Table of Contents
- Introduction
- Numeration
- Introduction
- Quantities in the Decimal System
- Numerals (Symbols)
- Union of Quantities and Numerals (Symbols)
- Additional Exercises in Numeration
- The Hundred Board
- The Seguin Boards
- Introduction to Operations Using the Change Game
- Golden Bead Chains
- Hierarchical Material
- Introduction to Other Mathematical Material
- Introduction to Memorization
- Introduction
- Addition
- Stamp Game Addition
- Memorization
- Strip Board (including Doubles)
- Games and Explorations using Bead Bars
- Addition Charts and Combination Card Exercises
- Passage from Chart I to Chart II
- Passage from Chart II to Chart III (the Whole Chart)
- Passage from Chart III to Chart IV (the Half Chart)
- Passage from Chart IV to Chart V (the Simplified Tables)
- The Bingo Game for Addition (using Chart VI)
- Bead Frame Addition
- More Memorization Exercises
- Further Explorations using Bead Bars
- Special Cases
- 0 – Calculating the Sum
- 1 – Calculating the Second Addend
- 2 – Calculating the First Addend
- 3 – Inverse of Case Zero
- 4 – Inverse of 1st Case, Calculating the Second Addend
- 5 – Inverse of 2nd Case, Calculating the First Addend
- 6 – Calculating the First and Second Addends
- Collective Activity:
- Individual Work:
- Word Problems
- Multiplication
- Stamp Game Multiplication
- Memorization Exercise
- Multiplication Boards (Bead Boards)
- Introduction and List of Materials:
- Initial Presentation:
- Multiplication Booklets
- Combination Cards
- Skip Counting (Linear Counting)
- List of Materials
- Initial Presentation
- Short Chain:
- Long Chain:
- Games of Comparison
- Bead Bar Multiplication
- Multiplication Charts and Combination Cards
- Passage from Chart I to Chart II
- Passage from Chart II to Chart III (the Whole Chart)
- Passage from Chart III to Chart IV (the Half Chart)
- The Bingo Game of Multiplication (using Chart V)
- Exercise
- Exercise
- Exercise
- Group Games:
- Multiplication By 10, 100, 1000
- Presentation:
- By ten
- By one hundred
- By one thousand
- Multiplication Boards (Bead Boards)
- Checkerboard – Geometrical Analysis of Multiplication
- Introduction to the Checkerboard
- Presentation:
- Games:
- Multiplication with the Checkerboard
- 1st level
- 2nd level-Small Multiplication
- 3rd level-Partial Products (this passage can be skipped)
- 4th level-Mental Carrying Over
- Multiplication and Drawing
- Introduction to the Checkerboard
- Bead Frame Multiplication
- Small Bead Frame
- Multiplication By 10, 100, 1000
- Multiplication with a One-Digit Multiplier
- Large Bead Frame-Multipliers of 2 or More Digits
- The Whole Product
- Partial Products
- Horizontal Golden Bead Frame
- The Whole Product
- Partial Products
- Carrying Mentally
- Small Bead Frame
- More Memorization Exercises
- The Snake Game
- Various Ways of Constructing a Product
- Small Multiplication
- Inverse Products
- Construction of a Square
- Multiplication of a Sum
- Analysis of the Squares-Binomial
- Analysis of the Squares-Trinomial
- Passage From One Square to a Succeeding Square
- Passage From One Square to a Non-Successive Square
- Skip Count Chains – Further Exploration
- List of Materials
- Construction of Geometric Figures
- Decanomial (a polynomial having ten terms) & The Construction of Chart I
- List of Materials
- Vertical Presentation
- Horizontal Presentation
- Angular Presentation
- Commuted Decanomial
- Part One
- Part Two-Building the Tower
- Variation on the 1st Method
- 2nd Method
- Part Three-Decomposition of the Tower
- Skip Counting Chains-Further Explorations
- Decanomial (a polynomial having ten terms) & The Construction of Chart I
- Numeric Decanomial
- Special Cases
- 0- Calculate the product
- 1- Calculate the Multiplier
- 2- Calculate the Multiplicand
- 3- Inverse of Case Zero – Calculate the Product
- 4- Inverse of The First Case – Calculate the Multiplier
- 5- Inverse of the Second Case – Calculate the Multiplicand
- 6- Calculate the Multiplier and the Multiplicand
- Activity: The Bank Game
- Word Problems
- Subtraction
- Stamp Game Subtraction
- Memorization Exercises
- Strip Board
- Introduction and List of Materials
- Initial Presentation
- Subtraction Booklets
- Combination Cards
- Decomposition of a Number
- Decomposition of a Number
with Zero as the Subtrahend
- The Snake Game
- Subtraction Charts and Combination Card Exercises
- Passage From Chart I to Chart II
- The Bingo Game of Subtraction (using Chart III)
- Exercise:
- Exercise:
- Exercise:
- Group Games
- Strip Board
- Bead Frame Subtraction
- Static Subtraction
- Dynamic Subtraction
- Calculating the Difference
a little more Abstractly- Presentation:
- Games:
- More Memorization Exercises (Special Cases)
- 0- Calculating the Difference
- 1- Calculating the Subtrahend
- 2- Calculating the Minuend
- 3- Inverse of Case Zero – Calculating the Difference
- 4- Inverse of the 1st Case- Calculating the Subtrahend
- 5- Inverse of the 2nd Case- Calculating the Minuend
- 6- Calculating the Minuend and the Subtrahend
- Collective Activity:
- Individual Activity:
- Word Problems
- Division
- Stamp Game Division – Single Digit
- Memorization Exercises
- Division Boards (Bead Boards)
- Introduction and List of Materials
- Initial Presentation
- Preparation for Presentation
- Presentation
- Division Booklets
- Division Charts and Combination Cards
- Chart I
- Bingo Game (Chart II)
- Exercise A:
- Exercise B.
- Exercise C.
- Group Game 1.
- Group Game 2.
- Division Boards (Bead Boards)
- Division By More Than One Digit
- Double Digit Division
- Intro. to Double Digit Division (on The Change Game)
- Double Digit Division on The Stamp Game
- Triple Digit Division
- Intro. to Triple Digit Division (on The Change Game)
- Triple Digit Division on The Stamp Game
- Double Digit Division
- Division Involving Zeros
- Division with Zero in the Dividend
- Division with Zero in the Divisor
- Group Division
- Single Digit Group Division
- Double Digit Group Division
- More Memorization Exercises
- Special Cases
- 0- Calculate the quotient
- 1- Calculate the Divisor
- 2- Calculate the Dividend
- 3- Inverse of Case Zero: Calculate the Quotient
- 4- Inverse of The First Case: Calculate the Divisor
- 5- Inverse of the Second Case: Calculate the Dividend
- 6- Calculate the Divisor and the Dividend
- Search for Quotients
- Prime Numbers
- Special Cases
- Division With Racks & Tubes
- Introduction
- Materials: racks and tubes:
- Small Division (1-digit divisor, 4-digit dividend)
- 1st level
- 2nd level
- 3rd Level – Group Division
- Big Division (2 or more digits in the divisor)
- 1st level:
- 2nd level:
- 3rd level-Group Division with a two digit divisor
- Long Division
- Division with Zero in the
Divisor
- Word Problems
- From Combination Cards
- Distributive vs. Group Division
- Divisibility
- 1. Introduction
- 2. Div. by 2
- 3. Div. by 4
- 4. Div. by 5
- 5. Div. by 25
- 6. Div. by 9
- Synthesis of Multiples & Divisibility
- Fractions
- Introduction
- Understanding What Fractions Are
- Understanding the Concept of Fractions
- Introducing Fractions Using the Fraction Skittles
- Introducing Fractions Using the Fraction Circles
- Putting Fractions in Order from a Whole to a Tenth
- Matching Fractions from a Whole to a Tenth
- Understanding the Parts of Fractions
- Writing Fractions and Finding Equivalencies
- Understanding Written Fractions
- Matching Fraction Tickets to Fraction Circles
- Constructing Fraction Circles to Match Fraction Tickets
- Finding Fraction Equivalencies
- Adding and Subtracting Fractions
- Adding Fractions with the Same Denominator That Add Up to One or Less
- Adding Fractions with the Same Denominator That Add Up to More Than One
- Introduction to Adding Fractions With Different Denominators
- Subtracting Fractions with the Same Denominator
- Introduction to Subtracting Fractions with a Different Denominator
- Multiplying and Dividing Fractions
- Multiplying Fractions By Whole Numbers
- Dividing Fractions By Whole Numbers
- Dividing Fractions By Whole Numbers when Equivalent Fractions Must Be Made First
- Geometry
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- Chapter One – Sensorial Exploration of Shapes
- Introduction to Geometry
- The Geometry Cabinet
- Introduction
- Presentation tray
- Triangles
- Rectangles
- Regular Polygons
- Circles
- Other figures
- Constructive Triangles – First Series
- First box
- Second box – Construction of Quadrilaterals
- Second box – Heads and Tails
- Trapezoid
- Third Box
- Chapter Two – Knowledge of Plane Figures and Details
- Introduction
- Fundamental Concepts
- Lines
- Types of lines
- Parts of a straight line
- Positions of a straight line
- Horizontal line – curved or straight?
- Straight line in a horizontal plane
- Two straight lines lying in a plane – coplanar lines
- Divergent and Convergent Lines
- Oblique and perpendicular lines
- Two straight lines crossed by a transversal
- Two parallel straight lines crossed by a transversal
- Angles
- Types of Angles and the Parts of an Angle
- Study of angles
- Vertical or Opposite Angles
- Measurement of Angles
- Presentation of the Montessori protractor
- Use of the Protractor
- Operations with Angles
- Addition
- Subtraction
- Multiplication
- Division – Bisecting an Angle
- Exercises in measurement and drawing of angles
- Operations with Angles
- Convex and reflex angles
- Research in the environment
- A new definition of an angle
- Plane Figures – Difference Between Closed Curve Figures and Polygons
- Classification Exercises
- Classification of closed curve regions and polygons
- A sensorial classification of convex and concave (re-entrant)
- Closed curve regions/polygons – convex/concave
- Classification Exercises
- Polygons – Triangles
- Triangles – Classification
- Triangles – Parts of the triangle
- Special nomenclature of the right-angled triangle
- Study of Quadrilaterals
- Classification
- Quadrilaterals – Types of trapezoids
- Quadrilaterals – Classification according to set theory
- Parts of the Quadrilateral
- Polygons With More Than 4 Sides
- Parts of Polygons
- Comparative Examination of Polygons
- Study of the apothem
- The polygon in relation to the first circle
- The polygon in relation to the 2nd circle
- The polygon in relation to the 1st and 2nd circles simultaneously
- From Irregular to Regular Polygons
- Construction of Polygons
- Circle – Level One
- Circle and its parts
- Relationship between a circumference and a straight line
- Relationship between two circumferences
- Relationship between a circumference and a straight line
- Relationship between two circumferences
- Chapter Three – Congruency, Similarity and Equivalence
- Chapter One – Sensorial Exploration of Shapes
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- Introduction to the Material – Squares
- Presentation of the Material – Triangles
- Presentation of the Concepts
- Similarity
- Equivalence
- Concepts in Action – Constructive Triangles – Second Series
- Triangular box
- Large hexagonal box
- Smaller hexagonal box
- Relationship between T1 and T2
- Difference and ratios between similar figures
- Sensorial demonstration of the difference between H1 and H2
- Equivalence between two rhombi
- Equivalence between the trapezoid and T2
- Ratio between circumscribing and inscribed figures
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