# Reasoning & explaining (MP2, MP3)

## 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

## 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

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

## 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

## Build a Cafe

As seen in Cross-Multiply? Not So Fast, this PowerPoint presents a series of real-world problems that students need to solve using their knowledge of ratios.

SOURCE: Doing What Works