Making Fractions Real: An RME Task

Recently, I’ve been investigating Realistic Math Education (RME).  I like the idea of building on what is real to the student.

Because I spend a lot of time thinking about fractions, I wanted to know how RME approaches them.  Luckily, Streefland wrote about his three-year teaching experiment in the Netherlands.

In the experiment, students were introduced to the “Fractured Family.”  The family encounters many experiences that require fractional thinking and proportional reasoning.  For example, they need to divide an omelet at lunch or share apples after school or bake cookies from a recipe.

It’s not necessary that students have experienced these situations themselves, but rather that they can imagine the adults and children in the family doing them.

Here’s one of the initial tasks students encounter.

When Anja and Monica Fractured come home from school they may have an apple each.  But what do you do about such a difference in size?


Here’s what I like about the task:

  • It’s a great context for introducing fair sharing.  Students know that it’s not fair if one child gets the big apple and one gets the small apple.
  • It’s a great context for talking about the unit.  Is one-half of the small apple the same size as one-half of the big apple?  Why are they both called one-half?
  • Using an imaginary family allows students to connect sharing with specific people they can imagine as opposed to the more abstract idea of sharing with unnamed people.
  • Students are encouraged to draw how they would share the apples.  At first students create very detailed drawings–drawing leaves and stems for the apples. But as they do more tasks, they move away from detailed drawings and use circles or rectangles to represent items.   The drawings become representations or models of the situation.  Eventually they become a mental model.

I’m not a big fan of calling the family fractured, but you can adapt this task and name the family anything you want.

I’m still making my way through the book, but I’ll be sure to share any other tasks that I find interesting.  I’d also love to know if anyone has any experience using RME tasks in their classes.

Want to read along with me?

Streefland, L. (Ed.). (1991). Fractions in realistic mathematics education: A paradigm of developmental research (Vol. 8). Springer.

2 thoughts on “Making Fractions Real: An RME Task

  1. galenaylor

    I really like that first task; as you said, there are many concepts that spring from choosing apples that are not the same size. The evolution of the students’ drawings mirrored the maturity of their thinking. Sometimes I think we don’t allow students the time it takes to go through this process, but instead try to help them get there faster. I look forward to hearing about more RME tasks. Instead of the Fractured family, how about the Fair Share family?

    1. Nicora Placa Post author

      I agree with you that we need to be a little more patient in allowing students to go through the process. It’s hard to do sometimes. I’m enjoying learning more about RME tasks–it’s nice to hear you are too. And I love the idea of calling them the Fair Share family!