Described is an activity that categorizes a two-digit number as "sneaky" if the continued process of taking the difference of the squares of its digits leads to a difference of zero. Other categorizations are determined by whether the difference process ends in a one-digit number or continues in a loop of numbers. (MDH)

Presents the template method developed by Galileo for calculating areas of geometric shapes constructed of uniform density and thickness. The method compares the weight of a shape of known area to the weight of a shape of unknown area. Applies this hands-on method to problems involving calculus, Pythagorean's theorem, and cycloids. (MDH)

Discussed is the classroom suitability of an open learning computer microworld centered around families of quadratic equations that provides a framework for exploring questions about parabolas to establish the link between the graphical and the algebraic representations of quadratic equations. (JJK)

Presents activities to create designs with different arrangements of square tiles, which gives students an opportunity to make conjectures about perimeter and to make convincing arguments to justify those conjectures. Includes worksheets. (MKR)