Do your students possess fraction sense? Fraction sense involves a deep, conceptual understanding of fractions as numbers. This goes far beyond simply shading parts of a whole or identifying numerators and denominators. It involves true, flexible understanding.

Errors in fraction calculations can often be traced back to poor fraction sense. For example, think of a student who might add three-fourths and three-fourths and get six-eighths.

This student is likely getting mixed up with a rule that he learned for adding the numerators only when adding two fractions with the same denominator.

But we don’t want our students to rely on a meaningless rule or procedure. We want them to actually understand fractions.

So how do we ensure that our students develop this fraction sense rather than having to rely on meaningless rules?

## Use Manipulatives and Visual Models

Fractions are an abstract concept for many kids, especially since they may not have much real-life experience with fractions yet. But concrete manipulatives can be a game-changer, making fractions easy to visualize and understand.

I love the circular foam fraction pieces for students to explore concepts like fraction addition/subtraction and equivalent fractions. They also make improper and mixed fractions simple to visualize.

Another amazing manipulative for fractions is Cuisinaire rods. Look at the examples below for just a couple ways these can be used.

Another visual that I love for fractions is bar models. Bar models can be used to make simple calculations more conceptual, or as an effective problem-solving tool. See this post on Instagram for more information on how to use them.

## Paper Folding

Simple paper-folding activities can take fraction concepts from abstract to concrete for your students. There is some prep involved to get these paper pieces ready for students, but the actual act of your students creating the fraction pieces will be well worth it.

To prepare for this activity each student will need several different square pieces of paper. I like to have different colors. In this picture, I used black as one whole. Then students can fold the blue piece in half. Each of these pieces represents one-half. The pink piece was folded in half, and then in half again. These represent one-fourth.

The act of folding and cutting is powerful, because it helps reinforce that one-fourth is half of one-half, one-eighth is half of one-fourth, etc.

BUT! Here’s the important part. You may be tempted to have students label the pieces as 1, 1/2, 1/4, etc. However, using them unlabelled will allow for far more deep thinking. For example, consider how these tasks might look:

• If the black piece represents 4, what does the blue piece represent? How about the pink piece?
•  Show one-half in three different ways.
• How does the orange piece relate to the black piece?
As you can see, using these pieces unlabelled will allow for some tremendous opportunities to rationalize and think deeply about fractions.

## Conduct Whole Class or Small Group Fraction Talks

Simply talking about fractions can have a profound impact on students’ understanding. This can be done in a whole class or small group setting and requires no prep or special materials.

For example, you could simply draw an image on the board, like the one here, and ask students what they notice about the drawing.

If students are stuck for ideas, prompts like these could help get the conversation started:

• What equations could we write to represent this drawing?
• How are these circles the same and different?

If you own my Math Conversations number talk resources, you’ll also find some great fraction talk slides in there.

Think of all the possiblities that students might come up with for this question. Maybe it represents 8 groups of one-fourth.

Maybe it represents two wholes and 8 groups of three-fourths.

When we start looking at how students might group the circles to add them together, there are loads of different options.

## Count By Fractions

Just like we can count by 1s, 2s, 5s, etc, we can count by fractions! This helps students see fractions as numbers.

I’ve made a few videos that you can use in your classroom to help your students make connections between the fractions and the visual representations.  See all available videos here.

## Make Fractions Meaningful and Relevant to Real Life

There is no better way to encourage true understanding than to relate fractions to how they are actually used in real life. Just think of all the amazing fraction skills we learn by baking! Here are just a few other examples of real-life experiences we can use to help our students understand fractions:

• Sports statistics
• Discounts at a store or restaurant
• Time (half of an hour, etc.)