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## Mathematical Explorations: Find the Distance: No Formula Necessary

This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics.

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## If Only Clairaut Had Dynamic Geometry Tools

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

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## Bird Boxes Build Content Area Knowledge

Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.

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## Capturing Thinking on the Talk Frame

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.

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## Using Tiered Explorations to Promote Reasoning

Address the needs of diverse learners with a class structure that is designed around a crime scene theme and based on student choice and perceptions of the math being studied.

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## Pattern-block frenzy

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes a set of lessons where sixth graders use virtual pattern blocks to develop proportional reasoning. Students' work with the virtual manipulatives reveals a variety of creative solutions and promotes active engagement. The author suggests that technology is most effective when coupled with worthwhile mathematical tasks and rich classroom discussions.

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## Informing Practice: Examples as Tools for Constructing Justifications

### research matters for teachers

Research explores how to help students build from, instead of building with, examples when justifying mathematical ideas.

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## A Little Area Challenge: A Sod Story

Implement this professional development workshop designed to help teachers excavate the concept of area, uncover misconceptions, and cultivate understanding.

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## A Super Way to Soak in Linear Measurement

After analyzing advertising claims regarding water shooters, students present their findings.

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## Math for Real: Packaging Golf Balls

### “when will I ever use this?”

A package of three golf balls provides the real-world scenario for this ratio and area activity.