Math Mammoth Square Roots & the Pythagorean Theorem - Miller, Maria

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Résumé :
Math Mammoth Square Roots & The Pythagorean Theorem is a relatively short worktext focusing on irrational numbers square roots and the Pythagorean Theorem and its applications. First students learn about taking a square root as the opposite operation to squaring a number. They learn about irrational numbers and how to find approximations to square roots both with a calculator and with a guess-and-check method. Students also practice placing irrational numbers on the number line using mental math to find their approximate location. Next the book has a review lesson on how to convert fractions to decimals. The following lesson has to do with writing decimals as fractions and teaches a method for converting repeating decimals to fractions. Then it is time to learn to solve simple equations that involve taking a square or cube root over the course of two lessons. After learning to solve such equations students are now 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 whether 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 book 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. Students also study a proof for the converse of the theorem which says that if the sides of a triangle fulfill the equation a2 + b2 = c2 then the triangle is a right triangle. Our last topic is distance between points in the coordinate grid as this is another simple application of the Pythagorean Theorem....

Biographie:
Maria Miller was born and grew up in Finland where she also received a master's degree in mathematics in 1997. She loves math and teaching, so becoming a math teacher was a natural career for her. Miller started writing math books in 2002, prompted by her experiences in tutoring homeschooled children. She felt the books they were using were inferior, especially when it came to conceptual understanding of mathematics, so she began to write books that focus on the concepts and the why of mathematics, though not forgetting the how and the needful practice. Over the years, her materials have become popular and appreciated, both among parents and teachers. In her free time, she likes walking, bicycling, swimming, reading, helping out with Inspire4.com, playing piano, and listening to music....

Sommaire:
Math Mammoth Square Roots & The Pythagorean Theorem is a relatively short worktext focusing on irrational numbers, square roots, and the Pythagorean Theorem and its applications. First, students learn about taking a square root as the opposite operation to squaring a number. They learn about irrational numbers, and how to find approximations to square roots both with a calculator and with a guess-and-check method. Students also practice placing irrational numbers on the number line, using mental math to find their approximate location. Next, the book has a review lesson on how to convert fractions to decimals. The following lesson has to do with writing decimals as fractions, and teaches a method for converting repeating decimals to fractions. Then it is time to learn to solve simple equations that involve taking a square or cube root, over the course of two lessons. After learning to solve such equations, students are now 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 whether 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 book, 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. Students also study a proof for the converse of the theorem, which says that if the sides of a triangle fulfill the equation a2 + b2 = c2 then the triangle is a right triangle. Our last topic is distance between points in the coordinate grid, as this is another simple application of the Pythagorean Theorem....