Search the California Content Standards

Cluster:
Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.]

Standard:
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.

Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]

Standard:
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).

Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]

Standard:
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. *

Cluster:
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]

Standard:
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.

Cluster:
Solve equations and inequalities in one variable.

Standard:
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Linear inequalities; literal equations that are linear in the variables being solved for; exponential of a form, such as 2^x = 1/16.]

Cluster:
Solve equations and inequalities in one variable.

Standard:
Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. CA

Cluster:
Solve systems of equations. [Linear systems]

Standard:
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Cluster:
Solve systems of equations. [Linear systems]

Standard:
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cluster:
Experiment with transformations in the plane.

Standard:
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Cluster:
Make geometric constructions. [Formalize and explain processes.]

Standard:
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.