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. SymbolQuantity SymbolQuantity A□C□□□ B□□D□□□□

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… a)AA b)BD c)BAD d)ABD e)A0A

9. Exploration 2.8 (cont’d) Examples: What comes before… a)D0 b)B00 c)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, do Part 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.