Tuesday, June 11, 2013

My Interactive Fraction Strip Quilt!

Have you ever used fraction tiles before? You might recognize them if you saw a photo so here is a link. Fraction tiles can be a very useful model in understanding fractions, however, math educators...be careful! Sometimes these tiles can hide the true understanding our students have about fractions. Who needs fraction tiles when you can have this gorgeous interactive fraction quilt that starts at the top (white) with one whole, and continues with (red) halves, (pink) thirds, (black) fourths, (green) fifths, (purple) sixths, (yellow) sevenths, (teal) eighths, (orange) ninths, (gray) tenths, light pink (elevenths), and dark purple (twelfths)?!

The free-motion quilting on the back highlights the unit fractions quite nicely. The greater the denominator the smaller the piece is!

In my college days, my math teacher gave us a task to create our own fraction pieces using felt. In conjunction with this, we also were solving equal-sharing problems with fractions, as well as other word problems involving various operations within a real-life context. As an adult, these types of problems were a real struggle for me because I didn't learn fractions through word problems and I always rushed to a solution with numbers while idiosyncratically mixing up procedures that were not even reasonable. Ugh! I even had to retake a previous math course for this very same reason. I literally could not explain why something made sense and just continually asked my teacher for the next step. I was a broken record stuck on the same sound, "Just tell me what to do next." I now realize that I deeply lacked conceptual understanding of mathematics.

I remember initially thinking the felt fraction assignment was a little weird and frustrating. However, I had come to learn a few things that helped me understand the word problems. Certain fractions were difficult to make and some were fairly easy. You could actually use the easy fractions to help make other fractions. For example, if you cut the halves in half, you now have fourths. Duh, right? Well, it was this experience of creating fractions (ME creating them) that helped me understand how to use the "felt model" to solve the real-world context problems. It became much easier for me to draw fractions to represent my solutions, and therefore, I could look back and use numbers to explain what I did.

These memories, both good and bad, burned an impression in my mind. It led to me create this fractional quilt as a symbol of my learning and beliefs to help give confidence to all people out there who feel or ever felt bad at math. The truth is, we can all learn and be successful at math when given the opportunity!

The quilt fabric was chosen to mimic the felt fractions I created, but to also resemble the wild assortment of colors found in a fraction tile set. I believe it is better for students to create their own fractions than to be handed plastic pieces that are pre-partioned. Once students create and understand fractional parts, then these fraction tiles can become a great tool for thinking. The problem is that many times students are imposed and forced into using models they don't understand. This often happens with fraction tiles and other models that we think are supposed to be helpful.

Additionally, this quilt is interactive! Look at all the ways I can fold it to prove and check equivalent fractions.

I can even place a line on the quilt to represent a benchmark fractions. I don't need to do the "butterfly" trick to determine whether 8/9 is larger than 2/3.  When students have a firm understanding (that they created) to understand the relationships between the numerator and denominator...this should be a no brainer. You don't need to write this down and solve it using some procedure, which sadly, many fourth or fifth graders already have been instructed that they need to do this. Instead, mathematical models (like this quilt), when understood, become strong mental models for thinking.
Here I have drawn some black lines for some common benchmark fractions: one-third, one-half and two-thirds. Consider them in relation to the other fractional parts on this quilt. Is it reasonable to say that seven-ninths is more, less or equal to one-third? Justify your reasoning. Now think about all of the fractions that are equivalent to one-half. What generalizations can you make about the fractions that are equivalent. Are there any patterns you noticed? What do you wonder about two-thirds?

Isn't this fun? These would be excellent and important discussions in an elementary classroom! Everyone should see math as fun, challenging and doable!

I'll leave you with more photos...

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