Ask most adults what makes fractions hard, and they'll mention the notation: why does 1/2 mean something completely different depending on whether you're adding, multiplying, or comparing it to 1/3? Montessori's answer is to remove the notation entirely for as long as possible, and let a child feel what a fraction actually is first.
The Fraction Circles
The core material is a set of ten metal insets, circles cut into equal pieces, one whole circle, one cut in half, one cut into thirds, all the way to a circle cut into ten equal pieces. A child physically handles these pieces well before ever seeing the symbol 1/2 written down. They can see, directly, that two halves make a whole, that a third is bigger than a quarter (which surprises almost every child the first time), and that pieces from different circles simply don't fit together the same way.
Why "A Third Is Bigger Than a Quarter" Matters
This single fact, that the larger the number on the bottom of a fraction, the smaller each piece actually is, is one of the most common and persistent points of confusion in later fraction work. Children taught fractions purely through written notation often never build reliable intuition for it, memorising a rule instead. A child who has physically compared a third-piece to a quarter-piece with their own hands rarely forgets which is bigger.
Building Toward Operations
Once quantity is secure, the same materials extend naturally into fraction addition, equivalence and even early multiplication: laying two quarter-pieces next to each other and seeing they equal a half, physically, before ever writing 1/4 + 1/4 = 1/2. Equivalent fractions, a persistent source of confusion when taught abstractly, become something a child can visually confirm rather than take on faith.
When This Typically Happens
Fraction work usually begins around age five or six with simple halves and thirds, and extends through age eight or nine into more complex operations, roughly matching the Primary Maths and early Elementary Maths stages at Mount Shine.
Conclusion
Fractions are hard mostly because they're usually taught as rules to memorise rather than quantities to feel. Give a child the physical pieces first, and the rules that come later stop being arbitrary, they become descriptions of something the child already understands.
Explore how this builds across the curriculum in our Primary Maths course, or book a trial class to see the fraction circles used directly.
Sources
- Association Montessori Internationale (AMI), for the reference Montessori fraction curriculum.
- National Council of Teachers of Mathematics (NCTM), on concrete models for fraction instruction.