Six different methods were used by students to solve the problem of finding the area of a given trapezoid. A seventh method used by textbooks is also discussed. (MP)

Calculators are seen to shift the student focus in problem-solving situations from "how to do it" to "what to do," by keeping computation from standing in the way when pupils write or solve problems. (MP)

Novel practice exercises for addition and subtraction using a special number puzzle called a number chain are suggested. (MK)

Having students find and cut out of graph paper the 12 pentominoes can provide an enjoyable exercise in perception, discovery, and double checking. The pentominoes can then be used to illustrate informally several geometric concepts. (SD)

A number of paper-folding activities are described. The activities illustrate geometric concepts, theorems, and construction techniques. (SD)

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

Alternative identification and instructional procedures are discussed. Instructors are warned against assuming an equivalence between the quantity of mathematical work a child demonstrates and the quality of that child's thinking. A need to integrate qualitative information is seen. Two types of activities for gifted pupils are detailed. (MP)

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

The activity described helps students develop facility in working with two-dimensional coordinate systems. Many students find the activity fascinating, so it can be used to motivate students to become involved in a number of explorations and to engender positive attitudes toward mathematics. (MP)

The Concept Game, which focuses on the attributes of parity, balance, majority, closure, and skip of seven-digit binary numbers, is described. Originally written as a computer program, the game is modified so that pupils can play with construction paper chips of just paper and pencil. (MP)

Teaching by learning activities is contrasted with teaching by objectives. Four types of learning activities are identified. (JT)

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 series of activities that focus on the process of measuring are presented. The material is designed to help children develop a concept of measurement by leading them through the processes used in establishing formal measurement systems over the centuries. (MP)

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

Alternative algorithms, "tricks," and shortcuts are viewed as ideally suited for inclusion in a systematic program of practice because of their motivational effect and the mental stimulation involved in discovering why they work. (MP)