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Common Core: Standard
Common Core: ELA
Common Core: Math
CCLS - Math: A.REI.4.b
- Reasoning With Equations And Inequalities
- Solve Equations And Inequalities In One Variable
- State Standard:
- 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 gives complex solutions and write them as a ± bi for real numbers a and b.
- Students extend their facility with solving polynomial equations to working with complex zeros. Complex numbers are introduced via their relationship with geometric transformations. The topic...
- Student Outcomes Students develop facility with graphical interpretations of systems of equations and the meaning of their solutions on those graphs. For example, they can use the distance formula to...
- Student Outcomes Students solve systems of linear equations in two variables and systems of a linear and a quadratic equation in two variables. Students understand that the points at which the two...
- Student Outcomes Students solve simple radical equations and understand the possibility of extraneous solutions. They understand that care must be taken with the role of square roots so as to avoid...
- Student Outcomes Students solve rational equations, monitoring for the creation of extraneous solutions.
- Students solve polynomial, rational, and radical equations, and apply these types of equations to real-world situations. They examine the conditions under which an extraneous solution is introduced...
- Topic A introduces polynomial expressions. In Module 1, students learned the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is...
- Student Outcomes Students use the quadratic formula to solve quadratic equations that cannot be easily factored. Students understand that the discriminant, b2 - 4ac, can be used to determine whether...
- Student Outcomes Students derive the quadratic formula by completing the square for a general quadratic equation in standard form, ax2 + bx + c = 0, and use it to verify the solutions for equations...
- Student Outcomes Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw...
- Student Outcomes Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a ≠ 1), as equivalent expressions in completed square form, a(x - h)2 + k. They build quadratic...
- Student Outcomes Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a = 1), in the equivalent completed-square form, a(x - h)2 + k, and recognize cases for which...
- Student Outcomes Students use appropriate and efficient strategies to find solutions to basic quadratic equations. Students interpret the verbal description of a problem and its solutions in context...
- Student Outcomes Students learn that equations of the form (x - a)(x - b) = 0 have the same solution set as two equations joined by “or:” x - a = 0 or x - b = 0. Students solve factored or easily...