Worksheets and instructions are given for this activity whose objective is to develop the relationship between the lengths of the sides of a triangle and its classification by angle. (MP)

An activity leading to the discovery of a property of primes is suggested for encouraging algebra students to make nontrivial conjectures. (MP)

Three examples are given illustrating the use of the calculator in problems where determining patterns and making conjectures are stressed. (MP)

The topics of angle construction, angle trisection, and regular polygon construction with only a straightedge and compass are discussed for angles with integer measure. (MP)

The notion that the area of an inscribed n-sided polygon approaches the area of a circle as n approaches infinity leads to some interesting limits involving trigonometric functions. (MP)

A method is developed for finding the equations of two circles that intersect at points with integral coordinates. Such equations are useful for the introducing systems of quadratic equations. (MP)

Solutions to difficult equations are illustrated with numerical techniques that can be used easily on calculators. Flowcharts and programs for computers and calculators are included. (MP)

Tree diagrams with numbers in a given pattern generate questions related to pattern recognition and number concepts such as binary numbers and exponentials. (MP)

A noncredit course is described in which the logic used in various episodes of "Star Trek" is analyzed to see whether or not it was valid. (MP)

An example is presented that can be used to introduce the study of limits of sequences through recursive formulas yielding square roots. (MP)

A proof is given of the irrationality of the square root of 2 which depends on notions of terminating and repeating decimals. (MP)

A class's struggle with the computer solution of a nontrivial problem is related. The use of algorithms allowed a trial-and-error approach.

A seemingly paradoxical situation is explained which tells of one baseball player having a higher batting average than a second player for two seasons, yet having a lower overall average. (MP)

Topics discussed include: maximizing the volume of a box, finding different size squares on a geoboard, the angles formed by the hands of a clock, and questions related to three consecutive integers. (MP)

The relationship between simple interest and compound interest is explored by using calculators to develop the required formula inductively and intuitively. (MP)