Mathematics

I. Great Lesson – The Story of Our Numerals

II. Numeration/Laws
1. Wooden Hierarchical Material
2. Commutative/Distributive Laws

III. Properties of Numbers
1. Multiples
2. Factors
3. Least Common Multiple
4. Greatest Common Factor
5. Divisibility

IV. Measurement

V. Operations with Whole Numbers
1. Long Multiplication
a. Large Bead Frame
b. Flat Bead Frame
c. Bank Game
d. Chequer Board
e. Geometrical Form of Multiplication
f. Algorithm for Multiplication
2. Long Division
a. Distributive
b. Group
c. Algorithm for Division

VI. Squares and Cubes of Numbers
1. Concept and Notation
2. Games with Squares and Cubes
3. Operations with Squares and Cubes Rules

VII. Squaring Powers of Numbers
1. Transformation of a Square
2. Passing from One Square to Another
3. Squaring a Sum
4. Extracting Rules for Squaring
5. Generalisations about Squaring

VIII. Cubing
1. Passing from One Cube to Another
2. Cubing a Binomial
3. Cubing a Trinomial

IX. Square Root
1. Concept/Language & Notation
2. Square Root Board
3. Extracting the Square Root
4. Special Cases
5. Abstraction and Algorithm

X. Cube Root
1. Concept/Language/Notation
2. Cube Root Using Chart
3. Extracting the Square Root
4. Special Cases
5. Abstraction and Algorithm

XI. Fractions
1. Concept and Notation
2. Equivalence
3. Operations
a. +/-/x/÷ Simple Cases
b. +/- with Different Denominators
c. x by a Fraction
d. ÷ by a Fraction

XII. Decimal Fractions
1. Presentation of Quantity & Symbol
2. Formation/Reading of Numbers
3. Operations
a. +/-/x/÷ Simple Cases
4. Conversion
5. Effect of x or ÷ on Powers of 10
6. Long Multiplication
a. Decimal Board
b. Decimal Chequer Board
c. Algorithm
7. Long Division
a. Distributive
8. Algorithm

XIII. Signed Numbers
1. Introduction
2. Operations
3. Rules

XIV. Powers of Numbers
1. Powers of Two
2. Exponential Notation
3. Powers of Ten
4. Operations Using Expanded Notation

XV. Non Decimal Bases

XVI. Ratio and Proportion

XVII. Word Problems
1. Distance/Rate/Time
2. Principal/Rate/Interest/Time

XVIII. Introduction to Algebra
1. Balancing Equations
2. Solving Word Problems

XIX. Numeracy