Revised July 2016 Essential Questions What are the characteristics of quadratic functions? How can you solve a quadratic equation? How can you use functions to model real-world situations? Enduring Understandings and Unit Goals EU #1: A quadratic function is a type of nonlinear function that models certain situations where the rate of change is not constant. o Graph various forms of quadratic functions. EU #2: Quadratic equations can be solved by a variety of methods. o Solve quadratic equations by graphing and finding square roots. o Solve quadratic equations by factoring. o Solve quadratic equations by using the quadratic formula. EU #3: Functions can be used to model and solve real-world problems. o Solve real-world problems using linear and quadratic equations.
Standards Common Core State Standards/College and Career Readiness Anchor Standards : CCSS.MATH.CONTENT.HSA.SSE.A.1: Interpret expressions that represent a quantity in terms of its context. CCSS.MATH.CONTENT.HSA.SSE.B.3.A: Factor a quadratic expression to reveal the zeros of the function it defines. CCSS.MATH.CONTENT.HSA.APR.B.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. CCSS.MATH.CONTENT.HSA.CED.A.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. CCSS.MATH.CONTENT.HSA.CED.A.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. CCSS.MATH.CONTENT.HSA.REI.B.4: Solve quadratic equations in one variable. CCSS.MATH.CONTENT.HSA.REI.B.4.B: Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. CCSS.MATH.CONTENT.HSA.REI.C.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. CCSS.MATH.CONTENT.HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. CCSS.MATH.CONTENT.HSF.IF.C.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* CCSS.MATH.CONTENT.HSF.IF.C.7.A: Graph linear and quadratic functions and show intercepts, maxima, and minima. CCSS.MATH.CONTENT.HSN.Q.A.2: Define appropriate quantities for the purpose of descriptive modeling. CCSS.MATH.CONTENT.HSN.Q.A.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities MSMHS 21 st Century Learning Expectations Competency 1: Read and write effectively for a variety of purposes. Competency 3: Make decisions and solve problems independently and collaboratively. Competency 5: Contribute to a positive learning environment with respect and responsibility. 2
Unit Content Overview 1. Quadratic Graphs and Their Properties (9-1) Standard Form of a Quadratic Function Identifying a Vertex Graphing y = ax 2 Graphing y = ax 2 + c 2. Quadratic Functions (9-2) Graph of a Quadratic Function Graphing ax 2 + bx + c 3. Solving Quadratic Equations (9-3) Standard Form of a Quadratic Equation Solving by Graphing Solving by Using Square Roots 4. Factoring to Solve Quadratic Equations (9-4) Zero-Product Property Solving by Factoring 5. The Quadratic Formula and the Discriminant (9-6) Using the Quadratic Formula Finding Approximate Solutions Choosing an Appropriate Method Using the Discriminant 6. Systems of Linear and Quadratic Equations (9-8) Solving by Graphing Solving using Elimination Solving using Substitution Solving with a Graphing Calculator Students will be able to Learning Objectives Graph quadratic functions of the form y = ax 2 and y = ax 2 + c (9-1) Graph quadratic functions of the form y = ax 2 + bx + c (9-2) Solve quadratic equations by graphing and using square roots (9-3) Solve quadratic equations by factoring (9-4) Solve quadratic equations by using the quadratic formula (9-6) Find the number of solutions of a quadratic equation (9-6) Solve systems of linear and quadratic equations (9-8) 3
Assured Learning Experiences Differentiated Instruction / Instructional Strategies: Daily Warm Up Activities Power Point Lecture with note-taking Guided Notes Flexible grouping Exit slips Graphic Organizers Creating authentic connections for students Rephrasing and restatement of information and concepts Accountable Talk Discussion Independent Problem Solving Collaborative Problem Solving Homework Smart Phone Profit Performance Task (practical application) o Rubric 3: Problem Solving Interdisciplinary Connection: Language Arts- Accountable Talk, Word Problems Assessments FORMATIVE ASSESSMENTS: Warm ups (SAT prep) ABCD Cards Whiteboards Mid-class check-ins Exit Slips Student-led instruction Homework Smart Phone Profit Performance Task o Rubric 3: Problem Solving SUMMATIVE ASSESSMENTS: Quiz on EU #1 Quiz on EU #2 Unit Test Smart Phone Profit Performance Task 4
Unit Task Unit Task Name: Smart Phone Profit Performance Task Description: Students will use information learned during this unit about the key features of the graphs of quadratic equations (EU #1), how to solve quadratic equations using several different methods (EU #2), and how to use quadratics to model real world situations (EU #3) compare and contrast profit functions for different companies selling smart phones. Students will be given information about each company in different forms (tables, graphs, etc.) and will be asked to write equations and sketch graphs for each of the profit functions. Students will use these equations and graphs to describe the long term trend in profit for each of the companies. They will use their data to choose a company that they would invest in. Students will finally write a reflection on the assignment describing which company has the best future and which method of solving and graphing they like the best. Evaluation: Rubric 3: Problem Solving Unit Resources Textbook (Charles, Randall I., Dan Kennedy, and Basia Hall. : Common Core. Boston, MA: Pearson, 2012) MSMHS School-wide Rubrics Internet databases Laptops 5