Misconceptions Associated With Fractions

I teach grades 7 to 12 all in once classroom.  I have a 7th grader who never learned about fractions but could do them with a calculator as long as it allowed him to do fractions. However, he couldn't tell if the answer from the calculator was correct.  I convinced him to try learning fractions by using fraction strips.  

Just this past Friday, I discovered he had misunderstood equality of fractions.  He uses those foam fraction strips and so he could squish some a bit so they seemed to be equal such as 3/4 = 7/10.  I had to take time to explain they could be split up evenly.  It left him a bit confused but I'm glad I saw the misconception.

Today, we'll look at other misconceptions that arise when students study fractions.  Some folks believe that fractions are only used in math, not realizing they are found in cooking, building, the size of tools, and so much more.  Knowing how to work with fractions is to have a real world skill.  In addition, although it seems as if fractions are a small part of mathematics, they are used over and over again in several forms.  When one understands fractions, it makes it easier to understand decimals, and percentages and the relationship among all three.

Students often think that the bigger the denominator, the bigger the fraction rather than understanding that the larger the denominator, the more pieces and each piece is smaller. Thus 1/2 is bigger than 1/4 which is bigger than 1/11. Speaking of denominators, students are taught to use the other denominator to find a common denominator when adding or subtracting.  An example might be 1/2 + 1/4 and they use 8 as the denominator rather than 4 which is the lowest common denominator. They learn this way of finding the denominator because elementary teachers often teach them something called the butterfly method.  I gather you would cross multiply to get the numerators while multiplying the denominators to get a common denominator.

Another misconception is that fractions must equal one or less, they cannot represent something bigger than one.  So when they are asked about 5/3, they have difficulty understanding it is one whole plus two thirds.   Of course, most students learn that fractions represent a part of a whole which is nice but it doesn't help students when it is time to learn about ratios, unit prices, division, or comparing two quantities. 

These are the big ones that I find students have when they get to middle or high school.  I have to go back and clarify the topic.  Let me know what you think, I'd love to hear.  Have a great day.