# Standards for Mathematical Content

## 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

## Focus on Fraction Operations

This PowerPoint covers the content of a staff development session for math coaches and teachers about how to teach fraction operations. Multiply or Divide? shows a portion of the workshop in which participants are working on the sample material, Multiply or Divide Problems.

FEATURING: RMC Denver Professional Development

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

## 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

## 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

## Learning and Teaching Linear Functions

These video-based resources help math teachers in grades 6–10 address “problems of practice” associated with the issues and challenges of teaching linear functions.

SOURCE: Nanette Seago, Judy Mumme, Nicholas Branca, WestEd

## Field Guide to Geometric Transformations, Congruence, and Similarity

Aligned with Common Core standards, this first-of-its-kind illustrated guide helps secondary school teachers and students understand geometric transformation, similarity, and congruence.

SOURCE: Nanette Seago, Patrick Callahan, Mark Driscoll, Jennifer Jacobs, Johannah Nikula