How I Wish I’d Always Taught Fractions
By John Bee
John Bee explores how fractions can be taught effectively in primary Maths
Fractions have always been one of those mathematical concepts that, if not handled carefully, can leave students feeling frustrated and confused. Over the years, I’ve seen students struggle with the idea of fractions and even question their own ability in maths because of it. The thing is it doesn’t have to be this way. If we, as teachers, get it right from the beginning, fractions can be a concept that not only makes sense but also builds confidence in learners.
I’ve often thought about how I would have done things differently had I known what I know now. This article is a reflection on my journey with teaching fractions—what worked, what didn’t, and how a deliberate focus on consistent representations helped me transform my students’ understanding. Whether you’re a newly qualified teacher or someone who has been in the classroom for years, I hope my experience encourages you to pause and reflect on how you teach this important concept.
The Initial Realization:
A few years ago, I started at a new school and, as with any new beginning, I wanted to get a sense of where my students were. I asked my Year 6 class a simple question: “What is a fraction?” The answers they gave—“a half,” “a quarter”—were examples of fractions, but none of them could define what a fraction really was. They couldn’t articulate that a fraction represents a part of a whole.
That was a turning point for me. I knew that if my Year 6 students couldn’t grasp this basic concept, I couldn’t jump straight into more advanced work. I decided to take them back and start from the beginning, and for the next seven weeks, I focused on rebuilding their foundational understanding. This wasn’t a quick fix, and it required revisiting fractions throughout the year, but it was worth the investment. Little by little, they began to develop a clearer understanding of what fractions represent.
Too Many Representations, Not Enough Consistency:
One of the biggest challenges I noticed in my own teaching—and now in my work as a school improvement adviser—is that we sometimes introduce too many different representations of fractions. On the surface, this seems helpful, but it can often lead to more confusion. When children are faced with multiple, disconnected ways of seeing fractions, they struggle to make connections to new ideas and build upon the structures they’ve learned.
Looking back, I realise that the inconsistency in representations was a barrier. Children would see fractions presented on circles one day, bar models the next, and then something entirely different the following week. It was too much. They needed a throughline—a consistent representation that could act as a scaffold for building new concepts. I developed the idea of a clear ‘flightpath’ to chart to progression of representations with fractions.
A Deliberate Shift: The Power of Number Lines:
That’s when I made the deliberate choice to centre my fraction teaching around number lines. It was a simple yet powerful shift. I began using number lines as a core representation for many of the small steps in teaching fractions. Before jumping into formal number lines, I introduced bead strings—both physical and animated—to help students grasp the concept of halves. From there, we transitioned to number lines with numbered intervals, both vertical and horizontal, as a natural extension.
The versatility of number lines became evident as we explored various fraction concepts. For example, when adding and subtracting fractions, I overlayed bar models on the number line so that students had a familiar representation to connect new learning. In one lesson, we used animated number lines to visualise fractions in the context of water bottles, measuring gauges, and other real-world applications. This consistency was key—it allowed students to see fractions in different contexts without losing sight of the structures they’d already mastered.
Connecting Representations: Bar Models and Number Lines
As I continued refining my teaching approach, I realised that one representation alone wasn’t always enough to convey the full depth of fraction concepts. However, rather than introducing an entirely new model, I found that linking familiar representations created a stronger foundation.
This is where bar models came into play, but with a twist: they were used in tandem with number lines. For example, when teaching students to add fractions like two-fifths and one-fifth, I overlayed the bar model on a number line divided into fifths. The number line provided the structure, and the bar model made the concept more tangible.
When it came to adding and subtracting fractions with different denominators, double number lines became a useful tool. By carefully animating the movement along these lines, students could visually grasp the idea of finding common denominators before adding fractions. These animations, which were used consistently across different lessons, made even the more abstract concepts accessible and concrete.
This combination of number lines and bar models was a deliberate strategy. It gave students the chance to move between different representations without ever losing the core idea. The coherence between the models allowed them to make connections, and, as a result, the learning stuck.
Avoiding Misconceptions
Misconceptions about fractions are easy to develop and hard to shake off. I’ve seen this time and time again in classrooms, both as a teacher and in my current role as a school improvement adviser. One common misunderstanding is around adding fractions. For example, children often think they can add both the numerators and the denominators: two-fifths plus one-fifth might mistakenly be thought of as “three-tenths.”
By using consistent representations like number lines, we can help avoid these pitfalls. When students saw the bar model overlayed on the number line divided into fifths, it reinforced the idea that only the numerators are added, while the denominator stays the same because it’s referring to the same whole. The visual representation made it clear that they were adding parts of the same size.
Similarly, when dealing with fractions that had different denominators, using double number lines helped show the need to find equivalent fractions with a common denominator. The animation of the double number line showed fractions being converted to a common base before addition, making this abstract step feel logical and intuitive for the students.
This method not only helped students solve the problems in front of them but also empowered them with a conceptual understanding that transferred to future problems. They didn’t just know how to add fractions; they understood why it worked that way.
Key Takeaways for Teachers
Reflecting on my journey with teaching fractions, there are a few key takeaways that I believe are worth sharing with other teachers.
First, consider the representations you use in your classroom. It’s easy to jump between different models—circles, squares, bars, and more—especially when the resources we use offer a variety of ways to teach fractions. But sometimes, too much variety creates a disconnect in students’ minds. Instead, focus on one or two versatile representations that can carry students through various fraction concepts. Number lines and bar models worked for me, but the key is consistency.
Second, build coherence across lessons. Don’t treat fractions as a set of isolated concepts. Instead, find ways to link new ideas back to what students have already learned. This creates a strong structure that students can continue to build upon, deepening their understanding over time.
Finally, I’d like to signpost you to some of the resources I’ve found incredibly helpful in developing these approaches. If you’re looking for more detailed ideas on how to use number lines, bar models, and other representations in a consistent way, visit my website, www.mrbeeteach.com. There, you’ll find resources, animations, and lesson ideas that can help you bring coherence to your fraction teaching.
Teaching fractions has been a learning journey for me, just as much as it has been for my students. I wish I’d always known the power of consistency when it comes to representations, but it’s never too late to refine our teaching practices. When we make deliberate choices about how we present mathematical ideas, we give our students the best chance to truly understand them.
By using representations like number lines and bar models consistently, we can avoid confusion, build stronger connections between concepts, and help our students see fractions not as a frustrating barrier, but as a manageable and even enjoyable part of their mathematical learning journey.
So, the next time you teach fractions, I encourage you to pause and reflect. What representations are you using, and how can they work together to build a coherent and lasting understanding? You might just find that making a small shift in your approach leads to big results in your students’ learning.
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