Printable Montessori materials for Montessori learning at home and school.
Printable Montessori Materials

Montessori Math Overview - Scope and Sequence

Learn about the Primary Montessori Math Program

Math is logic, sequence, order, and the extrapolation of truth. In the Montessori philosophy it's stated that the child has a 'mathematical mind' and an internal drive to understand the environment around them. It can therefore be said that children have an inborn attraction for math. Their minds are full of energy that propels them to absorb, manipulate, classify, order, sequence, abstract, and repeat. These tendencies are those which help the child to acquire a greater depth to his mathematical knowledge.  

It is the precision of the presentations and the exactness of the math materials that attract children to this area of the classroom. As well, children in the primary Montessori classroom are in the process (sensitive period) of fine tuning their perceptions. Children are sensitive to minute changes in order, sequence, and size. They will notice a teeny tiny bug in the crack of the sidewalk where as adults will walk by blindly without notice.

The exercises in the math area offer the children the 'keys' that they will need to send them on the road to further exploration and maturation of the mathematical mind. The ways in which the materials are ordered allows the children to complete full intellectual cycles that help them to achieve the freedom to become independent.

Math in the primary classroom is made up of many little details that form a whole, but each detail is complete unto itself. All early math exercises are worked at the sensorial level so as to ensure that the child relates the quantity to the symbol (example: Spindle Boxes).

Montessori Math - Numbers to Ten

The foundation of math is numbers to ten. The exercises in this section must be firmly rooted in the child before continuing through the math materials. The child learns the names of the numbers and the fact that each number represents a certain quantity. The child learns to associate the language, written symbol, and quantity of each number from 0 to 9. Sensorially he is shown even and odd numbers, as well, the child learns to fix a number in his mind and remember it after a long period of time.

The Decimal System

The Decimal System introduces the child to the bead materials and the associated cards for each category. The child learns that zero can give a greater value to a number, and he also learns the language of the larger numbers. The Collective Exercises show the child how to change (10 units/ones changes for 1 ten), and gives the child a sensorial impression of addition, multiplication, subtraction, division, and the relationship between the operations.

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The Teens and Tens

The section on Teens and Tens parallels the work with Association of Beads and Cards. The child learns to associate quantities, names, and symbols of the teens and tens. As well, the child is introduced to the colors of each individual bead bar which is important for future exercises. This section finishes off by consolidating the child's knowledge when he works on the linear and skip counting of the square and cube chains from the bead cabinet.

The Exploration and Memorization of Tables
This section focuses on the exploration and memorization of addition, subtraction, multiplication, and division tables. The tables that the children learn are limited in the fact that any given category of a question is not above the number nine. The materials in this area give the child the opportunity to explore essential number combinations for each mathematical operation and continue to move the child towards less concrete materials.

The Transitional Materials
These materials allow the child to re-examine all the concepts he has already learned. The child begins to realize that the materials hinder his efficiency and that he no longer requires the materials to do the operations. When the child reaches this point, he can now think abstractly.


The last section of the math area introduces the child to fractions and has the child explore the materials in order to discover the rules of each fraction operation.

If you are homeschooling your child and wish to have a little more theory, step-by-step direction on the presentation, and suggested age of when to present the Montessori Math materials you can purchase our Math Teaching Manual.

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Numbers to Ten
  • Number Rods
  • Sandpaper Numbers
  • Number Rods and Cards
  • Spindle Boxes
  • Numbers and counters
  • Memory Game of Numbers

Decimal System
  • Presentation with Beads
  • Presentation with Cards
  • Association of Beads and Cards
  • Formation of Complex Numbers with Beads
  • Changing Exercise - Bank Game
  • Addition  - Collective Exercise
  • Multiplication - Collective Exercise
  • Subtraction - Collective Exercise
  • Short Division - Collective Exercise
  • Long Division with Bows - Collective Exercise
  • The Stamp Game - Addition
  • The Stamp Game - Multiplication
  • The Stamp Game - Subtraction
  • The Stamp Game - Division
  • The Dot Game

Teens and Tens
  • 11 to 19 Beads Only
  • Teen Boards
  • Teen Boards and Beads
  • Ten Boards and Beads
  • Linear Counting 100 to 1000 Chains
  • Skip Counting

The Exploration and Memorization of Tables
  • Snake Game - Addition
  • Addition Strip Board with Charts #1 and #2
  • Addition Work Chart #3
  • Addition Work Chart #4
  • Addition Work Chart $5
  • Addition Work Chart #6
  • Negative Snake Game - Subtraction
  • Negative Strip Board with Subtraction Chart #1
  • Subtraction Work Chart #2
  • Subtraction Work Chart #3
  • Multiplication with bead Bars
  • Multiplication Board with Control Charts #1 and #2
  • Multiplication Work Chart #3
  • Multiplication Work Chart #4
  • Multiplication Work Chart #5
  • Unit Division Board
  • Division Charts #1 and #2

Transitional Materials
  • Small Bead Frame
  • Large Bead Frame
  • Short & Long Division with Racks & Tubes

  • Introduction to Fractions
  • Addition of Fractions
  • Subtraction of Fractions
  • Multiplication of Fractions
  • Division of Fractions
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