Materials Spotlight: The Wooden Hierarchical Material
December 9, 2024

The Wooden Hierarchical Material takes up a great deal of space in our primary and elementary classrooms, and for good reason! This key math material helps children understand the hierarchy of numbers and physically represents units through millions.


The Concrete Material


The Wooden Hierarchical Material comprises cubes, prisms, and squares that vary in size and color according to the different place values they represent. Units are green. Tens are blue. Hundreds are red. This pattern continues throughout the families or categories, so unit thousands are also green, ten thousands are blue, hundred thousands are red, and then unit millions are green. Units are represented as cubes, tens as prisms (or a line of ten units), and hundreds as squares (constructed from ten tens side-by-side). Due to this repeated pattern that is reinforced through shape and color-coding, children can visualize the structure of our decimal system.  


The Presentation to Children 


When we present the Wooden Hierarchical Material, we first connect with other math materials children have used, like the golden beads and the stamp game. In this way, children can build upon their prior knowledge of place value and how 10 of one category are exchanged for one of the next category (e.g. ten units become one ten). 


The material is constructed to reinforce the relationship between base-ten numbers in concrete form. As we place the blue ten bar to the left of the small green unit, we remind children how when ten units get together, they make a ten. We also point to the little green marks on the bar and use the unit to count that ten of the units make up the ten bar. Young children love double-checking this correspondence!


We repeat this process to show how ten of the blue ten bars correspond to the ten sections on the red hundred square. Then how when 10 hundreds get together, they make a thousand. When we place the green thousand cube to the left of the red square, we leave some extra space between them because we are starting a new family (or category). This green thousand cube is units of thousands, and we can continue the process with tens of thousands and hundreds of thousands. Children love getting to the green unit of the millions cube and often want to try to imagine or represent ten million, hundred million, and beyond!


The Many Benefits


Because children can physically explore how ten of the thousand cubes make a line that represents 10,000, just like ten of the unit cubes make a line that represents a 10, they develop a strong understanding of the hierarchical value of numbers and their position in the decimal system. Similarly, they can experience how ten 10,000s make up a 100,000, and ten 100,000s make a million! This physical manipulation helps them better grasp abstract mathematical concepts, such as the process of exchanging, exponential growth, and the concept of powers of ten.


As children develop their number sense, the Wooden Hierarchical Material strengthens their understanding of large numbers. The repetitive and visual nature of the material helps solidify children’s mental image of numbers and place values, making future math concepts easier to grasp.


Children’s Continued Work


When children are first introduced to the Wooden Hierarchical Material, we often play games, asking volunteers to show particular items (e.g., “Can someone show me the 10,000?"). In this way, we activate children’s reasoning minds and draw their attention to connections within the material. Once we ensure that the quantities and names are clear, children often like to explore the material further by considering what comes next after one million, making a connection to geometry (point, line, plane/square), measuring, and even labeling the material with the numeric symbols and written names for the different quantities. Children love to quiz each other as they place the cards showing “one million” or “1,000,000” on the correct item. 


Montessori in Practice


This work is great fun for our oldest primary children and youngest elementary students. They love to lay out the materials, explore the relationships, and label the quantities with numeral cards. Children develop an intrinsic love for mathematics in this self-directed learning and discovery process. 


The Wooden Hierarchical Material is one of many ways Montessori education helps children develop a deep, intuitive understanding of numbers, place value, and mathematical relationships. 


Visit our school to learn more about how Montessori supports strong math skills!



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Practical Life Has Purpose!
May 19, 2025
The Purposes of Practical Life in Montessori In a Montessori classroom, practical life activities play a foundational role in supporting children’s development, independence, and connection to their environment. Because children are actively absorbing and adapting to the world around them, everything we offer in practical life serves a developmental need. Supporting Independence One of the primary goals of practical life is to nurture children’s functional independence—the ability to care for oneself and the environment and interact meaningfully within a community. The first plane of development (0 to 6 years) is marked by a strong drive for independence, with children eager to do things for themselves. By the time a child enters the Children’s House (approximately ages 2.5 to 6), they have already made strides toward independence. However, they still require an environment that allows them to refine their skills. In the world, children generally encounter a number of obstacles to their independence: Household processes (e.g., cleaning dishes in the dishwasher) may be hidden or too complex. Tools are adult-sized and difficult for small hands to use. Movements happen too quickly for children to absorb (e.g., tying a shoe). The Montessori environment addresses these barriers by providing: Child-sized tools for daily activities, such as preparing food and caring for the classroom. A clear, ordered sequence of movements that children can observe and repeat. The freedom to practice skills at their own pace, allowing them to move from passive observers to active participants. Supporting the Sensitive Period for Movement We also recognize that young children are in a critical period for refining their control and coordination. So practical life activities are designed to help children refine their movements in purposeful ways, directing children’s attention and energy toward focused, intentional actions. Walking on the line of an ellipse develops balance and control. Pouring water from a basin to a bucket refines precision. Carrying a tray teaches careful, measured movements. One of the most challenging yet essential aspects of movement is control. It takes effort to stop pouring just before a cup overflows or use only a small drop of polish when shining an object. By engaging in these exercises, children strengthen their willpower and gradually master their own actions. Supporting the Sensitive Period for Order Children in the first plane of development have an innate need for external order, which is reflected in their surroundings and daily routines. Montessori environments support this in a variety of ways. We ensure that activities have a logical sequence of steps so as children learn new concepts, they can also rely on the sequencing. Materials are placed in a specific order on the shelves, moving left to right and top to bottom so children begin to internalize the same patterning we use for reading as they work through the easier and most concrete activities to the most challenging and abstract. Montessori activities are color-coded. For the youngest children this means that all of the items for something like window washing will have the same color which helps children keep the set together. As children get older the color-coding is designed to help them grasp concepts like place value in math or parts of speech in language. Once children internalize these structures, they gain confidence and independence, allowing them to complete tasks from start to finish without adult intervention. Assisting with Cultural Adaptation Practical life activities reflect real-world tasks that children observe in their daily lives. Children are naturally drawn to meaningful work—they want to help, imitate, and participate. For example, in Dr. Montessori’s early observations in San Lorenzo, she saw that children were fascinated by the gardener and the custodian, eagerly following and watching their work. Children see adults doing marvelous activities, and children want to learn the skills to participate! Through practical life activities, children engage in culturally relevant tasks that allow them to feel like valuable members of their community. Supporting Orientation Orientation is a fundamental human tendency—we all seek to understand our surroundings and how to function within them. Practical life exercises help children orient to the Montessori classroom by introducing essential routines. For example, we take the time to teach children things that might otherwise be taken for granted, such as: How to carry a chair properly. How to greet a friend. How to roll and unroll a work rug. How to ask for help. By taking time to demonstrate these tasks, we show respect for the child and provide the knowledge they need to act confidently in their space. Supporting the Development of Concentration Practical life activities serve as a gateway to deep concentration. The freedom to choose and repeat exercises allows children to follow their intrinsic motivation and work toward self-perfection. When children reach deep concentration, they experience: Joy and a sense of fulfillment. An increased connection to others. A natural reduction in undesirable behaviors. The ability to repeat an activity for as long as needed also supports children’s sensitive period for order and mastery. This is why practical life often serves as the first point of engagement for children in the Montessori classroom. Supporting the Development of the Will Practical life exercises help children develop willpower and self-control by bridging the gap between impulse and deliberate action. At first, children act on instinct, but through repeated exercises, they learn to: Act consciously and voluntarily. Perfect their actions through self-correction. Develop grace, courtesy, and social awareness. Whether through learning how to clean up a spill or preparing snack to share with others, children learn to control their impulses and consider the needs of others. Dr. Montessori beautifully summarized this transformation in The Discovery of the Child: “The grace and dignity of their behavior and the ease of their movements are the corollaries to what they have gained through their own patient and laborious efforts. In a word, they are ‘self-controlled,’ and to the extent that they are thus controlled, they are free from the control of others.” Practical life is far more than just pouring, scrubbing, and folding—it is the foundation for independence, concentration, order, and social development. These carefully designed activities help children orient to their world, refine their movements, and develop the willpower to act with purpose. By embracing practical life, we give children the tools to engage meaningfully with their environment, take ownership of their learning, and ultimately, become confident, self-sufficient individuals. Contact us to schedule a tour so you can see how young children use practical life activities in powerful ways!