# 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!

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.

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1. Sara says:

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!

1. Donna Boucher says:

Love hearing that this will further engage your kiddos, Sara! Thanks for your comment. ๐

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…

1. Donna Boucher says:

Oh, Kim, your comment makes my heart sing!! Your students are so lucky to have a teacher with your enthusiasm and passion for learning. ๐

3. Pam says:

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

1. Donna Boucher says:

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. ๐

4. Julie Sawyer says:

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. Donna Boucher says:

I’m great at reading minds, Julie! ๐

2. Rachel says:

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. Mrs. Jennifer Cimini says:

Thank you!

1. Donna Boucher says:

You’re welcome, Jennifer!

6. Chaya Phillips says:

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

1. Donna Boucher says:

Thanks for the sweet comment, Chaya! ๐

7. TheElementary MathManiac says:

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!

Tara
The Math Maniac

1. Donna Boucher says:

Absolutely, Tara! It’s also so much more powerful when kiddos construct ideas on their own.

Thank you Donna, for sharing. This is just what I need to supplement my unit for my LD students!

1. Donna Boucher says:

So glad to hear it! ๐

9. Mandy Lopez says:

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 ๐
Mandy

10. sewrachel says:

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!

1. Donna Boucher says:

So glad that this will be useful for your kiddos! Spare time? What’s that? Ha ha! ๐

11. Anonymous says:

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.

1. Donna Boucher says:

Thanks for sharing that!

12. Lopez Land Learners says:

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!

Susan

LopezLandLearners

1. Donna Boucher says:

Loved the picture of your kiddos playing Capture 4, Susan! Thanks for the shout out. ๐

13. Jennifer Brown says:

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.

1. Donna Boucher says:

Welcome, Jennifer! Good luck with the transition! ๐

14. Lori says:

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.

15. Danielle says:

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.

1. Donna Boucher says:

Wonderful, Danielle! I’m so glad this will be useful to you!

16. Dawn says:

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. Donna Boucher says:

Search on “fractions” using the Search By Topic feature on the right side of my website for additional articles on fractions. ๐

17. cheryl coffey says:

Thanks for the manipulatives to use to help my students understand equivalent fractions.

18. Judy says:

Thank you for making this easier for me to teach!

19. Reagen says:

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. Donna Boucher says:

Awesome! It’s always nice when something you need lands in your lap, right?

1. Olga says:

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

20. Shari B. Costanzo says:

This is exactly what I needed to enhance my lessons for review with my 3rd graders.

1. Donna Boucher says:

I’m so glad to hear it!