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Math I
General Outline
I Overview
II Numeration
III Multiplication
IV Division
V Fractions
VI Decimal Fractions
VII Introduction to Squares & Cubes
VIII Squaring & Cubing
IX Square Root & Cube Root
10
34
64
86
112
146
178
200
240
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
i
I Overview
Contents
AN OVERVIEW OF MONTESSORI MATHEMATICS:
10
11
The Montessori Mathematics Curriculum
The Early Childhood Mathematics Curriculum
The Elementary Mathematics Curriculum
p.
17
p.
13
11
23
Great Story:
II Numeration
Presentation:
p.23
Wooden Hierarchy Material
Presentation 1: First Arrangement
Presentation 2: Second Arrangement
p.
38
p.
38
Presentation 3: Introduction to Symbols
p.
36
34
36
Commutative and Distributive Laws of Multiplication
Exercise One: Number x a Number (Commutative Law)
Exercise Two: A Sum Multiplied by a Number (1 + 1) x 1
p.
41
p.
41
p.
43
Exercise Three: Multiplication of a Sum by a Sum (1+1)x(1+1) p.
43
Exercise Four: Multiplication of a Sum by a Sum with Signs & Cards
Exercise Five: Multiplying with Numbers Greater than Units
p.
45
39
Multiples
Lowest Common Multiples
Factors
Highest Common Factors
Measurement
Measurement of Length
p.
59
47
51
52
57
58
III Multiplication
Introduction
Other Measurments
Large Bead Frame
p.
66
p.
67
p.
67
p.
67
Presentation 1: Introduction to the Bead Frame
Presentation 2: Forming Numbers
Presentation 3: Bead Frame Paper
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66
62
Short and Long Multiplication
Presentation 1: One-Digit Multiplier
Presentation 2: Two-Digit Multiplier
p.
69
p.
71
69
73
p.
73
The Checker Board of Multiplication
Presentation 1: Introduction to Patterns and Placing Units
Presentation 2: Long Multiplication
p.
75
p.
75
Presentation 3: Multiplication Using Facts p.
75
Presentation 4: Long Multiplication with Partial Products
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
ii
Geometrical Form of Multiplication
Presentation:
p.
77
77
79
p.
79
Flat Bead Frame
Presentation 1: Introduction with a Two-Digit Multiplier
Presentation 2:
Recording Partial Product
p.
80
Bank Game
Presentation 1: One-Digit Multiplier
p.
81
p.
83
81
IV Division
Presentation 2: Two-Digit Multiplier
Long Division with Racks and Tubes
Presentation 1:
p.
87
p.
89
p.
91
p.
93
p.
94
Presentation 2: One-Digit Divisor with No Remainder
Presentation 3: Two-Digit Divisor with No Remainder
86
87
Presentation 4: One-Digit Divisor with Remainder and Writing Partial Quotients
Presentation 5: Two-Digit Divisor with Remainder and Writing Partial Quotients
Presentation 6: Special Cases
p.
95
Group Division with Stamp Game
Presentation 1: Short Division with a One-Digit Divisor
Presentation 2: Long Division with Two-Digit Divisor
Presentation 3: Long Division with a 3 Digit Divisor
Presentation 4: Holding Place with Zero
Presentation 5: Writing on Paper
p.
101
p.
101
p.
99
p.
97
p.
99
p.
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97
Presentation 6: Writing on Paper with a 3 Digit Divisor
Divisibility
Presentation: Divisibility by Two
Presentation: Divisibility by Three
Presentation: Divisibility by Four
Presentation: Divisibility by Five
p.
103
p.
105
p.
107
p.
107
103
Presentation: Divisibility by Eight p.
107
Presentation: Divisibility by Nine p.
107
Presentation: Divisibility by Eleven p.
109
Divisibility by Twenty-Five
p.
109
V Fractions
Introduction to Quantity, Symbol and Language
Presentation 1: Quantity
Presentation 2: Symbol
Presentation 3: Language
p.
114
p.
114
p.
115
112
114
Equivalence
Presentation 1: With Circular Insets
p.
117
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
117
iii
Presentation 2: With Divided Triangle and Square Insets
Presentation 3: With Constructive Triangles
p.
117
p.
117
Operations: Simple Cases
Presentation 1: Addition with Same Denominators
Presentation 3: Multiplication by a Whole Number
Presentation 4: Division by a Whole Number
Presentation 1: Addition
p.
125
p.
127
p.
127
p.
129
p.
129
p.
119
p.
121
p.
121
Presentation 2: Subtraction with Same Denominators
p.
123
119
Addition and Subtraction with Different Denominator
Presentation 2: Subtraction
125
Presentation 3: Leading to Abstraction
Presentation 4: Finding Common Denominators beyond the Scope of the Material
Presentation 5: Abstraction Using Common Denominator
Presentation 7: Applying P.F. to Find C.D. p.
129
Presentation 8: Reducing the Terms First to Find the Common Denominator
Presentation 6: Applying the Lowest Common Multiple to Find the Common Denominator p.
129
p.
131
Multiplication
Presentation 1: Sensorially Multiplying Fractions
Presentation 2: Writing on Paper
p.
136
p.
132
132
138
p.
138
Division
Presentation 1: Dividing a Whole Numbers by Fractions
Presentation 2: Dividing Fractions by Fractions p.
140
Presentation 3: Group Division
p.
142
p.
142
p.
142
Presentation 4: Division Using Cross Multiplication
Presentation 5: Leading to Abstraction
VI Decimal Fractions
Introduction:
p.
149
Word Problems
Notes on the Fraction Charts
Introduction to Decimal Fractions
Presentation 1: Presentation of Quantity p.
149
Presentation 2: Symbol Linked with Quantity
Passage Two
Presentation:
p.
153
p.
151
p.
151
Presentation 3: Formation and Reading of Quantity
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149
Simple Operations
p.
154
p.
155
p.
155
p.
155
Passage One: Addition p.
154
Passage Two: Subtraction
Passage Three: Multiplication by a unit
Passage Four: Division by a unit
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
154
iv
Multiplication of Decimal Fractions
Passage One: With a Multiplier Less Than One
Example I
Example II
Example III
p.
157
p.
157
p.
159
p.
160
p.
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157
Passage Two: Writing Partial Products
Presentation:
Presentation:
Example I
Example II
Example III
Presentation:
p.
161
Abstraction of the Rule for Multiplying Decimal Fractions
Division of the Decimal System
p.
162
p.
162
p.
163
p.
162
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162
Abstraction of the Rule for Dividing Decimal Fractions
p.
164
p.
164
p.
165
Passage One: Division by a Whole Number
Passage Two: Division by a Decimal
164
The Conversion of Common Fractions to Decimal Fractions
Presentation 1: Sensorial Conversion to Hundredths
Presentation 2: Conversion to Any Decimal Number
p.
166
p.
167
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169
The Decimal Checkerboard
Introduction to the Decimal Checkerboard
Presentation:
Presentation:
p.
169
p.
171
p.
171
p.
172
p.
173
p.
174
The Decimal Checkerboard p.
171
Passage One: Introduction
Passage Two: Multiplication
p.
169
Passage Three: Multiplication writing partial products p.
172
Passage Four: Multiplying on paper
Presentation:
Presentation:
Presentation:
p.
174
p.
175
p.
175
p.
176
p.
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p.
176
The Effects of Multiplication by Powers of Ten
The Effects of Division by Powers of Ten
The Relative Size of Terms When Multiplying Numbers p.
176
Passage One: Fractions Less Than One Times Whole or Mixed Numbers Greater Than One.
Passage Two: Decimal Fractions Less Than One Times Decimal Fractions Less Than One
Passage Three: Whole Number or Mixed Fractions Times the Same
The Relative Size of Terms When Dividing Numbers p.
177
Presentation:
p.
177
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
p.
176
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