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Wednesday, June 17, 2015

Beyond Pizza and Pies Book Study Part 2

Welcome to week 2 of our book study on Beyond Pizzas and Pies.  For more information this summer's book studies, check out this post.  If you need more convincing about how much this book has to offer, check out this short introduction video!

I am so excited that you are joining me on this journey to learn more about teaching fractions.  I know many folks are participating by following along.  Even if you are not caught up on the reading, please feel free to comment and share your own experiences with teaching fractions.

The posting schedule for Beyond Pizzas & Pies (all Wednesdays)
June 10th Chapters 1&2
June 17th Chapters 3&4
June 24th Chapters 5&6
July 1st Chapters 7&8

Chapter 3: Understanding Equivalency

I love the opening scenario in this chapter.  Kids following a procedure that their teacher taught them without any real understanding of the concept or context is so common in our current mathematics instruction.  If this teacher hadn't dug a little deeper and asked a context question like this one, they might never have known that their students had no understanding of the idea of equivalency.  I have had this happen to me and seen it happen to other teachers over and over again.  When you move from teaching procedures to teaching conceptually, it can be hard seeing how little your students understand.  

I am blown away by the video clips in this chapter and the entire lesson on measuring with Cuisenaire Rods.  I spend a lot of time on equivalency using area models and a number line but this lesson seems like a great way to bridge the two.  This lesson is simple and easy to replicate but seems like a brilliant way to look at equivalency and to move from an area model to a linear or number line model.  The follow up lesson where the rods are used on the number line also looks very effective.  These two lessons will definitely be a part of my students' work on equivalency next year.  

Fraction Kits: Friend or Foe?

I love the subtitle of this chapter.  I have a love/hate relationship with fraction kits.  When I first started transitioning to using more manipulatives and visual models, I thought fraction kits were the best thing ever.  Then I realized many of my students were using their fraction kits like calculators.  Something that was meant to be used as a tool to move them toward conceptual understanding was now being used as the only strategy they had for solving problems.  Since then I have been on a quest to find the right balance between hands on experiences and helping kids to develop mental models and conceptual understanding.  

I found the research the author conducted about using fraction kits to be similar to my own experience.  I love when this happens!  She talks about how she worked with 2 different groups of students on part-whole fraction ideas.  Cuisenaire Rods were used with both groups.  One group used them as a fraction kit where each piece was always the same fraction.  The other group used them with more flexibility where the whole would change and therefore the names of the other pieces.  The second group made more gains in their understanding than the first group.  When I started using pattern blocks in addition to fraction kits, I saw the same thing.  Although problems were initially harder for kids as the whole was changing, the developed a better understanding of fractions over time. 

Based on this reading and my own experiences, I think fraction kits still have a place and I will be keeping my making fraction strips lesson in third grade.  However, I will be adding the lessons in the book using Cuisenaire Rods and will continue to think about how to make sure students are not using fraction kits as calculators.  

I leave you with this quote from the end of the chapter:
"They (fraction kits) can support students' reasoning about fractions and help them make sense of basic fraction computation.  When used in a superficial way, however, fraction kits may lead students to develop superficial understandings of part-whole relations.  Students may come to understand fraction names such as one-fourth to be merely the name of a piece from a fraction kit, not a name that implies a specific mathematical relationship between a part and a whole." 

What are your experiences with fraction kits? How about teaching equivalency? Let us know in the comments below!  

Join us next week as we look at the importance of context in identifying the unit and making sense of fraction and decimal notation.  Be the first to see new posts by following my blog (look in the upper right hand hand column for ways to follow me) or my Facebook page.


  1. Another great post! Watching the video and reading your posts makes me long to go back to third and fifth grade just to explore fractions in these ways! I agree with you as far as fraction kits go. I think with any tool, there is the danger of students becoming too dependent on the tool. I think the variety of tools that were used in the video--number lines, pattern blocks, rods, and fraction kits help students understand fraction in different contexts. Ok---I must order this book!


    1. I love exploring fractions with third and fourth graders! Those are 2 of my favorite grades to teach partly because of how much fun we have with fractions. I like your point about using a variety of tools.

  2. I don't have the kids create fraction kits, we use the fraction pieces I bought. I worry like Sarah about the kids dependency on them. But reading this book and thinking about equivalency I can see the connection betw even using the rods and the fraction kits. To teach equivalents, we fold half and color one half, then fold it again, an talk about how 2/4 is now colored and so on. I write the fractions on the board as we fold and I have the kids make connections to the patterns created with the fractions.

    1. It is so interesting how many different options are out there for fraction pieces and fraction kits. If only having the right fraction pieces would make us super teachers, we would be set. It is so great to examine what we are doing and why we do it. Thanks for participating!

  3. Love this post! I have my kids make fractions kits from strips of construction paper, seems to help, and while they refer to them with fraction problems, they slowing use them less and less.

    1. Sounds like your students are doing a great job transitioning from a physical model to a mental one!

  4. I think I may have to find this book! One of our classes is having a great deal of trouble with multiple models of fractions. I love what you wrote about the research with the Cuisinair rods. Very interesting!