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-ArabicNumeration 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

3528

3(10x10x10) + 5(10x10) + 2(10) + 8(1)

3(103) + 5(102) + 2(101) + 8(100)

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. 113-122

However, everyone should be able to read and write Roman Numerals (p. 118).