Common Concepts Kids Forget - Part 3 - Adding and Subtracting Fractions

Making errors and trying new strategies are a natural part of the learning process in maths. However, if kids have an underdeveloped understanding of a certain concept in maths, like those in fractions, this may impede their progress.

Usually, misconceptions will not be corrected unless teachers and parents explicitly address them by instruction. Teachers need to be aware of misconceptions of their classes and individuals and then find an effective way to address them. Identifying misconceptions will require a purposeful diagnostic assessment and careful observation of what their students are thinking.

Common maths misconceptions in fractions
We understand that most kids find fractions particularly challenging.  The main reason for this is that they compare fractions from the common kinds of numbers they often worked with. They often forget how fractions work and how to work with them effectively.

In fact, most misconceptions in fractions come from the fact that kids try to draw associations with natural numbers. Natural numbers are those positive whole numbers like 1,2,4,12,110,255,670 etc. These are the kinds of numbers that most of our kids encountered from a young age and they spend a significant amount of time in early education learning about these numbers.

Students often forget how to add, subtract, multiply and divide fractions. There could be a few solutions to this dilemma:

• Introducing fractions and functions of fractions earlier
• Regulating use of a calculator more frequently in both lessons and assessments
• Introducing a ‘mini recap’ lesson at the beginning of each lesson, in which you spend 15 minutes with your class addressing a common misconception

Misconceptions in adding or subtraction fractions
A common mistake that kids often make is that they forget to find a common denominator before adding or subtracting fractions. In fact, they tend to treat the numerators and denominators as whole numbers.

For example:
Misconception: 2/3 + 5/6 = 7/9
The correct way is to add fractions by creating a common denominator and then adding the numerators. The right way of adding these fractions is written below.

Correct working: 2/3 + 5/6 = 4/6 + 5/6 with a total of 9/6 = 3/2 or 1 and 1/2

The same method applies to subtracting fractions. Many children make the mistake of subtracting the denominator as they would the numerators just like the example below:

Misconception: 5/7 – 1/4 = 4/3

You could address this misconception by finding the common denominator before subtracting the numerators, then just copying the common denominator to arrive at a solution just like below:

Correct Working: 5/7 - 1/4 = 20/28 - 7/28 to arrive at the solution of 13/28

Overall, this misconception needs to be continuously addressed and practiced so kids will know how to correctly add and subtract fractions. Now that school is running as normal in Victoria again, teachers will be able to more accurately address misconceptions within their classrooms.