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## Exploring Sequences Related to Medial Triangles

Sequences are an important topic—not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns that can be discovered with the use of dynamic geometry software (DGS) such as GeoGebra or Web Sketchpad. In addition, exploring sequences with DGS allows learners to formulate and test conjectures, an important mathematical process. In this article, I describe how my students used GeoGebra and geometric reasoning to visualize, discover, formulate,

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## Puddle Play!

For the Love of Mathematics

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## Changing the Rules to Increase Discourse

A second-grade teacher challenges the raise-your-hand-to-speak tradition and enables a classroom community of student-driven conversations that share both mathematical understandings and misunderstandings.

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## Perimeter and Beyond

A simple problem-solving exercise encourages teachers to “start small” to reveal how third graders understand multiple math concepts simultaneously.

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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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## Winning the “Hundred Years' War”

Arm your students for victory in the age-old battle to master subtraction with regrouping.

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## A smorgasbord of assessment options

Presented with a variety of palatable, inquiry-based, creative learning choices in geometry, this teacher and her fifth graders found tremendous satisfaction in meeting target goals for reasoning skills and taking important “next steps” in learning.

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## Early Childhood Corner: Storyboards for meaningful patterns

Patterns are an important element of developing children's mathematical reasoning. In elaborating ways in which “instructional programs from prekindergarten through grade 12 should enable all students to understand patterns, relations, and functions” (NCTM 2000, p. 90), the National Council of Teachers of Mathematics specifies that representing and interpreting patterns are skills that kindergartners through second graders should build toward developing a robust understanding of algebra.