The Pythagorean Theorem Workbook
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The Pythagorean Theorem Workbook
This is a relatively short workbook focusing on the Pythagorean Theorem and its applications. The Pythagorean Theorem is actually not part of the Common Core Standards for seventh grade. The Common Core places it in eighth grade. However, I have included it in this curriculum because it is a traditional topic in pre-algebra. That way, Math Mammoth Grade 7 works as a full pre-algebra curriculum while fully meeting (and exceeding) the Common Core Standards for grade 7. First, students need to become familiar with square roots, so they can solve the equations that result from applying the Pythagorean Theorem. The first lesson of the workbook introduces taking a square root as the opposite operation to squaring a number. The lesson includes both applying a guess-and-check method and using a calculator to find the square root of a number. Next, students learn how to solve simple equations that include taking a square root. This makes them fully ready to study the Pythagorean Theorem and apply it. The Pythagorean Theorem is introduced in the lesson by that name. Students learn to verify that a triangle is a right triangle by checking if it fulfills the Pythagorean Theorem. They apply their knowledge about square roots and solving equations to solve for an unknown side in a right triangle when two of the sides are given. Next, students solve a variety of geometric and real-life problems that require the Pythagorean Theorem. This theorem is extremely important in many practical situations. Students should show their work for these word problems to include the equation that results from applying the Pythagorean Theorem to the problem and its solution. There are literally hundreds of proofs for the Pythagorean Theorem. In this workbook, we present one easy proof based on geometry (not algebra). As an exercise, students are asked to supply the steps of reasoning to another geometric proof of the theorem, and for those interested, the lesson also provides an Internet link that has even more proofs of this theorem.
The Metaphysics of the Pythagorean Theorem
Explores Thaless speculative philosophy through a study of geometrical diagrams. Bringing together geometry and philosophy, this book undertakes a strikingly original study of the origins and significance of the Pythagorean theorem. Thales, whom Aristotle called the first philosopher and who was an older contemporary of Pythagoras, posited the principle of a unity from which all things come, and back into which they return upon dissolution. He held that all appearances are only alterations of this basic unity and there can be no change in the cosmos. Such an account requires some fundamental geometric figure out of which appearances are structured. Robert Hahn argues that Thales came to the conclusion that it was the right triangle: by recombination and repackaging, all alterations can be explained from that figure. This idea is central to what the discovery of the Pythagorean theorem could have meant to Thales and Pythagoras in the sixth century BCE. With more than two hundred illustrations and figures, Hahn provides a series of geometric proofs for this lost narrative, tracing it from Thales to Pythagoras and the Pythagoreans who followed, and then finally to Platos Timaeus. Uncovering the philosophical motivation behind the discovery of the theorem, Hahns book will enrich the study of ancient philosophy and mathematics alike.
Algebra I Workbook For Dummies
Author: Mary Jane Sterling
language: en
Publisher: John Wiley & Sons
Release Date: 2017-03-17
The grade-saving Algebra I companion, with hundreds of additional practice problems online Algebra I Workbook For Dummies is your solution to the Algebra brain-block. With hundreds of practice and example problems mapped to the typical high school Algebra class, you'll crack the code in no time! Each problem includes a full explanation so you can see where you went wrong—or right—every step of the way. From fractions to FOIL and everything in between, this guide will help you grasp the fundamental concepts you'll use in every other math class you'll ever take. This new third edition includes access to an online test bank, where you'll find bonus chapter quizzes to help you test your understanding and pinpoint areas in need of review. Whether you're preparing for an exam or seeking a start-to-finish study aid, this workbook is your ticket to acing algebra. Master basic operations and properties to solve any problem Simplify expressions with confidence Conquer factoring and wrestle equations into submission Reinforce learning with online chapter quizzes Algebra I is a fundamentally important class. What you learn here will follow you throughout Algebra II, Trigonometry, Calculus, and beyond, including Chemistry, Physics, Biology, and more. Practice really does make perfect—and this guide provides plenty of it. Study, practice, and score high!