The GOLDEN BEADS are used to give a concrete introduction to the decimal system. Like all Montessori materials they are tactile, attractive and easy to understand.
The material consists of Unit beads which are just individual beads, Ten bars which are short lengths of wire strung with ten beads, Hundred squares which are made of 10 ten bars wired together to make a square, and Thousand cubes which are made by wiring together 10 hundred squares. They are used to introduce mathematical concepts from counting to complex mathematical operations as well as help children visualise the mathematical and geometric patterns of numbers.
Cycle 1 : The child is first introduced to the beads at about age 4 to 4 ½ and the initial lesson uses a sensorial approach to distinguish each bead material by depth, weight and quantity. In time this brings the child to grasp mass and counting in higher numbers. This YouTube video demonstrates the first introductory lesson to a 4 year old. Link http://youtu.be/h2-OsKoYmrs
Cycle 2 & 3 : In Cycle 2, the work extends to more complex maths with the inclusion of the short & long bead. Cycle 2 children use them for dynamic addition, subtraction, multiplication and division and to comprehend the squaring and cubing of a number. The bead cabinet is done parallel to the golden bead materials (usually work starts in the last year of Cycle 1). The short and long chains are used for linear counting, including skip counting which is an activity for memorisation of multiplication facts as well as the concept of squares and cubes of numbers.
In Cycle 3, the Golden Beads are used to introduce and revise more complex concepts such as divisibility, squaring and cubing, extracting the square root or cube root of a given number, study of powers of numbers and the study of interest.
Curriculum: Mathematics—Decimal System
Initial purpose: To introduce the decimal system, ones or units, tens, hundreds & thousands. Introduce the names and quantity proportions.
Advanced purpose: Multiplication, using bigger numbers & shows exponents (index & power).
Age of child using material: Introduced from 4 - 4 1/2 years and then used onwards with increasing complexity.