The Montessori method has long been recognized for its unique approach to teaching children through practical learning experiences. One area where this approach is particularly evident is arithmetic. Montessori maths materials are specially designed to help children, usually aged between 4 and 6, to master complex operations and concepts. In this article, we’ll look at how these materials are used to teach arithmetic operations, fostering a deep understanding of numbers and their interrelationships in young learners.
Foundational Concepts in Montessori Arithmetic
Before diving into specific arithmetic operations, it’s essential to understand the foundational concepts that underpin Montessori math education. The Montessori method emphasizes the importance of learning through concrete experiences, which makes it an ideal approach for teaching children about numbers and their relationships. Some key concepts include:
 Number sense: Developing an intuitive understanding of the value of numbers and their relationships, as well as the ability to recognize and manipulate them in various contexts.
 Number symbols: Learning to associate numerical values with written symbols, making it possible to represent and communicate mathematical ideas.
 Decimal system: Understanding the base10 number system, which forms the foundation for most mathematical operations.
 Place value: Grasping the concept that the position of a digit within a number determines its value (e.g., the “3” in “30” represents thirty).
Concept  Description  Montessori Materials 

Number sense  Developing an intuitive understanding of the value of numbers and their relationships.  Number Rods Spindle Boxes Bead Stair 
Number symbols  Learning to associate numerical values with written symbols.  Sandpaper Numbers Number Cards 
Decimal system  Understanding the base10 number system.  Golden Bead Bead Chains Decimal Cards 
Place value  Grasping that the position of a digit within a number determines its value.  Golden Bead Stamp Game Large Number Cards 
Best Montessori Math Materials for Arithmetic Operations
With these foundational concepts in place, let’s explore how Montessori math materials can be used to teach specific arithmetic operations.

Addition with the Golden Bead Material
The Montessori golden bead material is a set of beads grouped in units (single beads), tens (strings of ten beads), hundreds (squares of 100 beads), and thousands (cubes of 1,000 beads). This material allows children to visualize the process of addition, as they physically combine bead quantities to form new values.
For example, if a student wants to add 23 and 45, they can represent each number using the appropriate combination of bead groupings. Next, they physically combine these bead sets and regroup them according to place value, resulting in a final sum of 68.
Material  Description 

Golden Bead Material  Beads grouped in units, tens, hundreds, and thousands to visualize addition. 
Number Rods  Colored rods that can be combined to represent addition of numbers. 
Bead Bars  Individual bars with beads that can be combined to visually represent addition. 

Subtraction with the Stamp Game
The Montessori stamp game is another versatile Montessori math material, consisting of colored tiles representing units, tens, hundreds, and thousands. To perform subtraction, students can use these tiles to represent two numbers and remove the smaller quantity from the larger one.
In the case of subtracting 27 from 43, a child would first lay out the tiles for each number. Then, starting with the smallest place value (units), they would remove the required quantity from the larger number, borrowing from higher place values when necessary. This handson approach helps solidify the concept of subtraction through concrete experience.
Material  Description 

Stamp Game  Colored tiles representing units, tens, hundreds, and thousands for handson subtraction. 
Subtraction Strip Board  A board with colored strips that helps visualize subtraction by removing strips. 
Bead Bars  Individual bars with beads that can be removed to visually represent subtraction. 

Multiplication with the Multiplication Bead Board
The Montessori multiplication bead board is a valuable tool for teaching multiplication, as it provides a visual representation of the times tables. The board features a grid of beads arranged in rows and columns, corresponding to the multiplicand (the number being multiplied) and the multiplier (the number by which it’s multiplied).
To perform a multiplication operation, a student places markers on the rows and columns that correspond to the factors. By counting the total number of beads covered by these markers, the child can determine the product. This handson approach helps students build a deep understanding of multiplication as repeated addition.
Material  Description 

Multiplication Bead Board  A grid of beads for visual representation of times tables and understanding multiplication. 
Bead Chains  Chains of beads that can be used to represent multiplication as repeated addition. 
Arithmetic Charts  Charts that provide a visual layout for multiplication problems. 

Division with the Montessori Division Board
The Montessori division board is designed to help children visualize and understand division by physically dividing sets of beads into equal groups. The board features a grid of beads that can be grouped using pegs or markers to represent the divisor (the number by which another number is divided) and the dividend (the number being divided).
For example, if a student wants to divide 28 by 4, they would place markers on four rows and distribute the 28 beads evenly among them. Through this process, the child can see that each row receives seven beads, revealing the quotient of the operation. This concrete experience gives students a better grasp of the concept of division as equal sharing.
Connecting Arithmetic Operations to Shape and Space
Beyond mastering arithmetic operations, Montessori math materials also help students explore the relationships between numbers, shape, and space. Materials such as the Geometric Cabinet, Fraction Circles, and Geometry Sticks provide opportunities for children to manipulate shapes, compare sizes, and discover patterns in a handson manner.
These experiences lay the foundation for more advanced mathematical concepts like geometry and measurement, building upon the arithmetic skills developed through Montessori arithmetic.