Fractions Day 4: Example–Counterexample!

What’s next with our fraction unit?

Fraction Warm Up Problem

Our “fractionfest” continued Friday by taking our investigations a little deeper.  We started our day by checking our their homework–how they divided the 5 x 5 grid into halves.  I asked students who thought they had interesting explanations to share on the document camera.

We had all sorts of fun talking about refining our “math talk” so that anyone would be able to clearly understand our ideas.  This is REALLY hard for my students, so I must remember to work in more modeling for them!

We then set out to really refine our thinking about what “1/2” really means.  I asked students to take a little time to make a mini poster (a common learning strategy in our room) to show me “5 ways to represent 1/2”. Represent is one of those words we try to use a lot–to make sure they understand how we can use word, numbers, symbols, and drawings to represent our thinking.  Today I asked them to really try to think outside the box and come up with 5 DIFFERENT ways to represent 1/2.  I wandered around looking at their ideas, hoping to get some information about where to head next in this unit. I noticed that most students were representing 1/2 by drawing different shapes (“wholes”) and dividing into two equal pieces.  There are so many more ways to represent fractions, so I need to find ways to get them exposed to them in the coming weeks.

Teaching Fraction Thinking

So what next?  After this, I felt it was time to review a skill we have dabbled in all year–creating examples and counterexamples.  I split the class into groups and assigned each a fractional part–thirds, fourths, and so on.  Each team was then responsible for designing a learning poster that represented their fractional part–but this time they needed to include five EXAMPLES and one COUNTEREXAMPLE.  I told them that their job was to create a poster that we would share–and the other groups would need to analyze their examples and find out which representation was the COUNTEREXAMPLE.

The students had a BLAST trying to find ways to subtly “trick” their classmates!  They had great discussions about what would make a representation accurate or inaccurate, what common misconceptions might trick their classmates, and really pushed each other to do accurate work.  We ran out of time to share, so I’ll have to report back next week!

***UPDATE***
This blog post is now a part of my comprehensive fraction unit available by clicking the image below.  Hundreds of teachers have now used it to change the way they teach fractions!