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

Introduction Mathematics was invented Numeral vs. Number Numeration system

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.

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

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

Expanded Notation (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)

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)

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