Visualizing Fractions {EQUIVALENT FRACTIONS FREEBIE}

visualizing fractions

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

How important is it that our students understand fractions? According to a study conducted by Carnegie Mellon University, it’s super important.

The research team found that fifth graders’ understanding of fractions and division predicted high school students’ knowledge of algebra and overall math achievement, even after statistically controlling for parents’ education and income and for the children’s own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication.

In other words, they found that it was the single most reliable predictor of success with higher math. Unfortunately, we don’t always do a good job teaching fractions for understanding. It’s a topic that is often “taught” using tricks and memorized procedures. So how can we do better?

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.

First and foremost, we have to provide students with lots of concrete and pictorial experiences so they can create mental pictures to draw upon when they encounter a fraction. When a student can visualize both one-eighth and one-fourth, it makes comparing fractions a whole lot easier. When the only image students can conjure up is symbols, they often apply faulty whole-number thinking and decide that one-eighth is greater than one-fourth because eight is greater than four.

visualizing fractions

Oftentimes, the use of manipulatives drops off in 3rd grade. There are a couple of reasons why that happens.

First, there is the misconception that manipulatives are for younger students. That stems from misunderstanding the concrete, representational, abstract (CRA) sequence of instruction. The use of concrete materials is not based on age at all. Students should have concrete experiences whenever they are introduced to new concepts, regardless of age. When students are introduced to foundational fraction concepts, like equivalent fractions in 3rd grade, the bulk of their instruction should be supported with a variety of fraction models—fraction tiles, number lines, fraction circles, etc. When they begin computing with fractions in 4th and 5th grade, they should again be supported with models. It’s even in the standards!

Another reason that upper elementary teachers often give for not using manipulatives is that they face a time constraint teaching their curriculum before state-mandated testing. I get it. But the argument is actually counterproductive. When we skip manipulatives and other visuals during instruction, we often find that students don’t retain what they’re taught. So then we end up spending precious time remediating skills because we rushed to teach them in the first place. When we slow down and give students the concrete experiences they need, it saves time in the long run.

Enjoy and remember that comments are greatly appreciated.

So, I have a couple of examples of using concrete or pictorial support for teaching equivalent fractions. First, check out this post for an exploration of equivalent fractions. There is a link to download the activity.

Next, I’ve created a little set of fraction picture cards with halves, fourths, eighths, thirds, and sixths that can be used in a variety of ways. You’ll find instructions for five different suggested uses.

Grab your equivalent fractions freebie download here.

19 Comments

  1. Christy

    Thank you for your freebie! Fractions are coming up soon, and I’ll be adding this to my plans!

    Christy
    Teaching In Oz

    Reply
    • Donna Boucher

      You’re welcome, Christy!

      Reply
  2. Suzy Q

    I bought the same clipart but did not do anything with it yet. We are also doing fractions right now, so this is perfect! Thanks for sharing.

    Reply
    • Donna Boucher

      That clipart is adorable, right Suzy? Glad the timing worked out for you. 🙂

      Reply
  3. Jami Smith

    Great freebie… Thanks! I love the illustration of the little guy holding the pizza.

    Reply
    • Donna Boucher

      Thanks, Jami! I’m in awe of clip artists and their talent. 🙂

      Reply
  4. Heather

    Perfect timing! My next unit after vacation is fractions, I’m so excited to add this to our math workstations…thanks so much! =)

    Reply
    • Donna Boucher

      Vacation?! Ours isn’t until mid-March. Jealous!:)

      Reply
  5. Tchur8

    Thanks for the freebie! We are working our way through fractions right now and anything hands-on works so well for my kiddos! Love…love…love your creations and ideas!

    Reply
    • Donna Boucher

      You’re welcome! Glad it will work out for your kiddos. 🙂

      Reply
    • Donna Boucher

      Thanks, Patti!! 🙂

      Reply
  6. Elaine

    Thank you! We start equi. fractions right after break!

    Reply
    • Donna Boucher

      Well, that was good timing, right? Hope you are enjoying your break, Elaine! 🙂

      Reply
  7. Jan

    Thanks for the great freebie- look forward to using it next year:-)

    Reply
  8. Diane

    What a great game! I love the nuts and bolts on the robot’s pizzas!

    Reply
  9. Anonymous

    Couldn’t have seen this at a better time! Plan on starting fractions with my students next week!

    Reply
  10. Taylor Rawlings

    Fractions are one of the most challenging aspects of math to understand and teach. I love the tiered model you generated. It allows students to go through the chain of events to grasp the concept of fractions fully. State testing is coming up, and I am becoming stressed about not getting everything in; however, I have been trying to tell myself it will all be fine to keep teaching with manipulatives. Your post reiterated my thinking. I cannot wait to use the resources!

    Reply
    • Donna Boucher

      You are exactly right! We often try to rush our instruction and our preparation for state testing. Going slowly and encouraging understanding will work every time! Good luck!

      Reply

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