# Standards for Mathematical Content

At Papillion Junior High School, seventh-grade students work in groups on a non-routine geometry problem. This sample material has a fencing task worksheet and photos of students’ presentations of their solutions.

SOURCE: Doing What Works

## Non-Routine Problem in Geometry

See how a class approaches Pre-Algebra Fencing Task, a non-routine geometry problem that challenges their mathematical reasoning.

FEATURING: Kathy Huggins, Papillion Junior High School (NE)

SOURCE: Doing What Works

## Focus on Ratios

This PowerPoint outlines the content of a development session for math coaches and teachers on teaching ratios, rates, and proportions. Understanding Ratios shows a portion of the workshop in which participants are working on the sample material, Ratio Problems.

SOURCE: Doing What Works

## Ratio Problems

Participants in the Understanding Ratios development session worked with this set of problems to strengthen their conceptual understandings. See Focus on Ratios for additional background.

SOURCE: Doing What Works

## 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