Three Ways to Represent Fractions

Three Ways to Represent Fractions


Why are fractions so hard?  Many children work well with whole number concepts, such as addition, subtraction, multiplication, and division, but struggle when it comes to working with fractions.  For many of us "fractions" are just hard.  This is why I remember very clearly from my teacher when it came to dividing fractions, she would say, "Don't ask why, just invert and multiply."  It wasn't until I became a teacher myself that I realized she told me this phrase over and over, because she didn't know why?  Fractions are just numbers.  We need students recognizing that fractions can be represented in several ways.  This blog recommends the top three ways to represent fractions.  The last two are supported strongly in textbooks, using a number line is a great way to support conceptual understanding of fractions.



#1 Represent a fraction using a number line.  Start with a larger number line and put 0 on the left end and 1 on the right end.  Ask, "Where does one-half belong?"  "Where does one-fourth or three-eighths belong?"  Getting students to see that fractions are a number and proper fractions are somewhere between zero and one.  For a math lesson plan go to




Once students have a strong understanding of working with fractions between 0 and 1, move onto improper fractions, "Where does four-thirds belong on the number line?" 







#2  Represent a fraction of part of a whole.  Start with simple diagrams, stressing that the size of the piece needs to be the same size.  Then move to more complex drawings.  Look at the progression below






#3 Represent a fraction as part of a set.  Use counters (two different colors) to represent fractions.