16 When Will I Ever Teach This?

ANCIENT NUMERATION SYSTEMS

One of the most fascinating parts of an MET course is the study of ancient systems. It is a great opportunity to look at history, not just of mathematics, but in general. Looking at systems with respect to place value, the concept of zero, and the symbols that were used is very useful as those ideas relate to our numeration system. Many students do not realize that a thorough understanding of ancient systems can provide an excellent foundation for our system and how to teach it.

Many of our students wonder why it is necessary to bother with ancient systems when these are not used anymore and we only teach our system in the schools. One very obvious reason is because it is in the school texts. However, all the reasons mentioned above are also excellent motivation for studying these systems.

The school text pages are from the Grade 3 book. There are also references to ancient systems in the teacher notes portions of the texts from grades 2 through 6. Not only can the topics be discussed for their mathematical significance, but you can also integrate the ideas into a social studies lesson with a multicultural approach. Looking at the mathematics of an ancient system, such as the Egyptian system, along with the culture and history of Egypt makes for a perfect integrated lesson.

Some books discuss a wide variety of not only ancient systems, but also of modern systems which use symbols different from our own. Again, a focus on a multi-cultural and integrated lesson is an added benefit to a traditional mathematics lesson.

Focus on Skills allows for practice with Babylonian, Roman, and Egyptian systems. Some MET books discuss other systems, but these seem to be the most common. We have provided the symbols for you as a reference. We tell our students not to worry too much about precision in re-creating the symbols. However, for students who enjoy artistic creations, drawing the symbols is fun and they really enjoy the art involved.

Focus on Concepts is mainly a writing assignment. Comparing and contrasting systems allows for a greater understanding of each system. By asking you to create your own numeration system and describe its features, it is a nice way to see if you understand the concepts. You also get to let your imagination and creativity be the focus of an assignment rather than just your mathematics skills.

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18 When Will I Ever Teach This?

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FOCUS ON SKILLS Name Ancient Numeration Systems

For problems 1 – 6, change each symbol into a number in our system.

1.

2.

3. CLXVI

4.

5.

6. CDXLVIII

For problems 7 - 9, convert each number to Egyptian, Babylonian, and Roman.

7. 437

8. 9731

9. 889