# Reasoning & explaining (MP2, MP3)

## Build-Up Strategies Worksheet

This worksheet provides practice problems that encourage students to use build-up strategies when working on ratio problems as shown in Cross-Multiply? Not So Fast.

SOURCE: Doing What Works

## Ratio

Students use counters or blocks to work out their responses to three problems and then represent their answers as shown in Cross-Multiply? Not So Fast.

SOURCE: Doing What Works

## Helping Students Debrief

Mark Driscoll provides practical advice on building students' habits of reasoning by structuring discussions using particular questions and written tools.

FEATURING: Mark J. Driscoll, Education Development Center

SOURCE: Doing What Works

## Monitoring the Problem-Solving Process

Listen to Sybilla Beckmann describe strategies for helping students monitor and reflect during the problem-solving process.

FEATURING: Sybilla Beckmann, University of Georgia

SOURCE: Doing What Works

## Developing Proportional Reasoning

This multimedia overview offers an introduction to students’ development of proportional thinking and its relationship to cross-multiplication. It describes recommended instructional strategies for solving problems related to ratio, rate, and proportion, including buildup and unit ratio strategies, and illustrates examples of real-world context for such problems. This recommended practice contains three tools to support the teaching and learning of ratio, rate, and proportion.

SOURCE:  Doing What Works

## Cross Multiply? Not So Fast

Eighth-grade co-teachers lead a class through activities involving ratios. Students use concrete materials, build-up strategies, and cross-multiplication to solve the real-world problems found in Ratio: Warm Up Activity, Build-Up Strategies Worksheet, and Build a Cafe: PowerPoint and Report.

FEATURING: James Ro and Jackie Price, Howard County Public Schools (MD)

SOURCE: Doing What Works

## Representing a Problem Visually

See how different groups of students use double number lines and other visuals to tackle "Frank's Problem," which involves figuring out the most efficient travel routes in terms of mileage.