Standards for Mathematical Practice

Multiple Interpretations of Fractions

Jonathan Brendefur describes how he helps teachers understand and teach different interpretations of fractions. He explains the importance of explicitly teaching about various interpretations and discusses how number lines can be used at each stage.

FEATURING: Jonathan Brendefur, Boise State University; and Eliza Hart Spalding School of Math and Technology (ID)

SOURCE: Doing What Works

Making Sense of Computational Procedures

Watch this multimedia overview to learn about the importance of focusing on conceptual understanding and procedural fluency with fractions operations and how they connect. The overview describes recommended instructional practices for developing understanding of computational procedures and ways to address typical student misconceptions.

SOURCE: Doing What Works

Learning to Think Proportionally

James Lewis discusses what it means to think proportionally and offers examples from everyday contexts. He describes the conceptual progression toward working with cross-multiplication and demonstrates using ratio tables as a tool for solving problems.

FEATURING: W. James (Jim) Lewis, University of Nebraska - Lincoln

SOURCE:  Doing What Works

Dumb Friends League Problem

Students work on this set of real-world problems about placing homeless dogs in animal shelters. The problems require comparison of fractions as seen in Grade 5 Number Talk.

SOURCE: Doing What Works

Grade 5 Number Talk

Follow a teacher’s lesson on adding and subtracting fractions using fraction equivalents and relationships. Children share their strategies for solving the problems described in Dumb Friends League Problem.

FEATURING: Cindy Matthews, Tollgate Elementary School (CO)

SOURCE: Doing What Works

Fractions on a Number Line

A fourth-grade teacher describes students’ challenges in moving from a part-whole interpretation of fractions to seeing them as numbers. Student pairs work on locating fractions and decimal and percent equivalents on a number line.

FEATURING: Vonda Franklin, Eliza Hart Spalding School of Math and Technology (ID)

SOURCE: Doing What Works

Multiply or Divide?

This staff development session provides suggestions for helping students understand fraction multiplication and division concepts. Follow the full session through Focus on Fraction Operations and Multiply or Divide Problems.

FEATURING: RMC Denver Professional Development

SOURCE: Doing What Works

Multiply or Divide Problems

Participants in the Multiply or Divide? staff development session on fraction operations worked with this problem set to strengthen their understanding of fraction multiplication and division concepts. See Focus on Fraction Operations for additional background.

SOURCE: Doing What Works

Focus on Fraction Operations

This PowerPoint covers the content of a staff development session for math coaches and teachers about how to teach fraction operations. Multiply or Divide? shows a portion of the workshop in which participants are working on the sample material, Multiply or Divide Problems.

FEATURING: RMC Denver Professional Development

SOURCE: Doing What Works

Ratio, Rate, and Proportion Problems

This collection of twelve ratio, rate, and proportion problems was contributed by the University of Nebraska's James Lewis and includes his comments on solutions and notes about the potential difficulties students may face.

SOURCE: Doing What Works