IXL - Indiana high school math standards

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Standards document:

2010 Common Core State Standards 2010 Common Core State Standards
2000 Indiana Academic Standards: Algebra I 2000 Indiana Academic Standards: Algebra I

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A1.1 Operations with Real Numbers

A1.1.1 Compare real number expressions.
- Numbers: Compare and order rational numbers (Algebra - A.2)
- Scientific notation: Compare numbers written in scientific notation (Algebra - W.2)
A1.1.2 Simplify square roots using factors.
A1.1.3 Understand and use the distributive, associative, and commutative properties.
A1.1.4 Use the laws of exponents for rational exponents.
A1.1.5 Use dimensional (unit) analysis to organize conversions and computations.

A1.2 Linear Equations and Inequalities

A1.2.1 Solve linear equations.
A1.2.2 Solve equations and formulas for a specified variable.
- Problem solving: Rate of travel: word problems (Algebra - O.4)
- Exponential functions: Exponential growth and decay: word problems (Algebra - X.3)
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.
- Solve equations: Solve linear equations: word problems (Algebra - J.8)

A1.3 Relations and Functions

A1.3.1 Sketch a reasonable graph for a given relationship.
A1.3.2 Interpret a graph representing a given situation.
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 Graphing Linear Equations and Inequalities

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.
- Linear functions: Slope-intercept form: write an equation from a graph (Algebra - S.6)
- Linear functions: Slope-intercept form: write an equation (Algebra - S.7)
A1.4.4 Write the equation of a line given appropriate information.
A1.4.5 Write the equation of a line that models a data set and use the equation (or the graph of the equation) to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.
A1.4.6 Graph a linear inequality in two variables.
- Linear inequalities: Graph a linear inequality in two variables (Algebra - T.3)

A1.5 Pairs of Linear Equations and Inequalities

A1.5.1 Use a graph to estimate the solution of a pair of linear equations in two variables.
- Systems of linear equations: Solve a system of equations by graphing (Algebra - U.2)
- Systems of linear equations: Find the number of solutions to a system of equations by graphing (Algebra - U.4)
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.
- Systems of linear equations: Solve a system of equations using substitution (Algebra - U.8)
A1.5.4 Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.
- Systems of linear equations: Solve a system of equations using elimination (Algebra - U.10)
A1.5.5 Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.
- Systems of linear equations: Solve a system of equations using elimination (Algebra - U.10)
A1.5.6 Use pairs of linear equations to solve word problems.

A1.6 Polynomials

A1.6.1 Add and subtract polynomials.
A1.6.2 Multiply and divide monomials.
A1.6.3 Find powers and roots of monomials (only when the answer has an integer exponent).
- Monomials: Powers of monomials (Algebra - Y.5)
A1.6.4 Multiply polynomials.
A1.6.5 Divide polynomials by monomials.
- Rational functions and expressions: Simplify rational expressions (Algebra - GG.3)
A1.6.6 Find a common monomial factor in a polynomial.
- Factoring: GCF of monomials (Algebra - AA.1)
- Factoring: Factor out a monomial (Algebra - AA.2)
A1.6.7 Factor the difference of two squares and other quadratics.
A1.6.8 Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

A1.7 Algebraic Fractions

A1.7.1 Simplify algebraic ratios.
- Ratios and proportions: Identify equivalent ratios (Algebra - C.1)
- Ratios and proportions: Equivalent ratios: fill in the missing number (Algebra - C.2)
A1.7.2 Solve algebraic proportions.

A1.8 Quadratic, Cubic, and Radical Equations

A1.8.1 Graph quadratic, cubic, and radical equations.
A1.8.2 Solve quadratic equations by factoring.
- Quadratic equations: Solve a quadratic equation by factoring (Algebra - BB.4)
A1.8.3 Solve quadratic equations in which a perfect square equals a constant.
- Quadratic equations: Solve a quadratic equation using square roots (Algebra - BB.2)
A1.8.4 Complete the square to solve quadratic equations.
- Quadratic equations: Solve a quadratic equation by completing the square (Algebra - BB.6)
A1.8.5 Derive the quadratic formula by completing the square.
A1.8.6 Solve quadratic equations by using the quadratic formula.
- Quadratic equations: Complete the square (Algebra - BB.5)
- Quadratic equations: Solve a quadratic equation using the quadratic formula (Algebra - BB.7)
A1.8.7 Use quadratic equations to solve word problems.
A1.8.8 Solve equations that contain radical expressions.
- Radical functions and equations: Solve radical equations I (Algebra - FF.3)
- Radical functions and equations: Solve radical equations II (Algebra - FF.4)
A1.8.9 Use graphing technology to find approximate solutions of quadratic and cubic equations.
- Quadratic equations: Characteristics of quadratic functions (Algebra - BB.1)
- Functions: linear, quadratic, exponential: Identify linear, quadratic, and exponential functions from graphs (Algebra - CC.1)

A1.9 Mathematical Reasoning and Problem Solving

A1.9 Students use a variety of strategies to solve problems.
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.
A1.9.2 Decide whether a solution is reasonable in the context of the original situation.
A1.9 Students develop and evaluate mathematical arguments and proofs.
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.
A1.9.5 Decide whether a given algebraic statement is true always, sometimes, or never (statements involving linear or quadratic expressions, equations, or inequalities).
- Solve equations: Identities and equations with no solutions (Algebra - J.7)
A1.9.6 Distinguish between inductive and deductive reasoning, identifying and providing examples of each.
A1.9.7 Identify the hypothesis and conclusion in a logical deduction.
- Logic: Identify hypotheses and conclusions (Algebra - HH.1)
A1.9.8 Use counterexamples to show that statements are false, recognizing that a single counterexample is sufficient to prove a general statement false.
- Logic: Counterexamples (Algebra - HH.2)