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## Generalizing and Skepticism: Bringing Research to Practice

Learn why generalizing is important but that overgeneralizing can be problematic.

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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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## A Repeat Look at Repeating Patterns

Working with repeating patterns is important for K–grade 2 students because of the connections they will make in later grades with related mathematical ideas.

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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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## Attending to Precision with Secret Messages

Introduce your students to a fun and innovative game to encourage precise communication

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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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## Cartoon Corner: When Will I Ever Use Math?

A cartoon highlighting occupational uses of mathematics is coupled with a full-page activity sheet.

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## Palette of Problems

A monthly set of problems is aimed at a variety of ability levels.

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## Let's Go to San Francisco

The Transamerica Pyramid building, shown in photograph 1, is San Francisco's most distinctive and well-known building. Photograph 2, taken from street level, shows a view looking up to the top of the building. Photograph 3, also taken at street level, shows pyramids incorporated into the overall design of the building.

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## License to Do Math with a Full Tank

Since its inception, the Mathematical Lens column has provided teachers with resources to use with their students to make connections between mathematics and the world around us through the use of photographs. The editors and the dozens of teachers who submitted material for columns have taken all of us on a journey around the world to discover where mathematics lives. These columns have offered teachers a license to do mathematics everywhere and to travel far with their students with a full tank of resources.