5 Ways to Visualize Fractions

Use these 5 ways to visualize fractions to show your students how fractions work with tangible examples.

Fractions are hard. They are!

As we begin working on fractions with our students, we sometimes forget just how much support is needed to take students from working with whole numbers to fractions.

For many students, just being able to understand the concept of fractions is really tough.

Fractions, in general, seem to feel a little more abstract for students, and they struggle to make the connection between how fractions act vs. whole numbers.

To help students understand fractions and to make them more tangible, we often teach fractions through visual representations.

When I introduce fractions to my students, I use the Fraction Envelope Book because it is full of visual representations of fractions, and the many examples are very helpful to students as they try to wrap their minds around this concept.

(If you’re unfamiliar with envelope books, click here to learn how these fun, interactive student resources are created!)

As we work through the Fraction Envelope Book, I teach my students 5 ways to visualize fractions, and I encourage them to use these methods as they continue to work with and develop their understanding of fractions and how they work.

All of the methods are similar, but being able to see the fractions in all these different ways, will show students that fractions don’t always look the same.

They are only a part of the whole, so the whole determines what the part will be (i.e., what the fraction will look like). For example, half a watermelon is way different from half a lime, even though both are fruits, green, and the same fraction. The whole (i.e., the fruit in this example) will change the look of the half.

Identifying Part and Whole

To begin, students need to get comfortable looking at a fraction and then identifying the top of the fraction (numerator) as the part and the bottom of the fraction (denominator) as the whole. In addition to being able to identify the whole, students need to understand that the number representing the whole is also equal to the total number of parts that make up the whole.

This is complex, which is part of the reason we use 5 ways to visualize fractions in the Envelope Book. For some students, simply getting to the point where they understand that the total number of parts is equal to the whole may take several different visuals to understand.

#1 | Fractions as Equal Parts of a Whole

The first way we visualize fractions is as equal parts of a whole.

To show students this, we write our fractions using the part over the whole with a horizontal line between the two. Then we create a block or array that first represents the whole.

Once students can ‘see’ the whole, we color in the appropriate number of boxes to create the ‘part’ or the fraction. We then spend time talking about how the colored part represents how much of the whole the fraction represents.

#2 | Fractions on a Bar Model

In this visualization, the whole is represented with a straight line of blocks, or a bar divided into equal parts.

Students will look at the whole number of parts (i.e., denominator) and use blocks to create a ‘whole’ bar (line of blocks) with that number of blocks.

The fraction is created by coloring in the number of blocks representing the part.

#3 | Fractions on a Circle Model

I really like working with a circle model because the circle is always the same. The part that is changing is how it is divided up. It’s fun to use pizza, or pie, or cookies to show this type of fraction.

For example, if the students are working with 4/6, they will split the circle up into 6 equal pieces and then color in 4 of them. If they are working with 8/12, they will split that same circle up into 12 equal pieces, but color 8 parts.

#4 | Fractions on a Number Line

Like a bar model, this way of visualizing fractions is done on a line, but this time, we’ve removed the boxes and just created a number line, where one side is labeled with a ‘0’ and the other with a ‘1’ to represent one whole. The number line is then divided into equal segments based on the number represented on the bottom of the fraction, or the denominator. Students identify how many of those pieces are needed to represent the part.

#5 | Fractions as Part of a Set

Lastly, we can visualize fractions as part of a set.

This is different than the other visualizations because this one shows the pieces as individual stand-alone things that are grouped to make a set rather than an actual whole shape.

For example, a group of 6 people could represent the whole when we’re working with a 4/6 fraction, and the part might be represented by the people wearing hats.

In a drawing, this might look like students drawing six individual smiley faces and then coloring 4 of them.

All of the visual fraction images in this post can be found inside this Fraction Envelope Book resource.

Additional Fraction Resources

As students begin to wrap their minds around fractions, we continue to work through the Fraction Envelope Book to compare fractions and add/subtract fractions. I supplement their learning with a variety of digital resources that allow me to assess whether my students have truly mastered this concept.

Here are some of my favorites!

Build a Rocket! Fractions Build It