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Would you rather…

Awhile ago, I ran across this nice blog written by John Stevens entitled, Would you rather?  His post from September 27th about pizza caught my eye, as it connected nicely to a lesson from Mathalicious (Domino Effect) that we were working on with some of our 8th graders.  However, at the time, things were hectic (aren’t they always), and I didn’t do anything more than write it down in my notebook.

Last week, while rummaging through my notebook looking for ideas to use for the fifth grade team to explore during today’s grade level conversation focused on Number and Operation-Fractions, I ran across my note about John’s blog,  And there it was, this nice question about pizza and fractions.  A perfect opener for us to use to begin the conversation about fractions.  (It feels as if we have been talking about fractions forever, and our kiddos are still not as confident with the reasoning and ideas as we would like them to be.  But we, their teachers, are not giving up and we spent the whole day working on putting together ideas and tasks that contain opportunities for kids to grapple with some foundation pieces, some background knowledge, and some new content that comes with the CCSS.)

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The grade 5 team chatted about John’s question this morning.  We liked the question he posed, and we really liked the structure of would you rather have this or that.  We decided that if we adjusted the question a bit we could have our students use fraction circles to explore the two options and justify their choice with mathematics.

We wanted to use his question as a starting point for a task progression for fifth graders.  Some of the ideas we want our students to explore are:

  1. the use of visual models to compare fractions
  2. the inverse relationship–the greater the number of slices the pizza is cut into, the smaller the size of each slice, and the smaller the number of slices the pizza is cut into the larger the size of each slice–why 1/10 is smaller than 1/2, even though 10 is a larger number than 2
  3. comparing fractions
  4. unit fractions
  5. equivalent fractions

So, we re-wrote the question to read:  Would you rather have 1 slice of 8 from a 10″ pizza or 1 slice of 10 from a 10″ pizza?

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Our first step was to do the task, independently, so we had a sense of what kind of reasoning and background experience students would need, and to determine if there was an entry point into the task so that all kids could be in the conversation. Then, we each set out our work.  We examined the mathematical reasoning our colleagues used to decide which piece  of pizza they wanted:  1/8 of a 10″ pizza or 1/10 of a 10″ pizza.

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We did have one person decide that she would rather have 1/10 of the 10″ pizza because it was smaller size slice and she was trying to eat a more healthy diet. (New Year’s Resolution and all that!)

Next, we discussed how to use the reasoning and thinking that organically occurred as a result of answering the question.  The list below describes some of the possibilities we discussed:

  • using fraction circles to determine which is more:  2/10 or 2/8 of a 10″ pizza, 3/10 or 3/8 of a 10″ pizza, 4/8 or 5/10 of a 10″ pizza, or 7/8 or 9/10 of a 10″ pizza
  • different ways (notation) to write 3/10:  1/10 + 1/0 + 1/10, or 3 x (1/10), or (1/10 + 1/0) + 1/0, or …
  • crafting True/False statements:  2/10 > 2/8 — Is this is true statement? How do you know?
  • using the would you rather question the way it was written with students who are ready to grapple with the area of a circle and other non-grade 5 content
  • using other visual models to explore the ideas listed in the first three bulleted items

Finally, we talked about the power of the question and the ideas and concepts that naturally arise–and that we might have missed some of them if we had not answered the question for ourselves.  So thanks, John, for sharing your idea with us.  It gave us a starting point for today’s conversation, and we put together ideas that create opportunities for kids to explore some of the ideas about fractions that can be frustrating if they don’t have the chance to grapple with them, to build their confidence and understanding.

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