Standards for Mathematical Content

Representations of Part-Whole Relationships

Listen to how a math coach works with second graders on fair sharing and fraction equivalence challenges. The lesson culminates with students exploring parts of a whole and equivalencies, completing Fractions With Cuisenaire Rods.


FEATURING: Sorsha Mulroe, Howard County Public Schools (MD)

SOURCE: Doing What Works

Recognizing Fractions as Numbers

Watch this multimedia overview explaining why number lines are recommended as a central representational tool to teach students about fractions and how teachers can help students understand fractions as numbers, relationships between fractions, and fractions as units of measure.


SOURCE: Doing What Works

Partitive and Measurement Fraction Problems

Dr. Brendefur uses two context problems to distinguish between partitive and measurement fraction problems. These two slides illustrate the differences between the two problems and demonstrate the approaches needed to arrive at the solutions. See the related media, Multiple Interpretations of Fractions.


SOURCE: Doing What Works

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

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