#### A1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

A1.1.2: Simplify square roots using factors.

A1.1.3: Understand and use the distributive, associative, and commutative properties.

A1.1.5: Use dimensional (unit) analysis to organize conversions and computations.

#### A1.2: Students solve linear equations and inequalities in one variable. They solve word problems that involve linear equations, inequalities, or formulas.

A1.2.1: Solve linear equations.

A1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

A1.2.4: Solve linear inequalities using properties of order.

A1.2.5: Solve combined linear inequalities.

A1.2.6: Solve word problems that involve linear equations, formulas, and inequalities.

#### A1.3: Students sketch and interpret graphs representing given situations. They understand the concept of a function and analyze the graphs of functions.

A1.3.1: Sketch a reasonable graph for a given relationship.

A1.3.3: Understand the concept of a function, decide if a given relation is a function, and link equations to functions.

A1.3.4: Find the domain and range of a relation.

#### A1.4: Students graph linear equations and inequalities in two variables. They write equations of lines and find and use the slope and y-intercept of lines. They use linear equations to model real data.

A1.4.1: Graph a linear equation.

A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

A1.4.3: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept of the graph are related to the equation.

A1.4.4: Write the equation of a line given appropriate information.

A1.4.6: Graph a linear inequality in two variables.

#### A1.5: Students solve pairs of linear equations using graphs and using algebra. They solve pairs of linear inequalities using graphs. They solve word problems involving pairs of linear equations.

A1.5.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

A1.5.3: Understand and use the substitution method to solve a pair of linear equations in two variables.

A1.5.4: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

A1.5.5: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

A1.5.6: Use pairs of linear equations to solve word problems.

#### A1.6: Students add, subtract, multiply, and divide polynomials. They factor quadratics.

A1.6.2: Multiply and divide monomials.

A1.6.4: Multiply polynomials.

A1.6.5: Divide polynomials by monomials.

A1.6.6: Find a common monomial factor in a polynomial.

A1.6.7: Factor the difference of two squares and other quadratics.

#### A1.8: Students graph and solve quadratic and radical equations. They graph cubic equations.

A1.8.2: Solve quadratic equations by factoring.

A1.8.4: Complete the square to solve quadratic equations.

A1.8.5: Derive the quadratic formula by completing the square.

A1.8.8: Solve equations that contain radical expressions.

#### A1.9: Mathematical Reasoning and Problem Solving

A1.9.1: Use a variety of problem solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.

A1.9.3: Use the properties of the real number system and the order of operations to justify the steps of simplifying functions and solving equations.

A1.9.4: Understand that the logic of equation solving begins with the assumption that the variable is a number that satisfies the equation, and that the steps taken when solving equations create new equations that have, in most cases, the same solution set as the original. Understand that similar logic applies to solving systems of equations simultaneously.

A1.9.7: Identify the hypothesis and conclusion in a logical deduction.

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.