The Arithmetic Materials ~ The Golden Beads ~ An Introduction to the Decimal System

Of all the materials that Maria Montessori created, perhaps the most brilliant of these is the Decimal System material also known as the Golden Beads.  Non-Montessori educational companies have tried to copy this material, yet it is never quite as beautiful as the original.

The Decimal System material consists of single golden unit beads, golden ten-bead bars (ten-bars), golden-hundred squares (hundred-square) and golden thousand-bead cubes (thousand-cube).  The ten-bars are ten individual units strung together on a wire.  The hundred squares are ten ten-bars wired together to form a square.  The thousand cubes are ten hundred-squares wired together to form a cube.

The Golden Bead Material - Introduction Tray

In the first presentation, the child is introduced to this material.  A unit bead is removed from the tray and introduced as one unit.  The child is invited to hold and examine it.

Examining the Unit Bead

A ten-bar is removed from the tray and introduced as one ten.  The child is told that it is made of ten units and invited to hold each bead and count it.  Ten units make one ten.

Examining the Ten-Bar

The hundred-square is removed from the tray and introduced as one hundred.  The child is invited to hold and examine it.  The child is told that the hundred square is made of ten-bars.  The child then takes a ten-bar and counts to see how many tens make one hundred.  Ten tens make one hundred.

Examining the Hundred Square

The thousand-cube is removed from the tray and introduced as one thousand.  The child is invited to hold and examine it.  The child is told that the thousand cube is made of hundred squares.  The child then takes a hundred-square and counts to see how many hundreds make one thousand.  Ten hundreds make one thousand.

Examining the Thousand Cube

The purpose of the Decimal System material is to make the child familiar with place value and the names of the decimal categories (units, tens, hundreds and thousands) and their relative proportions.  It illustrates that each decimal category is ten times the previous category. 

On another day, the child is shown where the Golden Bead Material is kept in the classroom.  The child is asked to bring various quantities of the material on a tray.

7 Units

4 Tens

Units, Tens and Hundreds

Once the child is familiar with the quantities, symbols are introduced for the decimal categories (number cards for the decimal categories units, tens, hundreds and thousands).

The Golden Bead Material - Symbol Introduction Tray

When the child is familiar with the symbols, they are matched with their quantities.

Matching Symbol and Quantity

These introductory lessons lead to the formation and reading of complex numbers (example - 3,246 with number cards and beads) and work with the operations (addition, subtraction, multiplication and division).  Further blog posts will discuss this progression.

This material is used extensively in the Montessori pre-school (casa) and early elementary.  It is introduced to children at 4 - 4 1/2 years of age.