Building Fraction Sense in Middle School

Fractions are an important foundation for higher-level math but can be challenging for students. For middle school educators, a key instructional task is helping students conceptually understand fractions—specifically, that fractions can be placed on a number line, that their size depends on the relationship between the numerator and denominator, and that there are infinitely many fractions between any two. The Teaching Fractions Toolkit offers practical resources to meet that need. Developed as part of a series of ten professional development toolkits from the Institute of Education Sciences, it is designed to help teachers strengthen fractions instruction with strategies they can use right away.

In this blog, learn about the core components of the toolkit and explore how it can support continuous improvement in fractions instruction—starting with just one hour a week.

Grounded in Evidence, Designed for Classrooms

This toolkit is built around three key recommendations from a What Works Clearinghouse practice guide developed by researchers and expert educators:

Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
Help students understand why procedures for computations with fractions make sense.
Develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems.

Toolkit at a Glance

Designed to be practical, flexible, and implementation-ready, the Teaching Fractions Toolkit includes six modules, organized into a total of 12 one-hour professional learning sessions, as well as an opening orientation. The toolkit also includes 12 hours of self-paced activities that teachers complete between professional learning sessions.

Each module includes opportunities to explore math tasks, analyze student work, plan and implement recommendations, complete interactive online activities. Professional learning is supported by ready-made tools such as videos, editable slide decks, lesson templates, teacher reflection tools, and formative assessments. The goal is to help teachers meaningfully apply evidence-based strategies in their own classrooms.

Module 1: Fractions on a number line

In this module, teachers explore strategies for helping students transition from whole-number reasoning to fraction reasoning. For example, participants might engage in the Fractions on the Number Line activity to explore how visual models can reinforce students’ understanding of fractions as numbers.

$Image of teacher pointing to pie chart, with text that reads: In Meeting 1A, teachers learn how to emphasize visual models and the number line to help students develop fraction understanding.$

$Image of teacher pointing to number line, with text that reads: In Meeting 1B: teachers learn how to use formative assessments and analyze student work to check for student understanding of fractions.$

Module 2: Understanding fraction addition and subtraction

This module focuses on addition and subtraction of fractions, emphasizing conceptual meaning before procedures. For example, participants might engage in the Estimating Fraction Sums and Differences activity using an online app to explore how number line models and estimation strategies can reinforce students’ understanding of fraction addition and subtraction

$Image of teacher pointing to dry erase tablet with text that reads: In Meeting 2A: teachers learn how to use area models, number lines, and other visual representations to help students understand adding and subtracting fractions.$

Teacher pointing to an addition problem, with text that reads: In Meeting 2B: teachers analyze student work and further explore activities to support student learning.

Module 3: Understanding fraction multiplication and division

Module 3 explores using real-world contexts with plausible numbers and the use of visual representations to improve students’ conceptual understanding of procedures for multiplying and dividing fractions. For example, in this module, participants might engage in the Exploring Paint Coverage task to use area models and real-world contexts to make sense of fraction multiplication.

$Teacher pointing to chalkboard, with text that reads: In Meeting 3A, teachers learn about applying strategies to solve fraction computation tasks using visual representations and reflect on the use of real-world contexts in problem solving.$

$Image of teacher pointing to chalkboard, with text that reads: In Meeting 3B: teachers review student work and discuss strategies to address common fraction computation misconceptions.$

Module 4: Implementation of fraction computation

Module 4 continues the focus on fraction division, including exploration of visual representations used for fraction division tasks and predicting and judging the reasonableness of answers for fraction division problems. As an example, participants could work on the Traffic Jam task to apply double number line representations to support understanding of fraction division in a continuous context

$Teacher pointing to lesson plan, with text that reads: In Meeting 4A, teachers examine the role of estimation in making predictions and collaboratively develop a lesson plan on fraction division.$

$Teacher pointing to a fraction division problem, with text that reads: In Meeting 4B: teachers discuss their experiences implementing the lesson plan created in the previous meeting and further explore visual representations for fraction division.$

Module 5: Understanding ratio, rate, and proportion

Module 5 focuses on developing students’ understanding of proportional relationships and using visual representations to solve ratio and rate problems. Participants in this module can explore strategies such as the buildup and unit ratio approaches in the Mixing Paint problem to deepen conceptual understanding of ratio and proportion before introducing cross-multiplication.

Teacher pointing to chalkboard, with text that reads: In Meeting 5A:teachers learn strategies and visual representations to solve ratio, rate, and proportion problems.

Teacher pointing to chalkboard, with text that reads: In Meeting 5B, teachers deepen understanding of strategies for solving the ratio, rate, and proportion problems.

Module 6: Implementation of ratio, rate, and proportion

Finally, to prepare for implementing this kind of problem, participants engage in activities like Ratio, Rate, and Proportion Strategies to compare approaches across multiple problem contexts and identify common structures in ratio, rate, and proportion problems. Then, they debrief their experience -- both with this type of problem and the learning community as a whole!

Image of two teachers talking, with text that reads: In Meeting 6A, teachers explore ratios, rates, and proportions using multiple strategies for use across problem contexts and engage in collaborative lesson planning.

Teachers celebrating, with text that reads: In Meeting 6B: teachers discuss their experiences of trying ratio, rate, and/or proportion problems with students and wrap up and celebrate this professional learning experience.

How to Use the Toolkits

All of the IES toolkits are implementation-ready and designed for use in professional learning communities (PLCs), with options for individual use if needed. The toolkits include:

Teacher’s guide

The teacher’s guide provides session agendas, and all activities. It also includes self-reflection tools and planning templates.

Facilitator’s Guide and Slides

The facilitator’s guide and slides offer detailed instructions for leading each PLC session.

School Leader’s Guide

The school leader’s guide supports administrators in helping teachers implement the toolkit.

Toolkit Website

The toolkit website hosts editable slide decks, videos, and downloadable resources.

To put evidence-based strategies into practice between sessions, teachers have the opportunity to try new strategies in class, reflect on their practice, and meet with coaches or peers to discuss progress and set goals.

Access the full toolkit here.