Montessori Mathematics – An Introduction

From the time children can pick something up, they are learning about mathematics. It is another way children view the world around them; understanding and expressing measurable relationships. The science of numbers is attractive to children, and they are conscious of quantity which they demonstrate as they begin to count. Maybe it’s the rocks they have collected on their hike or pieces of candy they received for Halloween.

The mathematics materials at Norbeck Montessori build upon each other in increasing complexity, which begins with the concrete and progresses towards the abstract. Mathematics is introduced in our Transitional Two’s classroom where the children first learn quantity as they are exposed to the symbol that represents the quantity. Eventually, this leads to a child incorporating quantity and symbols to perform more complex operations. As children progress through their Montessori journey, they will learn how to add, subtract, multiply, and divide. This process allows for the child to experience the thrill of discovery as part of a natural progression.

To simplify this area within the Montessori classroom, we have grouped the lessons into segments. Some lessons are given sequentially while others, parallel. First is the introduction to numbers, next, comes, the decimal system. After the decimal system is introduced and the concept is well understood, counting and numbers and memorization lessons are introduced- parallel to the decimal system lessons. Using mathematic material the child experiences order, coordination, concentration, and independence.

Introduction to Numbers

Norbeck Montessori’s Transitional Two’s classes are initially introduced to the quantity of numbers through sensorial mathematics lessons like the pink tower. All of the Montessori mathematic materials are introduced in sets of one through ten which prepares the child for counting, reinforces the value of quantity, illustrates the sequence of numbers and teaches the names of numbers. In the Primary Preschool classrooms, children begin to associate numeral and quantity. Lessons such as number rods, number cards, spindle boxes, and counters reinforce 1-10 sequential counting while introducing the concept of zero. This sets the stage for preparing the children for counting into the teens and growth towards abstraction.

The Decimal System

Do you remember when you first learned the difference between 1 and 10? Or that there is a number even bigger than 99? How does a child understand that each digit in a number has a different place called a decimal? Children using the golden bead materials are introduced to the decimal system. The child will learn the language of the decimal categories; units, tens, hundreds, and thousands and will visually learn the quantities. Lessons using beads, wooden cards, and wooden symbols reinforce the association of quantity and symbol, the visual impression of the decimal system, differences between place value, and assists in learning the sequence of larger numbers. Learning the operations of the golden bead material introduces the child to the concept and process of addition, subtraction, multiplication, and division. Children work with each other and develop an understanding of the process of exchanging while reinforcing place value and the child’s knowledge of quantity and symbol.

Counting and Number

These lessons help children understand the idea of place value and linear counting. The first lesson children are introduced to in this area is the Teen Board. This lesson introduces the children to the teens in a concrete form, reinforces the association of quantity and symbol and teaches the children to count the teens in sequence. This lesson is followed by the Ten Board, where children are introduced to tens. This reinforces place value and teaches the children how to count the tens, in sequence. These lessons are followed on by others such as the hundred board and skip counting.


This is likely the most difficult concept for children to grasp; however, there comes the point in mathematics that memorization is just needed. The number rods and colored beads, which are first shown with the introduction of numbers and the decimal system, can be used to reinforce the understanding of addition. Simply put out one number rod or colored bead bar + a second number rod or colored bead bar to demonstrate addition. Most of the same lessons for addition may also be applied to subtraction. For multiplication and division, we generally start by using the colored bead bars. For example, to demonstrate the concept of 3 x 3, we would show three, 3-bead bars to have the child develop an understanding of multiplication equations and see multiplication in a concrete form. For division, lessons like the bead boards are used. This lesson takes pieces (or what we call ‘skittles’) to show in a concrete fashion, how to divide a number. For example, to show 16 / 4, you would place 4 skittles at the top of the bead board and count out 16 beads. The child would then start at the top left of the board, under the first skittle and go across to the 4th skittle then start on the second row, again going across to the 4th skittle, until all beads are distributed. Then ask the child to count how many beads are under each skittle to determine that 16/4 equals 4.

The Montessori approach to math is so unique for so many reasons that the children actually get it! Lessons all go from concrete to abstract. This enables children not just to learn to count, but they also learn to perform more complex and abstract operations, allowing them to become problem solvers.

How to set up a simple at-home math center


Create a Simple Outdoor Math Station

Outdoor Math Station StumpObjective: Sorting, classifying & pattern recognition
Material needed:

  • Fallen leaves
  • Flat surface to work on (maybe try a stump!)

Gather at least 25 leaves of different colors and shapes. Sort the leaves into color groups, count how many leaves are in color group. Maybe try to a pattern by color or size, how many other patterns can your little once create?



Addition Fun

Addition Fun with Paper Towel TubesObjective: Concrete addition
Materials Needed:

  • One piece of poster board
  • Two paper cups
  • Two paper towel roll tubes
  • A basket or bowl
  • Beads, paper clicks, erasers, marbles
  • Marker to draw the plus sign
  • Packaging tape

Write down a few math problems they are working on at school. Have the child count out the beads (or whatever you are using) and have them put them in the first cup. Then, count out the second quantity of the problem and put it in the second cup. Watch as all the beads fall through the cups into the basket. Now, have the child count them all up.

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