Fractions: From Foundations to Operations

Methods and materials to teach fraction operations for meaning

Learn instructional methods and receive ready-to-go resources to help upper elementary and middle school students understand and retain fraction operation concepts, while deepening the understanding of basic fraction concepts. This course is designed to take you step-by-step through teaching the fraction operations both conceptually and procedurally, while incorporating basic fraction concepts.

Yes, You Can!

You CAN help your students feel comfortable with fractions!

Without feeling 

  • overwhelmed 
  • stressed, OR
  • deciding to 'just let them use a calculator.'

Do You LOVE Teaching Fraction Operations?

Or do you feel like fractions are a nightmare?

Every time they pop up, your students might freeze and say things like 

  • "I can't do fractions."

  • "There's a fraction...what do I do???"

  • "I hate fractions!"

  • "I have no clue."

And then, maybe they give up. They write something on their paper that has fractions in it and they try to move on. 

OR, they beg to use the calculator (even if they aren’t quite sure HOW to enter the problem into the calculator). 

And sometimes, being frustrated, you do let them just use the calculators, because you have to move on… have SO much to cover…you don’t have time to get to the root understandings of all the fraction things….and the students will eventually use the calculators for fractions anyway.

If your 5th, 6th, 7th, or even 8th-graders are having trouble with fraction operations, it’s time to switch things up.

Why is Teaching Fraction Operations Such a Challenge??

For starters, there’s a good chance you were never taught HOW to teach fractions and fraction operations!

A survey of math teachers revealed that their undergraduate programs didn’t really prepare them to teach math in general, much less prepare them to teach fraction operations with a conceptual approach.

Many teachers stated that they learned how to teach math from other teachers….and when you’re a new teacher, it can be easier to just teach the way they other teachers are teaching……there’s so much to get used to when you start teaching.

But are other teachers' fraction operations methods teaching students procedures or concepts?

In Number Talks, Fractions, Decimals, and Percentages, the authors cite a study by Li and Smith (2007) that stated:

  • 93% of prospective middle school teachers could solve 7/9 ÷ 2/3 procedurally

  • BUT only 52% could correctly answer ‘How many 1/2 are in 2/3?’

  • Teachers’ lack of conceptual understanding affects students’ understanding of what fraction division means

Fractions ARE Hard

Truthfully, many students struggle with fractions or fraction operations at some point. 

You probably see this struggle every year.

(And the past couple of years have NOT helped!)


One study of Algebra 1 students (81% of whom had strong parental support) found:

  1. about 48% couldn’t find the sum of 5/12 and 3/8
  2. their most common errors included: 
  • not being able to find a common denominator
  • adding numerators and adding denominators

If students are taught procedurally rather than conceptually, they can easily get confused as they learn about new operations. 

And many of your students may have been taught with just procedures before they came to you.

BUT, it's not too late to help your upper elementary and middle school math students get on the right track with their fractions.

If you want to help your students...

  • Understand what fraction operations mean

  • Successfully complete and explain operations with fractions 

  • Improve their fraction flexibility

  • Retain their understanding of concepts throughout the year

  • Develop a deeper understanding of number relationships

  • Feel more confident and less stressed when they encounter fractions in other contexts...

                                                    …you’re in the right place.

Who is this course for?

Before I share all the details, you're probably wondering if this course is a good fit for you.

This course is for you if you're an upper elementary or middle school math teacher and... 

  • you find yourself looking for fraction tips every year, OR

  • you're looking for new ways to teach any of the fraction operations, OR 

  • your students have fraction gaps you're not sure how to address, OR 

  • you want your students to develop a deeper understanding of what fractions are and what fraction operations mean, AND

  • you're willing to start 'weaving' fractions into math class when you aren't 'teaching fractions'

Thank you for this course!

" I am the Middle School Math Instructional Coach for a small K-8 district and will definitely be sharing these two methods with our teachers. Thank you for this course!"

Judy G

Instructional Coach

I am almost done with the course and have thoroughly enjoyed it! My two biggest take-aways were the Ladder Method and dividing fractions using the Common Denominator. I am the Middle School Math Instructional Coach for a small K-8 district and will definitely be sharing these two methods with our teachers. Thank you for this course!

This course is for you if...

  • You find yourself feeling frustrated because your students don't seem to understand what fractions even ARE. You want to minimize those understanding gaps while teaching your curriculum.

  • You're teaching fraction operations for the first time (or 2nd or 3rd!) and are looking for strategies to help your students learn both the meanings and the processes.

  • Teaching fraction operations isn't in your curriculum, but you ALWAYS have to review them because of the other contexts that require students to know fraction operations (like solving equations). Maybe you're looking for new ways to approach this.

  • You've been teaching fraction operation 'rules' because that's how you were taught, and you want to learn strategies to teach fraction operations differently.

  • You're an instructional coach, looking for new strategies to share with your teachers.

  • You want to save the planning time you spend searching here and there for fraction tips and resources that might help your students. You need a program with methods and materials all in one place.
  • You're ready to invest in your development as a math teacher.

What's Included:

35 video lessons covering:

  • fraction basics 
  • how to incorporate review of the basics into the teaching of operations
  • various methods for teaching all four fraction operations
  • how to incorporate representations into teaching fraction operations

90-page course workbook 

  • download as one whole book and bind the pages OR download them separately as you work through each lesson

45-page student workbook

  • includes 17 student activities from the lessons plus organizer and notes pages
  • pages can be downloaded as one whole book or you can download them as you work through each lesson

12 Hour Professional Development Certificate

  • provided upon course completion

In this course, you'll learn about...

Including representations along with computation when teaching fraction operations, relying less on just teaching the 'rules'

Activities that help students explore fractions and fraction operations to find meaning.

Weaving fractions into class when you aren't 'teaching fractions,' to reduce time gaps student often experience before getting back to fractions at a new grade level.

Methods and materials to address students' gaps and difficulties with basic fraction concepts.

Course Curriculum

  • 1

    Welcome to the course!

    • Welcome!

    • How to use this course

  • 2

    Module 1: Helping Students Master Fraction Basics

    • M1 L1: Introduction to Teaching Fraction Operations

    • M1 L2: Improper Fractions and Mixed Numbers

    • M1 L3: Using the Ladder Method

    • M1 L4: Comparing Fractions

    • M1 L5: Simplifying Fractions: 3 Methods

  • 3

    Module 2: Adding and Subtracting Fractions with Unlike Denominators

    • Module 2 Overview

    • M2 L1: Eliminate the Butterflies

    • M2 L2: Fraction Addition & Subtraction: What Does It Mean?

    • M2 L3: Estimating

    • M2 L4: Finding Least Common Denominator – Three Methods

    • M2 L5: Adding & Subtracting Unlike Fractions

    • M2 L6: Adding Mixed Numbers

  • 4

    Module 3: Subtracting Mixed Numbers

    • Module 3 Overview

    • M3 L1: Subtracting with Mixed Numbers "Groundwork"

    • M3 L2: Using Partial Differences

    • M3 L3: Subtracting with Regrouping

    • M3 L4: Subtracting With Improper Fractions

  • 5

    Module 4: Multiplying Fractions and Mixed Numbers

    • Module 4 Overview

    • M4 L1: Fraction Multiplication: What Does it Mean?

    • M4 L2: Multiplying Whole Numbers and Fractions

    • M4 L3: Multiplying Fractions by Fractions

    • M4 L4: Multiplying Fractions and Mixed Numbers

    • M4 L5: Multiplying Mixed Numbers by Mixed Numbers

  • 6

    Module 5: Dividing Fractions and Mixed Numbers

    • Module 5 Overview

    • M5 L1: Fraction Division: What Does it Mean?

    • M5 L2: Dividing Whole Numbers and Fractions

    • M5 L3: Common Denominators to Reciprocals

    • M5 L4: Dividing Fractions by Fractions

    • M5 L5: Dividing Mixed Numbers

  • 7

    Module 6: Fitting it All In

    • M6 L1: Summary of Operations

    • M6 L2: Fractions in Other Contexts

    • M6 L3: Resources & Fitting Fraction Concepts In

    • Closing Lesson

  • 8

    QA Session Recordings

    • QA Session Links

    • QA Session 1

    • QA Session 2

    • QA Session 3

    • QA Session 4

"This course is excellent for anyone who teaches middle school math!"

The first teachers are finishing up this course and this is what they have to say...

5 star rating

Great Course

Judith Goodfriend

This course is excellent for anyone who teaches middle school math. Whether a new teacher or seasoned veteran, there are great ideas and excellent goodies to...

Read More

This course is excellent for anyone who teaches middle school math. Whether a new teacher or seasoned veteran, there are great ideas and excellent goodies to use in the class.

Read Less
5 star rating

For Newbies & Veterans

Jennifer Jaques

Whether you are new to teaching fractions, are just looking for a better understanding of fractions and teaching them, or just need a good refresher. This c...

Read More

Whether you are new to teaching fractions, are just looking for a better understanding of fractions and teaching them, or just need a good refresher. This course is great from beginning to end.

Read Less
5 star rating

Thorough Course

Laurie Schorno

This course covered everything from basics to complex. The speed of the course was perfect, especially since you could stop/review as needed. I appreciate th...

Read More

This course covered everything from basics to complex. The speed of the course was perfect, especially since you could stop/review as needed. I appreciate the additional resources AND the ability to come back to refresh!

Read Less
Watch Intro Video

Check out a snippet from Module 4, Lesson 4 Multiplying Fractions & Mixed Numbers

Bonus Items

Over 25 student resources to help you implement methods from the course. 

These include:

  • notes pages
  • number lines
  • fraction strips
  • problem solving
  • fraction cards 
  • game ideas

AND two special resources for incorporating fractions on a daily basis:

  • 120 Days of Fraction Spiral Review
  • Fraction Operations Math Dates

Four bonus vidoes with over an hour of additional content:

  • Teaching Decimal Operations
  • Fraction, Decimal, Percent Conversions
  • Problem Solving Strategies
  • Using Spiral Review


  • How is this course presented?

    Each lesson includes a prerecorded video, with teaching strategies and examples. Note-taking guides are provided for each lesson, along with student versions of the examples used in lessons.

  • Do you accept purchase orders?

    Yes. Please email me at

  • What if I don't teach all the fraction operations? Is this still for me?

    Yes! You may only be required to teach fraction division (as I did in 6th grade), but you may end up reteaching addition, subtraction or multiplication when students encounter fractions in other contexts (like solving equations). You may have NO fraction operation instruction in your curriculum, but still find that you need to teach them in 'non-fraction' contexts.

  • Will I receive a certificate of completion?

    Yes! When you finish the course, you'll receive a certificate showing you completed 12 hours of online learning.

  • Will I be able to access the course materials right away?

    Yes! All modules will be available as soon as you enroll and you can access any lessons and resources immediately.

  • What if I have questions during the course?

    I am always available, via email or in the course discussion area on Thinkific.

  • I'd like to help my child with fractions and fraction operations. Would this course be helpful?

    Definitely! If you're a parent supporting a child who would benefit from supplemental work with fraction concepts (or you're a homeschooling parent), this course will be helpful.

Money-back Guarantee

I hope you'll love this course, but if you work through the first module or two and feel the course just isn't right for you, you can receive a refund within 7 days of purchase.

I can't wait to share the strategies that helped my students. I'm excited to provide you with everything you need to help your students and save you precious planning time during the year! Let's get started on this fraction journey together:-)