1. 2-4 Numeration Remember to Silence Your Cell Phone and Put It In Your Bag!

2. Introduction Mathematics was invented Numeral vs. Number Numeration system

3. Hindu-Arabic Numeration System 1. All numbers are constructed from ten basic symbols or digits. 2. It uses grouping by tens. 3. The position of a symbol in a numeral determines the value it represents. 4. There is a representation for zero.

4. Models of Place Value – Proportional Models Multi-base Pieces Unit Long Flat Block or Cube Base Ten Blocks Unit - One Long – One Ten Flat – One Hundred Block or Cube – One Thousand

5. Models of Place Value – Nonproportional Models Money Penny – One Dime – One Ten Dollar – One Hundred Colored Chips Example Red Chip – One Blue Chip – One Ten Yellow Chip – One Hundred Green Chip – One Thousand

6. Expanded Notation 3528 3(10x10x10) + 5(10x10) + 2(10) + 8(1) 3(10 3 ) + 5(10 2 ) + 2(10 1 ) + 8(10 0 ) 3(1000) + 5(100) + 2(10) + 8(1)

7. Nondecimal Bases You are responsible for: 1. Writing and counting in base 2, 3, 4, 5, 6, 7, 8, and 9 2. Changing a numeral from a given base (2, 3, 4, 5, 6, 7, 8, or 9) to a base ten numeral 3. Changing a base ten numeral to a numeral in a given base (2, 3, 4, 5, 6, 7, 8, or 9)

8. Other Early Numeration Systems You may omit pp. 113-122 However, everyone should be able to read and write Roman Numerals (p. 118).