Write and solve one-step linear equations in one variable.
Write and evaluate an algebraic expression for a given situation, using up to three variables.
Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.
Solve problems manually by using the correct order of operations or by using a scientific calculator.
Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)².
Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.
Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.
Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
Graph functions of the form y = nx² and y = nx³ and use in solving problems.
Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.
Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.
Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.
Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x - 5) + 4(x - 2) = 12.
Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.
Students graph a linear equation and compute the x-and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.
Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.
represents and solves real-world problems graphically, with algebraic expressions, equations, and inequalities.
uses algebraic problem-solving strategies to solve real-world problems involving linear equations and inequalities.
uses systems of equations and inequalities to solve real-world problems graphically, algebraically, and with matrices.
Write and evaluate mathematical expressions that correspond to given situations.
Write, solve, and graph one- and two- step linear equations and inequalities.
Works backward with two-step function rules to undo expressions.
Solve problems given a formula.
Apply the Commutative, Associative, and Distributive Properties to show that two expressions are equivalent.
Construct and analyze tables, graphs and equations to describe linear functions and other simple relations using both common language and algebraic notation.
Formulate and use different strategies to solve one-step and two-step linear equations, including equations with rational coefficients.
Use the properties of equality to represent an equation in a different way and to show that two equations are equivalent in a given context.
Create and interpret tables, graphs, and models to represent, analyze, and solve problems related to linear equations, including analysis of domain, range and the difference between discrete and continuous data.
Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.
Use tables, graphs, and models to represent, analyze, and solve real-world problems related to systems of linear equations.
Identify the solution to a system of linear equations using graphs.
Translate among verbal, tabular, graphical and algebraic representations of linear functions.
Compare the graphs of linear and non-linear functions for real-world situations.
Solve linear equations in one variable that include simplifying algebraic expressions.
Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.
Solve literal equations for a specified variable.
Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.
Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.
Solve and graph the solutions of absolute value equations and inequalities with one variable.
Rewrite equations of a line into slope-intercept form and standard form.
Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form.
Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line.
Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line.
Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.
Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph.
Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology.
Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods.
Solve real-world problems involving systems of linear equations and inequalities in two and three variables.