The following ideas are shared: (1) a low-stress subtraction algorithm that eliminates the traditional borrowing process, and (2) an approach to graphing circular functions that looks at the process of modifying simple functions as a series of shifting, sliding, and stretching adjustments, with its biggest advantage viewed as its generality. (MP)

Graphs are viewed as extremely useful tools in communication, which enable readers to see at a glance facts that might take several paragraphs to describe adequately. An ability to read graphs critically is seen to be an important objective for any elementary curriculum, and ways to introduce them are presented. (Author/MP)

An instructional sequence for teaching graphing that has been extensively field tested in kindergarten through grade six is detailed. The material begins with point graphs, employs a movable y-axis to begin with minimal clutter, and has graphs constructed before reading graphs is required. (MP)

It has been found that students gain much greater insight into routine calculations with business formulas when such work is viewed in the light of graphing concepts. Ten problems are presented that illustrate how three specific objectives in a unit on graphing in a business mathematics course have been met. (MP)

The lesson details an approach to teaching positive and negative numbers which uses number pairs and generates inverses that initially avoid any mention or use of negative signs. The material moves pupils from development of key concepts to the use of more standardized notation for number operations. (MP)

Five reasons why graph work is effective are given, followed by suggestions for making bar, picto-, and line graphs. (MS)

The activities presented deal with representing student-collected information by means of reusable teaching aids such as pictorial graphs, tally charts, bar graphs, and circle graphs. Directions for making three of the teaching aids described are included. The activities are seen as supplements to drill and practice. (MP)

A class of seldom-seen real-world applications of high school mathematics is described. The problems considered are viewed as more substantial than ordinary word problems and thus are thought to require a greater commitment of time and energy. Suggestions for student extensions of the project are made. (MP)

How graph paper has been used to illustrate the algorithm for division of fractions is presented. The combined use of graph paper and an overhead projector can make the presentation even more convincing. A review of whole number division is recommended prior to the lesson. (MP)

This publication contains the substance of all papers submitted at the fall 1974 Association of Teachers of Mathematics in New England (ATMNE) conference. As the title indicates, the focus of the publication is directed toward mathematical applications. The 25 papers cover topics ranging from applications at the elementary school level to those…