The first chapter of the seventh unit in this SMSG series discusses perpendiculars and parallels; topics covered include the relationship between parallelism and perpendicularity, rectangles, transversals, parallelograms, general triangles, and measurement of the circumference of the earth. The second chapter, on similarity, discusses scale…

A theory of psychophysics is discussed that enlarges the classical theory in three general ways: (1) the multidimensional nature of perception is made explicit; (2) the transformations of the theory are interpreted geometrically; and (3) attributes are distinguished from sensations and only partially ordered. It is shown that, with the enlarged…

Development of a second-grade mathematics instructional unit is discussed in terms of activities, evaluation procedures, and results of evaluation. The report is organized by topic. Behavioral objectives are followed by descriptions of activities and materials used. Topics include: review of symbols, pictorial representation of numbers, writing…

This teacher's guide for a semester course in trigonometry is prepared for use with the text "Plane Trigonometry with Tables" by E. R. Heineman. Included is a daily schedule of topics for discussion and homework assignments. The scope of each lesson and teaching suggestions are provided. The content for the course includes trigonometric functions,…

The plans for a field test of teaching tenth grade plane geometry through transformations is described. Text and homework materials have been written, and teachers have been trained. Eight intact classes are now being taught utilizing the materials. Data to be collected will include: (1) teacher descriptions of the course via questionnaire; (2)…

This is the second volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

This is the third volume of a series produced by the New York State Education Department. Originally developed by four local school districts, the mathematics objectives and sample items included were not intended to be official or comprehensive but rather to be used as an aid to teachers in constructing curricula and in making classroom goals…

This is volume five of a series produced by the New York State Education Department. Originally developed by four local school districts, the mathematics objectives and sample items are not intended to be official or comprehensive, but to be an aid to teachers in constructing curricula and in making classroom goals clear and precise. The document…

This fifteenth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 13. A time allotment for each of the chapters in Units 13 and 14 is suggested. Then, for each of the chapters in Unit 13, a guide for the selection of problems is provided, the goals for that chapter are discussed, the mathematics is explained,…

This sixteenth unit in the SMSG secondary school mathematics series is the teacher's commentary for Unit 14. For each of the chapters in Unit 14, a guide to the selection of problems is provided, the goals for that chapter are discussed, the mathematics is explained, some teaching suggestions are given, the answers to exercises are listed, and…

Results of operations on the Pythagorean formula are interpreted pictorially to yield interesting art forms. (MP)

A nine-point plane coordinated by the field of integers modulo three is examined using motion geometry. The conceptual advantages of teaching this geometry are emphasized. (MP)

Discusses some theorems and properties of figures produced when circles are tangent to one another. (GA)

The development of square units for area and cube units for volume is discussed with emphasis that switching focus from one physical property to another is involved as opposed to simply multiplying units. (MN)

A classroom activity is described where students divided circular regions into equal sections and reassembled them to determine the formula for the area of a circle. Using an odd number of sections (Instead of an even number) changes the shape of the reassembled pieces but still gives rise to the same formula. (MN)