School Blog

Montessori Math

Montessori curriculum is based on giving children exposure to concrete materials first, then giving them incremental opportunities to build more abstract concepts.  

What do we mean by concrete?  The children are able to hold a material in their hands.  Montessori Math is unique in that math skills are developed through hands on materials first.  They physically hold, carry and manipulate materials to gain a complete understanding of the concept of quantity.  

Children initially experience concrete 1-10 concepts in Sensorial by doing activities such as the Pink Tower, Brown Stairs, Red Rods, Knobbed and Colored Cylinder.  All of these activities have ten physical components to them (10 cubes, 10 stairs, 10 cylinders, etc.).  While we do not count these components, children work with them and unconsciously experience what 10 items feel like.  The materials are carried individually to a workspace on the floor, built or organized, then returned, one piece at a time, to their proper location in the classroom.

Montessori math materials stem directly from the Sensorial materials by utilizing the physical feel of 1-10, then adding the more abstract idea of a symbol: the number that corresponds to the physical quantity.

Number recognition is taught after the concrete materials are introduced, then the two concepts are paired together.  In this manner, children develop a thorough understanding of not only numbers, but what those numbers represent.

Examples of Early Montessori Math materials include:

The Red and Blue Rods

The Spindle Boxes

Cards and Counters

and the Short Bead Stair.

When concepts of 1-10 are mastered, children move onto concepts of Teens, Tens, Hundreds and Thousands using the same process of introducing the concrete material first, then learning the symbol or number that represents the quantity, then pairing the two concepts together.

The materials are symbolic or representative of something else (a number, perhaps), and that symbolism changes over time until children are ready to let go of the materials and find solutions on paper or even in their heads.  This idea of mastering a skill without the assistance of materials is what we refer to as abstraction. 

When a child is ready to learn about basic operations, there are plenty of materials to support them.  Montessori math uses the golden bead material; first to build numbers into the thousands.  For example a single golden bead represents 1, a group of 10 beads are strung together in a straight line for 10, and 100 beads are affixed into a flat square.  The thousand cube is as large as 1,000 of the original single ‘1’ bead.  Once a child is able to build a visual representation of a number, the beads are used to teach basic operations.  Young children are able to add, subtract, multiply, and divide numbers into the thousands using this material.  They first learn with static problems – that is, with no exchanges – and then move on to more complex, dynamic problems.  They quickly learn that ten 1s is equal to one 10, and they do this by holding those numbers in their hands.

Long and Short Chains are a continuation of the short bead material.  These materials incorporate sequential counting that can also be used for skip counting which, in turn, aids building addition and multiplication skills.

In this manner, math concepts are easily understood and students are able to practice a wide variety of functions.


“Thankfulness is the beginning of gratitude.  Gratitude is the completion of thankfulness.  Thankfulness may consist merely of words.  Gratitude is shown in acts.” – Henri Frederic Amiel

The holiday season has many themes. In this year of loss and uncertainty, perhaps the most important is gratitude. Students in our Upper Elementary program have been learning that gratitude is not just saying “thank you” and having good manners, but it is an intentional act. 

One of our teachers, Ms. Krista, taught students ways to show gratitude during one of her Growth Mindset lessons. The students were paired up to design skits to show the acts of gratitude. Each pair was given an act of gratitude and they prepared a skit to perform for the rest of the class. The rest of the class had the opportunity to guess what act of gratitude they were portraying in their skit. 

The acts of gratitude were the following: 

  • being an active listener, giving out compliments 
  • making eye contact, giving detailed examples of appreciation
  • being thoughtful of others, how to give a virtual hug (COVID style)
  • being gracious when challenged, offering congratulations (even when you are not the winner) 
  • volunteering to help others with difficult tasks
  • showing patience. 

All of these acts show gratitude for the community in which we live. 

How will you and your family show your gratitude this season? 

Art is Essential 

Due to budget deficits, schools throughout the nation are finding ways to cut their spending, and often the first thing to be removed from the curriculum is art. At Foothills Montessori School, we are committed to offering art education. We see the value in arts education and appreciate the significance it can have on student development. There is evidence that supports it helps our students to develop stronger academic skills, improve their decision-making processes, foster inventiveness, and help build self-confidence. These are the things we want for every student that joins our community. 

We asked our art teacher, Ms. Angela, what the goal of our art curriculum is for our students and she said, “The goal at FMS has been to support fundamental academics, supplement our cultural curriculum, and bridge gaps by developing new ways of seeing.  At a young age, children begin to communicate through artistic expression.  Long before they are able to read and write, they tell stories through their artwork.  Creativity through expression in the arts helps to improve innovative thinking for our students at every level.  It’s the ‘out of the box’ thinking that provides so many areas for growth. Students exposed to the arts become adults with improved focus, decision making skills, self-confidence, and civic engagement.”

During our spring school closure in 2020, Foothills Montessori continued to provide our art curriculum remotely. The art curriculum was delivered through project-based challenges. Project-based challenges in the arts allow our students to devise strategies for problem solving. As teens and adults, life is full of trials and obstacles.  Determination and commitment gained through project-based learning helps prepare our students for future challenges.  No matter their level of development, their capacity expands.

In closing, the Brooking’s Institute did extensive research and published an article in 2019 on the impact of the arts educational experience.  Their findings determined that arts education not only positively impacted emotional and social outcomes for students by fostering greater compassion for others; but it concluded that the students they researched had 13 percent higher standardized writing scores*.  Our students create magic everyday with their creativity and dedication to their arts based projects- many of which become treasures or family keepsakes.  The true beauty in arts education is that those experiences are helping to frame our future.  Students that become strong leaders, inventors, designers, communicators, and citizens.  Whatever they choose to become on their path, the arts provide them with tools to use for a lifetime.

*Brian Kisida and Daniel H. Bowen Tuesday, February 12, 2019