Fractions Aren't Scary!

I thought I'd try something a little different today.

I've been out a lot lately for collaborative inquiries (professional development), both for math and blended e-learning.  We are gearing up to launch a blend of e-learning with live-action teaching, and I have been so overwhelmed with ways to bring tech into the classroom that I thought it was time to try something a little different.

Since I haven't been in my classroom for a full week since before the March break (that's insane - I was at a hub, a conference, a meeting, and a hub!), I knew that just giving them the question would be okay, but that I really needed to WOW! them.  From what I've been looking at, they are "getting" fractions to varying degrees.  They are extremely comfortable drawing fractions, and many can talk about equivalent fractions when they are "easy to manipulate" numbers, like 10/100 being the equivalent to 1/10.  Some can even tell me that if it is 10/100, then it is 10%, which is also 0.1, or 0.10.  PERFECT!  But, I need to make sure that this understanding is concrete and not flukey, so I thought I'd probe a bit.

The question today was wide open.  I was looking to see if they could do what I mentioned above - could they represent the fraction as an equivalent, in a decimal, or as a percentage.  While most didn't really give me that information, I realize now that the question may have led them to drawing pictures.  Here it is:

Nick is going on a trip.  His mom bought him a gigantic sub, and he needs to figure out how to make it last over the full day trip, with no other stops!  That means it will be his snacks and meals.

What fractions could represent how much he will eat each time?  Explain how you know.  Are there other ways to express those fractions?

Many students became caught up in how big the sub needed to be.  They were concerned with the measuring aspect.  Others were trying to figure out how often he would eat (one group was successful in finding this out, actually).  I would say that 99% of the class (that's a guess, and just my way of saying that pretty much all of them, so don't nail me later on doing some poor math!) didn't extend their thinking beyond showing me a circle split into however many snacks and meals he would have.  I did see some interesting things though.  I'll show you those in a minute.

You are likely wondering, "What did he do that was so different?  He just asked a question - nothing new!"

You would be correct!  Except, before I showed them the question, I interrupted their independent reading with this trailer:

It was a great way to grab their attention and whet their appetites for the upcoming question.  It made them giggle and engaged them in the math.  It made an "authentic situation" a little more authentic.

I created it in about 4 minutes using my iPhone.  I grabbed the kids from the classroom during my prep time and snapped some photos - they had no idea what it was for.  I used my question to input the text, and then that was it!  Using the "Trailer" option instead of "New Project," I was able to throw everything together with the fun template graphics and music.  The only downfall was that I couldn't change the number of photos, the length of them, or anything else.  I highly recommend using this from time to time!  It is easy, and the kids can even use it to showcase their thinking (in fact, one group was making a grand effort to use their own iPods to record their work, but we ran out of time and they didn't get to finish).

Here is some of their work.  It is not, by any stretch of the imagination, mind-blowing.  It is, however, a good dose of reality in what they know, can do, and how well they were able to read my mind.  Next step for me?  Be a little more explicit in what I ask, since they didn't go down my road this time.

This student showed his thinking using percentage and the original fraction!

This student's work is well organized, and includes a mini legend.  There is a lot of effort going into figuring out another way to show the fraction, but the student requires some "hard teaching time" now. 

These students re-interpretted the question.  They knew that the snacks would be smaller than the meals, so they split the sub equally and then took each half, splitting one half into thirds, and one into halves, to create more fractions.  Interesting approach!  It is well laid-out.  However, they still haven't shown the fractions in more than one way.

With some prompting, this student was able to find equivalent fractions using multiplication.  We used this example in our class consolidation to see how to grow the fractions.  Then, we moved into simplifying them, working backwards by dividing.  I think they are starting to really, truly see it.  Fractions don't need to be scary!

It's not about changing everything you do as a math teacher - it's about small additions and adjustments.    The trailer didn't revolutionize how they saw the problem.  It did help excite them about math again, and break up another Thursday.  A little shift is important - it's the technological equivalent to a body break!