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## Talking about the Greek Cross

Meaningful discourse occurs when tasks are chosen carefully and when the teacher steps back and allows students to move to the forefront of their own learning.

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## Informing Practice: A Hybrid Perspective on Functions

### research matters for teachers

Formal notions of function, which appear in middle school, are discussed in light of how teachers might complement the input-output notion with a covariation perspective.

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## A Geometric Path to the Concept of Function

Transformations using dynamic software can provide a unique perspective on a common topic.

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## Tiling the Cube

The Tiling Tubs task is a middle school activity published in NCTM's Navigating through Algebra in Grades 6-8. Students examine a drawing that shows a square hot tub with side length s feet. A border of square tiles surrounds the tub, with each border tile a 1-foot square. Students determine the number of border tiles required to surround the tub and express that number in as many ways as they can, thereby creating various equivalent algebraic representations. A valuable component of Tiling Tubs is its requirement that students contextually justify their algebraic representations. Students also realize that more than one correct representation and justification exists.

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## A Vehicle for Bivariate Data Analysis

Top-selling cars in America can be the catalyst that drives an analysis of data.

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## Dilations and the Equation of a Line

Track students' understanding of proportional reasoning by combining transformational geometry, similar-triangle reasoning, and linear relationships.

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## All Talk and More Action

Students' understanding of proportional relationships become apparent during an algebra project that focuses on constructing mathematical arguments.

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## Quick Reads: Posters: More Than Just for Looks

### a good idea in a small package

Posters, commonly employed for decoration, can be used to introduce and practice new concepts and help assess student learning.

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