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# Changing the Face of Math Education Book 1 Chapter 4

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Number Base Numeration Systems
4.1 Introduction…56
4.2 Hindu-Arabic Numeration System…57
4.3 Other Number Base Numeration Systems Where the Base is Less Than 10…60
4.4 Other Number Base Numeration Systems Where the Base is Greater Than 10…65
4.5 Expressing a Numeral in Standard Form…67
4.6 Changing a Base Numeral from One Base to a Different Base…69
4.7 Practice Exercises for Chapter 4…73

In this chapter, you will be introduced to a variety of number base numeration systems. This will give you the opportunity to gain a more complete understanding of our numeration system, how other number base numeration systems are similar to ours and how they are used today or could be used. Using material from this chapter would be an interesting way to view mathematics from a different perspective while practicing number sense. Also, computers use base 2 and base 16 numeration systems.

Base ten numeration system should be introduced as students learn to add, subtract, multiply, and divide whole numbers. You could introduce certain aspects of other numeration systems early but, I would not go into detail until middle school or later. I would take a single day now and then throughout the year and introduce certain aspects about one system as an interesting, abstract, fun activity. This could be used on a day before a vacation or at the end of the year.

Material in this chapter is an interesting way to have students view mathematics from a different perspective while practicing their number sense. You could also have students add and subtract in other number bases to see if they understand the conceptual approach to addition and subtraction. Another reason would be the fact that computers use base 2 and base 16 numeration systems.

Keep the problems simple and manageable, do not try to be too creative with your problems. Students should be expected to understand the concepts behind a number base numeration systems and be able to move from one base to another with ease. This should be an interesting, intriguing, and challenging section. The goal is for the student to understand how other number base numeration systems work similar to our system.
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