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Common Core Curriculum Map 2012-2013 Common Core Unit Name: Quadratics Unit Number: 3 Enduring Understanding: Students will reason both abstractly and quantitatively in order to solve and graph equations that have a degree of two as their largest exponent. Answers will be real and imaginary defined by the complex number system. Quadratics are modeled in real-world scenarios such as construction, navigation, engineering, sports, manufacturing, business, and physics. Students attend to precision when finding real and imaginary numbers. Students will look for and express regularity in repeated reasoning when determining the simplified powers of i. Standard F.IF.4 A.CED.2 A.REI.4b F.IF.8a A.SSE.3b A.REI.4a N.CN.1 N.CN.2 N.CN.7 A.SSE.2 Essential Questions A.SSE.2 Can I factor expressions that are quadratic in form? F.IF.8a: Can I factor and complete the square in a quadratic function to show and interpret zeros, extreme values, and symmetry in the graph? A.REI.4a: Can I complete the square on a quadratic equation and transform it into the vertex form of the parabola and derive the quadratic formula? N.CN.1: Can I find a complex number in the form of a + bi? Can I find i^2, i^3, i^4, and i^99? N.CN.2: Can I use properties and operations on complex numbers? N.CN.7: Can I solve quadratic equations with real number coefficients that have complex solutions? A.SSE.3b: Can I complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines? A.REI.4b: Can I solve quadratic equations by taking square roots, completing the square, quadratic formula, and factoring while recognizing complex solutions? A.CED.2: Can I create and graph equations in two or more variables? F.IF. 4: Can I interpret and sketch key features (intercepts, increasing or decreasing intervals, relative maximums or minimums, symmetries, end behavior, periodicity) of functions that model relationships between two quantities? Pacing Guideline 11 Days Key Academic Vocabulary Axis of Symmetry Coefficient Complete the Square Complex Conjugates Complex number (imaginary and real) Decreasing Interval Discriminant Double Root End Behavior Factoring i, i^2, i^3, i^4 Imaginary number Increasing Interval Local Maximum Local Minimum Parabola Perfect Square Trinomial Principal Square Root Product Property of square Roots Pythagorean Theorem Quadratic equation Quadratic expression 1 Common Core Curriculum Map 2012-2013 Quadratic Formula Quadratic Function Quotient Property of square Roots Rationalizing the Denominator Standard Form of a Quadratic Equation Vertex Vertex Form of a Parabola Zero Product Property Zeros, X-Intercepts, Solutions, Answers, Roots Suggested Resources by Unit Location of these resources Forming Quadratics http://map.mathshell.org/materials/lessons.php?taskid=224&subpage=c oncept Holt Algebra II Textbook Ch. 5.1,.5.2, 5.3, 5.4, 5.5, 5.6 2