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Fractions with Unequal Partitions

If you are looking for a fresh take on teaching fractions with lessons that help students overcome common misconceptions and develop deep understanding, you’ll definitely want to check out Beyond Pizzas & Pies: 10 Essential Strategies for Supporting Fraction Sense, Grades 3-5!

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.

It was my source for this lesson. You might also like this post about using geoboards to teach deep conceptual understanding of fractions.

If you asked a handful of 3rd graders (and possibly 4th and 5th graders…) to name the fraction represented by the shaded part in the model below, many would say one-third.  What misconception are they operating under? Yes, one part out of three parts is shaded, but are the parts equal?

This is an important understanding that students must develop as they work with early fraction concepts. We often only show students wholes that are already equally divided, and we assume they realize the importance of the parts being equal. But until they actually work with unequally partitioned figures, we can’t be sure.

To introduce this lesson, I created a SMART Notebook file with seven different slides showing unequally partitioned figures, like the one shown below.

The smaller square off to the side is an infinite clone. Touching and sliding the smaller figure will create a clone (copy). On each slide, students should use the smaller figures to determine how many of the shape it will take to cover the larger figure.

The figures in this activity also provide a great way to work in some geometry vocabulary review. For example, the figure shown above is a square, but it is also a quadrilateral, a parallelogram, a polygon, a rectangle, and a rhombus.

Grab the Notebook file here.  I also created a Student Think Sheet with the same shapes as in the Notebook file, so students can use it to sketch out their thoughts. Grab that here.

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  1. I love reading your blog. It really gets me thinking about fractions. We will be starting this in about a week with our first graders. I notice this post is for 3rd-5th grade. Do you think this would a concept that we need to touch on in first grade as well?
    Curious Firsties

    1. First grade should really be developing the understanding of fair shares, rather than formal fraction language. For example, understanding what that ‘halves’ mean two equal parts and ‘fourths’ means four equal parts. That idea that the parts must be equal.

  2. You are fantastic. I love this activity and I am so appreciative that you so willing to share your expertise and knowledge. Thank you so much for an invaluable fraction activity. You and ( The ElementaryMathManiac- Tara) are my mentors. I have learned so much from you Donna.

  3. I have this book Beyond Pizzas and Pies I will be pulling it out. Thanks for reminding me of the great resources.

  4. I am so happy to have stumbled across this! I have this book and am working on the first chapter with my class. I Googled unequally partitioned areas in hopes that I could find a student sheet I could modify to go with that chapter, and your site came up with a student sheet I don’t have to change AND a SmartBoard lesson to boot! I was beyond thrilled. I am already a follower on Pinterest, and now I will be a blog follower as well. Thanks so much for this resource! 🙂

  5. I would love an updated version, too. My district does not have the application to open the notebook file either. Do you think you could turn it into a PDF? Thanks!

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