Montessori Matters

The Golden Beads

The cornerstone of the Montessori mathematics curriculum is the Golden Beads. They are in use at all age levels. Essentially, the Golden Beads are the concrete representation of our place value hierarchy, the foundation of our mathematics. (When first invented, the Montessori Golden Beads were shimmering glass beads strung on wires. Sadly, now they are opaque plastic—or, in the case of some thousand cubes, just wooden blocks.)

With the Golden Beads, the child is given an introduction to our decimal system with the single unit bead, the ten-bar (ten beads strung on a wire), the hundred square, and the thousand cube.

Next, the child learns “counting through”: “This is one unit, two units, three units”… until we get to nine units. “And if we had one more, we would have ten.” Then we show how to exchange the ten separate beads into one ten-bar.

You can imagine how this continues: counting out the tens until we get to nine ten-bars. And, if we had one more, we would have ten ten-bars, which we can exchange for a hundred square. When the child has facility with this, we introduce the number cards that are treated the same way, but now we are presenting the written symbols for 1, 10, 100, and 1000. Again, we do the counting through exercise.

Children love the lesson that follows: the Bird’s Eye View! The child places all the numeral cards (1-9; 10-90; 100-900; 1000-9000)in vertical columns (units at the right, as when we write the numerals) and then sets out the quantities for each in Golden Beads. It may take most of the morning, but what an accomplishment for the four- or five-year-olds doing this!

Elementary students entering at a primary grade (i.e. first or second) also do the Bird’s Eye view, since they will not have en.countered this before, and it is eye-opening for them, too.

Many happy hours can then be spent with the Bank Game. This is a group exercise. The teacher asks for a child to go get a particular number, such as 4,372, and the child goes to the Golden Bead “Bank”, assembles that quantity on a tray, and returns to the teacher.

In reverse, the teacher shows a quantity, and the child must give the name. A more advanced lesson combines the beads with the numeral cards for the exact same exercise.

After the Bank Game, mathematical operations commence. Children learn addition—three or four children are asked to get a quantity, and these are added together, and the sum is determined. Multiplication follows addition, as the natural step. As the children become proficient, division is added to the repertoire (retrieving a quantity and then sharing it among the children equally).

The Golden Bead activities continue into the elementary grades. All basic operations are presented initially with the GoldenBeads before the child moves into the symbolic manipulation of the quantities (with number tiles or color-coded pegs).

Oh, yes, did I mention that the numeral cards are color-coded throughout? Units are always green, tens are always blue, hundreds are always red; then we repeat with thousands always green, etc.

Elementary students learn, using the Golden Beads, compound multiplication, then geometric multiplication (you probably called this long multiplication in school). We also present division by partition (sharing) and division by quotition (forming equal portions). Beyond the four basic operations, we also use the Golden Beads to introduce squaring of numbers and finding square roots of large numbers.

A Montessori elementary class will also have color-coded beads that are a bit smaller for going the “other” direction—representing tenths, hundredths, thousandths, for operations with decimal fractions. With such a firm basis in the entire decimal hierarchy from their preschool and primary elementary grades, upper elementary students breeze through operations with decimal fractions.

The Golden Bead repertoire of teachings is a golden treasure to your child’s life-long mathematical understandings.