Standards for Mathematical Practice

Ratio Problems

Participants in the Understanding Ratios development session worked with this set of problems to strengthen their conceptual understandings. See Focus on Ratios for additional background.


SOURCE: Doing What Works

Understanding Ratios

This professional development session for teachers and coaches demonstrates strategies for teaching ratio, rate, and proportion concepts. Follow the full session through the PowerPoint, Focus on Ratios, and the set of Ratio Problems.


FEATURING: RMC Denver Professional Development

SOURCE: Doing What Works

The Concepts Behind Operations

David C. Geary describes how to build students’ understanding of the concepts underlying operations with fractions, common misconceptions that children have, and what can be learned from their errors.


FEATURING: David C. Geary, University of Missouri

SOURCE: Doing What Works

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