The Pythagorean Theorem and Baseball

ONE OF THE MOST IMPORTANT THEOREMS IN THE WHOLE REALM OF GEOMETRY

A Webquest for 7th Grade Mathematics

INTRODUCTION / THE TASK / THE PROCESS / EVALUATION / CONCLUSION / TEACHER PAGE

INTRODUCTION

The Pythagorean Theorem is one of the most important theorems in the whole realm of geometry. With this Theorem we can measure distances "indirectly" (without using a tape measure to measure from one point to another). The measures of the sides of a right triangle are involved with two of the measures needing to be known. Knowing the measures of the two sides, the Pythagorean Theorem helps find the measure of third side. This webquest will link the students to PowerPoint slides with animation and web sites that provide for understanding by using animation. CURRICULUM STANDARDS 9.D.3 Compute distances, lengths and measures of angles using proportions, the Pythagorean theorem and its converse. Why This Goal Is Important: Geometry provides important methods for reasoning and solving problems with points, lines, planes and space. The word "geometry" comes from Greek words meaning "measurement of the Earth." While we use modern technology and employ a wider variety of mathematical tools today, we still study geometry to understand the shapes and dimensions of our world. The applications of geometry are widespread in construction, engineering, architecture, mapmaking and art. Historically, geometry is a way to develop skill in forming convincing arguments and proofs. This goal of developing a means of argument and validation remains an important part of our reasons for studying geometry today.

THE TASK

The distance between each of the consecutive bases is 90 feet. How far does the catcher have to throw the ball from home plate to second base?

You will be linked to sites to give the necessary background of the right triangle. After familiarizing yourself with the right triangle, a few PowerPoint slides and web sites will be used to show the Pythagorean Theorem through animated illustrations. There will be a few examples shown to help you get started with solving the "Baseball Distance" problem with the Theorem.

THE PROCESS

Linking to PowerPoint, you will review some information needed to understand the right triangle. Once this is mastered you will proceed to "The Pythagorean Relationship" site that will help you understand the relationship between the sides of the right triangle. Scroll down until you see the bold letters RIGHT TRIANGLES and follow the directions through that illustration. After finishing that, scroll back up to the top and follow the directions through this illustration. Now some Necessary Basic Skills need to be reviewed. It's time to consider real life situations where the Theorem is used and to get more practice. Now you will have the necessary tools to solve the problem presented above concerning the baseball diamond. This PowerPoint Calculator may be used at any time during the Process.