UNIT 3 - Equations and Inequalities
Section 3.1: One Step Equations
Section 3.2: Two Step Equations
Section 3.3: Multi-Step Equations
Section 3.4: Variables on Both Sides
Section 3.2: Two Step Equations
Section 3.3: Multi-Step Equations
Section 3.4: Variables on Both Sides
CCSS Addressed - Foundations of Algebra 2013-2014
N.Q.1 :: Use units as a way to understand problems and to guide the solution of multi‐step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
N.Q.2 :: Define appropriate quantities for the purpose of descriptive modeling.
N.Q.3 :: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
A.CED.1 :: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A.CED.2 :: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-APR.1 :: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A.REI.10 :: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
A-REI.11 :: Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y =g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g.,using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
A.REI.12 :: Graph the solutions to a linear inequality in two variables as a half‐plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half‐planes.
N.Q.2 :: Define appropriate quantities for the purpose of descriptive modeling.
N.Q.3 :: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
A.CED.1 :: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A.CED.2 :: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-APR.1 :: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A.REI.10 :: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
A-REI.11 :: Explain why the x‐coordinates of the points where the graphs of the equations y = f(x) and y =g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g.,using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
A.REI.12 :: Graph the solutions to a linear inequality in two variables as a half‐plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half‐planes.
CCSS Addressed :: Algebra Year 2 of 2
Equations and Inequalities:
Students
will perform algebraic procedures accurately.
A.A.21 :: Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable
A.A.22 :: Solve all types of linear equations in one variable
A.A.23 :: Solve literal equations for a given variable
A.A.24 :: Solve linear inequalities in one variable
A.A.25 :: Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable.
A.A.26 :: Solve algebraic proportions in one variable which result in linear or quadratic equations
A.A.27 :: Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
A.A.28 :: Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression
A.A.21 :: Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable
A.A.22 :: Solve all types of linear equations in one variable
A.A.23 :: Solve literal equations for a given variable
A.A.24 :: Solve linear inequalities in one variable
A.A.25 :: Solve equations involving fractional expressions Note: Expressions which result in linear equations in one variable.
A.A.26 :: Solve algebraic proportions in one variable which result in linear or quadratic equations
A.A.27 :: Understand and apply the multiplication property of zero to solve quadratic equations with integral coefficients and integral roots
A.A.28 :: Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression