Understand A-REI.1 Explain each step in solving a i) Tasks are limited to quadratic i) Tasks are limited to simple solving equations simple equation as following equations. rational or radical equations. as a process of from the equality of numbers reasoning and asserted at the previous step, explain the starting from the assumption reasoning that the original equation has a solution. Construct a viable argument to justify a solution method. Solve equations A-REI.4b Solve quadratic equations in i) Tasks do not require students to i) In the case of equations that and inequalities one variable. b) Solve write solutions for quadratic have roots with nonzero in one variable quadratic equations by equations that have roots with imaginary parts, students write inspection (e.g., for), taking nonzero imaginary parts. However, the solutions as a ± bi for real square roots, completing the tasks can require the student to numbers a and b. square, the quadratic formula recognize cases in which a and factoring, as appropriate quadratic equation has no real to the initial form of the solutions. equation. Recognize when Note, solving a quadratic equation the quadratic formula gives by factoring relies on the complex solutions and write connection between zeros and them as a ± bi for real factors of polynomials (cluster numbers a and b. Cluster A-APR.B is formally assessed in Algebra II. Solve Systems of A.REI.6 Solve systems of equations Tasks have real-world context. Tasks are limited to 3x3 Equations exactly and approximately systems (e.g. with graphs), focusing Tasks have hallmarks of on pairs of linear equations in modeling as a mathematical two variables. practice (less defined tasks, more of the modeling cycle,
Understand solving equations as a process of reasoning and explain the reasoning 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. i) Tasks are limited to quadratic equations. i) Tasks are limited to simple rational or radical equations. Solve equations and inequalities in one variable A-REI.4b Solve quadratic equations in one variable. b) Solve quadratic equations by inspection (e.g., for), 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 gives complex solutions and write them as a ± bi for real numbers a and b. i) Tasks do not require students to write solutions for quadratic equations that have roots with nonzero imaginary parts. However, tasks can require the student to recognize cases in which a quadratic equation has no real solutions. Note, solving a quadratic equation by factoring relies on the connection between zeros and factors of polynomials (cluster Cluster A-APR.B is formally assessed in Algebra II. i) In the case of equations that have roots with nonzero imaginary parts, students write the solutions as a ± bi for real numbers a and b. Solve Systems of Equations A.REI.6 Solve systems of equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables. Tasks have real-world context. Tasks have hallmarks of modeling as a mathematical practice (less defined tasks, more of the modeling cycle, Tasks are limited to 3x3 systems
A2_UP_U1_Polynomial_Rational_and_Radical_Relationships_Dec_27.docx