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 Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form, (x) = a(x  h)2 + k in Topic B. The strategy known as completing the square is...

 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...

 In Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex...

 In Topic D, students are formally introduced to the modeling cycle (see page 61 of the CCLS) through problems that can be solved by creating equations and inequalities in one variable, systems of...

 Throughout middle school, students practice the process of solving linear equations (6.EE.5, 6.EE.7, 7.EE.4, 8.EE.7) and systems of linear equations (8.EE.8). Now, in Topic C, instead of just...

 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 completedsquare 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 discover that the multistep and exact way of solving 2x  5 = 3x + 1 using algebra can sometimes be avoided by recognizing that an equation of the form f(x) = g(x) can...

 Student Outcomes Students investigate a problem that can be solved by reasoning quantitatively and by creating equations in one variable. They compare the numerical approach to the algebraic approach...

 Student Outcomes Students use systems of equations or inequalities to solve contextual problems and interpret solutions within a particular context.

 Student Outcomes Students create systems of equations that have the same solution set as a given system. Students understand that adding a multiple of one equation to another creates a new system of...

 Student Outcomes Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically.

 Student Outcomes Students recognize and identify solutions to twovariable inequalities. They represent the solution set graphically. They create two variable inequalities to represent a situation...

 Student Outcomes Students recognize and identify solutions to twovariable equations. They represent the solution set graphically. They create two variable equations to represent a situation. They...

 Student Outcomes Students interpret equations like 1/x = 3 as two equations “1/x = 3 ” and “x ≠ 0 ” joined by “and.” Students find the solution set for this new system of equations.

 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...

 Student Outcomes Students solve two inequalities joined by “and” or “or,” then graph the solution set on the number line.

 Student Outcomes Students describe the solution set of two equations (or inequalities) joined by either “and” or “or” and graph the solution set on the number line.

 Student Outcomes Students learn ifthen moves using the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.

 Student Outcomes Students learn “ifthen” moves using the properties of equality to solve equations. Students also explore moves that may result in an equation having more solutions than the...