Fractions

The teaching and learning of fraction concepts is often quite complex. Many teachers were not themselves taught the critical mathematical concepts underlying fractions when they were students. (Remember the tricks?) Even in their professional training, many teachers have not had opportunities to engage in deep learning dedicated solely to fractions. Although understanding and mastery of fractions have critical implications for mathematical proficiency, these concepts and skills are not consistently prioritized in teacher preparation or professional development. 

Further, the world around us bombards our students with images and language about fractions that work against our efforts. Have you ever heard someone say, when splitting a treat, “I want the bigger half!”? By definition, however, halves are equal. Imagine how confusing that language is for students beginning to build fraction understanding. They see drawings of fruit pies and pizza pies and are asked repeatedly to shade in parts of these pies. Does this help them see that a fraction is a number in and of itself, or does it reinforce the incorrect belief that a fraction is only a piece of a number, just a numeric slice of a whole pie?

Many students struggle with fractions, but students of color, students from families experiencing poverty, and English learners are less likely to have access to effective instructional practices, appropriate individualized supports, or teaching practices and materials that reflect their identities. To implement the study of fractions more equitably, we must consider student supports, culturally relevant content and practices, and aligned instructional materials. This means that educators must have a deep knowledge of fraction content and instruct in ways that value all students’ backgrounds, languages, cultures, points of view, knowledge, and skills. You’ll find these essential elements of teaching fractions throughout this collection.

Supporting Social, Emotional, and Academic Development in Mathematics. It is clear that not only must attention be spent on fraction understanding and students’ academic development but we must also attend to their social and emotional needs. In this document, you will find a more detailed description of how to do this, including sample actions to support student agency, identity, and belonging.

Coherence Map. The Coherance Map was incredibly useful in the design of this fraction learning experience. Here is a brief video, created by the Washington Core Advocates, that highlights the Coherence Map as a tool.

Coherence Map Fraction Activity. Use this activity to look at standards across grade levels. Within each standard, spend some time reading the focus standard, excerpts from the Progression document relevant to that standard, and tasks that fall within the standard. Consider: what are the connections between standards and the downstream implications of students understanding fraction value based on unit thinking?

Fraction Guidance for Educators.  Teaching of fraction content across individual classrooms and schools can vary dramatically. If your students seem to stumble when working with fractions, they might be missing some foundational fractions concepts. This guidance document is designed to help you identify some traditional practices that may be impeding student learning, and to provide ideas for alternate approaches. 

If you pose the question, “Are fractions numbers, and how do you know?” you might be surprised by the responses and rationales you get. The misconceptions you will find in these answers are indicative of what makes both the understanding and teaching of fractions complex. Throughout the following grade-level collections of tasks, you’ll find resources to support the thinking behind confident (and accurate) answers.

Yes, a fraction is a number because it may be placed on the number line.

As the story of fractions unfolds, it is important to stay connected to the progression laid out by the standards themselves, dig deeply, and allow for exploration and sensemaking. The unit fraction plays a critical role in this learning and is featured prominently within each grade-level collection. The grade-level collections intentionally highlight the number line over bar models and circular models to emphasize fractions to prior work with whole numbers, and do not include every NF standard or fully address the aspect of rigor in a single grade.

Coaches and instructional leaders do important work to support teachers and students engaging with fractions content. The resources below are intended to help ensure high-quality professional learning and coaching.

Question the Image Fraction Activity.  Use this professional learning activity to examine and discuss possible images and visuals you and your students may encounter in fraction units of study. Are the fraction images students are presented with supporting their learning or impeding their understanding?