Fractions Day 4: Example--Counterexample! - The Teacher Studio: Learning, Thinking, Creating

Fractions Day 4: Example--Counterexample!

teaching fractions

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.
fraction lessons

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 know I need to find ways to get them exposed to them in the coming weeks.

A few did branch out a little . . .
This student had all sorts of interesting ways to represent 1/2 (including the little stick figure that he drew "1/2 dressed").  Got to love the mind of some 9 year olds . . .

Here is our finished "collection" of mini posters . . .

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!

Next blog post--how did the students respond to the question, "Which is bigger, 1/2 of a grape or 1/2 of a strawberry?"  
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!  


  1. Do you know how much you are making my heart swoon by reading these posts? I am totally in love reading through the past few days and let me tell you I was nodding my head and cheering along through the entire first part. I can't wait to see how their learning posters turn out! This is an AWESOME lesson that I am sure will stick with them forever!

    1. are so sweet! It's been a fun first week of the unit! :)

  2. I love the "example" "counter example" concept. Did you create that?

    1. Well...I wouldn't say I created it, but I do ask my students to do that kind of thinking whenever I can--to really show that they can have real clarity in their thinking.

  3. Gotta say you're leaving us hanging here, Meg!!! I want to see their posters - and their answers to the question about the grape and the strawberry :)

    1. OH my goodness...the grape problem. for more on that one.

  4. I loved this post! I need to totally have a 'fractionfest' in my class! We haven't done fractions yet this year and reading your fraction posts have given me SO many ideas!

    I even had to grab your button for my blog! I believe in teachers CONNECTING and sharing great information!

    Love it!!

  5. Nice post, fractions are a difficult concept. But you have got those kids thinking.


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