“When young children first encounter the racks and tubes material, it gives them another concrete entry point to understand what division really means. They are not just looking at an abstract numerical expression; they can feel the quantity in their hands and see what equal sharing looks like as it happens. One of the greatest values of the material is the process of trading. As they move hundreds into tens, and tens into units, they begin to understand place value in a very real way and see what is actually happening during division. It creates a solid foundation because the mathematics is no longer just abstract symbols; it is physical, visible, and logical. These experiences connect the action of dividing with the meaning behind numbers.”
Kelly Jonelis, Adolescent Program Director and Math Teacher
Materials Spotlight: Racks and Tubes
At first glance, the Racks and Tubes material is striking. Rows of glass tubes filled with color-coded beads, boards, cups, and small figures invite curiosity and concentration. Children are naturally drawn to it, both for its beauty and for the sense that something important is happening here. This is where division becomes something they can see, touch, and truly understand.
Racks and Tubes introduces children to the idea of sharing a quantity equally and discovering what one share receives through long division. While other activities, such as the Elementary Stamp Game lesson, highlight grouping division, how many groups can be made. The Racks and Tubes lesson focuses on fair sharing through distribution. Together, our multiple approaches give children a complete picture of what division means and help them choose the strategy that fits a problem best.
Each element of the material reinforces place value. The racks hold test tubes of beads organized by units, tens, hundreds, thousands, and beyond. Cups hold the dividend, the number being divided. Boards and small figures represent the divisor, the number of groups. As children work, they share beads one at a time, distributing them equally among the groups.
The process is deliberate and hands-on:
- They build the dividend using the racks and cups.
- They represent the divisor with individual figures on boards.
- They share beads one at a time, equally, to each part of the divisor.
- They stop when sharing is no longer possible and then see what remains from that category.
- They then bring down the next category of beads to continue the sharing process.
Each step answers a real question. Can we distribute equally again? What does one unit get? What happens when we run out? What do we do with what is left? Instead of being told to “bring down the next digit,” children literally bring down the next set of beads. Remainders are not abstract ideas. Remainders are the beads still sitting in the cup.
🎥 Watch the video to see our students working with racks and tubes and making long division come alive!
Long division becomes a story they can follow with their hands.
One of the most meaningful aspects of this work is how naturally it leads toward abstraction. At first, children record only the final answer. Over time, they begin to note the intermediate steps and partial remainders. Eventually, they discover that multiplying the quotient by the divisor shows how much has been used at each stage. In this way, the traditional long division algorithm grows out of their own experience. By the time children begin solving division problems on paper, the process already makes sense. It reflects what their hands have done again and again.
Racks and Tubes strengthen a deep understanding of place value, support logical sequencing, and build patience, precision, and trust in one’s own reasoning. At Wheaton Montessori School, children come to see that complex equations can be solved step by step, and that they are capable of working through problems with confidence.
