Rainbow Pooping Unicorns

Two years ago, I began a journey that turned out to be far less positive than I had imagined.  This year, I find myself if a position that could not be more opposite.  The job is the same, but the location, grade, and experience are totally different.  There are still plenty of times I've found myself questioning my effectiveness and career choice, but already, in just two short week, I've had multiple experiences where I've thought "this is it!  This is what teaching is and it's glorious!"  I commented to my colleague that sometimes it seems as though unicorns are prancing through my classroom.  She replied "and they're pooping rainbows."

With the freedom to make my own professional decisions, a little inspiration from Tracy Zager's Becoming the Math Teacher Teacher You Wish You'd Had, and the Math Twitter Blog-O-Sphere (#mtbos) community, things are moving right along in room 125.  We start our year learning about equivalent fractions, comparing fractions, and fractions greater than one.  I was blown away by all of the fabulous ideas and thoughts students have shared along the way.  Just take a look at a couple of the interpretations of building fractions equivalent to one half.

After a morning of standardized testing and a somewhat ineffective class involving note taking and practice problems, I decided it was time to reboot.  For my last class of the day, I handed out index cards cut in half.  Under the white board, I had a clothes line number line with 0, 1/2, and 1 marked.  Students were asked to write a fraction between 0 and 1 on their index card and then order them from least to greatest in their groups. Some students weren't sure what "a fraction between 0 and 1" meant, so they were asked to just consider the types of fractions we'd been working with to write their own. When the finished, they came to the front and had a seat on the rug with their index cards.    The objective for this lesson was to look at ordering fractions, but it turned into much more when students had enthusiastic discussions about where each fraction should be placed.  We used benchmark fractions to start, but the more fractions added to the line, the more debate there was about placement.  Discussion organically evolved into finding ways to know for sure we had the fraction in the right place (common denominators) and whether using the number of unit fractions from a whole was a reliable method for comparison.

Some students created fractions greater than one which led to conversations about how to recognize when a fraction is greater than one and how to convert it to a mixed number (is this a term we're not using any more?) by recognizing how many pieces make a whole and what is left over.  The number line grew, but here are a few shots from early on in the process.

 

It was refreshing to facilitate respectful discussions about math that were well informed and showed what students really knew, as well as what they were just starting to form an understanding about.  Students also learned that I was not going to confirm their answer, but that their peers were going to share why they agreed or why they disagreed.  Students who were comfortable with the lesson created much more challenging fractions to place.  Those who were less confident created and placed more common fractions with the aid of their classmates. The activity was repeated with all 4 of my classes and equally as successful in each.

My experience is not all unicorns pooping rainbows, but the success and authenticity of this lesson has encouraged me to work hard to create more like it as often as possible.  And it has made my weekend a whole lot more enjoyable!