Rethinking Fractions

Introducing Rethinking Fractions: 8 Core Concepts to Support Assessment and Learning 

This resource will help students to develop a deep understanding of

• unit fractions (the base of all fractions); and
• the eight core concepts (the keys to unlocking fractions understanding).

For educators, this resource will help you to assess students’ understanding and possible misconceptions via the use of targeted, field-tested questions and recommended next steps that

• reveal student understanding; and
• respond to student needs (with precise and differentiated tasks and instruction).

The 8 Core Concepts

Eight core concepts form a trajectory of learning that moves generally from foundational to more complex ideas. The trajectory is designed to help students form strong schemas and mental representations of fractions, allowing them to work with increasingly difficult fractions ideas with understanding.

Core Concepts 1 to 4 lay a strong foundation for understanding fractions, while Core Concepts 5 to 8 allow students to apply this understanding to more complex thinking about fractions. Although the core concepts move in a direction of increasing complexity, they do not act as a linear prescription for learning. Rather, relationships across the core concepts allow us, as educators, to identify students’ needs and support their learning by moving among concepts.

What's in the Book?

The book consists of two sections.

Section A

Chapters 2 through 4 give you background information on why fractions are important and the long-term value of teaching fractions with an emphasis on unit fractions; the types of reasoning that support fractions understanding; and an overview of each of the eight core fractions concepts that are developed in the book.

Section B

There are eight core concepts in this resource. Each concept is explored in its own chapter that includes the following components:

• A detailed explanation of the core concept
• Two or more quick-to-use assessment questions to gain a better sense of what students understand about the concept. Sample student responses provide insights into how students might respond to a question and what their response may tell you about their understanding. Based on student responses, next steps outline suggestions for follow-up and point to a task (or tasks) to extend student understanding.
• Two or more classroom tasks that focus on deepening student understanding of the core concept. These tasks include:
• an overview;
• a description of the mathematics in the task; a clearly defined task sequence;
• questions to pose during the task;
• precise instruction notes;
• suggestions of what to look for as students engage with the task; and notes about what we observed during field testing.

What’s on the Website?

The website is accessed via a unique code that is printed on the inside front cover of your book. It contains both necessary and supplementary material to the book, and includes

• line masters with the individual assessment questions from the book as well as parallel questions that can be used for variety;
• line masters needed to complete the tasks;
• full assessments, with support to help you choose the right assessment according to your goals and the age/stage of your students;
• tools to analyze student results from the assessment questions;
• a glossary of selected mathematical terms used in this book
• curriculum maps that identify how the core concepts are aligned with mathematics curricula across Canada as well as with NCTM standards.