# Modeling & using tools (MP4, MP5)

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Effective Problem-Solving Instruction

This summary describes a wide range of research-based recommendations for guiding instruction in problem solving. Three important strategies that apply at all grade levels and in all areas of math are: use of visual representations, encouragement of multiple approaches to solving problems, and linking mathematical and algebraic notation to intuitive approaches.

*SOURCE: *Doing What Works

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Problems

In the media piece, *Connecting Mathematical Ideas to Notation*, Sybilla Beckmann presents two examples of problems showing how students can connect mathematical concepts and notation. This sample material has the problem statements along with the solution ideas given by Beckmann.

*SOURCE:* Doing What Works

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Connecting Mathematical Ideas to Notation

Sybilla Beckmann uses two different problems to demonstrate how to develop mathematical concepts and present mathematical notation in problem-solving situations.

**FEATURING:** Sybilla Beckmann, University of Georgia

*SOURCE: *Doing What Works

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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

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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

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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

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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

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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

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Partitive and Measurement Fraction Problems

Dr. Brendefur uses two context problems to distinguish between partitive and measurement fraction problems. These two slides illustrate the differences between the two problems and demonstrate the approaches needed to arrive at the solutions. See the related media, *Multiple Interpretations of Fractions*.

*SOURCE: *Doing What Works

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Multiple Interpretations of Fractions

Jonathan Brendefur describes how he helps teachers understand and teach different interpretations of fractions. He explains the importance of explicitly teaching about various interpretations and discusses how number lines can be used at each stage.

**FEATURING: **Jonathan Brendefur, Boise State University; and Eliza Hart Spalding School of Math and Technology (ID)

*SOURCE: *Doing What Works

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