A teacher in my Facebook group described number stories with fractions as a double Achilles heel. And it’s the perfect analogy. Teaching fractions on their own can be challenging enough. And many students already struggle to understand what a story problem is asking when dealing with whole numbers. Putting them together can feel like a recipe for disaster.

Today, I’m breaking down one approach to help your students with their reading comprehension of number stories with fractions.

The challenge

There are a few struggles that come up every time I work with teachers. The most common one? Instead of slowing down to figure out what the problem is asking, their students pluck out the numbers, pick an operation, and solve. 

To ensure student comprehension, we have to slow them down and engage in conversations about what’s happening in the story. That’s why many of the resources I’ve created involve question stems. One of the most critical discussions you can have is around the math main idea.

The math main idea

Kids are used to talking about the main idea when it comes to reading texts. It’s our job to help translate this skill to reading math stories. The math main idea refers to the action or operation that occurs based on the given situation in a story problem. 

If you’re new to Structures of Equality (SoE), I encourage you to pause and read about how to find the math main idea of a number story. You can also see it in action in this brief video.

Once students are familiar with finding the math main idea in number stories with whole numbers, you can create explicit connections to problems with fractions. Rather than being overwhelming, these problems become manageable. Let’s dive into an example.

Example number story with fractions

A 5th-grade teacher shared this number story with me. She asked me how to help her students with their comprehension.

I have 3 1/4 cups of flour. If I use ½ of it for a recipe, how much is left?

If your students are like most kids I’ve worked with, they get a deer-in-the-headlights look as soon as they see fractions. In this problem, we can take the fractions out without impacting comprehension. (This isn’t always true with fractions so think through each number story carefully before using this strategy.)

Scaffolding for understanding

Here’s the progression I suggest to approach this problem. First, you can show the students the number story without the numbers. Ask questions such as:

• Who is this story about?
• What’s happening in the story?
• Can you visualize this story in your head?
• What’s the math main idea? (They are using part of the flour. A total is being decomposed.)

Once it’s clear that your students have the math main idea, it’s time for more context. As a reminder, this was our original problem:

I have 3 1/4 cups of flour. If I use ½ of it for a recipe, how much is left?

It’s likely the fractions will still be overwhelming at this point. In the example below, I replace 3 ¼ with a whole number and ½ with the word half. This is way less scary for kids but still has the same main idea.

If we hadn’t already discussed it, I would ask them what structure we could use to represent this situation. After we concluded Parts Equal Total, we would visually represent this version of the problem.

Notice the labels for the parts differentiate which part of the flour was used and which part of the flour is left. I’d continue to encourage kids to picture this happening in their heads. Now, we can introduce 3 ¼ and make explicit connections between the visual representation that used a whole number.

By this stage, your kids will likely have a much clearer understanding of what the problem is asking. This is where it might start to get a little tricky. Instead of the total being shown as one whole, we decompose 3 ¼ into 3 + ¼, or  1 + 1 + 1 + ¼. 

This representation helps students see the ¼ cup and its relationship to 1 cup. It also allows them to see ½ of ¼, solidifying conceptual understanding around the multiplication of a fraction and another fraction.

Now, they have multiple access points to approach this problem and can use the strategy of their choice to come up with a solution.

A few tips

I believe in quality over quantity. Developing reading comprehension and helping students make sense of math stories is not a quick or easy task. Building your kids’ confidence when teaching fractions, especially in the context of number stories, takes time. 

• Give your students time to grapple with one problem as opposed to multiple problems.
• Talk through what’s happening in number stories without solving them.
• Take your time. This problem can be done in one class period or over multiple days as a warm-up.

Conclusion

Breaking problems down so they are more manageable is an effective way to help your students understand number stories with fractions. By taking the numbers out, you can help students focus on the context first. Then, gradually build your way back to the problem as originally written. It won’t be quick or easy, but it will be worth it.

If you haven’t implemented SoE in your classroom yet, it will take additional time for your students to internalize the ideas above. And you’ll probably have lots of questions as you get started. I’d love to have you as part of our Facebook community where I’ll personally answer every question you have. Join us!