Math 302A section 5

January 27, 2009 0011 0010 1010 1101 0001 0100 1011 2 1 4 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 0011 0010 1010 1101 0001 0100 1011

Exploration 2.8 group Alphabitia systems class Alphabitia system 2 1 4 Exploration 3.1 (Addition and Subtraction using the class Alphabetia system) Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 Teach us about how your system is designed.

2 1 4 Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 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) 2 1 4 Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 We will need a common class Alphabetia system to use. Theres something special about this system! (Well discover this a bit later.) 2

1 4 Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 Class Alphabitia system: Symbol Quantity Symbol A

C B D Well use 0 as a placeholder. Quantity 2 1

4 Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 Place value system (no gaps required) 5 is important number Counting: using visual aids A, B, C, D, A0, AA, AB, 2 1

4 Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 Examples: What comes next after a) AA b) BD c) BAD d) ABD e) A0A 2 1

4 Exploration 2.8 (contd) 0011 0010 1010 1101 0001 0100 1011 Examples: What comes before a) D0 b) B00 c) D0D0 2 1 4

Exploration 3.1 0011 0010 1010 1101 0001 0100 1011 Addition & Subtraction in Alphabetia 2 1 Together, well do Part 1 #2a. Either write the explanation in words or draw pictures explaining. 4

Exploration 3.1 (contd) 0011 0010 1010 1101 0001 0100 1011 With a partner, do Part 1: #3 do the first three. Part 2: #3 do a, e, and i. 2 1 4 Homework 0011 0010 1010 1101 0001 0100 1011

Exploration 3.1 Part 2 #3: do b, f and j. Explain your thought process carefully for each of these. 2 1 4

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