This seventh unit in the SMSG junior high mathematics series is the teacher's commentary for Unit 5. A time allotment for each of the chapters in Unit 5 is suggested. Then, for each of the chapters in Unit 5, the objectives for that chapter are specified, the mathematics is discussed, some teaching suggestions are provided, the answers to…

This eighth unit in the SMSG junior high mathematics series is the teacher's commentary for Unit 6. A time allotment for each of the chapters in Unit 6 is suggested. Then, for each of the chapters in Unit 6, the objectives for that chapter are specified, the mathematics is discussed, some teaching suggestions are provided, the answers to exercises…

Equations or systems of equations can be associated with letters of the alphabet printed in the coordinate plane. Messages can be coded and decoded with a computer or by hand. (SD)

Described is mathematics used by the ancient Babylonians and recorded on tablets which have been dated 3000-2000 B.C., and 700-500 B.C. (SD)

Students were presented with the problem of finding all magic squares of order three. (SD)

Convex polyhedra having square or triangular faces are analyzed algebraically. (SD)

Photographs such as those included in this article can be used to provide activities related to measurement of velocity. These activities are less artificial and expensive of time and materials than most instructional approaches to velocity. (SD)

Experimenting with weights in a two-pan balance can be used in a series of activities on application of trigonometry. (SD)

This activity unit leads students to discover facts related to the maximum area enclosed by figures with given perimeters. Three worksheets are included. (MP)

Personality variables and teachers' ratings will explain more than 50 percent of the variance, with the latter being the most significant and economical method for predicting mathematical achievement of seventh graders. (MP)

Described are results obtained by students investigating double-diagrams, including discoveries of properties and accompanying proofs. (MP)

A method for finding any integral root of a number using a four-function calculator is given, along with a justification of the method and root-finding exercises. (MN)

In order to solve a functional equation, one must identify possible functions that satisfy a given equation. This paper seeks to convince the reader that students in high school could be exposed profitably to certain functional equations. Several examples of functional equations are given and discussed. (Author/MP)

A computation learning lab was planned, implemented, and evaluated as a way of helping learners conquer computation problems. Features include: emphasis on a premotivation activity; the use, on a regular basis, of eight instructional strategies; and active parent support. The lab students showed dramatic gains. (MP)

Classroom activities that provide meaningful practice, and at the same time motivate students, are the subject of this article. Several activities appropriate for first-year algebra are discussed; e.g., a prepared matrix of algebraic numbers, cross-factor puzzles, and number tricks. (MP)