A+World+of+Number+Systems

= A World of Number Systems = by Joe Todaro, Curriculum Developer & Consultant (jtodaro@pacbell.net) In the same way that learning a foreign language can help you better understand your mother tongue, learning about a variety of number systems can help students become "fluent" in the base-ten system. For example, the idea of place value is a cornerstone of K-12 mathematics. Comparing number systems that use place value to systems that do not use place value can give students deep insight into the workings of our familiar base-ten system.

Here are some of the Internet's best resources for taking students on a journey through the world of number systems.

When youngsters first learn to count, they typically think of 17 as a symbol representing 17 objects. It is simply "the thing that comes after 16." Later, as they begin to understand the base-ten number system, they see that the number 17, which is composed of a 1 and 7, represents 1 ten and 7 units. This is an essential understanding. Before having students explore number systems, check their knowledge of our base-ten system by having them use base-ten blocks to represent numbers. For example, ask students to use the virtual blocks at these sites to show the numbers 4, 40, 45, 405, and 450.
 * Beginning With Base Ten**


 * [|Base 10 Blocks]
 * [|Using Base 10 Bloocks]
 * [|Virtual Manipulatives: Base Blocks]

Other than ten, the most common number-system base is two. In fact, the base-two (or binary) system, which consists of nothing but 0's and 1's, is the foundation of very computer's CPU. Rather than giving students a detailed explanation of binary numbers, consider having them investigate the following sites on their own. Have students keep track of their findings as they experiment with decimal-binary conversions and then ask them to explain binary numbers in their own words.
 * Binary Numbers**


 * [|The Binary System]
 * [|Binary & Decimal Numbers]
 * [|Decimal / Binary Conversion Tool]
 * [|Decimal and Binary Equivalence]

For many students, Roman numerals are the first alternative number system that they see. Unlike our base-ten system, Roman numerals do not include the idea of zero. also, the position of a numeral can indicate that it is added to or subtracted from an adjacent numeral. After students have experimented with the converters, games, and calculators at the following sites, have them work in small groups to prepare a two-column chart showing the pros and cons of Roman numerals.
 * Roman Numerals**


 * [|Roman Numeral Converter]
 * [|Roman Numerals]
 * [|Easy Roman Numerals]
 * [|Compvter Romanvs]

The Babylonian number system, developed around 1900 BCE, is often regarded as the world's first place-value system. That is, the value of a numeral depended on its position within a number, just as in our modern-day system of Arabic numerals. Unlike our system, however, the Babylonians used 60 as a base. Have students visit the sites below and then ask them to write some large numbers using the Babylonian system. This may help students recognize one of the drawbacks of the system - the lack of a symbol for zero!
 * Babylonian Numbers**


 * [|Babylonian Numerals]
 * [|Bablylonian Mathematics]

The Maya were one of the first civilizations to incorporate the concept of zero into their number system. The site provided below offers a straightforward introduction to this number system as well as an interactive converter near the bottom of the page. give students a chance to convert several base-ten numbers to Mayan numbers. Then have them discuss the advantages of having a symbol for zero in a number system.
 * Mayan Numerals**


 * [|Mayan Mathematics]

The Egyptian numbers system is a base-ten system that does not use place value. As such, it presents a valuable contrast to our everyday number system. The Egyptian math site includes an overview and some word problems (click on the link near the bottom of the page). Use the problems to give students a taste of mathematics in the time of the pharaohs!
 * Egyptian Numerals**


 * [|Egyptian Math]
 * [|Egyptian Numbers]
 * [|Egyptian Calculator]

Although much of today's written Chinese uses Arabic numerals, the traditional Chinese number system is still in use and well worth investigating in the classroom. share the following sites with students. Then ask, Is the Chinese number system a base-ten system? Does it use place value? Does it include a symbol for zero? Have students present their responses to these questions and encourage them to give specific examples of Chinese numbers to support their answers. The Numbers and Counting site will help students learn to draw and pronounce Chinese numerals for user in their presentations.
 * Chinese Numerals**


 * [|The Chinese Numeration System]
 * [|Numbers and Counting]