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## Visualizing Equations Using Color Tiles

Algebraic reasoning is often promoted through an analysis of and generalizations about patterns that appear in mathematics, in nature, or in everyday situations (Driscoll 1999; Kieran 2006; Lee 1996). In accordance with this tendency, the Common Core (CCSSI 2010) emphasizes finding patterns and expressing such regularity in repeated reasoning as an important mathematical practice. NCTM (2000) also recommends that students participate in patterning activities by asking them to describe numeric and geometric patterns; generalize patterns to predict what comes next while providing a rationale for their predictions; and represent patterns in multiple ways, including drawings, tables, symbols, and graphs.

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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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## Connecting Representations: Using Predict, Check, Explain

Although educators agree that making connections with the real world, as advocated by Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014), is important, making such connections while addressing important mathematics is elusive. We have found, however, that math content coupled with the instructional strategy of predict, check, explain can bridge such real-world contexts. In so doing, this procedure supports the research-informed teaching practices of using evidence of student thinking and aiding meaningful mathematical discussion.

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## Informing Practice: Mathematical Practices That Promote Twenty-First Century Skills

Skills that students will need in the twenty-first century, such as financial literacy, are explored in this classroom-centered research article.

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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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Consider four important elements of setting up challenging mathematics problems to support all students' learning.

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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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## Math for Real: Comfortable Construction

### “when will I ever use this?”

Finding the best step and tread for stairs provides the real-life tie in to this activity on slope and graphing.

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## Isle of Cats

What happens with cat populations when they are not controlled? Consider the case of Aoshima Island in Japan. Aoshima Island is called a cat island: Its cat population is 130 and growing; its human population is 13. The cats live in colonies and are fed and cared for by people who live on the islands.