Materials Highlight: The Fraction Insets

Meagan Ledendecker • December 13, 2021
Young child with apple slicer/corer

For this month’s Materials Highlight we bring you the fraction insets: a beautiful set of metal templates resting on slanted wooden trays. As you can see in the photo above, the insets range from one whole through tenths, and each piece has a small knob allowing children to move them easily.

 

But before we get to the insets, perhaps we should back up just a bit.

 

Prior to an introduction to fractions, the child has had extensive instruction and experiences with numeration being based on the unit. One unit (or one, one whole, etc.) has been the basis by which they have learned to count, skip count, add, and subtract. Young children have also gotten to use the fraction insets to create beautiful designs, experimenting with constructing with tenths and sixths and halves. As the child comes to the end of Children’s House or begins elementary, they are ready to learn how to divide a unit and name those parts.

 

An Introduction

It’s important to note that while the most commonly used and popular fraction insets are circular, there are also triangular and square fraction insets. It’s important for guides to refer to this at times so the children have an understanding that anything may be divided, not just circles.

 

The first time children use the insets they are encouraged to observe what they notice, and they develop the concept that each inset is a family of sorts. “These are the thirds, these are the sixths, etc.”

 

The guide will make a point to use intentional language to create a firm basis in understanding: “This circle is divided into four equal parts. We call them fourths.” The guide will write out “fourths” as well as “/4” as children are able to verbally express their understanding.

 

The Numerator

During the course of this lesson, the guide doesn’t actually use the term numerator just yet. What is emphasized is that while the children previously learned the family names of each inset, the focus will now shift to individual pieces. Examples will be shown using the material, and both verbal and written expressions will accompany each.

 

For example: “This is one third, or ⅓.” “This is four fifths, or ⅘.” This may be the end of the lesson, or, if the children seem to grasp the concept quickly and easily, it may be combined with the third presentation.

 

The Third Presentation

The third presentation is essentially a culminating review of what has been covered so far. The children may take turns matching labels with fractions to show their understanding. The critical piece is that the guide will now formally name the numerator and denominator.

 

There is a lot of opportunity for practice and extension work at this point. Children may trace and label fractions, make booklets or charts, work together to match labels, and so on. This work typically happens at the end of Children’s House or during the first year of Elementary.

 

Equivalence

This is an exciting lesson for children. Once they have a firm grasp on naming fractions, the guide will introduce equivalence. The one whole circle will be removed from its frame and the two halves will be put in its place. The guide will show the child how one whole is equal to two halves. This will be repeated with similar equivalencies: 3/3=1, 4/4=1, etc.

 

Next, smaller equivalencies will be discovered. The guide will try and fit a piece into a number of different spots, proving where it does and does not fit. Children will learn several simple equivalencies, such as 2/6=1/3 .

 

As with the previous skill, there is plenty of opportunity for exploration and extension in regard to equivalencies. This is arguably one of the most important foundational fractions skills.

 

Operations with Fraction

Once a child has a firm grasp of fraction basics, they are ready to learn operations. Another material often used in the elementary is called the fraction box, which includes small plastic replicas of the red circular fraction pieces. Skills include:

  • Addition and subtraction using the same denominator
  • Multiplying fractions by whole numbers
  • Dividing fractions by whole numbers
  • Addition with different denominators
  • Addition with more than two addends
  • Subtracting with different denominators
  • Multiplying whole numbers by fractions
  • Multiplying fractions by other fractions
  • Dividing whole numbers by fractions
  • Dividing fractions by fractions

 

Moving to Abstraction

Use of materials when teaching fractions is critical; we believe Montessori students excel later in life with more complicated math concepts because they have such a strong foundation in the basics. Rather than memorizing rote procedures they are physically manipulating quantities with their hands, giving them a deeper understanding of why we do what we do.

 

One cannot rely on materials forever, though, and there comes a time when the child is prepared to move onto abstraction.

 

This is often achieved by the guide again showing an operation with the material while also writing out the pencil and paper process simultaneously. In fact, children will often come to this learning independently. They are able to make the connections as they master skills. If not, the guide is there to show them the way. There comes a point in the elementary years when a child no longer needs to rely on the materials to determine the answer to a problem. In fact, using the materials becomes cumbersome, and they are eager to put the materials aside.

 

Want to learn more? We encourage you to reach out and set up a time to observe. Reading about Montessori education is important and enlightening, but the very best way to understand is to see for yourself.

By Meagan Ledendecker February 23, 2026
One of the quieter, less visible practices in a Montessori elementary classroom is the Child-Guide conference. You may never see it listed on a schedule or mentioned in a weekly update, yet it plays a profound role in children’s experience at school. Relationship Comes First The primary purpose of these conferences is to establish, maintain, and strengthen the relationship between the adult and each child. This focus shifts the dynamic from a teacher looking for faults or scolding about unfinished work. Rather, it’s a collegial conversation that enables children to take an active and engaged role in their own education. These connective conversations are grounded in relationship-building because when children feel emotionally safe and genuinely respected, they are far more willing to reflect, stretch themselves, and take responsibility for their growth. Every Child, as Often as They Need Montessori Guides aim to meet regularly with every child, but what “regularly” looks like can vary based on individual needs. Some children benefit from a longer, more formal conference every few weeks. Others need brief, frequent check-ins, sometimes lasting only a minute or two. These short moments might look like a quick conversation at the beginning of the morning, a gentle pause beside a table, or a quiet walk across the room together. The length of the meeting is not what matters. What is important is the message it sends: “I see you. I know your work. I care about how this is going for you.” What Happens in a Child-Guide Conference? While conferences vary based on each individual and the moment, they often include: The child bringing their learning journal or work (finished and unfinished) The guide bringing observational records A shared look at what has been accomplished Gentle reflection on what still feels unfinished Planning for what might come next Scheduling new lessons or presentations Support with larger projects: breaking them into steps, mapping timelines, imagining the finished product This collaborative time also provides an opportunity to experiment with new strategies (“Would you like to try creating a prioritized list?”), celebrate successes (“You worked so hard on your presentation! How did it feel to share your work?”), and reflect upon challenges (“It seems like you’ve been feeling a bit stuck in your research project. Tell me more about what is going on.”). Learning to Define “Finished” One of the most freeing lessons children learn in Montessori is that not every piece of work must be finished to an adult’s standard. Sometimes children accomplish exactly what they set out to do, and continuing would add nothing meaningful. Other times, interest has naturally ended, and letting go is healthy. This is not about lowering expectations. It is about honoring children’s internal sense of completion and learning when to release what no longer serves a purpose. Trusting Children’s Self-Assessment A cornerstone of these conferences is trust. Guides listen carefully to how children assess their own work and articulate their goals. When an adult truly accepts children’s self-assessment, something powerful happens: children begin to see themselves as capable, thoughtful, and worthy of being taken seriously. Children often receive more from the tone and sentiment of these meetings than from the actual content discussed. The Whole Child Matters Because Montessori education is concerned with the whole child, conferences may naturally move beyond academics. A Guide might gently offer support with social dynamics or ask about recent struggles during outdoor time. These moments provide a safe space for children to reflect on their own social, emotional, and physical development, and to recognize that there is a network of support. When Relationships Need Repair Even in the most thoughtful classrooms, relationships can become strained. What matters is how adults respond. It is never too late for a Guide to sit with a child and say, honestly: “I’ve been thinking about how we’ve been interacting recently, and I’d love to brainstorm with you about what I could do differently.” When an adult takes responsibility, without demanding the child do the same, something shifts. Trust begins to rebuild. Real dialogue becomes possible. Children learn from this modeling. In time, after they feel safe, they often step forward to take responsibility themselves. What Children Are Really Learning Through these quiet, intentional meetings, children learn that:  their thoughts and feelings matter, adults can be trusted, mistakes are part of growth, reflection leads to independence, and relationships can be repaired. And while these conferences may happen quietly in a corner of the classroom, their impact echoes far beyond it. This is true preparation for life. To learn more about the long-term benefits of Montessori, visit us here in Lenox, MA!
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