# Mathematics

Short Name:
Math

## 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 Conceptual Basis for Fractions

This multimedia overview introduces how children’s intuitive understandings of sharing and proportion can serve as a foundation on which to build formal instruction of fraction concepts.

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

## Web Shots for Spiderman Problem

Students use the worksheet to record findings from exploration with Cuisenaire Rods as they build a foundation for working with equivalent fractions. Their work is shown in Solving a Real-World Fraction Division Problem.

SOURCE: Doing What Works

## Same Parts, Different Whole

A fourth-grade teacher’s lesson on finding fractional parts of rectangular arrays and a group of objects requires students to compare the same fractional parts of different-size wholes.

SOURCE: Doing What Works

## Fractions With Cuisenaire Rods

Students use the worksheet to record their explorations of equivalent fractions using Cuisenaire Rods. Their work is shown in Representations of Part-Whole Relationships.

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

## 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