A.REI.1 Explain each step in solving a Ability to identify the simple equation as following from the mathematical property (addition equality of numbers asserted at the property of equality, distributive previous step, starting from the assumption property, etc.) used at each step that the original equation has a solution. in the solution process as a Construct a viable argument to justify a means of justifying a step solution method. A.REI.4 Solve quadratic equations in one Ability to solve literal equations variable. for a variable of interest 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) b. Solve quadratic equations by inspection Students in Algebra 1 must be able to recognize Ability to solve quadratic (e.g., for x2 = 49), taking square roots, when quadratic equations do not have real equations using various completing the square, the quadratic solutions. methods and recognize the formula and factoring, as appropriate to the most efficient method initial form of the equation. Recognize Examples include or . Ability to use the value of the when the quadratic formula reveals that the discriminant to determine if a quadratic equation has real In Algebra 2, they will use knowledge of the quadratic equation has one “no solutions”. (major) complex number system to find the complex double solution, two unique solutions. solutions or no real solutions
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.
A1_U4_UP_Eq_Exp_Jan_15.docx