Step-by-Step: Adding Fractions Using Montessori Fraction Materials
Teaching children how to add fractions can feel abstract, especially when they are moving from hands-on Montessori materials towards written fraction equations. In this Montessori fraction lesson, I’ll show you step by step how to teach adding fractions using Montessori fraction circles and fraction pieces, beginning with fractions that have the same denominator before moving on to different denominators and equivalent fractions. This lesson is suitable for Montessori elementary classrooms, homeschool maths and children who benefit from seeing fractions concretely before working more abstractly.
Adding Fractions with Montessori equipment helps students visualise what parts of a whole look like. Using hands on materials the child is able to make a visual imprint of what certain fractions look like.
Not sure if your child is ready for this lesson?
Fraction lessons make much more sense when children have the earlier maths foundations securely in place.
If you are trying to work out what should come before this lesson — or what to teach afterwards, download my free Montessori Maths Scope & Sequence for ages 3–12.
It gives you a broader view of Montessori maths across the 3–6, 6–9 and 9–12 cycles while still leaving room to follow each individual child.
The lesson - SAME DENOMINATORS
Prior to this lesson students will need to
- have been introduced to different fractions and practised drawing them into booklets for example drawing 1/6 or 1/4
1) Have some task cards with various addition equations on them
2) Have the montessori fraction pieces (the box of different pieces works best)
3) Take out a large fraction such as a third. Ask student what it is. Do you know how many of these make a whole? If they don't tell the student the answer
4) Today we are going to do an equation with thirds but it won't quite equal a whole
5) Write 1/3 + 1/3 on a piece of paper. Place 1/3 on the table and then get out another third. Say what you are doing I had 1/3 now I am adding another third.
6)How many thirds do I have now 2/3
4) repeat with another fraction e.g. 2/4 + 1/4.
5) Students then practise different equations with addition activities
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The lesson - DIFFERENT DENOMINATORS - one change
Prior to this lesson students will need to:
- Be very fluent in adding fractions with the same denominators
- Be fluent with equivalent fractions click the link to see my lesson on equivalent fractions.
1) Get out 1/3 and two sixth pieces.
2) Ask the students if these can be added
3) If needed prompt about equivalent fractions are there any pieces here we could change to being something else?
4) Let's change the third. It is the same as 2/6
5) We could rewrite this as 2/6 + 2/6
6) That is 4/6
7) Repeat with another equation this time bring to the students attention that you are changing the larger fraction (the one with the smaller denominator) into smaller pieces.
8) Use the fraction addition activities
The lesson -DIFFERENT DENOMINATORS - two changes
1) Take out 1/2 and 1/5 Have the student try and add them together using the equipment to help them
2) Stop and look at the written equation. Say to the students I can see this one has a denominator of 2 and this one has a denominator of 5. I know that 2 and 5 are both in the 10x table. I think if I can get both of these denominators to be 10 I could add them together
3) Write 1/5 = _/10 Say I have multiplied the bottom number by two. I will do the same to the top to make it fair this means I have 2/10
4) I will do the same with the 1/2. Write 1/2 = _/10. Say I have multiplied the bottom number by five. I will do the same to the top to make it fair. This means I have 5/10.
5) Add the numbers together
6) I have 7/10
7) Practise with the fraction tickets.
Keep Exploring Montessori Fractions
If your child is working on adding fractions, it can help to keep building the ideas around equivalence, fraction size, mixed numbers and fractions of an amount. Here are some related Montessori fraction lessons and follow-up resources you may find useful.
Related Montessori Fraction Lessons
- Equivalent Fractions: What Do Students Need to Know? – a practical look at how to build equivalent fraction understanding with Montessori materials.
- How to Teach Improper Fractions with Montessori Materials – a hands-on lesson for helping children connect improper fractions and mixed numbers.
- Teaching Fractions of an Amount with the Montessori Stamp Game – a practical way to use familiar Montessori maths materials to explore fractions of quantities.
Ready-to-Use Fraction Materials
If you want children to practise these ideas independently after the hands-on lesson, these Montessori-inspired fraction resources can help.
- Montessori Fraction Addition Task Cards – practice adding fractions with like and unlike denominators.
- Adding Fractions with Mixed Denominators Task Cards – ideal when children are ready to use equivalent fractions and common denominators.
- Montessori Equivalent Fraction Task Cards – hands-on and visual practice moving from fraction circles into equations.
- Montessori Ordering Fractions Activities – useful follow-up work for comparing and ordering fractions.
Want a larger collection of fraction work?
The Montessori Fraction Bundle brings together fraction task cards, clip cards, equivalent fraction work, ordering activities, fractions of an amount, visual materials and other follow-up work for ages 6–12.
Not sure where fraction work fits in the bigger Montessori maths sequence?
You can also download my
free Montessori Maths Scope & Sequence for ages 3–12
to see how fractions connect with place value, operations, decimals and other Montessori maths work.