By Kathryn Chval, John Lannin, Dustin Jones, Barbara Dougherty

Do your students suppose that 1/3 is greater than 1/2, since 3 is greater than 2? Do they believe that having “halves” means having two, and only two, congruent “pieces” of a whole?

What tasks can you offer — what questions can you ask&#151to determine what your students know or don’t know — and move them forward in their thinking?

This book focuses on the specialized pedagogical content knowledge that you need to teach fractions effectively in grades 3–5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions — not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts.

Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of fractions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.

About the Series:

You have essential understanding. It’s time to put it into practice in your teaching.

The Putting Essential Understanding into Practice Seriesmoves NCTM’s Essential Understanding Series into the classroom. The new series details and explores best practices for teaching the essential ideas that students must grasp about fundamental topics in mathematics&#151topics that are challenging to learn and teach but are critical to the development of mathematical understanding.

Classroom vignettes and samples of student work bring each topic to life, and questions for reader refl¬ection open it up for hands-on exploration. Each volume underscores connections with the Common Core State Standards for Mathematics while highlighting the knowledge of learners, curriculum, understanding into practice, instructional strategies, and assessment that pedagogical content knowledge entails. Resources and tasks are available at www.nctm.org/more4U.

Maximize the potential of student-centered learning and teaching by putting essential understanding into practice