Montessori math materials are perhaps the most compelling materials that grant access to complex math in early childhood. The Golden Bead material is the quintessential math material since it makes it possible for children as young as 4.5 to work within the decimal system (base 10 system). Children go through a series of presentations that progressively lead them to associating concrete quantities (golden beads) to abstract symbols (numeral cards). Children learn that one golden bead is 1, one 10-bead bar is 10, one 100-bead square is 100, and one 1000-bead cube is 1000. They can visualize and feel the quantities which they will manipulate while working with numbers. Later, children are invited to associate numeral cards to the bead material, which they understand are simply “pictures” that represent quantities. Children will eventually go through the 45-Layout (also known as Bird’s Eye View) which provides an organized concrete layout of numbers 1-9, 10-90, 100-900, 1000-9000. The same layout is built using the numeral cards, and is then combined with the concrete bead material. After much practice, children then may be ready to work with the four arithmetic operations: addition, subtraction, multiplication, and division.
Practice and consistency are the keys to understanding and retention, therefore we developed a series of Addition and Subtraction Activity Sets to accompany our Golden Bead Bank Game. In order to aid children to work with the Golden Bead material, our Activity Sets are designed incrementally, which ensures that no gap of learning is occurring. Our cards progressively introduce children to the various situations that they may encounter when working with addition and subtraction. The Activity Sets consist of a series of exercises that requires no exchange (static addition/static subtraction). Other cards provide opportunities to work on exchanging beads, and moving beads across categories (place value). .i.e.: 8 units + 8 units require exchanging 10 units for one 10-bead bar. The child would be left with six units, and one 10-bead bar would be moved to the “ten” category. Below, you will see illustrations of how effective our Golden Bead Material Activity Sets are.
Materials
- Golden Bead Bank Game (acrylic, 7mm, fused 100 squares and 1000 cubes), which consists of:
–9 Thousand Cubes, 45 Hundred Squares, 45 Ten Bars, 45 Individual Beads, 2 trays, 1 Wooden Decimal Cards with Symbols, 2 sets of Wooden Number Cards (1-9000)
- Upgraded Version: Golden Bead Material (8 mm Individual Acrylic Beads, Plastic Cards)
- Introduction to the Decimal System (1A and 1B)
- Golden Bead Materials (Quantity) Addition Activity Set #1 (1A-1D)
- Golden Bead Materials (Quantity and Symbol) Addition Activity Set #2 (2A-2D)
- Golden Bead Materials (Quantity) Subtraction Activity Set #1 (A1-D1)
- Golden Bead Materials (Quantity and Symbol) Subtraction Activity Set #2
- Optional: Command Box & Place Value Mat: Thousands
How to Use the Materials
Introduction to the Decimal System (1A and 1B)
Our first Golden Bead Activity Set is Introduction to the Decimal System (1A and 1B). It includes preliminary work to introduce the decimal system. Children are provided a set of cards (A1) with visuals that indicate the materials to go fetch at the Golden Bead Bank with a tray. They bring the Golden Bead materials and name them aloud, for example: 4 units, 3 tenths, 2 hundreds, 1 thousand. This work can be done with the help of an adult or an older child. The second set of cards (B1) invites children to use the numeral cards to create “New Numbers” and fetch the indicated quantities at the Golden Bead Bank. The “New Number” appears from the merging of all numeral cards, which reveals a large number to fetch (e.g.: 4, 30, 200, 1000 numeral cards are merged to form 1,234). Children must go fetch the quantities for the numerals indicated on the cards. The control for errors on the back should suffice to inform children about the quantities they should have.
With a tray, children go fetch the quantities represented on the card (top). A written version of the symbols (numerals) is represented on the back of the card (bottom). 
Numerals on top (new number)
and quantities at the bottom
Golden Bead Materials (Quantity) Addition Activity Set #1
Our second recommended set is Golden Bead Materials Addition Activity Set #1. This set consists of 40 addition exercises. Cards 1A-1B are with images of the material (static and dynamic addition.) Cards 1C-1D of this set are in the text format (dynamic addition, zeros in the sum and addends.) Children use the Activity Cards to build addition problems. They become accustomed to gathering 2 addends, and merging the 2 addends to find the sum. They simply refer to the visuals on the activity card to go fetch the quantities they need using a tray.
This work can be done with a partner where two children, each in possession of a tray, go fetch one of the two quantities indicated on the activity card. The work is laid out on a mat with the units to the far right, preceded by the tenths, hundreds, and thousands to the far left. The work is incremental since it begins with static additions (no carrying over) and continue with dynamic additions (carrying over, exchanging), and additions that include zeros.
Golden Bead Materials (Quantity and Symbol) Addition Activity Set #2
Our third recommended set is Golden Bead Materials Addition Activity Set #2. This set consists of 40 addition exercises and a presentation card. The work requires the use numeral cards. Cards 2A-2B are static and dynamic addition. Cards 2C-2D of this set are dynamic addition, zeros in the sum and addends. Instead of relying on the visual quantities to create equations, children work with numeral cards (symbols). Children use the small numeral cards and lay them out on 2 separate mats as they have been demonstrated by an adult in the preliminary lessons. Using 2 trays, children go fetch the two addends indicated on the activity card. They bring the Golden Bead material from the bank and bring it to the working mat. By merging these two quantities of beads, children create the sum. On the back of the card is the visual representation of the sum.
While Set A1 offers work with static additions, Set A2 contains dynamic additions. Set C2 and D2 lead children to working with abstract addends and to form sums with numeral cards as well.
Golden Bead Materials (Quantity) Subtraction Activity Set #1
Our fourth recommended set is Golden Bead Materials Subtraction Activity Set #1. Children need to have worked through Golden Bead Materials Addition Activity Set #1 and #2 before working with this set. This set provides visuals on cards for children to build equations. Children go fetch beads materials at the Golden Bead Bank. They bring the subtrahend to the working mat and form the equation visually. Children are now ready to subtract (take away) the minuend from the subtrahend they collected. The minuend is represented with shaded graphics on the activity cards. This indicates that this part must be taken away. Once children have subtracted the minuend from the subtrahend, they are left with the difference. A visual of the difference is provided on the back of the activity card.
Subtrahend represented at the top Minuend represented at the bottom 
Children bring the subtrahend from the Golden Bead Bank 
Children remove the minuend and are left with the difference
Golden Bead Materials (Quantity and Symbol) Addition Activity Set #2
Our fifth set is Golden Bead Materials Subtraction Activity Set #2. Children need to have worked through Golden Bead Materials Subtraction Activity Set #1 before working with this set. This set consists of 40 subtraction exercises and a presentation card. The equations are with numeral cards and answers are with images of material (static and dynamic with borrowing.) Cards 2C-2D in this set are with numeral cards for both the equation and difference (dynamic subtraction, zeros in the equation). This set presents equations using numeral cards. Children can build the equation using the numeral cards sets. After laying out the equation, they can go fetch the Golden Bead Material at the Golden Bead Bank. Using the concrete materials, children solve the equation and find the difference. A visual of the difference is provided on the back of the activity card.
Conclusion
After going through this progressive set of cards, children will have a solid decimal system foundation. Their next work will be working with multiplication and division using the Golden Bead Materials, as well as the Stamp Game.
