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MS 104 Unit Plan 6 Unit Name: Looking for Pythagoras Essential Question: How do we solve for missing sides and angles of triangles? Grade: 8 Duration: 5 weeks Big Ideas/Enduring Understandings: Find and understand square and cube roots Use the Pythagorean Theorem to find missing sides of right triangles Use the Pythagorean Theorem to find distance on a coordinate plane Explore special right triangles Common Core Learning Standards: 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions 8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system 8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x squared = p and x cubed= p where p is a positive rational number. Evaluate square roots or small perfect squares and cube roots of small perfect cubes. Student Objectives: 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 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 REGENTS Activities/Tasks Investigation 2: Squaring Off Find and estimate square and cube roots, graph square root and cube root equations Investigation 3: The Pythagorean Theorem Use the Pythagorean Theorem and its converse Find Pythagorean Triples Investigation 4: Using Real Numbers Explore sets of numbers (whole, integer, rational, irrational) Approximate irrational numbers 8th Grade Activities/Tasks 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 Benchmark 5: Performance Task: Fencing and Grassing Key Terms/Vocabulary: Square root Cube root Pythagorean Theorem Converse Hypotenuse Legs Irrational Rational Resources: CMP3: Looking for Pythagoras Glencoe Math Common Core Mathematics Big Ideas Math