Uncomplicating Fractions

December 3, 2024|Education, Math

As an educator, I took pride in my math-teaching background. Math and I weren’t always friends, though. Back in school, the only numbers I cared about were the ones I used to call friends (back when minutes were free after 9 p.m.) and the ones I earned for doing chores.

But teaching math changed everything—it made me like it…and even love it. Still, I could relate to students who didn’t feel the same way. One student, Devin (not his real name), hated division with every fiber of his being. And I’m not exaggerating. Whenever he brought division homework to me, he’d groan and mutter, “Ms. Ebonique, I hate division.” 

One day, Devin handed me a worksheet full of problems like 5÷6 and 10÷3—division problems with answers that were fractions. He was confused and already defeated before he started. I’d seen this reaction before. In fact, I’d heard a chorus of moans and groans from many students whenever fractions and/or division came up, but this moment solidified something for me. 

Spongebob Squarepants. ”Thinking Reaction GIF.” GIPHY.com. 20 Nov 2024. Click the image for link.

I needed to figure out two things:

1. Why do students typically struggle with fractions?

2. What are the best ways to teach them these skills, especially when it comes to dividing fractions?

After research, reflection, and experience, I have some answers. 

Part I. Understanding Fraction Interpretations

Students may struggle with fractions because they do not understand that there are different fraction interpretations. Fractions are numbers, AND they can also represent several ideas depending on the context. According to Teaching Student-Centered Mathematics. Grades 3-5 by Van de Walle, Karp, Lovin, and Bay-Williams (2018), students often encounter the following interpretations: 

1. Part-Whole: A fraction represents a part of a whole, like cutting a pizza into 8 slices and eating 3 slices (⅜​). 

2. Measurement: This involves identifying an amount of a continuous unit (length, area, volume, or time) and then comparing that amount to a whole unit that is equal to 1. Example: ½ of a mile. 

3. Division: This interpretation leads directly to equal shares. Fractions are division problems, like 5/4​, which means dividing 5 items among 4 groups.

4. Operator: Fractions act as instructions, like “find ⅓ of 9.” 

5. Ratio: A fraction can show the relationship between two quantities, like 2 red apples for every 3 green apples (⅔)

Recognizing these interpretations helps students make connections between fractions and their real-world applications.

Let’s dive into a practical way to think about fractions as “fair share” division and how to help students like Devin see them in a new light.

Part II. Fractions as Division Problems

Tabitha Carro. "Untitled." FlapJack Educational Resources. 20 November 2024. https://flapjackeducation.com/2013/03/comparing-fractions-with-play-do.html#front-page-2

At their core, fractions represent division. Recently, I discovered from a webinar hosted by Make Math Moments Academy that a division problem with 2 whole numbers can use the “fair-share” division concept. This concept recognizes problems like 4÷7 as # of items divided by # of sharers, i.e., 4 items being shared equally amongst 7 people. Another example is the fraction 5/4,​ meaning 5 sandwiches are being divided among 4 friends. But how does that translate to a fair share for each person?

Partitioning to Solve

Let’s start by visualizing. Picture 5 sandwiches divided among 4 friends.

• Mathematically, 5÷4 gives us the same result as the fraction 5/4​.

• To figure out one friend’s share, we can also think of it as ¼ x 5—we’re finding ¼ of the 5 sandwiches. 

• The result? Each friend gets 5/4​, or one and a quarter sandwiches.

This process helps students connect the ideas of division and fractions in a practical way.

Part III. Fair Share Division Word Problems

Here are two more word problems that reinforce the idea of fractions as “fair share” division, along with step-by-step solutions.

Problem 1: Sharing a Pizza

Six friends are sharing four pizzas equally. How much pizza does each person get?

Step-by-Step Solution:

1. Represent the situation as a division problem: 4÷6.

2. Write this as a fraction: 4/6

3. Simplify the fraction if possible: 4/6  = ⅔ 

4. Interpret the result: Each person gets ⅔ of a pizza

Problem 2: Splitting Candy

You have 9 pieces of candy to share equally among 5 friends. How much candy does each person get?

Step-by-Step Solution:

1. Represent the situation as a division problem: 9÷5.

2. Write this as a fraction: 9/5

3. Convert the fraction greater than 1 to a mixed number: 9/5 = 1 4/5

4. Interpret the result: Each person gets 1 full piece of candy and 4/5 of another piece.

Why “Fair Share” Matters

Teaching fractions as “fair-share” division makes this abstract concept tangible. Students see fractions not as numbers that float in isolation but as solutions to real-world problems—like splitting pizzas, candy, or even time.

By grounding fractions in relatable scenarios, we can help students approach them with confidence and curiosity. Because, in the end, who doesn’t love a fair share? 

Do you have favorite strategies for teaching fractions? Share them in the comments!

References:

Lehman, Y., Orr, J., & Pearce, K. (2024, October 8). How to Teach Division Involving Fractions. Make Math Moments Academy. https://makemathmoments.com/division-fractions-1/?mc_cid=53d29d20a2&mc_eid=b3020c4144

Van De Walle, J. A., Karp, K. S., Lovin, L. H., & Bay-Williams, J. M. (2018). 12/Exploring Fraction Concepts. In Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (3rd ed., Vol. 2, pp. 216–249). essay, Pearson. 

Share this post: