The Power of Models to Help Your Students Really Understand Fractions

Have fractions ever made you feel stupid?  I feel like the answer to this question from the overwhelming majority of us is a resounding YES!  I’ll never forget the day fractions made me feel seriously stupid.  I was helping my dad with a woodworking project.  He needed a piece of wood cut and had pulled a tape measure down the length of the wood on one end.  He handed me a pencil and said, “hey Nat, can you make a mark at 15 ⅝ of an inch?”  Sure I thought, of course I could do that. And I should have been able to, but there I was, a 16-year-old straight A student, sweating with embarrassment as I desperately looked for a number on the tape measure that read 15 ⅝ only to realize that there was only 15 and 16.  I could find 15 ½, why couldn’t he have just asked for that one?!  Geez!  So many little black tick marks, none of them labeled!  How was a person supposed to know where ⅝ is?!  And how did my dad who went to school in 1950 something and I did not?!  

I’ll tell you how.  It’s because no one had ever taught me that fractions could be modeled with anything other than a shape and I had nothing to draw upon to help me reach the conclusion that the space on the tape measure between 15 and 16 could be divided into eight equal parts just like a circle could be divided into eight equal parts. I’m afraid this is still happening inside classrooms today and is one of the major culprits in our student’s lack of fraction sense and overall math proficiency.  

Advantages of a Model-Based Approach to Fractions

Remember, math proficiency is not just measured by computational or procedural skills, but rather that combined with their ability to interpret, solve and explain real world problems. Two critical things can help change how students approach, and ultimately understand, fractions:

1. Understanding that a fraction represents part of a whole—and that “whole” can be anything, not just a shape.
2. Learning fractions through multiple models, each with specific strengths for solving different kinds of problems.

When students use different types of models to visualize and manipulate fractions, it bridges the gap between abstract numbers and relatable concepts. It’s not about memorizing rules but developing a fraction sense that sticks. 

3 Types of Fractions Models

Here are three types of fraction models every teacher, tutor, or homeschooling parent should use to help build confident learners. Each one has its own advantages in helping students visualize important fraction concepts, and together they are a powerful set of tools to create a deep understanding of fractions overall. 

#1 - Area Models (aka Shapes)

The area model is perhaps the most familiar to us. These are visuals where a shape—typically a circle, rectangle, or square—is divided into equal parts. 

Best Applications: Area models are perfect for solving fraction problems where the whole is concrete and can be represented by a shape.  

Example Problem: Emma baked a rectangular tray of brownies and cut them into 12 equal pieces. She ate 3 pieces, and her brother ate 2 pieces. What fraction of the brownies did they eat together? Use an area model to represent the parts of the brownie they ate and the parts that are left.

#2 - Number Line Models

Number line models divide each interval between whole numbers on a number line into equal parts with fractions marked along the way. Number line models help students see how fractions relate to one another and to whole numbers. 

Best Applications: Understanding how to label fractions on a number line is a powerful tool for comparing and ordering fractions.  When it comes to fraction word problems, number lines are extremely helpful for solving problems that involve finding fractional amounts of more abstract concepts like distance and time.

Example Problem: Emma jogged along a trail that was ⅓ of a mile long.  If she jogged the length of the trail 6 times, how many miles did she jog?

#3 - Set Models

Set models take fractions beyond shapes and numbers into real-world collections. Here, a “whole” is represented by a group of objects, like counters, cubes, or even fruit. Set models teach students that fractions are part of any set of items—not just shapes or numbers.

Best Applications: Teach students to sketch out a set model when solving problems that ask them to find a fractional amount of a group of objects or even people.

Example Problem: Camryn has 9 friends attend her birthday party.  ⅓ of her friends gave her money for her birthday present.  How many friends gave Camryn money? 

When students have the right fraction sense, suddenly, the world makes a whole lot more sense. They can not only solve textbook problems—but they can also apply that knowledge to the world around them and even understand measurements on a tape measure like 15 ⅝ inches. 

Resources for Teaching Fractions

Whether you're a teacher or homeschooler, we’re here to help you teach fractions with models.  Check out our free fractions resources as well as our 3rd grade level fractions lessons that provide you with everything you need to teach these concepts including fractions guides, posters, anchor charts, Google Slides lessons ready for you to teach and lots of NO PREP worksheets.

• Fractions with Area Models - 3rd Grade Lesson Bundle
• Fractions on a Number Line - 3rd Grade Lesson Bundle
• Fractions as Set Models - 3rd Grade Lesson Bundle
• 3rd Grade Fractions Super Bundle with 6 Complete Lessons