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Alphabetia Systems Exploration: Designing a Unique Numerical System

Join the class Alphabitia system exploration to understand the design of a special numerical system. Learn the distinction between quantity and numeral representation, importance of consistency, and the use of placeholders. Discover the significance of the Alphabetia system with examples and counting techniques using visual aids A, B, C, D, A0, AA, AB, and more. Engage in Addition and Subtraction with Alphabetia, working on various exercises in pairs. Improve your understanding of this innovative system through thoughtful explanations and drawings. Dive into a fun and educational journey of exploring numerals and quantities in a unique way.

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Alphabetia Systems Exploration: Designing a Unique Numerical System

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  1. January 27, 2009 “A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort.” -Herm Albright

  2. January 27, 2009 • Exploration 2.8 – group Alphabitia systems – class Alphabitia system • Exploration 3.1 (Addition and Subtraction using the class Alphabetia system)

  3. Exploration 2.8 (cont’d) • Teach us about how your system is designed.

  4. Exploration 2.8 (cont’d) • Remember, there is a distinction between a quantity (“number”) and the symbol we use to represent the quantity (“numeral”). • It is important that we have only ONE way to represent a number. • It is also important that we can continue our system (i.e. given a number, we can determine what comes next)

  5. Exploration 2.8 (cont’d) • We will need a common class Alphabetia system to use. • There’s something special about this system! (We’ll discover this a bit later.)

  6. Exploration 2.8 (cont’d) Class Alphabitia system: We’ll use “0” as a placeholder.

  7. Exploration 2.8 (cont’d) Place value system (no gaps required) 5 is important number Counting: using visual aids A, B, C, D, A0, AA, AB, …

  8. Exploration 2.8 (cont’d) Examples: What comes next after… • AA • BD • BAD • ABD • A0A

  9. Exploration 2.8 (cont’d) Examples: What comes before… • D0 • B00 • D0D0

  10. Exploration 3.1 Addition & Subtraction in Alphabetia • Together, we’ll do Part 1 #2a. • Either write the explanation in words or draw pictures explaining.

  11. Exploration 3.1 (cont’d) With a partner, doPart 1: #3 do the first three.Part 2: #3 do a, e, and i.

  12. Homework • Exploration 3.1 Part 2 #3: do b, f and j. Explain your thought process carefully for each of these.

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