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Unwrapping CCSS Mathematics Example – High School A.REI.4. Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form ( x p)2 q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x 2 49 ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a bi for real numbers a and b. Concepts: Need to know about quadratic equations in one variable Vocabulary Quadratic equation Forms of quadratic equations x2 p; x2 25 x2 bx c; x2 4x 25 ax2 bx c 0; x 2 8x 6 0 ( x h) 2 4 p ( x p)2 q; ( x 3) 2 25 Methods of solution Inspection Square roots Complete the square Quadratic formula Factor 2/22/2012 11:03 AM Document1 Note: This example is used in conjunction with another file: Unwrapping the Math Standards Types of solutions (quadratic formula) Real Complex Skills: Be Able to Do Solve quadratic equations in one variable Use the method - completing the square Derive the quadratic formula Solve by inspection ( x 2 25 ) Solve by taking square roots Solve by completing the square Future uses, conics, trig functions, zeros, etc. Solve by using quadratic formula How to derive it. Solve by factoring Lots of hints, patterns, and effective practice. Recognize that QF may give complex solutions (using the quadratic formula) Target: only as it applies to QF at this point. Write complex solutions as a bi (using quadratic formula) Target: only as it applies to QF at this point. Big Ideas 1. Quadratic equations can be written in various forms. 2. There are various methods we can use to solve quadratic equations. 3. The quadratic formula can be derived by manipulating the form ( x p)2 q 2/22/2012 11:03 AM Document1 b 2 b2 c ( x ) ( ) 2 2a 4a a Note: This example is used in conjunction with another file: Unwrapping the Math Standards Essential Questions 1. 2. 3. 4. What is a quadratic equation? How can algebra be used to solve quadratic equations? How many solutions can quadratic equations have? How can we decide which method to use to solve quadratic equations? Topics or Context: Lessons, Activities, Units of Instruction Quadratic equation unit - solving Text – 9.1-9.7 TRP practice problems Teach each method, but make sure to connect them. ….. Strategies/Activities Completing the Square Notes – Prepare for Completing the Square Peer teaching – Solving by completing the square … Peer teaching =Factoring quadratics form Since completing the square is kind of tricky, use the peer teaching (with effective notes) to practice. Prepare for it FIRST by reviewing prior skills. x 2 bx c Peer teaching =Factoring quadratics form ax 2 bx c ….. Assessments HW Activities Practice test Unit tests 2/22/2012 11:03 AM Document1 Make sure instruction, HW, activities, and assessments are all connected and coherent. Note: This example is used in conjunction with another file: Unwrapping the Math Standards