Mathematics Manual 1 - Linear Counting - - Decimal System - - Memorization of Operations - Dr. Pamela Zell Rigg Copyright 2004 Montessori Research and Development 16492 Foothill Boulevard, San Leandro, CA 94578-2105 (510) 278-1115 FAX (510) 278-1577
INTRODUCTION 1. Statement of Philosophy
TABLE OF CONTENTS CHAPTER 1 INTRODUCTION...1 CHAPTER 2 LINEAR COUNTING...2 THE NUMBER RODS... 3 THE SANDPAPER NUMERALS... 9 THE NUMBER RODS AND NUMERALS... 12 THE SPINDLE BOXES... 15 THE NUMERALS AND COUNTERS... 18 THE MEMORY GAME WITH NUMERALS AND COUNTERS... 21 LINEAR COUNTING... 23 THE SHORT BEAD STAIR... 24 SNAKE GAME: SEARCH FOR TEN... 25 TEEN BOARD: QUANTITY... 28 TEEN BOARD: SYMBOLS... 30 TEEN BOARD: QUANTITY AND SYMBOLS... 32 NUMBER RODS - TEEN PRESENTATION... 35 TEN BOARD: QUANTITY... 37 TEN BOARD: SYMBOLS... 39 TEN BOARD: QUANTITY AND SYMBOLS... 41 ONE HUNDRED CHAIN AND LABEL... 44 ONE THOUSAND CHAIN AND LABELS... 46 ONE HUNDRED CHAIN AND ONE THOUSAND CHAIN... 49 ONE HUNDRED BOARD AND NUMERALS... 50 SQUARING CHAINS: ONE THROUGH TEN... 52 CUBING CHAINS: ONE THROUGH TEN... 54 CUBING CHAINS LAYOUT... 56 CHAPTER 3 BASE TEN... 57 INTRODUCTION TO THE DECIMAL SYSTEM: QUANTITY... 58 INTRODUCTION TO THE DECIMAL SYSTEM: SYMBOLS... 60 THE DECIMAL SYSTEM: ASSOCIATION OF QUANTITY AND SYMBOL... 62 FORMATION OF NUMERAL CARDS... 66 ADDITION WITH THE GOLDEN BEADS... 67 REGROUPING WITH THE GOLDEN BEADS FOR ADDITION AND MULTIPLICATION... 71 SUBTRACTION WITH THE GOLDEN BEADS... 73 REGROUPING WITH THE GOLDEN BEADSFOR SUBTRACTION AND DIVISION... 75 MULTIPLICATION WITH THE GOLDEN BEADS... 78 DIVISION WITH THE GOLDEN BEADS (ONE-DIGIT DIVISION)... 82 DIVISION WITH THE GOLDEN BEADS (TWO-DIGIT DIVISOR DECURIAN DIVISION ). 86
INTRODUCTION TO THE STAMP GAME... 90 FORMATION OF QUANTITY IN STAMPS... 92 ADDITION WITH THE STAMP GAME... 89 SUBTRACTION WITH THE STAMP GAME... 94 MULTIPLICATION WITH THE STAMP GAME... 96 DIVISION WITH THE STAMP GAME....97 THE DOT BOARD: ADDITION... 103 INTRODUCTION TO THE BEAD FRAME... 106 INTRODUCTION TO THE BEAD FRAME WITH THE GOLDEN BEADS... 108 INTRODUCTION TO THE BEAD FRAME WITH NOTATION PAPER... 111 READING AND WRITING NUMBERS ON THE BEAD FRAME...114 ADDITION WITH THE BEAD FRAME...115 SUBTRACTION WITH THE BEAD FRAME...116 CHAPTER IV MEMORIZATION... 118 INTRODUCTION TO MEMORIZATION WORK...119 INTRODUCTION TO THE ADDITION STRIP BOARD... 120 ADDITION STRIP BOARD... 122 ADDITION CHART 3... 128 ADDITION CHART 4 (THE HALF TABLE)... 131 ADDITION CHART 5 (SIMPLIFIED CHART)... 133 ADDITION CHART 6 (BLANK CHART)... 135 ORAL GAMES FOR THE MEMORIZATION OF ADDITION... 138 ADDITION SNAKE GAME... 140 BEAD BARS FOR THE MEMORIZATION OF ADDITION... 142 BEAD BARS: COMMUTATIVE LAW... 144 BEAD BARS: MULTIPLE ADDENDS... 146 BEAD BARS: ADDENDS LARGER THAN TEN... 147 BEAD BARS: ASSOCIATIVE LAW... 149 BASIC FORMATS FOR ADDITION... 155 ADDITION STORY PROBLEMS... 16 INTRODUCTION TO THE SUBTRACTION STRIP BOARD... 158 SUBTRACTION STRIP BOARD... 160 ORAL GAMES FOR THE MEMORIZATION OF SUBTRACTION... 171 BASIC FORMATS FOR SUBTRACTION... 163 SUBTRACTION STORY PROBLEMS... 175 SUBTRACTION SNAKE GAME... 177 INTRODUCTION TO THE MULTIPLICATION BEAD BOARD... 180 MULTIPLICATION BEAD BOARD... 182 MULTIPLICATION BEAD BOARD: PREPARED EQUATION SLIPS... 184 MULTIPLICATION BEAD BOARD: COMBINATIONS OF NUMBER... 186 MULTIPLICATION CHART 3... 187
MULTIPLICATION CHART 4... 188 MULTIPLICATION CHART 5 ( BINGO CHART or BLANK CHART )... 190 ORAL GAMES FOR THE MEMORIZATION OF MULTIPLICATION... 193 BASIC FORMATS FOR MULTIPLICATION... 195 MULTIPLICATION STORY PROBLEMS... 196 SNAKE GAME FOR MEMORIZATION OF MULTIPLICATION... 198 CUBING CHAINS FOR THE MEMORIZATION OF MULTIPLICATION... 200 BEAD BARS FOR THE MEMORIZATION OF MULTIPLICATION... 206 CONSTRUCTION OF THE DECANOMIAL... 218 POWERS OF NUMBERS... 227 FURTHER EXPLANATION - POWERS OF NUMBERS... 231 INTRODUCTION TO THE UNIT DIVISION BOARD... 233 UNIT DIVISION BOARD... 235 DIVISION BEAD BOARD... 241 DIVISION CHART 1... 242 DIVISION CHART 2... 243 DIVISION STORY PROBLEMS... 247 RELATIONSHIPS OF MULTIPLICATION AND DIVISION... 249 ORAL GAMES FOR THE MEMORIZATION OF DIVISION... 250 BASIC FORMATS FOR DIVISION... 252