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A2-A-1-1

Page history last edited by Tashe Harris 6 years, 2 months ago

A2.A.1.1 Represent real-world or mathematical problems using quadratic equations and solve using various methods (including graphing calculator or other appropriate technology), factoring, completing the square, and the quadratic formula. Find non-real roots when they exist.

In a Nutshell

Students will explore the different methods of solving quadratic equations. They become confident in their ability to solve quadratics and can easily switch between methods when necessary to come to a solution. When a real solution is not possible, students understand the solution will be a non-real root. They will recognize that a particular solution may not be applicable in the original context.

Student Actions	Teacher Actions
Students will develop strategies to select the appropriate method for solving a quadratic when solving a second degree function, and they will be able to question the reasonableness of their solution. Students engage in the idea of roots within a quadratic. They will develop a flexible conceptual understanding that zeros, solutions, x-intercepts and roots are the same numbers but each term is used in different contexts. Students will be able to transfer the information between multiple representations. Students will develop procedural fluency by discussing the various connections between the different strategies for solving quadratic function and develop a conceptual understanding of the connection of quadratics to real-world problems. Students expand their knowledge of roots in a quadratic equation to include complex solutions and develop a conceptual understanding of why complex solutions come in pairs. Students will develop mathematical reasoning as they discuss, write, read, and/or interpret real-world scenarios in terms of a quadratic function.	Provide the students a variety of real-world problems which involve finding the solution of a quadratic function. Pose purposeful questions that focus on making connections among mathematical representations of the numerical solution of zeros, roots, solutions, or x-intercepts. Facilitate meaningful mathematical discourse: Give students time to discuss and explore the advantages and disadvantages of each method of solving a quadratic function. Pose purposeful Questions: Pose purposeful questions that allow students to determine under what circumstances solutions to a quadratic equation are not real. Use and Connect Mathematical Representations: Engage students in making connections between the graphical representation of a quadratic function and the number of real zeros it has. Build procedural fluency from conceptual understanding: Build procedural fluency from conceptual understanding by providing students with a variety of tasks that connect the methods of solving quadratic equations to the number and type of solutions the quadratic equations will have. Allow students to choose from a variety of methods, which may include the use of technology, to solve the problems and to present their findings.
Key Understandings	Misconceptions
Solve quadratic equations by factoring, completing the square, graphing or using the quadratic formula to find real or non-real roots. Interpret the meaning of roots or lack of roots when using technology. Explain the meaning of quadratic roots within the context of a real world problem. Create a mathematical model for a real world situation and interpret the solutions with the context of the original problem.	Students do not factor properly, identifying factor pairs of the last term and use those without checking if they add up to the middle term. For example, a student might see x² + 6x + 9 and factor it incorrectly as (x9)(x+1). Students may correctly identify factors m and n of c, but not realize that m+n=b Students do not put quadratic equation in ax²+bx+c=0 format before solving it. Students do not apply the quadratic formula properly, they forget the negative at the beginning and/or they do not divide all the numerator part of the quadratic equation by 2a. Students complete the square on one side of the equation and forget to balance the equation on the other side or they might loose the second solution when taking the square root. Students complete the square on one side of the equation and forget to balance the equation on the other side. Students lose the second solution when taking the square root. For example: