Tuesday, February 25, 2014

"Fraction of" problems

Nicora Placa's latest post has motivated me to blog about a method we've used for helping kids develop some conceptual understanding for what happens when they find a fractional part of a set.  She calls them "tape diagrams".

We start with fraction tiles.

We have lots of these in my school.  I think the previous math specialist got a special deal on them.  

We have the kids make booklets.  They trace the bars.  Each page has a whole bar, and then the whole made with unit fractions.  I like them to write both the fraction and the words, and a number line as well.  

   Most kids will make it through the eighths, and some will go all the way to the twelfths.  This takes about a period.  But it's worth it.

We have the kids make up their own "fraction of" problems.  We check them over and then have the kids write them on index cards.  In order to solve this problem, you need 18 counters and your thirds page.  I really like how this looks, because the kids can now see that the set of 18 is the "one whole".  We've transformed the whole from a candy bar, or a brownie, to a set of individual objects.
Now it's just a matter of dividing the 18 counters into 3 equal sets.

We've collected lots of cards like these.  I've used these with third, fourth, and even fifth graders.  After a while they can transition into using drawings, which look like Nicora's "tape diagrams".  And now when we talk about the relationship between the numerator, denominator, and the whole number, we have a concrete model to look at.

And they're self-checking, so you don't have a pile of papers to correct!


  1. This is great Joe! I love how you show the transition from students using concrete materials to them using diagrams to represent their actions. I also love how the students make sense of their own work and don't need the teacher to tell them if they are correct.

  2. Thanks Nicora. The self-checking, kid-generated problem index card activity is something I've been using for a while and it transfers really well. In this activity there were actually two sets of cards: the yellow ones had manageable numbers and problems that could all be solved using the tile booklets, and then there were pink ones that had "challenge" problems with larger numbers and fractions not represented in the booklets.

  3. Joe, I love the way that you had the students create these booklets that they can use with different "fraction of" problems. My district has been using bar diagrams for awhile now, but some of my students still struggle with using them. Like Nicora said, you did a fantastic job transitioning the students from using concrete materials to the bar diagrams. Thank you for this outline. I can't wait to try this in my classroom on Monday!

    1. Thanks Tamara! Please let me know how it's going.