Discovering 3 by 3 magic squares, using numbers 1 through 9, is presented as a learning activity on three different levels. (MP)

Properties of a given array of numbers are discussed and some sample activity cards involving discovery of number patterns are presented. (MP)

Activities for calculating experimental and theoretical probabilities are presented. Worksheets designed for duplication for classroom use are provided. Suggestions are given for additional problems that could be generated from the original simulation, and answers to questions on the worksheets are included. The activities simulate parachute…

Relationships among the sides are developed for right triangles whose sides are in the ratios 1:3, 1:4, and 1:5. The golden ratio appears in the results which can be used in secondary mathematics. (DC)

Describes a mathematics trail created on the campus of Exeter Academy and in the town of Exeter, New Hampshire. A series of problems and puzzles enabled teachers to teach mathematics outdoors. Novel questions were created to permit students to look at things from a different perspective. Participants were often inspired to create questions of…

Discusses six examples that discover supplementary geometry theorems by using three elementary theorems about the relationships between angles and intercepted arcs in circles. Topics in the examples include angles formed by parallel lines and the sum of the interior angles of triangles, convex quadrilaterals, star polygons, and hexagons. (MDH)

Four specific problems are presented, discussed, and extended to illustrate how diverse instructional strategies, materials, and resources can be used to develop problem-solving skills. (MP)

A set of activities geared towards decoding messages by evaluating algebraic expressions and discovering coding rules by analyzing pairs of coded messages is presented. (MP)

Learning activities based on a geometrical puzzle that consists of rearranging triangles and trapezoids are used to teach concepts involving area. (MP)

Presents three investigations that extend the problem of counting the number of squares on a grid in two dimensions to an analogous problem of counting the number of cubes in a three-dimensional cubic array. (MDH)

Presented is the solution to the problem of calculating the probability of winning or losing a game played by moving a counter from the center of a hexagonal grid according to the number shown after the toss of a die. The exercise is an example of an interesting mathematical investigation. (MDH)

The author describes a dialogue with his three-year-old daughter about numbers. He discusses aspects of mathematics education and how his views about how students acquire mathematical knowledge have changed. (MP)

Gives an example of an open exploration using trigonometric relationships in which the law of cosines can be deduced from the law of sines. Discusses the characteristics and value of the exploration process. (MDH)

Presents the problem of finding the maximum area of a quadrilateral when three of the four sides are given. Incorporates several parts of the secondary school precalculus curriculum into the solution. Develops the formula to solve the problem. (MDH)

Investigates the question concerning the maximum number of lines of symmetry possessed by irregular polygons. Gives examples to illustrate and justify the generalization that the number of lines of symmetry equals the largest proper divisor of the number of sides. Suggests related classroom activities. (MDH)