# Standards for Mathematical Practice

## 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

## 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

## Number Lines

Yukari Okamoto describes the misconceptions that students have about fractions and how to help them understand fractions’ place in the number system. She demonstrates instructional approaches with number lines and number strips to expand beyond the part-whole approach to teaching fractions.

FEATURING:  Yukari Okamoto, University of California, Santa Barbara

SOURCE: Doing What Works

## Matching Visuals to Purpose in Problem Solving

Asha Jitendra shows and discusses the role of different types of visualizations in problem solving, especially their usefulness for students struggling with math.

FEATURING: Asha Jitendra, University of Minnesota

SOURCE: Doing What Works

## Algebraic Notation in Problem Solving

Ken Koedinger provides examples that demonstrate the importance of bringing mathematical notation into the problem-solving process.

FEATURING:  Ken Koedinger, Carnegie Mellon University

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