
"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 primary 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)?
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 for preschool and kindergarten. 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 Abstract.
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Our oldest started with her preschool curriculum resources 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. If you'd like to start from the beginning, you can check out Montessori math at home. It outlines a lot of the skills she acquired and materials she worked with during her first year of homeschool.
In Montessori Math, concepts are taught using concrete methods and materials. As concepts are mastered, lessons slowly move from concrete to abstract.
An example of this would be the child starting with the Montessori Golden Beads as they explore the decimal system and operations, including addition, multiplication, subtraction, and division. After the child has mastered operations with the Golden Beads, they move on to the Stamp Game, and then the Bead Frame.
Each step in this progression introduces a new layer of abstraction to the child. Moving from concrete to abstract allows students to understand advanced math concepts more fully and relies less on memorization and the interpretation of abstract ideas.
Montessori Math: Concrete to Abstract
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
- Montessori Golden Beads with Numeral Cards
- Stamp Game
# Recognition, # Quantity, & Sequencing to 100
- Colored Bead Bars with FREE Montessori Matching Trucks printable
- Montessori Golden Beads with Numeral Cards
- Teen Bead Hanger
- Teen and Ten Boards
- 100 Board and Printable Extension (Save 16% off your first purchase from Montessorikiwi here)
- Colored Bead Chains with Skip Counting Printable
Operations (+, x, -, /)
- Colored Bead Bars
- Dinosaur Operations Printable
- Addition Strip Board
- Addition Snake Game with Addition Snake Game Printable Bundle
- Multiplication Bead Board
- Multiplication Snake Game
- Subtraction Strip Board
- Golden Beads with Numeral Cards and 4 Digit Equation Printable
- Stamp Game with 4 Digit Equation Printable (Save 16% off your first purchase from Montessorikiwi here)
free NBA game!
What's Their Average?
Calculate the average for each NBA player.
Free NBA Averages Word Problems
Use the Montessori stamp game to calculate the averages described in each word problem. Kids can check their answers to see how they did. All answers are in whole numbers. There are no decimals in this printable. Simply cut out the question cards and place them on the shelf next to the Montessori stamp game for easy access.
Geometry
- Geometric Solids with Nomenclature Cards & Printable Extension - check out Sensorial Materials: Montessori Geometric Solids
- Geometric Cabinet with Control Chart & Form Cards
- Constructive Triangles
- Spielgaben
- Art Materials - check out Montessori Art and Handwriting Space
Fractions
- Fraction Skittles with Fraction Sorting Extension (Save 16% off your first purchase from Montessorikiwi here)
- March Madness Math printable pack
- Just about any household item you can use to demonstrate the concept
Measurement
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- Outdoor Practical Life in the Garden & Measurement Printables (Save 16% off your first purchase from Montessorikiwi here)
- Animals of the World Measuring Tape (Get $15 off your first Waseca Biomes purchase.)
- Days/Months/Years: Perpetual & Linear Calendar
- Money & Money Nomenclature Printable
Favorite Montessori Math Activity Right Now:
- Addition Snake Game
How to Play the Addition Snake Game
- 3 y.o. builds the Snake according to the printable Task Card
- 5 y.o. shows 3 y.o. how to exchange the Colored Beads for the Golden Beads
- 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.
Current Math & Geometry Spaces:
We 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.
The Geometry materials are in the sensorial area, after the pink tower. This includes the geometric solids, the constructive triangle boxes, and the geometry cabinet.
Topics to Introduce Next
- Money Shelf Work - Dollar Counting Board
- Graphs Using Art
- Subtraction Snake Game
- More Abstraction Using the Small Bead Frame
Math Books
Explore a variety of math topics with this collection.
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.
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.
More Montessori Math Resources
Free Guide to the Sensorial Materials
To the iconic Pink Tower and Geometric Solids
Montessori Homeschool Course:
- Homeschool of the Redwoods: Montessori Homeschool Course for Ages 2.5-6
Want to Learn More About All Things Montessori?
Thanks for stopping by!
- Kristin
Montessori Math: Concrete to Abstraction
List of Montessori Math materials & printables for preschool and kindergarten. Montessori Golden Beads, Geometry, etc.
Materials
- Montessori Golden Beads with Numeral Cards
- Stamp Game
- Colored Bead Bars
- Montessori Matching Trucks printable (FREE)
- Teen Bead Hanger
- Teen and Ten Boards
- 100 Board
- 100 Board Printable Extension
- Colored Bead Chains
- Skip Counting Printable
- Colored Bead Bars
- Dinosaur Operations Printable
- Dinosaur Word Problems Printable
- March Madness Math Printable Pack
- Colored Bead Stamps
- Addition Strip Board
- Addition Snake Game
- Addition Snake Game Printable Bundle
- Multiplication Bead Board
- Multiplication Snake Game
- Subtraction Strip Board
- 4 Digit Equation Printable
- Sumblox
- Math Facts Booklets Printable
- Watercolor Times Table Petals
- Geometric Solids
- Geometric Solids Nomenclature Cards
- Geometric Solids Sorting Printable Extension
- Geometric Cabinet
- Geometric Cabinet Control Chart
- Geometric Cabinet Form Cards
- Constructive Triangles
- Spielgaben
- Art Materials
- Fraction Skittles
- Fraction Sorting Extension
- Practical Life in the Kitchen - Recipe for Kids (FREE)
- Outdoor Practical Life in the Garden
- Animals of the World Measuring Tape
- Measurement Printables
- Analog/Digital Clock (Montessori Learning Clock)
- Perpetual Calendars
- Linear Calendar
- Money
- Money Nomenclature Printable
- Money Work - Dollar Counting Board
- Graphs Using Art
- Subtraction Snake Game
- Small Bead Frame
Tools
- See Materials List
Instructions
- The Decimal System can be taught using the Montessori golden beads, stamp game, and eventually the bead frame.
- Number Recognition, Number Quantity, and Sequencing to 100 can be taught using the colored bead bars with trucks printable, the golden beads with numeral cards, the teen bead hanger, the teen and ten boards, the hundrred board and printable extension, and the colored bead chains with skip counting printable.
- Operations (+,x,-,/) can be taught using the colored bead bars, dinosaur operations printable dinosaur word problems printable, colored bead stamps, addition strip board, addition snake game with snake game printable bundle, multiplication bead board, multiplication snake game, subtraction strip board, subtraction snake game, golden beads with numeral cards and 4-digit equation printables, stamp game with the same 4-digit equation printables, sumblox, math facts booklets, and watercolor times table petals.
- Geometry concepts can be introduced and reinforced using the geometric solids with nomenclature cards and printable sorting extension, geometric cabinet with control chart and form cards, constructive triangles, the spielgaben, and art materials.
- Fractions can be taught using the fraction skittles with fraction sorting extension, and household items such as food.
- Various types of measurement can be taught using practical life in the kitchen (free recipe), outdoor practical life, measurement printables, animals of the world measuring tape, Analog/Digital Clock (Montessori learning clock), perpetual calendars, a linear calendar, money and money nomenclature printable, dollar counting board, and graphs using art.
Notes
Full Lesson Info and Pictures at: https://happyhomeschooladventures.com/montessori-math-concrete-to-abstraction/
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