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Arithmetic
Cards and Counters
the Stamp Game
Combination of Quantities & Symbols
Spindle Box
Small Number Rods
Philosophy:
Arithmetic is the science of computing using positive real numbers, more specifically, the process of addition, subtraction, multiplication, and division. Little children are naturally attracted to the science of numbers. Mathematics, like language, is the product of the human intellect and the nature of a human being. Mathematics arises from the human mind as it comes into contact with the world and as it contemplates the universe and the factors of time and space. It undergirds the effort of the human to understand the world in which he lives. All humans exhibit this mathematical propensity, even little children. It can therefore be said that humankind has a mathematical mind.
By age four, the child is ready for the language of mathematics. A series of preparations have been made. The child has established internal order, they have developed precise movement, established the work habit, and is able to follow and complete a work cycle. The child has the ability to concentrate and has learned how to follow a process and use symbols.
The mathematical material gives the child his own mathematical experience and to arrive at individual work. There are some teacherdirected activities but these are followed by individual activities. The Exercises in arithmetic are grouped and there is some sequential work and some parallel work. The first group is Numbers through Ten. The experiences in this group are sequential. When the child has a full understanding of numbers through ten, the second group, The Decimal System, can be introduced.
The focus here is on the hierarchy of the decimal system and how the system functions. It also starts the child on the Exercises of simple computations, which are the operations of arithmetic. The third group will be started when the decimal system is well underway. This third group, Counting beyond Ten, includes the teens, the tens, and linear and skip counting.
The fourth group is the memorization of the arithmetic tables. This work can begin while the later work of the decimal system and the counting beyond ten exercises are continued.
The fifth group is the passage to abstraction. The Exercises in this group require the child to understand the process of each form of arithmetic and to know the tables of each operation. There is again an overlap. The children who know the process and tables for addition can begin to do the addition for this group. They may still be working on learning the tables for the other operations and these will not be taken up until they have readiness.
Exercises:
Numbers to Ten

Number Rods

Sandpaper Numerals

Number Rods and Number Cards

Spindle Boxes

Cards and Counters

Memory Game of Numbers
Decimal System

the Introduction to the Golden Beads

Golden Beads  counting Through the Hierarchies

Counting Golden Beads

Introduction to the Large Number Cards

Large Number Cards  Counting Through the Hierarchies

Identifying Large Number Cards

Formation of Large Number Cards with Beads

Combination of Golden Beads and Large Number Cards (Bird's Eye View)
Teens and Tens  Teens

Formation of Quantities 1119 with ten bars and short bead stair

Formation of Symbols 10  90 with teen boards

Combination of Quantities and Symbols to form 1119
Teens and Tens  Tens

Formation of Quantities 1099 with ten bars

Formation of Symbols 10  90 with ten boards

Combination of Quantities and Symbols 1090 with ten bars and boards

Formation of 11  99 with ten bars, unit beads, and ten boards
Teens and Tens  Counting

Linear Counting

Skip Counting
Decimal System Continued

Changing Exercise

Addition with the Golden Beads

Multiplication with the Golden Beads

Subtraction with the Golden Beads

Division with the Golden Beads

The Stamp Game  Introductory Exercise

The Stamp Game  Addition

The Stamp Game  Multiplication

The Stamp Game  Subtraction

The Stamp Game  Division
Exploration and Memorization of Tables

Addition Snake Game

Addition Strip Board

Addition Charts 3,4,5, and 6 (blank)

Negative Snake Game

Negative Strip Board

Subtraction Chart 2 and 3 (blank)

Multiplication Bead Bar Layout

Multiplication Board

Multiplication chars 3, 4, and 5 (blank)

Unit Division Board

Division Charts 1 and 2
Passage to Abstraction

The Dot Game

The Small Bead Frame