Learning Fractions

Learning fractions

Understanding fractions can be difficult, as can teaching them. We are all familiar with the picture of pizza slices, but this alone doesn`t cover the many different aspects of fractions. In this article I explain which visual aids for the different aspects of fractions can support a student as they progress through the school stages.

Fractions as parts of a whole

In year 1, students learn about and of a shape. Folding paper shapes or cutting fruit are good hands-on methods to learn about this. It is important to make sure both halves are the same size. With paper folding you can also show that a quarter is the same as halving and halving again.

As a student progresses, folding paper can again show how halves, quarters, and eighths and 16ths relate to each other. Moving on to pictures, that classic pizza image, or a cake or chocolate bar is ideal for showing how a fraction is a part of a whole. As a student becomes older, the pizza can become a pie chart and the chocolate bar can become a divided rectangle.

Fractions as a number

Students start with this vital concept in year 2 by learning to count in fractions. (e.g. , 1, 1 , 2, 2 , 3, ). Pointing to a 0-10 numberline at the same time can help students visualise what these fraction numbers are worth as they count.

Numberlines really are a great way to demonstrate that fractions are numbers and how they relate to other numbers. Students can use them themselves to compare and order fractions. For example, , 8/4, 19/4 can be plotted on a 0 to 10 numberline.

As students start to learn about decimals (such as 0.5) and improper fractions (such as 16/3) and other types of numbers, these can also be added to numberlines and compared to each other.

Equivalent fractions

As a student learns about fractions, they will start to be able to recognise that some fractions are equivalent (worth the same amount).

As they learn about quarters and halves, a pizza divided into 2 slices compared to a pizza divided into 4 slices will demonstrate that and 2/4 are equivalent. As they plot fractions on a numberline they will see that some numbers, such as 5/5, 4/4 and 1 are equivalent. As children move into year 4 they will be expected to draw their own diagrams to show that fractions are equivalent, using pizzas or chocolate bar type shapes.

Another key visual aid for comparing fractions and identifying equivalent fractions is a fraction wall. It is a great activity for children to create their own fraction wall by folding strips of paper, colouring them, labelling them and gluing them down to build their own wall. They can then use this wall to visually see that 2/8 is the same as or that 1/8 is smaller than 1/3.

A key point students need to recognise for equivalent fractions is that the numerators and denominators are always in the same proportion (i.e. you multiply them both by the same amount to get an equivalent fraction). This will enable children to go on to learn to simplify fractions and to convert a fraction to an equivalent one in order to change the denominator.

Fractions representing division

In year 3, children learn 1/10^th is the same as dividing by 10. Students will move on to learn that a fraction such as can represent 3 divided by 4. The numerator relates to multiplication and the denominator relates to division. This can be shown visually by sharing 3 pizzas between 4 friends.

Fractions of a quantity or amount

I think one of the hardest parts of learning fractions can be to understand that a fraction can be used as an operator to calculate a quantity. For example a year 4 child might be asked what is 1/3 of 45? or what is 4/5 of 80? It is easy to say all you need to do is divide by the denominator and multiply by the numerator . However, if a child doesn t yet understand the relationship of fractions with multiplication and division as above, this will be meaningless to them.

Children begin in year 1 by finding and of a quantity. They can use sets of beads, cubes, berries or sweets and share them equally between 2 or between 4 people. Using pictures, small circles can be used to represent these items and students can progress to calculations such as of 20.

By using these visual aids as students learn about fractions, their understanding will become deeper. They will have a solid foundation to build on and visual images to relate to as they progress their fractions learning in secondary school.