Labels are Important

And so it begins.  My excitement is difficult to contain.  This year, I have been granted the opportunity to change grade levels and districts.  After many years of teaching primarily 7th grade math, I'll be getting to know some 5th grade mathematicians.  Using what I know about the math that 7th and 8th graders need to know, I hope to inspire a love of math and learning in this new group of humans I have been entrusted to educate.

This week, Building Math Minds is hosting a Virtual Math Summit, where Pre K - 5 educators are engaging in cyberspace about many ideas that impact student learning and classroom practices.  After viewing just 15 minutes of the first presentation I chose to view, I came upon this.  Graham Fletcher of gfletchy.com presented a situation involving 5 oranges cut into quarters.  Here's a screen shot:

In my experience and teaching, I would have expected an answer of 20.  I asked family members to answer as well.  All of us said 20.  One person said they multiplied by 4, another said they flipped the fraction and multiplied.  I was immediately struck by the denominator of 4, not just because of the image, but because Graham said that the answer was twenty, one-fourths.  In later communication with Graham, he would reveal that the solution should say 20/1, which made a whole lot more sense to me, but I am left thinking about two things:

If 5 is a whole number, and you're dividing into 1/4 size pieces, does it make sense that you have 20 whole pieces?

Labels are so important in understanding context and solutions.  

That first question was initially raised because of the solution on the slide, but even with the corrected solution of 20/1, I'm still thinking about how both 5 and 20 are whole numbers, but 20 is used to represent  a quantity of parts.  This could be tricky for students for sure.

In 5th grade, fractions are abundant.  Teaching 7th grade, I had taken for granted that students had already formed the necessary foundation to understand these sorts of answers.  Looking back, most clearly had not.  This image will be embedded in my brain as I take on the new challenge of educating 5th graders.  It will be an important task to ensure that students develop a solid understanding of what unit fractions are (1/2, 1/3, 1/4, ...  fractions with a numerator of 1) and how they relate to our solutions.  In this scenario, each piece is 1/4 and there are 20 of them.

As I look at the image above, I'm also struck by how many questions students could pose if the equation were removed, and how many patterns could be observed.  I'm excited and inspired to work with 5th graders and cannot wait to facilitate their mathematical journey's this year!