John Prince

The current published story of 'Goldilocks and the Three Bears' has been modified several times since the original tale was told in the early 1800's. This paper will modify the story again, but using matrices. All solutions of linear systems have either a common solution, or not. In many courses, no further work is completed if no common solution exists. Based on the solution(s) to a linear system, there are three system models to consider. The 'just-right' one solution, the 'too hot' many solutions, and the 'too cold' optimal solution not likely satisfying any equation. This paper will present the solving of a linear system using the adjoint matrix. If no common solution exists, the corresponding optimal solution will be determined. For a linear system with three or less equations, the solution can certainly be completed using 'pencil-and-paper' methods. For a larger number of equations, software methods will be used.

This book explores and examines mathematics and its role in elementary education. Strategies are given for teaching mathematical principles including problem solving and its integration with other subject areas. Math is not 'just one problem after another', but most questions can be answered using several different methods. Some methods of thinking are more inventive and elegant than others, but all accurate methods will agree on both a reasonable initial estimate and the final answer.

Students will naturally ask, "When will I use this stuff?" With some mathematical concepts, the answer will be a definite "Never!" However, it is very likely you will require trigonometry in some form. You may only need some of the trigonometry topics, but applications similar to the ones contained in this book will probably be required. One of my students worked with a construction firm. He was required to determine whether or not the dump trucks would be in any danger of hitting the overhead hydro wires, preferably with an accurate solution. This book is designed to teach the skills required to be successful solving problems involving triangles. It is suitable for an independent learner, a student in a class, parent, tutor, or for a teacher.