# 6-9 Math Album

• Introduction
• Numeration
• Multiplication
• Stamp Game Multiplication
• Memorization Exercise
• Checkerboard – Geometrical Analysis of Multiplication
• 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
• 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
• 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 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
• 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
• 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 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
• Chapter One – Sensorial Exploration of Shapes
• 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
• Subtraction
• Multiplication
• Division – Bisecting an Angle
• Exercises in measurement and drawing of 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
• Polygons – Triangles
• Triangles – Classification
• Triangles – Parts of the triangle
• Special nomenclature of the right-angled triangle
• Classification
• Quadrilaterals – Types of trapezoids
• Quadrilaterals – Classification according to set theory
• 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