CoUrSe ModUle SUMMary and UnpaCkIng of StandardS | 67A-REI.B.4 Solve quadratic equations in one variable.
b. Solve quadratic equations by inspection (e.g., for x^2 = 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.
A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing
on pairs of linear equations in two variables.
A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two
variables algebraically and graphically. For example, find the points of intersection between
the line y = -3x and the circle x^2 + y^2 = 3.
G-GPE.A.2 Derive the equation of a parabola given a focus and directrix.
Instructional Days: 14Student Outcomes
Lesson 22: Equivalent Rational Expressions
● (^) Students define rational expressions and write them in equivalent forms.
Lesson 23: Comparing Rational Expressions
● (^) Students compare rational expressions by writing them in different but equivalent
forms.
Lesson 24: Multiplying and Dividing Rational Expressions
● (^) Students multiply and divide rational expressions and simplify using equivalent
expressions.
Lesson 25: Adding and Subtracting Rational Expressions
● (^) Students perform addition and subtraction of rational expressions.
Lesson 26: Solving Rational Equations
● (^) Students solve rational equations, monitoring for the creation of extraneous solutions.
Lesson 27: Word Problems Leading to Rational Equations
● (^) Students solve word problems using models that involve rational expressions.
Lesson 28: A Focus on Square Roots
● (^) 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 apparent paradoxes.
● (^) Students explain and justify the steps taken in solving simple radical equations.
Lesson 29: Solving Radical Equations
● (^) Students develop facility in solving radical equations.
Lesson 30: Linear Systems in Three Variables
● (^) Students solve linear systems in three variables algebraically.
Lesson 31: Systems of Equations
● (^) 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 graphs of the equations intersect
correspond to the solutions of the system.