Montessori Math: Concrete to Abstraction

Montessori Math Stamp Game Addition Work

“One of the most basic principles of Montessori mathematics is that students always learn new concepts with concrete materials. Montessori’s math materials are designed to lead your child step by step from the most concrete representations to pure abstraction.”

– Michael Duffy

– Interested in learning more about Montessori Math and the materials found in one of the most exciting areas of a Montessori classroom or homeschool?

– Planning for Fall and want some insight on what you’ll need for the next few years of early childhood education (3-6)?

– Are you, like I was, wondering what your little ones should learn once they understand number quantity and number recognition up to 10?

As we wrap up the rest of the official school year, this is a good time to share the second part of our daughter’s progression in Math. In other words, what happened after mastering number sense (# recognition, # quantity, and 1-1 correspondence) for quantities up to 10. More specifically, we’re going to share her journey in Montessori Math: Concrete to Abstraction.

If you’d like to start from the beginning, then you can find the first post here. It outlines a lot of the skills she acquired and materials she worked with during her first year of homeschool. She started preschool at 2.5. Her math journey included a lot of open-ended play with materials such as blocks, working with her sensorial materials, and gaining skills such as one-to-one correspondence.

Montessori Math: Concrete to Abstraction

If you’re getting organized and researching the types of Math materials you want to have available as shelf work for your students, then this is the post for you! Here’s a broad overview of what we have covered so far, including what materials we used for each category, and the printables (including a freebie) we are enjoying.

Some materials are listed under more than one category. Therefore, those are the ones you’re going to get the most mileage out of. The best part: these materials will be useful for the Elementary years as well! As a result, whatever materials or printables you do purchase, you have the piece of mind of knowing your kids will likely get a lot of use from them. I don’t know about you, but that makes all the difference for us when deciding what and where to spend.

Decimal System

  • Golden Beads with Numeral Cards
  • Stamp Game

# Recognition, # Quantity, & Sequencing to 100

Montessori Math Kids learning teen numbers with truck matching activity
Montessori Math Kids matching quantity to numbers with truck matching game
  • Golden Beads with Numeral Cards
  • Teen Bead Hanger
  • Teen and Ten Boards

Operations (+, x, -, /)

  • Colored Bead Bars
Montessori Math Addition using colored beads and dinosaur printable
 Montessori Math Kid sorting answers to Dinosaur printable activity
  • Colored Bead Stamps
  • Addition Strip Board
Montessori Math Addition Strip Board for Fact Families
Montessori Math Addition Snake Game Building the Snake
  • Multiplication Bead Board
  • Multiplication Snake Game
  • Subtraction Strip Board
Montessori Math Stamp Game Addition Work


  • Geometric Cabinet with Control Chart & Form Cards
  • Constructive Triangles
  • Spielgaben


Montessori Math Fraction Sorting Extension
  • Just about any household item you can use to demonstrate the concept


  • Days/Months/Years: Perpetual & Linear Calendar

Their Favorite Activity Right Now:

  • Addition Snake Game

How Do You Play the Addition Snake Game?

Montessori Math Addition Snake Game with Printable Activity- Building the Snake
  • 3 y.o. builds the Snake according to the printable Task Card
Montessori Math Kids exchanging colored beads for golden beads in Montessori Addition Snake Game
  • 5 y.o. shows 3 y.o. how to exchange the Colored Beads for the Golden Beads
Montessori Math Kids Evaluating Sum in Montessori Addition Snake Game
  • 5 y.o. demonstrates how to evaluate the sum by ordering the beads and adding: 3 tens + 1, and then compares the answer to the value on the back of the printable Task Card for control of error

Control of error is also included by counting the colored beads in the far left box. These types of activities that our kids can do together are everyone’s favorite. They don’t mind taking turns and they enjoy the exchange of ideas that takes place organically when problem-solving together.

Our Current Math & Geometry Spaces:

Montessori Math Space
Montessori Geometry Space

We don’t use a bead cabinet so we’re able to save a lot of space in that respect. We also rotate the shelf work in our Math area so we are able to function with one shelving unit for our two oldest. You’ll notice we keep the earlier Math works on the lower shelves and the more advanced work higher up. This works well for our family and our littles ones.

Soon, We Will Introduce:

  • Money Shelf Work
  • Graphs Using Art
  • Subtraction Snake Game
  • More Abstraction Using the Bead Frame

In Conclusion

As with most things Montessori, the Three Period Lesson, repetition, and observation are the cornerstones to success. So far, we have found having a mix of materials and printables is what works best for us.

While there are several different Math topics to cover for ages 3-6, and it can seem daunting, it actually works really well because variety means our kids never get bored. As a result, they show persistent interest in Math. In fact, our Math shelves get more consistent traffic than any other area of our homeschool. We don’t include all of the materials you would see in the Math area of a traditional Montessori classroom since we do not need to provide for as many students in a homeschool setting.

What else would you include in your Montessori Math collection? Do you consider this a minimal amount of Math materials or is your collection more trimmed down than ours? Let me know.

If you want to see more of what we’re up to in our homeschool, subscribe to our blog at the top!

More Montessori Math in Our Homeschool

More of What We’re Up To

Want to Learn more about Montessori Math & how to implement it in your homeschool?

Best Montessori Math Book:

Montessori Homeschool Course:

Want to Learn More About All Things Montessori?

Thanks for stopping by!

– Kristin


Getting organized for Fall & researching the types of Math materials you'll want for your homeschool? Here’s a broad overview of what we covered, what materials we used, and the printables (including a freebie) we enjoy. #montessori #homeschool #montessorimath