Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…

Providing student choice and opportunities for independent study are recognized as viable differentiation techniques. Daily homework sets that contain more demanding problems even though not required allow the teacher to provide challenge without incurring undue stress. The modest incentive of some homework bonus points is enough to whet the…

This article describes one seventh-grade teacher's classroom efforts to integrate traditional exercises from different content areas to form more robust questions that provide genuine problem-solving opportunities for students. These exercises are illustrated by connecting the Pythagorean theorem with a variety of prealgebra topics. Since the…

Students use computer software to construct personalized fractal art. (Contains 7 figures and 1 table.)

This article describes an activity in which students plot collections of ordered pairs according to prescribed set conditions. The coordinate plane sets can have rich variety, and their construction fosters critical thinking, attention to detail, and algebraic reasoning. (Contains 3 figures.)

Uses spreadsheets and programmable calculators to investigate limiting behavior in number patterns. (YDS)

Uses the zooming technology of graphing calculators and certain graphing software to help middle school students extend their understanding of slope to curved graphs. (ASK)