Math is all around us and, for a young child, words like “more, less, not enough, and share” are part of daily life.  Math is also inherently abstract.  It is a language of precision that takes years to master, but at its core are the basic foundations all children need to learn: counting, numeral identification, and basic mathematical operations. Let’s take a look at the Montessori math curriculum for the primary class and see how we do it.

A Tactile Experience

Montessori math materials create a tactile experience for the child. Manipulatives allow the child to use their sense of touch to grasp mathematical concepts of quantity. Materials are generally made of wood and are painted pleasing colors, when necessary. They have weight to them, which helps small hands and muscles understand that 1 is less than 10 and 1000 is more than 100. Smooth wooden rods and heavy cubes work to ensure that the child develops a concrete understanding of quantity.

Some materials are made of glass. These shiny, glass beads appeal to the tiny fingers that will count them precisely and handle them carefully. From the youngest to the oldest child, the colorful glass beads hold their appeal through the years. Younger children use them for simple counting lessons: single units, teen numerals, and tens to one hundred.  Older children have lessons on skip counting, addition, subtraction, and even square numbers and cubed numbers; all with the same shiny beads!

Quantity and Numeration

The numeral “5” represents a quantity of five units. Children learn that “1” means a single unit, “2” means two units, “3” means three, etc. There are several materials in the Montessori math curriculum that are used for practicing matching a quantity to its numeral. Children memorize the numerals in order, identify them randomly, and understand concepts like “zero.” Some examples include:

• Spindle box – introduces the concept of “zero” as one box remains empty while the others are filled
• Number rods – the length of the wooden rods progress from the smallest rod (10cm long) to the longest rod (1m) and are marked in colored sections from one to ten
• Cards and Counters – small items are counted out and matched to numerals indicated on a card

Introduction to the Decimal System

The Golden Beads are the primary Montessori math material used to introduce a child to the decimal system. Glass “unit beads” and “ten bars” are paired with wooden “hundred squares” and “thousand cubes” to create a hands-on learning experience that teaches place value up to 9, 999. 

The Golden Beads are a flexible set of materials that are used for multiple lessons, which include:

• Introduction to the decimal system – naming each place value and comparing the quantity of each part (units, tens, hundreds, thousands)
• The 45-Layout – setting up quantities from 1 unit to 9 units, then 10 to 90, 100 to 900, and 1,000 to 9,000. Numeral cards for each are matched with the quantity, represented by the Golden Beads. The name “45-layout” refers to the 45 unit beads, 45 ten bars, 45 hundred squares, and 45 thousand cubes that are required to complete the activity.
• Introduction to mathematical operations – addition, subtraction, multiplication, and division are all introduced with the Golden Beads

Mathematical Operations

Over the course of their three years in the Montessori classroom, a child is introduced to the four mathematical operations in a variety of ways and with a variety of materials. Because the Montessori math curriculum moves from concrete to abstract, the understanding of math operations develops over time.  Children physically add, subtract, multiply, and divide with manipulatives, before moving on to memorizing math facts.

The Golden Beads (large manipulatives) and Stamp Game (smaller manipulatives) are used for computing numbers up to 9,999. Small beads, strip boards, and finger charts are used to encourage memorization of math facts and to introduce concepts like the commutative property (3 + 4 = 4 + 3 or 6 x 7 = 7 x 6). 

Additional Math Lessons for Kindergarten

Here at Children’s House, we maintain mixed-age classrooms. This means that any child who is ready to receive a new, more advanced math lesson, will have the opportunity to do so. This applies to any of the materials listed above. It is not uncommon for an older child to work alongside a younger classmate, showing what they know. Teaching a friend to do a new lesson is a reinforcement of the lesson itself.

There are, however, a few exceptions. We reserve some of the more abstract concepts for the kindergarten year. These lessons are taught in small groups with individual practice to follow:

• Time – introduction to the clock and telling time to the hour and half-hour
• Money – identifying the different coins and bills and learning their value and practice counting money
• Measurement – learning how to use a ruler and tape measure to measure inches and feet
• Temperature – understanding the thermometer and how to track the weather 
• Calendar – learning the days of the week, months of the year, and seasons in order

The Montessori math materials provide years of hands-on learning for the Montessori child. After three years in the classroom, most children will have a solid foundation of quantity, place value, and the mathematical operations. They are ready to move on to elementary and the wider world of math!

Additional Resources:

• Montessori Math Materials – Kingsley Montessori School, Boston MA
• Montessori Basics: How Math Progresses Through the Levels – Hollis Montessori School, Hollis NH

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• Eat the Cake! The Importance of the Montessori Kindergarten Experience
• Why are Montessori Classrooms Mixed Age?