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Trousdale County Schools Focused Lesson Plan 2015-16 Teacher: Canaan Bowman Unit Name: Quadratic Equations and Models Unit #: 4 Unit Length: 5 weeks Week: 11/16 – 11/23 Week 4 of 5 Subject: Core Math II Tennessee State Standard(s) to be taught: (Write the entire standard) N-Q.2 – Define appropriate quantities for the purpose of descriptive modeling. N-CN.1 – Know there is a complex number i such that 𝑖 2 = −1, and ever complex number has the form 𝑎 + 𝑏𝑖 with 𝑎 and 𝑏 real. N-CN.2 – Use the relation 𝑖 2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. N-CN.7 – Solve quadratic equations with real coefficients that have complex solutions. A.SSE.2 – Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). A-CED.1 – Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-REI.1 – Explain each step in solving a simple equation s following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.4 – Solve quadratic equations in one variable. 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. I Can Statements : I can solve quadratic equations with real and imaginary solutions. I can determine from a function’s graph the type and number of zeros. I can graph a quadratic function. I can operate on complex numbers. I can solve application problems with complex numbers. I can solve and model with quadratic equations. Accommodations for students, both regular and special populations : Extra practice time may be given using InteractMath technology online. One-on-one and/or peer tutoring. Re-take quizzes on which students perform poorly. Unit Vocabulary: factor, zero-factor property, perfect-square trinomial, difference of squares, square root, product property of radicals, quotient property of radicals, completing the square, quadratic formula, discriminant, real solutions, non-real solutions, imaginary numbers, imaginary unit, complex number, pure imaginary unit, correlation, exponential function, exponential regression, line of best fit, linear regression, quadratic regression Daily Agenda Monday Bell-ringer: Quadratic Equations (Various Methods) and Solution Types/Graphing/Vertex Formula Notes/Examples over Imaginary Numbers Practice Problems (HW) Resources, Technology, Formative and/or Summative Assessments, Assignments, and a Daily Activity for citing text based evidence in conversations and/or writing Resources: Integrated II Text, Bell-ringer Technology: TI nSpires, MOBI Assessment: questioning/observation during student work Assignments: Imaginary Solutions to Quad. Equation HW 1 Tuesday Go over HW Modeling Problems Quiz – Quadratic Equations (Real and Imaginary Solutions) Go over MIST Practice Test Resources: Integrated II Text, Modeling Problems, Quiz Technology: MOBI, TI nSpires Assessment: homework, observation/questioning, quiz Wednesday Bell-ringer: Modeling Problem (MICA-based) Notes/Examples over Complex Numbers Practice Problems (HW) Assignments: Resources: Integrated II Text, Bell-ringer Technology: MOBI, TI nSpire Assessment: observation/questioning Thursday HW Quiz Continue Practice Problems with Complex Numbers and Quadratic Equations (HW) MICA Practice Test Assignments: Complex Number HW Resources: Integrated II Text, MICA Technology: MICA, MOBI, TI nSpires Assessment: homework, observation/questioning, MICA Test Friday Go over HW Quiz – Complex Numbers and Quadratic Equations MICA Practice Test Assignments: Complex Numbers and Quad. Eq. HW Resources: Integrated II Text, Quiz, MICA Technology: MOBI, TI nSpires, MICA Assessment: homework, Quiz, MICA Test, observation/quesioning Assignments: 2