Once a child has mastered the concept of 1-9, the concept of 0 and the basic idea of putting groups together and separating groups (adding and subtracting), they are ready to work with 4 digit numbers.

**Primary:**Mathematics begins at or close to the child's 4th birthday:

**Numbers 1-10 - 4.0-4.5**

Number
Rods

Sandpaper
Numerals (ciphers)

Number
Rods and Cards

Spindle
Boxes

Zero
Activity

Cards
and Counters

Memory
Game of Numbers (Chit Game)

**Decimal System - 4.5-5.5**

Introduction
to the Decimal System

Introduction
to the Bead Material

Introduction
to the Card Material

Formation
of Numbers

Change
Game (with golden beads - exchanging; the Bank Game is an elementary work with colored cards)

Addition
with the Golden Beads

Subtraction
with the Golden Beads

Multiplication
with the Golden Beads

Division
with the Golden Beads

Long
Division with Bows

Stamp
Game Addition

Stamp
Game Subtraction

Stamp
Game Multiplication

Stamp
Game Division

Dot
Game

Word
Problems

**Counting - 4.5-5.0**

Teens
Stage I: Teen Boards 11-19

Teens
Stage II: Teen Boards 11-19

Teens
Stage III: Teen Beads and Boards 11-99

Tens
Stage I: Tens Boards 10-90

Tens
Stage II: Tens Beads and Boards 10-90

Tens
Stage III: Tens Beads and Boards 11-99

Linear
Counting: Stage I – Hundred Chain

Linear
Counting: Stage II – Thousand Chain

Skip
Counting

**Memorization - 5.0-6.0**

Addition
Snake Game

Addition
Strip Board

Addition
Charts

Subtraction
Snake Game

Subtraction
Strip Board

Subtraction
Charts

Multiplication
with Bead Bars

Multiplication
Board

Multiplication
Charts

Unit
Division Board

Division
Charts

**Passage to Abstraction - 5.5-6.0 (leads into elementary as well)**

Small
Bead Frame

Wooden
Hierarchical Material

Large
Bead Frame

Division
with Racks and Tubes

**Fractions - 4.5+**

Introduction
to Fractions

Fraction: Simple Operations

(there is also design work with the fraction materials, leading to concepts of equivalencies - design work begins shortly after introduction to the metal insets)

__Elementary__- covering ages 6-12 years:**I. Introduction**

5th Great Lesson: The Story of Numbers

**II. Early Work - Numeration**

Wooden Hierarchical Material

Large Bead Frame: Introduction

Exercises I-IV

Commutative and Distributive Laws of Multiplication

Multiples

Least Common Multiples

Factors

Last Steps of Least Common Multiples to Abstraction

Divisibility: by 2, 5, 25

By 4, 8

By 3, 9, prime numbers, 7, 11

Measurement

**III. Operations**

Long Multiplication

Large Bead Frame

Bank Game

Flat Bead Frame

Checker Board: Exercises 1 & 2

Geometrical Form of Multiplication

Category Multiplication

Long Division

Distributive Division with Racks and Tubes

Group Division

Group Division & Word Problems w/ the Fraction
Material

**IV. Squares and Cubes of Numbers**

Prerequisites to Squares and Cubes of Numbers

Notation of Squares

Notation of Cubes

Games 1-3

Game 4: Decanomial
Square

Paper Decanomial

Sums Using Squares and Cubes

**V. Fractions**

Introduction to Fractions (review if received in primary)

Equivalence of Fractions

Simple Operations

Addition & Subtraction of Fraction w/ Different
Denominators

Exercises Leading to Abstraction of the
Above

Multiplication of a Fraction by a Fraction

Division by a Fraction

Notes on the Fraction Charts

**VI. Decimal Fractions**

Quantity

Symbol Linked to Quantity

Formation and Reading
of Quantities

Operations

Conversion of Common Fractions to Decimal Fractions

Effects of Multiplying or Dividing Numbers by Powers of 10

Multiplying a Decimal Fraction by a Decimal Fraction

Introduction to the Decimal Checkerboard

The Decimal Checkerboard

Relative Size of Terms in a Multiplication Problem

Relative Size of Numbers When You Are Dividing

Division of a Decimal Fraction by a Decimal Fraction

Leading to Abstraction of Multiplication of Decimal Fractions

Division of a Decimal Fraction on Paper

**VII. Squaring and Cubing**

Squaring

Transformation of a Square, Ex 1-6

Passing From One Square to Another

Squaring a Sum

Squaring with a Hierarchical Value

Cubing

Passing From One Cube to Another

Cubing a Binomial

Cubing a Trinomial

Cubing a Quadrinomial

Cubing a Trinomial having Numerical Value

The Story of the Three Kings

Cubing a Number with Decimal Value

Square Roots

Introduction to the Concept

Exercises 1-3

Backtracking

Passages to Abstraction

Special Cases

Rule

Cube Roots

Concept

Exercise 1

Exercise 2: 3 digit roots

Exercise 3: Last Steps Towards Abstraction

**VIII. Other Topics**

Signed Numbers

Powers of Numbers

Powers of 2

Powers of 3

Powers of 10

Operations Using Exponential Notation

Expanded Power Notation

Operations Using Expanded Power Notation

Other Number Bases

Numeration

Operations

Conversion

Ratio and Proportion

Word Problems

Introduction to Word Problems

Distance/Velocity/Time

Principal/Interest/Rate/Time

Introduction to Algebra

UPDATE: See a math topic missing? Browse our other Montessori Nuggets, as I have upcoming Nuggets on this topic; then post in comments and I'll reply with where it is found within the albums --- not all Mathematics topics are found in the math album ;)

Be sure to check the reaction boxes below this post - this provides me some feedback of what you'd all like to see!

Excellent post. Thank you for putting it all into a concise outline. Hope to see more "Table of Contents" for other areas of study.

ReplyDeleteMore coming :) I am looking to do each one as a combination of primary and elementary to show the complete flow from one plane of development to the next.

ReplyDeleteIf you (or anyone) has a particular area you'd like to see addressed that would fit with the theme here, please let me know. In particular along the lines of "top questions for new Montessori parents or teachers - or those seeking information on Montessori". :)

This is so useful post! Thank you!

ReplyDeleteStill learning here... we started Montessori "late" (always parented in the 'style' but haven't formally homeschooled Montessori until my son was about 5 ish). Does that mean I'm destined to constantly catch up with him? Even now at 5.5 y.o. he resists academics (sitting down to read on his own and is still struggling with memorizing numbers - 0 thru 9 is pretty good, but is just now starting to get a handle on teens & up recognition). I'd like to continue Montessori, but I worry that if the tools I have will no longer work since he's out of the sensitive periods, I may need to seek out an alternative.

ReplyDeleteBy the end of your first year of elementary, it won't be "playing catch up" so much - you'll see :)

ReplyDeleteThere is a point where you have to let go of everything he COULD have had in primary because he is moving into the second plane and the quality of his needs change.

At 5, they like humor, they like games. I had 5 and 6 year olds during my student teaching who were "behind" so to speak; I had them start over with the sensorial album and focused on the games - they ate it up! Especially when there was a little trick or catch for us all to laugh about in the end.

For mathematics materials - the core materials continue into elementary (golden beads, colored bead bars, chains/cubes/squares, fraction insets); and while there is a remediation section, again, at some point he just moves on to the next thing and he will be totally FINE.