A.REI.1 Explain each step in solving a simple equation as 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. Ability to identify the mathematical property (addition property of equality, distributive property, etc.) used at each step in the solution process as a means of justifying a step 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. (major) Ability to solve literal equations for a variable of interest b. Solve quadratic equations by inspection (e.g., for x2 = 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 reveals that the quadratic equation has “no real solutions”. (major) Ability to solve quadratic equations using various methods and recognize the most efficient method Ability to use the value of the discriminant to determine if a quadratic equation has one double solution, two unique solutions or no real solutions Students in Algebra 1 must be able to recognize when quadratic equations do not have real solutions. Examples include or . In Algebra 2, they will use knowledge of the complex number system to find the complex solutions.
The following skills/understanding developed in Middle School should support students in learning “Operations with rational and irrational numbers”: In 8th grade students Having already extended arithmetic from whole numbers to fractions (grades 4-6) and from fractions to rational numbers (grade 7), students in grade 8 encountered particular irrational numbers such as or Operations with rational and irrational numbers In Algebra II students will use operations with rational and irrational numbers to simplify complex numbers. The following skills/understandings developed in Middle school should support students in learning “Quadratic Equations in One Variable”: Solving one-variable linear equations Understanding of and ability to work with rational and irrational numbers Fluency with properties of numbers. Ability to generate equivalent expressions and equations Fluency with operations with rational numbers is an expectation at the 7th grade level. In Algebra I Unit 1 students solved linear and Quadratic Equations in One Variable In Geometry students will need to be fluent in solving quadratic equations in one variable to apply geometry concepts. In Algebra II Unit 1 students will solve quadratic equations with real coefficients that have complex solutions.
a.APR.1 A.sse.3 A.REI.4 This link provides access to tasks created with support from the Bill and Linda Gates foundation for the Mathematics Assessment Program. Questions #3-5 Solving Quadratic Equations in One Variable A.sse.3 A.REI.4 This link provides access to tasks created with support from the Bill and Linda Gates foundation for the Mathematics Assessment Program. Question #2 A.APR.1 This link provides access to tasks created with support from the Bill and Linda Gates foundation for the Mathematics Assessment Program. Question #2 Solving Quadratic Equations in One Variable A.sse.3 A.REI.4 A.CED.1 This link provides access to tasks created with support from the Bill and Linda Gates foundation for the Mathematics Assessment Program. Questions 2 and 3 invovle sorting functions question, multiple solutions Rearrange formulas to highlight a given interest A.CED.4 This task requires students to solve literal equations for a variable of interest.
Resources This section contains links to materials that are intended to support content instruction in this unit. Topic Standards Addressed Link Notes Graphing equations in two variables A.CED.2 This is a link to a program to graph a given equation. Teacher types in equation and the program graphs it for you. Solving quadratics A.SSE.3 A.REI.4 Provides a review of factoring and quadratic formula as well as some practice problems. Solving quadratics A.SSE.3 A.REI.4 Click on “Algebra”. Applicable activities include Algebra 4 Algebra Quiz Function Flyer Unit 4 A.SSE.3 A.REI.4 A.CED.1 A.CED.2 A.APR.1 A.SSE.1 You will need to create an account, which is free and you will get access to many lessons. Just run a search on the topic you are looking to teach. {Search: nonlinear systems for a lesson on solving systems with quadratics} Solving quadratic equations A.SSE.3 A.REI.4 Math 101: College Algebra course, scroll down to factoring with FOIL, Graphing Parabolas and Solving Quadratics. There are videos for a variety of lessons with quadratics. When you click on the topic to pull up the video, a time line for the video is underneath. You can skip to a specific topic. There is also a quiz
(c) Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with integer exponents. equivalent form of the expression reveals something about the situation. ii) Tasks are limited to exponential expressions with rational or real exponents. Understand the relationship between zeros and factors of polynomials A-APR.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. i) Tasks are limited to quadratic and cubic polynomials in which linear and quadratic factors are available. For example, find the zeros of . i) Tasks include quadratic, cubic, and quartic polynomials and polynomials for which factors are not provided. For example, find the zeros of Create equations that describe numbers or relationships 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. i) Tasks are limited to linear, quadratic or exponential equations with integer exponents. i) Tasks are limited to exponential equations with rational or real exponents and rational functions. ii) Tasks have a real-world context. Understand solving equations as a process of A.REI.1 Explain each step in solving a simple equation as following Tasks are limited to quadratic equations. i) Tasks are limited to rational or radical equations.