The Montessori Math Progression

In Montessori math, not only are topics taught differently than in traditional education, but the order (or sequence) of introduction is different. What does the progression of learning look like in Montessori math? Let’s find out!

Basic Content: The following topics are introduced roughly in order, starting when a child turns four (or later, depending on their interest and readiness):

1. Numbers 0-10: Like traditional education, Montessori starts formal math education with the numbers from 0-10. Unlike traditional education, Montessori waits until the child is four to start this introduction and focuses on a deep and holistic understanding of quantity.
2. Numbers 1-9999 (the decimal system): The second of unit of Montessori math study diverges sharply from traditional education. Children use the Golden Beads to develop a “birds-eye” view of quantity, building and writing numbers into the thousands. This experience follows the “concrete to abstract” pathway- children gain a physical impression of the decimal system (the “overview”) which then allows them to more precisely place individual numbers.
3. Teens and tens: When a child has mastered most of the decimal system unit (and can reliably build and say the names of four digit numbers), they move onto working with teens and tens. Compared to traditional education, this seems out of sequence and maybe even a little backwards, but there is good reason for postponing this topic. These numbers, especially the teens, have irregularity in their naming patterns (whereas the naming convention for hundreds and thousands is predictable). By waiting until children understand building and naming large numbers, Montessori education provides children with a stronger internal model within which to place these numbers.

Advanced Content: After showing their understanding of the decimal system (tens, hundreds, thousands) and their ability to read and write teens and tens, a child’s math learning intensifies. The order of topics below shows a rough outline of the order of introduction, but children will be working on many of the topics at the same time. These topics are introduced between 4.5 and 6 years old in a Montessori classroom, depending on a child’s interest and readiness.

1. Linear and Skip Counting: Children practice counting, first linearly to 100 and 1000 (using the golden bead chain) and then skip counting with the short and long bead chains. In addition to practicing fact families (which are important in multiplication), children also begin to develop an understanding of “squares” and “cubes”.
2. Introduction to Operations: Around the same time a child is working on skip

counting, they also begin working on the four operations- addition, subtraction, multiplication and division (in that order). Montessori uses a unique “story” method and hands on manipulatives to help children perform operations on four digit numbers from the beginning. Ideas like carrying and borrowing are introduced early on and become intuitive for even young children during this progression. When a child has shown a solid understanding of one operation, we introduce the next operation while also continuing to move them forward on the first operation progression. This means that, in a Montessori classroom, a child may be working on all four operations at once- just at different levels of understanding and abstraction.

1. Memorization of facts- The Montessori progression from concrete to abstract naturally moves a child towards fact memorization- no flash cards needed! The memorization lessons happen at the end of each operation progression- this means a child can fluently work with four digit numbers before they are asked to calculate single digit facts.

Table One: A sample learning progression for a five year old, showing work on different topics at different levels at the same time.

1. Fractions– A bit of an outlier, the fraction sequence is still incredibly important and

1. powerful. This is one of the math materials that we actually introduce before four (usually around three and half), although only in a sensorial way… aka, as a series of puzzles. Once a child turns five and has had ample experience working with whole numbers, they learn the names of fractions and begin preforming all four operations on fractions with the same denominator.

So what does this mean for families that are not currently enrolled in a Montessori program If this progression seems complication and you’re not sure where to start, that’s okay. Here’s the take-away:

• The Montessori math sequence is different from the traditional learning timeline. One of our programs may touch on math concepts from multiple different public school grades.
• Montessori math progresses from concrete, hands on learning to more abstract tasks. Understanding the stroy behind a more “complicated” idea often comes before a child is asked to memorize.
• While skills build, a child does not need to do every course in order. This is especially true of older children. If your child meets the prerequiste skills, they are ready for that cours’s content.

If you’re ready to get started but don’t know where to start, or if you’re looking to target a specific skill (for example, multiplication fact mastery), please reach out. We’d be happy to help you find the perfect course to meet your family’s needs.

Finally, if you’re curious about the individual skills taught in each course and how they compare to the Common Core State Standards, here is a summary document. Please note that this document only covers the Children’s House (3-6 years old) lessons- the Elementary progression is coming soon!