Calculations with fractions are perceived as abstract and difficult for many children. It’s important to let the children experiment and try for themselves in everyday situations to become familiar with the concepts.
Learning fractions develops proportional thinking, that’s to say how we perceive size. Calculations with fractions lay the foundation for doing algebra and probability, and without this base it’s hard to advance within mathematics. This is one of the reasons we at Zcooly developed our game Piece of Cake in collaboration with National Center for Mathematics (NCM) in Sweden to help kids with fractions.
What are fractions?
Fractions describe parts of a whole or parts of several wholes. It’s imperative to keep in mind that these parts are all of the exact same size. Fractions lay the foundation for understanding decimals and percentages.
Building an understanding for fractions is a process where knowledge gradually expands and deepens. Fractions demand a high capacity for abstraction.
Four fundamental facts for fractions:
All parts must be of equal size for them to be parts of a fraction.
The denominator shows how many parts a whole has been divided into.
The bigger the denominator is compared to the numerator, the smaller the fraction is: each part is smaller.
The numerator shows how many parts of the whole we have..
And why are fractions difficult?
According to NCM fractions can be difficult to understand because there are so many different ways of interpreting and writing numbers – for example 1.25, 125%, 5/4 and 1 1/4. The most common issue children have when starting to learn fractions is that they don’t realize the pieces have to be the exact same size. At the same time, it usually works as long as you stick with halves and fourths considering in these cases we’re halving in iteration. Eights are also results of continued halving and are usually easy for children to understand. The problems usually arise with thirds. An example is when dividing an apple in three by cutting it in half and then cutting one half in half. The resulting fraction is 1/2 apple and 2/4 of an apple, not three thirds (1/3, 1/3, 1/3). The division property of equality needs to be taught from the beginning.
Misconceptions and difficulties with fractions for kids
There are often misconceptions on the size of numbers when they are depicted as fractions. One such misconception is that a large denominator means that the fraction is a larger number or that if the denominator is 9 that means that the number is almost a whole.
Children know that 9 is bigger than 3 and assume that one ninth is big and one third is pretty small. That’s not correct – 1/3 is bigger than 1/9. Compare the circles below:
Another difficulty with fractions is that two fractions can look completely different, but still convey the same number or parts of a whole. Take for example 1/2, 2/4 and 3/6.
To be able to compare fractions, children need to understand that parts of a fraction are equally large parts of a whole (the division property of equality).
A fraction plank is a great way to compare and make clear the size of fractions. You can make one at home by drawing on a piece of paper and color like below.
Practice together at home!
There are a multitude of ways to talk about fractions at home to make it easier for the kids to understand! For example, you can talk about how when you cut the pizza/chocolate cake in four equally large pieces you have four fourths. How do you then make eights? If you eat 1/2, you have 1/2 or 2/4 or 4/8 left. Through this simple activity you can introduce your child to using fractions.
Learn fractions in Piece of Cake
When your family subscribes to Zcooly, you have access to all the educational content in the game. In Piece of Cake, accessed through Josanna (who’s eyeing the competition on the island Sasmandu), your children can learn how to use fractions and develop their spatial understanding.
If you have more than one child, all of them can explore Zcooly’s world of learning with their very own avatar and separate progressions.