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## Cracking Codes and Launching Rockets

This historically significant real-life application of a cryptographic coding technique, which incorporates first-year algebra and geometry, makes mathematics come alive in the classroom.

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## Punch Up Algebra with POWs

An action research study focuses on the teaching strategies used to facilitate Problems of the Week.

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## Fostering Algebraic Understanding through Math Magic

Meaningful context motivates students to appreciate the usefulness of variables, expressions, equations, and symbolic transformations.

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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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## Teaching Straight-Line Graphs Using Autograph

Students often have difficulty with the topic of straight-line graphs. Perhaps they cannot relate to the abstractness of the concepts involved. Perhaps the sheer number and complexity of the skills required—reading algebra, substituting values, rearranging formulas, dealing with negative numbers, understanding coordinates and fractions—magnifies any misconceptions or weaknesses that students may have in other areas of mathematics, rendering them unable to come to grips with the topic as a whole.

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## Learning Algebra from Worked Examples

Presenting examples of both correctly and incorrectly worked solutions is a practical classroom strategy that helps students counter misconceptions about algebra.

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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.

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## The Sound of Thunder

You may have heard that if you are outside and see a flash of lightning, you can estimate the distance between you and the lightning strike fairly well by counting the number of seconds that pass between the lightning flash and the clap of thunder. The rule of thumb is that for every 5 seconds that pass before you hear the thunder, the lightning strike is 1 mile away.

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## Weaving Mathematical Concepts through Native American Baskets

The stunning natural beauty of Arizona, New Mexico, southern Colorado, and Utah is indicative of the American Southwest and is reflected in Southwestern baskets. Many Southwestern basket weavers use coiling as their method of construction (see fig. 1). The following problems relate mathematics to the art of basket weaving, with an emphasis on coiling.

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## Capturing Mathematical Curiosity with Notice and Wonder

Capturing students' own observations before solving a problem propelled a culture of sense making by meeting needs typical of middle school learners.