Patent US 5,281,145

The pictorial image transforming manipulatives are instructional visual aid devices adapted for use to demonstrate visually the applications of deductive reasoning in proving most of the geometry theorems in conjunction with a geometry course. The manipulatives can also be used to display visually many graphs which represent algebraic linear equations and inequalities in two variables, and compound inequalities on a number line. These applications of mathematical systems for demonstrated algebraic linear graphs, and other graphs, are designed in conjunction with algebra textbooks. Each device uses one or more transparent overlays which rotate, translate, translate and rotate, flip over, or flip over and rotate to another position relative to a stationary underlaid plate. The manipulative devices are adapted for use on the overhead projector or for use in direct demonstration without a projector. These devices can be produced in small sizes for student use or in large blackboard sizes. The function of these manipulatives is to demonstrate visually a mathematical concept, a geometry theorem, a geometry problem, or a family of algebraic linear graphs.