Activities that allow students to represent patterns concretely before showing the patterns in color on paper are presented. Three basic activities are described, with suggestions made for extensions that allow further pupil exploration of multiples. Student discovery of relationships not found by the teacher is expected. (MP)

Pumpkin seeds are counted after students convert pumpkins to jack-o-lanterns. Among the activities involved, pupils learn to count by 10s, make estimates, and to construct a visual representation of 1,000. (MP)

Described is a study in which three instructional approaches were applied in second grade classes. Discussed are proportional materials, nonproportional materials, nonproportional materials with pictorial models. Findings, results, and recommendations are presented. (CW)

Students are given a computational rule to follow for the first set of problems and must then discover the rule for the second set. Four worksheets for grades 1-8 are included. (MNS)

Four activities are described which focus on consumer awareness and judgment using data collection and judgment skills involving data from footwear. Worksheets for data collection and activities at home and at school are included. A set of ratings of sneakers from "Consumer Reports" magazine is provided. (CW)

Describes four activities for grade levels K-3, 4-5, and 6-8 and for the family that explore statistical concepts using a manipulative familiar to students-SKITTLES candies. Concepts explored include frequency graphs, data collection and analysis, probability, measures of central tendency, averaging, and correlation coefficients. Includes…

Presented are suggestions for increasing the efficient use of the transition board while reducing its overall size. Discussed are the construction and preparation of the boards. Teaching addition and subtraction using these materials is described. (CW)

Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

Doing (addition and multiplication) and undoing (subtraction and division) are illustrated through drawings and sentences. Combinations of operations are also included. (MNS)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

Presents six strategies to develop appropriate mathematical applications for middle school children: (1) change the name; (2) make problems appealing; (3) encourage group work; (4) let students generate story problems; (5) encourage a positive attitude; and (6) keep students motivated. Illustrates strategies with three examples involving…

Considerations of the history of similar techniques and the structure of the method itself are used to discuss this question. (MP)

A discussion is given of a method of finger reckoning in which the numbers one through ten are represented by one's fingers. (MP)

A method of multiplying using fingers is described and an explanation given. The method is then generalized to other number bases. (MP)

Directions are given for preparing a puzzle that may be used to provide practice in computation. (MP)