Linear Counting: Montessori Materials

The Montessori math materials are perhaps the most ingenious apparatuses used in the early childhood years. Not only are they aesthetic and sensorially appealing to children, but each apparatus is designed with longevity and they provide access to abstract math through sensorial means as well. Montessori math materials tend to have direct purposes that are obvious to a common observer, when in fact, they are preparing children for greater works in the next coming years.

Linear Counting
Teen Boards with Beads

In this post, we are presenting the Colored Bead Stairs, the Colored Bead Stair Hanger, the Teen Boards, and the Teen Beads Box. These materials are preparatory materials that lay the foundation for linear counting, the skill of counting from 1 to 1000. What they all have in common is the use of Colored Bead Bars. The Color Bead Bars consist of nine color-coded bead bars clustered using a metal wire ranging from one through nine: one-red, two-green, three-pink, four-yellow, five-light blue, six-purple, seven-white, eight-brown, and nine-dark blue. Below, we will talk about three engaging ways to set foundation for linear counting for children ages three to five.

Colored Bead Stairs

The Colored Bead Stairs on a tray are introduced in the primary level to children around ages 3.5 to 4. By clustering beads together, children are able to integrate quantities of beads as a whole entity. In traditional education, children can be offered separate objects to represent numbers. Sometimes, they are even offered different objects for different numbers. For instance, they are presented with one stick, two acorns, three leaves, so on and so forth. Children might not be seeing the continuum, the growth within the sequence of numbers. By using wired beads, children are using a consistent visual to understand how numbers are formed, and how they relate to one another. The color coding was added to accelerate numbers manipulation in later mathematical concepts. At first, children learn to count the beads in each bar, and associate the spoken language that goes with the beads. For instance, an adult introduces the beads by naming the number of beads, then the color. Later, an adult introduces the symbols associated with the bead bars. For this purpose, we offer a tray with colored pencils and charts (click here).

Colored Bead Stair Hanger

The Colored Bead Stair Hanger is a sensorial math extension that is well appreciated by children. It consists of a wooden frame on a tray, with hooks and with two receptacles in the front and back. The receptacles host numbered tiles one through nine, and wooden strip with numbers, which serves as control for errors. Children are invited to use the control for errors to learn the proper sequencing of the numbers one through nine. They then associate the bead bars by hooking them below each numbers. This is the way children are connecting abstract learning (numbers, symbols) and concrete learning (beads, quantities). At this stage, one might ask children the color of eight, and the child will respond brown. The point isn’t to learn a combination of colors associated with number, but to learn quantitative impressions on children through the tactile and visual senses. Children visually know that brown is bigger than pink, therefore, they know that eight is bigger than three. This color coding not only leaves impressions on children, but they also accelerate their math processing when working with arithmetic operations. For instance, children will work on addition beads. They will not be counting how many beads are in one bar, but they will systematically know the amount of beads based on colors. The Colored Bead Stair Hanger is an excellent material that visually strikes children by making the number sequence obvious which requires no explanation.

Teen Boards

The Teen Boards set is another sensorial math material that utilizes the color-coded bead bars to introduce how teen numbers are formed. The Teen Boards consist of two large and narrow vertical boards with the number 10 written nine times. Tiles numbered one through nine are to be inserted in the vertical board, revealing how teen numbers are formed. For instance, by inserting the numbered tile one, children are witnessing how teen numbers have a static tenth that remains constant, and how only the unit place changes. Children are invited to organize the tiles in order by inserting them one by one in their respective places. They are also provided with the language (eleven, twelve, etc.) The work is quite intuitive, and is easily achieved by children after a demonstration.

Teen Boards
Teen Boards and Colored Bead Box

Teen Beads Box

Following this work, children are presented with an association of the quantities to the symbols. Again, children are visualizing how numbers are formed using the Teen Beads Box. They add golden ten bead bars to the left of the board, and add a colored bead bar to match the unit place. They visualize that eleven is a ten and a one together. They are invited to verify this statement by counting the beads.

Later, the same method will be used to learn about the tens using the Tens Boards.

The Montessori method has a unique way to present sensorial math to children in a concrete manner that provides them early access to working with arithmetic operations (addition, multiplication, subtraction, and division). They gain a deeper understanding of numbers, their quantity, and their place value. In addition, the beads’ color coding is consistently used through the entire math curriculum from ages three to twelve, promoting the development of the children’s mathematical mind.

Please visit our website at www.alisonsmontessori.com to check out our extension works using the colored bead bar materials.

Linear Counting

Linear Counting