* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Topic/ Theme/ Duration Pythagorean Theorem
Mathematics of radio engineering wikipedia , lookup
Infinitesimal wikipedia , lookup
Large numbers wikipedia , lookup
Mathematical proof wikipedia , lookup
John Wallis wikipedia , lookup
History of trigonometry wikipedia , lookup
Location arithmetic wikipedia , lookup
Ethnomathematics wikipedia , lookup
Mathematics and architecture wikipedia , lookup
Non-standard analysis wikipedia , lookup
History of mathematics wikipedia , lookup
Central limit theorem wikipedia , lookup
Foundations of mathematics wikipedia , lookup
Georg Cantor's first set theory article wikipedia , lookup
Vincent's theorem wikipedia , lookup
Wiles's proof of Fermat's Last Theorem wikipedia , lookup
Four color theorem wikipedia , lookup
Fundamental theorem of calculus wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Real number wikipedia , lookup
Fermat's Last Theorem wikipedia , lookup
List of important publications in mathematics wikipedia , lookup
Proofs of Fermat's little theorem wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
Unit Plan Mathematics Unit: 6 Grade: 8 Solve one‐variable linear equations, including cases with infinitely many solutions or no solutions Solve problems involving volumes of cones, cylinders, and spheres together with previous geometry work, proportional reasoning and multi‐ step problem solving in grade 7 Pythagorean Theorem Topic/ Theme/ 6 weeks Duration How do we solve for missing sides and angles of triangles? Essential Question(s) Find and understand square and cube roots Key Student the Pythagorean Theorem to find missing sides of right triangles Learning Objectives Use Use the Pythagorean Theorem to find distance on a coordinate plane Standard Explore special right triangles Skills 8.G.6( ). Explain a proof of the Pythagorean Theorem and its converse. Explain a proof of the Pythagorean Theorem and its converse. Resources CMP Looking for Pythagoras Glencoe Chapter 5: Lesson 5, Inquiry Lab Tell whether a triangle is a right triangle 8.G.7( ). Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Use the Pythagorean Theorem to find missing side lengths 8.G.8( ). Apply the Pythagorean Use the Pythagorean Theorem to Common Core Mathematics CC 8-9, 3.2, 3,3 Big Ideas Math: 7.3, 7.5 CMP Looking for Pythagoras Glencoe Chapter 5: Lesson 6 Apply the Pythagorean Theorem to real-world and word problems Common Core Mathematics 3.3 Big Ideas Math: 7.3, 7.5 CMP Looking for Pythagoras Theorem to find the distance between two points in a coordinate system. find distance between points on a coordinate plane and in real world problems Glencoe Chapter 5: Lesson 7 Common Core Mathematics 3.4 8.NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers; locate then approximately on a number line diagram. 8.EE.2: Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. Vocabulary Sequence of Key Learning Activities Big Ideas Math: 7.3, 7.5 CMP Looking for Pythagoras Glencoe Common Core Mathematics 3.4 Big Ideas Math: 7.4 CMP Looking for Pythagoras Glencoe Common Core Mathematics 3.4 Big Ideas Math: 7.1, 7.2, 7.3, 7.4, 7.5 right triangle, leg, hypotenuse, right angle, Pythagorean Theorem, square root, squared, formula, proof PYTHAGOREAN THEOREM Understand and apply the Pythagorean Theorem Develop strategies for finding the distance between two points on a coordinate grid Explain a proof of the Pythagorean Theorem Use the Pythagorean Theorem and its converse to solve a variety of problems Use the Pythagorean Theorem to find the equation of a circle with its center located at the origin REAL NUMBERS Understand that the set of real numbers consists of rational and irrational numbers Interpret square roots and cube roots of numbers by making use of their related geometric representations Activities/Tasks Relate the area of a square to the side length of the square Estimate the values of square roots Estimate the values of cube roots Relate the volume of a cube to the edge length of the cube Compare numbers that can be represented as fractions (rational numbers) to numbers that cannot be represented as fractions (irrational numbers) and recognize that the set of real numbers consists of rational and irrational numbers Represent rational numbers as fractions and as terminating decimals or repeating decimals Recognize that irrational numbers cannot be represented as fractions and are nonterminating, nonrepeating decimals Recognize that the square root of a whole number that is not a square is irrational Locate irrational numbers on a number line Use and understand properties of rational and irrational numbers Investigation 1: Coordinate Grids Review of the coordinate plane and finding distance on it (1.1 and 1.2) Investigation 2: Squaring Off Find and estimate square and cube roots Investigation 3: The Pythagorean Theorem Use the Pythagorean Theorem and its converse Find distance on the coordinate plane Investigation 4: Using Real Numbers Approximate irrational numbers Explore special triangles Assessments Note: Standards in bold are identified as major standards. Standards with checkmarks are standards recommended for greater emphasis 4