F is for Fractions
There are certain topics in maths which bring a sense of dread by just mentioning them and fractions is most definitely one of them. Fractions can seem intimidating, with their numerators, denominators, and various rules, but fear not! Let’s be like a fraction and break this down (bad maths pun).
Fraction comes from the Latin word, fractus, which means “broken”. When used in everyday language, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters.
A fraction consists of two parts: the numerator and the denominator.
numeratordenominator
The numerator represents the part of a whole, while the denominator represents the total number of equal parts that make up that whole. Confusing? Think of it like this, in the fraction ½, 1 is the numerator (the part) and 2 is the denominator (the whole).
Something I did not learn until I became a teacher, was the line of the fraction also represents something, it means divide. This is useful to know for two reasons; it helps the understanding of what a fraction is and helps when we use it in more complicated situations later on. So when you see 42 divided by 6 this can also be written as:
426
Fractions are presented as early as Year 1 in the National Curriculum which may seem early. But if we think of fractions as part of division, children are likely to be more successful as they can pair knowledge of division to this topic. When we are finding a half of something, we are in fact dividing it by 2.
One effective way to help children grasp fractions is by utilising everyday objects like pizzas, pies, or even candy bars to visually represent fractions and bring the use of fractions into the real world. For instance, if you cut a pizza into eight slices and your child eats two slices, ask them what fraction of the pizza they've consumed. This hands-on approach helps solidify the concept in a tangible way. It is important to try and make your slices as equal as possible. This will help avoid the common misconception that cutting something in half can result in 2 unequal pieces, which I saw recently when I met with an adult learner.
Showcasing real-world applications of fractions can also pique your child's interest. Whether it's dividing a recipe in half, calculating discounts during shopping, or sharing toys with siblings, fractions are everywhere! Pointing out these instances helps children understand the relevance of fractions in their daily lives.
This can then be progressed to visual aids and manipulatives, such as fraction bars, circles, or even simple drawings can help children visualize the relationship between different fractions. Encourage your child to experiment with these tools, comparing fractions and understanding concepts like equivalent fractions and addition/subtraction of fractions.
Teacher Perspective
As a Maths teacher I too often see pupils shy away from fractions, even A-Level Students, preferring to write 0.36 rather than 9/25, even though 9/25 would be much more obvious to square root or, if it is in an equation, to solve.
This year I am teaching a low ability Year 7 class and although pupils experience fractions in Year 1, it is clear that most still do not understand fractions 6 years later. This could be because schools move through concrete, pictorial to abstract far to quickly (often pushed on by the need to meet National Curriculum aims). We as educators need to not be afraid to push back in certain areas because what is the purpose of covering adding fractions or fractions of amounts if a pupil doesn’t fully grasp what a fraction is. Often I see answers to ¼ + ¼ = 2/8. I feel this is primarily due to the fact that pupils have missed something when they first approach fractions. Intuitively the answer 2/8 does not make sense as 2/8 is ¼. Using manipulatives it can be easier to see that ¼ + ¼ = 1/2
With my Year 7s we have used a whole host of manipulatives to help with different aspects of maths, including fraction walls which helped them recap what a fraction was. We then moved on to virtual manipulatives (Big shout out to Mathsbot.com for free virtual manipulatives for anything you could think of) with pupils drawing fraction bars using the squares in their books. Once they are secure in this knowledge we can move onto manipulating fractions using these skills.
