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

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

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

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)

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.)

Exploration 2.8 (cont’d) Class Alphabitia system: We’ll use “0” as a placeholder. SymbolQuantity SymbolQuantity A□C□□□ B□□D□□□□

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, …

Exploration 2.8 (cont’d) Examples: What comes next after… a)AA b)BD c)BAD d)ABD e)A0A

Exploration 2.8 (cont’d) Examples: What comes before… a)D0 b)B00 c)D0D0

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

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

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