Montessori Math Tools and Materials – Kinesthetic-Tactile Learning

Raising children in a world built on mathematical principles, to form and nourish understanding and practice of fundamental math, is a must in parenthood.

While there are many Montessori materials and tools we use and recommend, elementary algebra lessons are special!

A child’s mind comfortable with mathematics and mathematical games is capable to perceive, adapt, and make sense of the technological merry-go-round world we live in.

At Montessori Nature, we preach Montessori education for a reason. The set of distinctive teaching techniques and Montessori tools are highly effective to convey to younglings an easy-to-understand grasp of mathematics.

Animals and their homes montessori nature sort matching free printables sign up

Montessori methods and tools stand for exploration, experience, and knowledge of math concepts and order, sequence, measurement, calculations, and exactness through indirect preparation and repetition of activities with specific scientifically developed didactic materials.

Montessori math tools support children to gain math skills naturally via hands-on, visual, and physical impressions and play.

When taught math this way, baby students learn how to attach concrete knowledge coming from their surrounding environment to abstract math concepts. This way, children practice observation skills and a better mental representation of the world unlike how most adults learn.

Applying such teaching and active learning techniques in the education of children helps achieve exponential progress, behavior management, gentlemanship in boys (and girls too), and nourishes independence, comments tutor professional Eliza Morrison Nimmich.

So, here’s a THOROUGH list of Montessori math tools and materials of common use. These are perfect to challenge and stimulate the mind of a child!

Here starts the list,

Number Rods

Identical to sensorial red rods, number rods are a set of ten wooden bars with different lengths, each corresponding to a number.

  • The shortest rod is red, and it’s 10-cm long.
  • Each of the following rods is 10-cm longer than the previous.
  • Every 20 cm or up long rod is divided into sections of 10-cm which are alternating red and blue segments with the first section always being red.
  • The number of segments on a rod is apparent.
  • It represents which number in the set is the bar itself.

Number rods are one of the first math tools to use when you teach Montessori elementary math. It’s also a great material to practice hands-on Montessori at home.


Sandpaper Numerals

Sandpaper numbers are a basic yet essential addition to your Montessori toolset that introduces numerals 0 to 9 to prepare youngsters to identify and read.

The Montessori math sequence set consists of 10 green boards, each showing one number from 0 to 9, created from sandpaper. With its specific texture, the instrument invites children to touch, explore, memorize, and identify numeric symbols.

Sandpaper Numbers – Extension Cards

I created these Winter and Spring-themed extension cards for preschool and pre-K children to practice one-to-one correspondence and number formation.

Hands-on match-up math activity with pegs featuring watercolor clipart. You have the option to choose a print or cursive font style.

Learning to Count 0-10 Math Cards English & Spanish Winter Theme

Learning to Count 0-10 Math Cards English & Spanish Spring Theme

Spindle Box

The spindle box helps the student to grasp the idea that the symbols represent a certain quantity of objects and reinforces an early learning one-to-one correspondence math skill.

Cards and Counters

Cards are great for reading, but also for algebra, counting, and even multiplication.
Relatively simple, yet fundamental, the next addition to our list of Montessori math tools are DIY sets of 10 cards, each with a number from 1 to 10 on it, and 55 round, red dots the size of a nickel to represent the numeral.

The sequence requires space to arrange the set, so it’s usually neatly organized on a mat on the floor. Cards are arranged in a nice straight line with a bit of space in between.

There are specific locations for counters, too. Depending on whether the number they represent is odd or even, children arrange cards differently.

Montessori cards and counters help children:

  • learn that each number consists of different quantities
  • explore the concept of odd and even numbers
  • develop a natural sense of order

“Christmas books are the perfect math play for the holiday season”, comments professional Christina Hill, “so you better prep in advance in case you haven’t and get a pair ready for this year”, she adds.

Knobless Cylinders

Full Set of the Knobless Cylinders
It’s a great tool to help younglings grasp dimensions and the many ways to creativity.

I created fun knobless cylinder extension cards, especially for the Christmas season.

Christmas Themed Knobless Cylinder Extensions

Bead Stair

The bead stair math set consists of cards, each with a number from 1 to 9, and a set of colored bead chains. Each chain has a particular number of beads that corresponds to a number from 1 to 9.
This Montessori tool for learning math does an amazing job of teaching children how to associate quantities with numerals, practice one-to-one correspondence, and count objects.

Bead Chains

The bead chain cabinet is an impressive and eye-catching addition to the Montessori math toolset and classroom.

And parents often ask:

  • How to use Montessori math beads?
  • How many beads do I need for Montessori math?
  • How much wire will I need for Montessori math beads?

The answer is: Prepare to lose a lot!

A large cabinet that holds various colored bead chains is helpful for a number of lessons, especially for advanced students. Bead chain cabinets help youngsters understand relations between numbers and advance from fundamental counting to complex algebra.

Constructed as a tactile tool, the Montessori bead cabinet allows children to count hands-on and interact with numbers. Beads contribute not only to mental progress but to develop of fine motor skills, as well.

Golden beads – Decimal System

The bead tray tool is part of introductory lessons in Montessori math.

It contains only golden beads. There is always one single unit and the others are combined in orders of tens: a ten bar, a square/tile of 100, and a cube of 1000.

The bead tray helps youngsters attach exercises to the knowledge of the decimal system and lays foundations for complex math operations, such as multiplication, and more.

Place Value Cards and Mats with Interesting Facts contain 50 place value matching sets and 50 place value mats with interesting facts in Geography, Science, Music, Art, and History. Students can learn fascinating facts and practice memorizing dates and numbers associated with different subjects in a fun and engaging way. It also combines building students’ comprehension skills and encourages them to conduct further research based on the facts that they’ve learned.

Place Value Cards and Mats

Bead Frame

The bead frame resembles an abacus, but it has only four rows of beads, representing units, tens, hundreds, and thousands.

The color of beads is different in every row. The first row has green beads, the second – blue, the third – red, and the fourth – green again.

The category of each row is marked on the frame. The bead frame helps children transit to a more exciting understanding of the decimal system, concepts of place value, and numerical powers.

Stamp Game

We continue with an example of an abstract alternative to golden beads – the Montessori stamp game.

While it’s similar to golden beads, this math tool is still different enough to intrigue a child. Instead of beads, the stamp game includes identical tiles, some labeled with the numbers 1, 10, 100, and 1000, and wooden skittles along with counters.

Some of the bits in the set are red, and the rest are blue. The tool allows a wide range of Montessori math manipulations.

Teen & Ten Boards

These are two technically different Montessori math toys, but they have similar features and functions.
The teen board has ten rows and each begins with the number 10 written on the frame.

The tool consists also of a set of tiles with the numerals 1-9.

The tiles are made to fit the board rows, so when inserted they change the number 10 to any of the teen numbers.

So, this Montessori math tool introduces the concept of teen count to a child and helps develop a true understanding of how they form.

The ten board works in the same fashion, except that only the first row starts with 10, and the number changes on each of the following by ten.

These math toys show impressive results when combined with Montessori counting beads for exploring relationships between numerals and quantities to learn the sequence from 10 to 99.

You can read more about how to create your own bead bars and DIY Seguin Boards here.

Christmas Themed Math Beads Addition Cards

Arithmetic Boards

A must when teaching Montessori math lessons – arithmetic boards!

They represent the relationship between numbers and the sums of different manipulations in a holistic way, she adds.

Explore work, and practice with arithmetic boards help youngsters memorize and carry out simple operations, which is crucial to advance in math.

Also Calendars

Montessori calendars are not the best fit in terms of math, but they can be playful and exercise digits, too.

You can view all available calendars here.

In the spirit of Montessori, besides the amazing tools listed above, the best way to learn is through nature and counting collections of seashells or pebbles as a hands-on summer activity.

Montessori math tools & materials, final thoughts

Montessori math tools are a part of a well-researched, developed, and timeless educational system and methods that help children become independent, motivated, intelligent, and inspirational adults. According to experts, education from an early age is fundamental to the parent-child bond and the ability to learn fast as younglings get in class, and leads to a passion for STEM games in the upper classes. If you feel like the youngster needs a push, be it for math, cleaning, or any other chore at home or outside, apply the secret weapon of motivation quotes! They work great to keep children on track with persistence.

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About Anastasia - Anastasia is an early childhood teacher and the founder of Montessori Nature - a blog about Montessori living and learning and nature-based explorations. With many years of experience working in a Montessori environment and homeschooling her children, she directed her passion for all things Montessori and nature into creating educational resources. You can learn more here and browse her printables on Teachers Pay Teachers.