Part of what makes learning fractions tricky is that there at least three unnatural things to learn:

  1. The written language of fractions
  2. The spoken language of fractions
  3. The math of fractions

I work in a third grade classroom right now and I’ve heard a bunch of kids say something like the following:

a third


“This is a third.”

Why? There’s an enormous mushing that goes around with “fourth” and “four,” with “third” and “three.”

Related(?) mistake: 4/6 is equivalent to 1/3

Maybe that isn’t related, but I heard it out of a kid who thought a third was 3/4, so it’s probably connected somehow. Maybe you guys can figure out how.

  • Michele Torres

    Are they reading it as a ratio?

  • Jaclyn

    let´s see – there are three shaded squares so those three shaded sections are one chunk of three, and three is related to the word third so its a chunk, one third; that means the student is not looking at the whole square made of 4 pieces, but just focused on the three shaded parts

  • Irene Pham

    When the student said “a third”, what comes to my instinct is “a third of something” or “one third of something” as “a hundred” means “one hundred” to me. Thus, I assume the student referred to the 1/3 that is not shaded. However, what the kid who thought a third was 3/4 completely turned my understanding upside down. I think when they said “third”, they meant “three”, or the three shaded area. “A third” could also mean to him/her as “a group of three things”. Coming back to the mistake that 4/6 is equivalent to 1/3, when the student convert 4/6 into 2/3 by dividing both 4&6 by 2 and draw this as a picture where there are 3 cubes total and 2 are shaded and 1 is not, they now call the picture “a third”, which is equivalent to 1/3 in my understanding.

  • Julie

    This student is not taking in to account of the whole shape. The student said it is a third because 3 of the squares are shaded in and left out one, which is not shaded in. it seems like this student does not fully understand fractions that is drawn out visually. Or the student might of meant three and not a third, these terms maybe confusing for this student. I would practice drawing out small fractions with this students to help him or her understand the concept behind it.