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Concrete Learning for Equivalent Fractions

Fractions are such an abstract concept, and children need lots of concrete and representational (pictorial) experiences to really understand the meaning of a fraction. Concrete learning also allows students to explore concepts and build understandings of their own, rather than having information delivered to them from a teacher.

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This activity for exploring equivalent fractions is perfect for third-grade students who have already worked with fractions as parts of wholes, as parts of sets, and on a number line. Often, when exploring those concepts using manipulatives, students have already noticed and commented on fractions that show the same amount. In other words, they have already discovered that equivalent fractions exist on their own! This activity can be used in a small group lesson or as a workstation.

Now, think about how the Standards for Mathematical Practice are embedded in this activity. Students are using tools (manipulatives) and models (sketching the fractions) to represent and explore the fractions. They are looking for structure when asked to make observations about what all the fractions equivalent to one-half have in common. At the conclusion of the activity, they will discuss their ideas with fellow mathematicians, so they will be justifying their solutions and critiquing the reasoning of others. And, since it’s building on what they already know about fractions and the teacher is not doing a direct teach, I’d say it also incorporates problem-solving. That’s a lot of Practices packed into one activity!

Provide students with concrete models for equivalent fractions

After exploring fractions equivalent to one half, students go on to explore additional fractions–there are four of these sheets in all.

The sheets are sized to be used with standard fraction tiles, but I realize everyone doesn’t have that resource, so I made a fraction strip kit that you can print (in either color or B&W), cut out, and use with the activity.

Provide students with concrete models for equivalent fractions

Download the fraction activity sheets and fraction tiles here. ย As always, I’d love to read your comments!!


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  1. I also teach third grade. I’m in the middle of teaching the equivalent fractions and only had the black and white tiles. I’m so excited that you made these in colors. I can’t wait to let my students cut these out and visually use them. Thank you so much for making this happen!

  2. I just bought those fraction tiles this summer, Donna. See how much you’ve taught me?! I teach sixth grade and the kids have SO LITTLE conceptual understanding of fractions–equivalent or otherwise. This is the first year I have taught it from “the ground up.” We have done drawings, number lines, various manipulates and I am constantly asking: Can you say it in a different way? We made a flip chart on the Promethean board so they could actually move the giant pieces…
    On Friday, someone asked: Isn’t 23 hundredths the same as two tenths and three hundredths? I almost fell off my chair!
    Thanks for always being inspirational…

    Finding JOY in 6th Grade

    1. Oh, Kim, your comment makes my heart sing!! Your students are so lucky to have a teacher with your enthusiasm and passion for learning. ๐Ÿ™‚

  3. Thank you for sharing. The fraction strip kit is such a bonus! I enjoy reading posts on building the conceptual. Keep them coming :)!

    1. My pleasure, Pam! I know we are very fortunate to have the actual tiles, and I wanted everyone to be able to use the activity. ๐Ÿ™‚

  4. Thanks so much, Donna! This lesson is coming up at the end of the week, and I was thinking about the need for an activity sheet to go with the fraction strips. So glad you did the work for me ?)

    1. I am getting observed tomorrow and wanted to use these fraction tiles (I just got them!!) but wasn’t quite sure how to organize it! Thank you so very much! THIS IS PERFECT!

  5. My students love your activities! The posters you sent are a big hit too! Thank you for all you do for us.

  6. This is a wonderful way to help kids construct their own knowledge! Love how well this would work as a workstation so kids can go at their own pace. Thanks for sharing!

    The Math Maniac

  7. Oh, I love this! I’m a third grade teacher and we’re in the middle of fractions right now! Do you have any resources (either in your store or something your teachers used) for teaching fractions on a number line? I’d love to see/buy them!!

    Thanks ๐Ÿ™‚
    The 4th Grade Journey

    1. Hey, Mandy! The only thing in my store that has number lines is really only to reinforce the benchmarks of 0, 1/2, and 1. It’s not really reading fractions on a number line. I did a SMART Notebook activity for my 3rd grade teachers. Look for a blog post maybe later tonight or tomorrow. ๐Ÿ™‚

      Here’s the product, if you want to check it out: http://www.teacherspayteachers.com/Product/Fraction-Cards-for-Benchmarks-of-0-12-and-1-with-Activities-194633

  8. Just finishing up our fractions unit in 4th grade, but the test showed me that some of my darlings still don’t quite get it. This will be used during extended learning to help them see it a different way. Gotta keep that spiral going!
    Thanks for such great descriptive posts. There are lots of great teacher produced products out there, but often do not come with the why/how, or at least not detailed. And when you have a spare moment (hah ahahhaha) more stuff for the older babies!

  9. The Georgia Department of Education has some great fraction tasks for third grade and so does North Carolina department of Education. Just FYI…. You can use fraction tiles with most all of them.

  10. YAY!! Just what I need. We used your Capture 4 Equivalent Fractions this week and I really got a clear picture as to who needed some extra concept practice. I hope everyone goes and downloads your game. I just gave you a shout out on my blog! Thank you for activities that are meaningful and definitely engaging!



  11. Love this blog! As I am moving from kindergarten to 3rd grade I am overwhelmed with the math curriculum that I will be teaching. Thank you for the ideas.

  12. Thank you. I love how the fractions are written the correct way. I bought a foam set and didn’t realize they were incorrect. I cant wait to use these this new year.

  13. THANK YOU! I am getting my Intervention Specialist license and am currently in a field setting teaching fractions…this worksheet is going to come in handy for my kiddos who need lots of visuals and manipulatives.

  14. Thank you for always sharing. I am a Curriculum Coach and enjoy seeing activities that you have posted and reading ideas that you have implemented. Fractions are difficult for our students, so I plan to share with them next week since 3rd – 5th are all in a fraction unit. Do you have any tips, other than this activity, that helped push that light on?

    1. Search on “fractions” using the Search By Topic feature on the right side of my website for additional articles on fractions. ๐Ÿ™‚

  15. Thank you so much for this great resource! I was on Amazon about to buy a class set of fraction tiles when I stumbled upon this resource. It has made my life easier and will help make teaching equivalent fractions less intimidating for me!

      1. Exactly what I needed!! My son struggles with equivalent fraction area and finally heโ€™ll use something helpful for him. Thank you !!!

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