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FAYETTE COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 8 Topic 8H Big Idea(s) Pythagorean Theorem Pythagorean Theorem Converse and the Pythagorean Theorem Distance on the Coordinate Plane Understand and apply the Pythagorean Theorem. What enduring understandings are essential for application to new situations within or beyond this content? Essential Question(s) What questions will provoke and sustain student engagement while focusing learning? Enduring Standard(s) Which standards provide endurance beyond the course, leverage across multiple disciplines, and readiness for the next level? How do models help solve math problems? Why is the Pythagorean Theorem considered to be the most important mathematical equation? Enduring Understandings The Pythagorean Theorem can be used both algebraically and geometrically to solve problems involving right triangles. There is a relationship between the Pythagorean Theorem and the distance formula. Both the Pythagorean Theorem and distance formula can be used to find missing side lengths in a coordinate plane and real-world situation. How to solve simple and complex linear and literal equations with one solution. Finding the square root of a number is the inverse operation of squaring that number. Finding the cube root of a number is the inverse operation of cubing that number. Right triangles have a special relationship among the side lengths which can be represented by a model and a formula. Pythagorean Triples can be used to construct right triangles. How to simplify radicals and solve quadratic equations. Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Curriculum and Instruction 2014-2015 Page 1 of 4 FAYETTE COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 8 Standards for Mathematical Content Geometry Understand and apply the Pythagorean Theorem. 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. Supporting Standard(s) Which related standards will be incorporated to support and enhance the enduring standards? Instructional Outcomes Standards for Mathematical Content Geometry Understand and apply the Pythagorean Theorem. 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. Essential Vocabulary I can… explain a proof of the Pythagorean Theorem and its converse. identify the parts of a right triangle. use a^2+b^2=c^2. determine the hypotenuse of a right triangle given it’s legs. determine a missing leg of a right triangle, given the hypotenuse and a leg. determine the unknown side lengths in right triangles in realworld and mathematical problems (2D and 3D) using the Pythagorean Theorem. use the Pythagorean Theorem to find the distance between two points in the coordinate plane. Students who demonstrate understanding can… explain a proof of the Pythagorean Theorem and its converse. determine the unknown side lengths in right triangles in realworld and mathematical problems (2D and 3D) using the Pythagorean Theorem. use the Pythagorean Theorem to find the distance between two points in the coordinate plane. Essential Vocabulary What vocabulary must students know to understand and communicate effectively about this content? converse - The interchanging of the "if" and "then" parts of a conditional statement. What must students learn by the end of the unit? Performance Expectations What must students be able to do by the end of the unit to demonstrate their mastery of the instructional outcomes? Pythagorean Theorem - "The theorem that relates the three sides of a right triangle: a^2 + b^2 = c^2". right triangle - A triangle in which one angle is a right angle. The relation between the sides and angles of a right triangle is the basis for trigonometry. Curriculum and Instruction 2014-2015 Page 2 of 4 FAYETTE COUNTY PUBLIC SCHOOLS District Curriculum Map for Mathematics: Grade 8 Supporting Vocabulary Triangle Inequality Theorem hypotenuse leg Common Core Glossary http://www.corestandards.org/Math/Content/mathematicsglossary/glossary/ Curriculum and Instruction 2014-2015 Page 3 of 4 Subject and Grade Level Unit Title Summative Assessment of Learning Mathematics 8H Pythagorean Theorem In what way will students meet the performance expectations to demonstrate mastery of the standards? Instructional Outcomes How will the instructional outcomes be sequenced into a progression of learning? Learning Activities What well-designed progression of learning tasks will intellectually engage students in challenging content? Formal Formative Assessments What is the evidence to show students have learned the lesson objective and are progressing toward mastery of the instructional outcomes? Integration Standards What standards from other disciplines will enrich the learning experiences for the students? Resources Resources What resources will be utilized to enhance student learning? Curriculum and Instruction 2014-2015 Page 4 of 4