan Numeration System as an activity on a shortened day, or the day before a break to add interest and intrigue to mathematics.