This paper describes an Eight-dimensional methodology for teaching inventive and innovative problem solving. It has been developed and taught as part of an on-going course at Florida Atlantic University titled: "Introduction to Inventive Problem Solving in Engineering", and has been sponsored in part by the National Science Foundation (NSF) and the National Collegiate Inventors and Innovators Alliance (NCIIA). The Eight-dimensional problem solving methodology is a systematic approach that stimulates innovation by effectively using both sides of the brain. The methodology is a unified approach that builds on comprehensive problem solving knowledge from industry, business, marketing, math, science, engineering, technology, and daily life. It allows to quickly generate unique, and high-quality multiple solutions in a short period of time. Problems are not constrained to a particular profession or subject, and may be used by individuals and teams. The methodology works extremely well in brainstorming sessions. It is easy to teach, learn and use. This new methodology has been taught using hands-on activities that include more than 250 different 3-D mechanical puzzles, many games, brain-teasers, LEGO® Mindstorms competitions, and design projects, each of which illustrates principles and strategies in inventive problem solving. These activities allow for self-paced, semi-guided exploration that improves self-esteem and encourages questioning and daring. The Eight-dimensional methodology has been recently evaluated with encouraging results.