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Math II
General Outline
I Powers of Numbers
II Negative Numbers
III Non-Decimal Bases
IV Word Problems
V Ratio & Proportion
VI Algebra
1
15
27
45
65
83
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
i
Contents
I Powers of Numbers
A. Powers of 2 2
Presentation:
Passage One: Introduction p.2
Extension I: Terminology
Extension II: Exploration with Bases Other than Two
Passage Two: Different Unit Size p.6
Passage Three: Hierarchical material p.8
1
B. Exponential Notation
Presentation:
10
II Negative Numbers
Passage One: Behavior of Exponents when Multiplying Number of the Same Base p.10
Passage Two: Behavior of Exponents when Dividing Numbers p.12
A. Addition Using Negative Numbers
Presentation:
16
p.16
15
Passage One: The Snake Game with Negative Numbers and Negative Changing
Passage Two: Writing p.18
Passage Three: Introduction to the Ten Bar p.18
B. Subtraction of Sign Numbers
Presentation:
20
p.22
Deriving the Rule for Subtracting Sign Numbers
C. Multiplication of Sign Numbers
Presentation:
D. Division of Sign Numbers
25
Presentation:
24
III Non-Decimal Bases
A. Numeration
29
Passage One: Numeration
Part A: Counting on a strip p.29
Part B: Bases larger than 10 p.29
27
B. Operations in Bases
31
Part A: Addition p.31
Part B: Subtraction p.33
Part C: Multiplication p.35
Part D: Division p.36
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
ii
C. Conversion from One Base to Another
37
Part A: To convert a number from any base to base 10 p.37
Part B: To convert from base 10 to another base p.39
Part C: Changing to bases larger than 10 p.41
Part D: Changing bases using the base chart p.42
Example I:
Example II:
Example III:
IV Word Problems
A. Introduction to Word Problems
B. Distance, Velocity and Time
47
Presentation:
Passage One: Introduction p.47
Passage Two: Solving for Distance p.47
Level One
Level Two
Level Three
Passage Three: Solving for Velocity p.49
Level One
Level Two
Level Three
Passage Four: Solving for Time p.52
Level One
Level Two
Level Three
46
45
C. Principal, Interest, Rate and Time
Presentation:
Passage One: Introduction p.53
Passage Two: Solving for Interest p.54
Level One
Level Two
Level Three
Passage Three: Solving for Rate p.56
Level One
Level Two
Level Three
53
Passage Four: Solving for Principal
Level One
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
iii
Level Two
Passage Five: Solving for Time
Level One
Level Two
Level Three
p.62
V Ratio & Proportion
A. Ratio
66
Presentation: Introduction
65
Passage One: Introduction p.66
Passage Two: Introduction to the Language p.66
Passage Three p.68
Passage Four p.68
Passage Five: Exploring the Idea Arithmetically p.68
Passage Three:
Passage Four:
Passage Six: Ratios Written as Fractions p.70
Passage Seven: Stating the Ratio Algebraically p.71
Passage Eight: Word Problems p.72
Example A
Example B
Example B Algebraically
Example C
Example C Arithmetically
Example C Algebraically
B. Proportion 77
Presentation: Introduction
Exercise One: Determining if Something is in Proportion p.78
Exercise Two: Proportion Between Geometric Figures p.78
Exercise Three: With 3 Dimensional Figures p.79
Exercise Four: p.80
C. Calculations with Proportion
81
Exercise One: Arithmetically p.81
Exercise Two: Algebraically (for older children) p.81
Exercise Three: Applications p.82
Example I
Example II
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org
iv
VI Algebra
A. Introduction to Algebra
84
83
Exercise One: Balancing an Equation p.84
Exercise Two: Balancing an Equation When Something is Taken Away p.85
Exercise Three: Balancing an Equation When Something is Multiplied p.85
Exercise Four: Balancing an Equation When it is Divided p.85
B. Operations With Equations
86
Exercise One: Addition p.86
Exercise Two: Subtraction p.86
Exercise Three: Multiplication p.86
Exercise Four: Division p.86
C. Algebraic Word Problems
Example I: p.87
Example II: p.87
Example III: p.87
Example IV: p.88
Example V: p.88
Example VI: p.88
Example VI: p.89
Example IX: p.89
Example X: p.90
Example XI: p.90
Example XII: p.90
87
Copyright 2009 | Jonathan Feagle
www.FreeMontessori.org

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