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Two practical strategies for unlocking fractions: A preview of the Teaching Fractions Toolkit

REL Midwest
May 21, 2024
By: Melinda Griffin, Belema Ibama-Johnson

A computational understanding of fractions in 6th grade lays the groundwork for later success in math, which in turn equips students for a range of in-demand careers in science, technology, engineering, and math (STEM). In this blog post, we highlight two evidence-based strategies teachers can use to help 6th-grade students demystify fractions and equip themselves for success in both math class and life. The strategies are from our forthcoming Teaching Fractions Toolkit, which is set for release in 2026. An immediate opportunity is available, however, for a limited number of schools and districts to receive advance toolkit resources and professional development at no charge by joining our study evaluating the toolkit.

Practical strategies for teaching fractions

Watch our Teaching Fractions Toolkit webinar to learn more about the practical strategies featured in this blog post."

The Teaching Fractions Toolkit offers actionable insights and practical strategies for implementing the recommendations in the What Works Clearinghouse (WWC) practice guide Developing Effective Fractions Instruction for Kindergarten Through 8th Grade. The strategies featured here relate to two of the five recommendations in the practice guide:

  • Recommendation 3 emphasizes the importance of helping students grasp the logic behind fraction computations.
  • Recommendation 4 underscores the need to cultivate students' conceptual understanding before introducing procedural methods such as cross-multiplication for solving ratio and proportion problems.

To address the recommendations, teachers can use these practical strategies to bridge the gap between students' conceptual understanding and procedural fluency when working with fractions.

Practical Strategy 1: Use tape diagrams to visualize fractions operations

The first strategy connects to Recommendation 3 in the WWC practice guide, which notes that providing a visual representation of a problem can help students "draw out" the solution. One way to do this is through the use of tape diagrams.

Practical strategy: Tape diagrams are helpful when considering the whole versus the parts of a relationship in contextual problems. Problem: A pitcher holds five glasses, and the serving size is 3/5 of a glass. How many servings are in a pitcher of orange juice? Tape diagram image: Gray bar segmented into five sections to represent 5 glasses of orange juice. Below this bar, is a second bar that is the width of one segment (1 glass of juice). This second bar is segmented into five sections, three of which are orange, to represent one serving (3/5 of a glass). Answer: 5 divided by 3/5 = 8 1/3. The pitcher (5 glasses) holds 8 1/3 servings or enough to serve 8 people

Students may have used tape diagrams when working with whole numbers in earlier grades, and the same approach can be helpful when working with fractions. In the example problem, students need to determine how many servings are in a pitcher of orange juice. The pitcher holds five glasses total, and the serving size is 3⁄5 of a glass. A student can use a tape diagram to visualize the whole (five glasses of orange juice) and the serving (3⁄5 of a glass).

After students map out the problem with a tape diagram, they can consider how their visual model relates to the formal notation (5 ÷ 3⁄5=?). In this example, there are 8 1⁄3 servings in 5 glasses of orange juice. Students can then reference the tape diagram to learn how to interpret a remainder in context, such as how many people this pitcher of juice would serve. In this case, the pitcher would serve 8 people as there is not enough juice for another full serving.

Practical Strategy 2: Use double number lines to visualize rate problems

This strategy connects to Recommendation 4 in the WWC practice guide, which suggests that students use and discuss alternative strategies for solving ratio, rate, and proportion problems. One approach is to use double number lines to visualize rate problems.

Practical strategy: When solving rate problems, use a double number line to help visualize time versus distance. Problem: You are in a traffic jam on the freeway and want to know how long it will take to reach the next exit.?You timed your progress and found you can travel 4 miles in 1 hour.?If you continue at this speed, how many hours will it be until you reach the next exit, which is 6 miles away? Double number line image 1: Top number line depicts miles and bottom number line depicts time. The tic marks indicate that 1 mile = 1/4 hour; 4 miles = 1 hour; and 6 miles = 1 1/2 hour. Double number line image 2: Shows an orange bar segmented into 6 sections. The first four sections are each labeled '0.25'. Above the bar, the first four sections are labeled as a group as 4 miles; all 6 sections are labeled as a group as 6 miles. Below the bar, the first four sections are labeled as a group as 1 hour and the last two sections as 1 1/2 hour Answer: 1 1/2 or 1.5 hours

As with tape diagrams, many 6th-grade students have previously encountered number lines when working with whole numbers. So moving to a double number line to visualize comparisons builds on a tool and strategies that many students already know.

In this example, students are in a traffic jam and need to determine how long it will take them to reach the next freeway exit (6 miles away) at their current speed (4 miles an hour). Students can use double number lines to visualize the time needed to reach the total distance.

As another example, students could use the same strategy to consider two students who read at different speeds (pages per minute). Using a number line, they could map out which of the students will first finish a 20-page book chapter.

Recommendation 4 in the WWC practice guide aligns with mathematical practice standards, such as persevering in problem solving, justifying one's own reasoning, and critiquing the reasoning of others. Through discussions with other students about how to solve a problem and whether their solutions make sense, students build their conceptual understanding of rates and proportions. This understanding is critical to moving into work with functions in high school algebra and exploring similar figures and trigonometric ratios in high school geometry.

Preview of the toolkit's components

The Teaching Fractions Toolkit will provide a suite of resources to help teachers learn and apply practical strategies and instructional approaches for fractions. Here's a peek at what's included.

Six professional development modules for 6th-grade math teachers support the use of evidence-based practices in fractions instruction. Each module includes synchronous and asynchronous activities as well as classroom resources to support lesson planning, student work analysis, the use of formative assessment probes, and reflection on classroom practice. In addition, teachers will learn to use interactive apps to visualize fractions operations.

Facilitator guide

This three-part image shows the cover of the Module 1 Facilitator Guide and two pages from the guide, showing the Meeting 1A agenda, resources, and facilitator directions

Participant workbook

This three-part image shows the cover of the Module 1 Participant Workbook and two pages from the working, showing Handout 1: Name the Point Exploration and the Module 1 Interim Activities

Resources for administrators and math leaders build educator understanding of the five recommendations in the related WWC practice guide as well as how to support teachers in implementing the recommendations. The resources include three informational videos, three handouts, a checklist for district and school conditions, and materials to support the facilitation of teacher professional development modules.

Interactive apps

This two-part image shows examples from the interactive app for Locating Fractions on a Number Line and Comparing Rational Numbers - Fractions.

Opportunity to partner with REL Midwest

School districts are invited to join REL Midwest's study evaluating the Teaching Fractions Toolkit to receive professional development and early access to the toolkit resources. This study will be conducted during the 2024/25 school year. Schools and districts will receive the toolkit professional development and resources at no charge. In turn, teachers and district leaders will help collect data to evaluate the implementation of the toolkit and its outcomes for teachers and students.

Participating 6th-grade math teachers will have opportunities to engage with experts in the field, gain knowledge about strategies and tools for teaching fractions, and help refine the toolkit resources.

"Very well worth it! You will get amazing insight into teaching various math concepts and interactive tools to help your students understand the why behind what they are learning. Highly recommend." -- 6th-Grade Teacher Participant

If you are interested in participating in this study, you can reach out directly to Jennifer Anthony at janthony@air.org or fill out our interest form to learn more.

Related resources

For more information on the Teaching Fractions Toolkit and our work in the region, browse the following REL Midwest resources:

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