Building fraction understanding through hands-on learning
In episode four of the AAMT x We Support Hands-On Learning video series, Allan Dougan and Professor Catherine Attard discuss a topic that strikes fear into the hearts of students and teachers alike. Yep, it’s fractions.
But why do fractions have such a bad reputation? Allan explains that they’re often the first time young people encounter numbers that are less than one, and that’s a genuinely difficult concept to get your head around. Add to that the fact that fractions have multiple models and multiple ways of being expressed.
But as Allan and Catherine show in this episode, with the right foundations and the right materials, fractions don’t have to be the villain of the maths classroom.
Hands-on maths: Exploring fractions with materials
Paper folding is a wonderfully simple starting point. Fold a square in half, now you have two halves that make a whole. Fold it in half again: four quarters. This activity also shows how two halves can look completely different and still both be halves, as long as they’re equal parts of the same whole.
Fraction bars (or fraction walls) are a classroom staple for good reason. Allan demonstrates with magnetic fraction bars, showing how equivalence becomes immediately visible: two quarters line up exactly with one half. One whole matches two halves etc. Children can see the relationships rather than just being told about them. This visual understanding is what makes the concept stick.
Catherine highlights the importance of lots of hands-on, concrete manipulation for fraction understanding. “It’s something teachers need to take time with. If you develop misconception around fraction understandings and they get skipped over, it’s very hard to fill those gaps later on.”
Teacher insight: Developing fraction sense
Placing fractions on an open number line builds a strong sense of magnitude in a way that’s hard to achieve otherwise. Children can visibly see that a bigger denominator doesn’t mean a bigger fraction. E.g. fifths are smaller than quarters because the whole has been cut into more pieces. Seeing it is far more convincing than being told.
Counting by fractions is another worthwhile activity to build in. Zero, one half, one, one and a half, two. Then try it with thirds or quarters. It reinforces the role of the numerator and denominator in a way that feels natural rather than abstract.
Teacher takeaway: Ideas for your classroom
Catherine sums things up well. “Concrete, concrete, concrete. Lots of manipulation, lots of different fraction models, lots of conversion, lots of mathematical reasoning, lots of appropriate language.”
Fractions certainly are a LOT. But the key is flexibility – in the models you use, and in the way you use them. Give children the time and space to really explore, address misconceptions as they come up, and resist the urge to rush to the abstract.