# Introduction to the Decimal System: Golden Bead Material & Decimal Cards

### What is the Decimal System?

The decimal number system, which we commonly use, employs digits ranging from 0 to 9. In this number system, the base number is 10, signifying that there are a total of 10 different digits available for representing numbers.

In Montessori, the decimal system is a cornerstone of mathematical education. It serves as the foundation for understanding numbers and place value, paving the way for more advanced mathematical concepts. This system is not just about numbers; it’s about nurturing a deep comprehension of how our numerical system works.

### Introduction to the Decimal System

Prior to this, the child should have lots of exploration of numbers one through ten to acquire a solid grasp of various fundamental concepts, including quantity, numerical symbols from 0 to 10, the association between quantity and symbols, and the notion of zero.

This early exposure also indirectly imparts insights into the four fundamental mathematical operations, sequential order, and the distinction between odd and even numbers. At this stage, children comprehend that quantity is composed of individual units.

In our Montessori approach, we typically progress from Numbers 1-10 directly to the decimal system, bypassing the intermediary step of working with numbers in the teens and tens. However, it’s important to recognize that some children may benefit from an alternative route, initially engaging with the more straightforward numbers before moving on to larger quantities.

Many children find the manipulation of large quantities with our bead materials particularly engaging. The decision to transition to the decimal system aligns with the child’s absorbent mind, sensitive periods for order, language development, and refinement of the senses. It allows us to introduce bead materials on a primarily sensory level, where the child can visually appreciate the relative differences in volume, supporting the development of the mathematical mind.

### Principles to Remember

1. Hierarchies and Categories:

Recognize that the decimal system is structured around hierarchies and categories. The three primary categories are units, tens, and hundreds. These categories repeat in each hierarchy, whether you’re working with the simple hierarchy or larger ones like thousands and millions. Understanding this hierarchical structure is fundamental to grasping the decimal system.

2. Comprehensive Understanding:

Resist the urge to move on to mathematical operations prematurely. It’s essential to ensure that the child fully comprehends the categories before introducing operations like addition, subtraction, multiplication, and division. Patience is key, even if it may feel repetitive.

Be aware that children may occasionally confuse the terms “hundreds” and “thousands.” In such cases, it can be helpful to explicitly count the zeroes to reinforce the distinction between these categories.

4. Speaking Whole Numbers:

Teach children that when saying whole numbers out loud, the word “and” is not used. The word “and” is reserved for discussing fractions, ensuring clarity in language usage.

### Introduction to the Golden Beads

The first material introduced is the golden bead presentation tray, which contains one representative of each category: a single unit bead, one ten-bar, one hundred-square, and one thousand-cube. In our teaching, we prefer the use of glass beads for a more profound sensory experience. By presenting this material, the child gains an initial understanding of the varied scales of these components. These materials are designed to visually and tangibly represent the concept of place value.

The wonder of golden beads lies in their ability to demonstrate place value. Each component represents a different place in the decimal system, allowing children to see how numbers are composed of units, tens, hundreds, and thousands. This tangible representation makes the abstract concept of place value concrete and comprehensible.

Armed with new information of hundred and thousand, the child can extend their understanding up to one million. They accomplish this by counting these components just as they did with the numbers 1-10, with a clear progression from 1-9 tens to 10 tens (equivalent to 1 hundred), and so forth.

The beauty of this material lies in the fact that the child is never compelled to count beyond 10, as adding 1 to 9 of one category naturally yields 1 of the next. This approach ensures that the child counts with genuine comprehension and meaning.

Occasionally, children may struggle to recall the names of the newer categories, specifically “hundred” and “thousand.” To reinforce this knowledge, we engage in many fetching games designed to solidify their understanding of these terms.

### Introduction to the Decimal Cards

Decimal cards are another valuable tool in the Montessori classroom. These cards visually represent numbers, reinforcing the concept of place value introduced through golden beads. Decimal cards are typically color-coded to help children distinguish between different place values.

Units: green
Tens: blue
Hundreds: red
Thousands: green

### Combining Golden Beads and Decimal Cards or the Formation of Numbers

Golden beads and decimal cards complement each other seamlessly. Children can pair the tactile experience of manipulating golden beads with the visual representation of numbers on decimal cards. This dual approach enhances their understanding and helps consolidate their knowledge of the decimal system.

### DIY Golden Bead Cards and Decimal Cards

As an alternative approach to introducing the decimal system in Montessori education, one can explore the use of DIY golden beads and DIY decimal cards. These homemade materials offer a cost-effective way to provide children with hands-on experiences in comprehending the intricacies of the decimal system.

Crafting DIY golden beads and DIY decimal cards using paper or cardstock allows for a personalized and creative touch to the learning process. Though using alternative golden beads may not give the same impression in both appearance and weight, this DIY approach of also the decimal cards not only promotes resourcefulness but also encourages educators and parents to actively engage in creating educational materials that facilitate a deep understanding of mathematics for young learners.

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