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Topic: Equations and inequalities 

Mathematics

 Standard 8.  Understands and applies basic and advanced properties of functions and algebra
  Level II (Grade 3-5)
   Benchmark 4.Understands the basic concept of an equality relationship (i.e., an equation is a number sentence that shows two quantities that are equal)
    Knowledge/skill statements
     1.Understands the concept of an equation
   Benchmark 5.Solves simple open sentences involving operations on whole numbers (e.g., ? + 17 = 23)
    Knowledge/skill statements
     1. Understands the concept of an open sentence
  Level III (Grade 6-8)
   Benchmark 1.Knows that an expression is a mathematical statement using numbers and symbols to represent relationships and real-world situations (e.g., equations and inequalities with or without variables)
    Knowledge/skill statements
     1.Understands the concept of a mathematical expression
     2.Understands the role of numbers in math expressions
     3.Understands the role of variables in math expressions
     4.Understands the concept of an inequality
     5.Understands the role of symbols in math expressions
   Benchmark 5.Solves linear equations using concrete, informal, and formal methods (e.g., using properties, graphing ordered pairs, using slope-intercept form)
    Knowledge/skill statements
     1.Understands the concept of a linear equation
     2.Solves linear equations using knowledge of properties
     3.Solves linear equations by graphing ordered pairs
     4.Solves linear equations using slope-intercept form
     5.Solves linear equations using concrete methods
     6.Solves linear equations using informal methods
     7.Solves linear equations using formal methods
   Benchmark 6.Solves simple inequalities and non-linear equations with rational number solutions, using concrete and informal methods
    Knowledge/skill statements
     1. Solves simple inequalities using informal methods
     2. Understands the concept of a non-linear equation
     3. Solves simple non-linear equations using informal methods
     4. Understands the concept of an inequality
     5. Solves inequalities using concrete methods
     6. Solves non-linear equations using concrete methods
   Benchmark 10.Solves simple systems of equations graphically
    Knowledge/skill statements
     1.Solves simple systems of equations graphically
     2.Understands the concept of systems of equations
  Level IV (Grade 9-12)
   Benchmark 2.Uses expressions, equations, inequalities, and matrices to represent situations that involve variable quantities and translates among these representations
    Knowledge/skill statements
     1.Understands the relationship between inequalities and equations
     2.Transforms inequalities to equations
     3.Understands the relationship between equations and matrices
     4.Represents equations in matrix form
     5.Understands the relationship between expressions and equations
     6.Understands the relationship between expressions and inequalities
     7.Understands the relationship between expressions and matrices
     8.Understands the relationship between inequalities and matrices
     9.Understands the concept of an algebraic expressions
   Benchmark 5. Solves polynomial equations (e.g., find the real or complex roots of a quadratic equation) using a variety of methods (e.g., symbolically, graphically, numerically).
    Knowledge/skill statements
     1.Understands the concept of polynomials
     2.Understands the concept of roots
     3.Solves polynomial equations symbolically.
     4.Models real world problems using polynomial equations without the use of technology.
     5.Solves real world problems using polynomial equations with the use of technology.
     6.Solves polynomial equations by finding the real roots of a quadratic equation.
     7.Solves polynomial equations by finding the complex roots of a quadratic equation.
   Benchmark 7.Uses a variety of models (e.g., written statement, algebraic formula, table of input-output values, graph) to represent functions, patterns, and relationships
    Knowledge/skill statements
     1.Represents functions using graphs
     2.Represents functions using table of input/output values
     3.Represents functions using algebraic formula
     4.Represents functions using written statements
     5.Represents functions using models
     6. Represents patterns using graphs
     7.Represents patterns using table of input/output values
     8. Represents patterns using algebraic formula
     9.Represents patterns using written statements
     10. Represents patterns using models
     11. Represents relationships using graphs
     12. Represents relationships using table of input/output values
     13. Represents relationships using algebraic formula
     14. Represents relationships using written statements
     15.Represents relationships using models
   Benchmark 11.Uses a variety of methods (e.g., with graphs, algebraic methods, and matrices) to solve systems of equations and inequalities
    Knowledge/skill statements
     1.Solves systems of equations using graphs
     2.Solves systems of equations using matrices
     3.Solves systems of equations using algebraic methods
     4. Understands the concept of systems of inequalities
     5.Solves systems of inequalities using algebraic methods
     6.Solves systems of inequalities using graphs
     7.Solves systems of inequalities using matrices
   Benchmark 13.Adds, subtracts, multiplies, and divides polynomials
    Knowledge/skill statements
     1.Adds polynomials
     2.Subtracts polynomials
     3.Multiplys polynomials
     4.Divides polynomials
   Benchmark 14.Understands the meaning of and writes equivalent forms of expressions, equations, inequalities, and relations, including all of their parts(e.g., terms, factors, coefficients).
    Knowledge/skill statements
     1.Understands the meaning of expressions.
     2.Understands the meaning of equations.
     3.Understands the meaning of inequalities.
     4.Understands the meaning of relations.
     5.Writes expressions in equivalent forms.
     6.Writes equations in equivalent forms.
     7.Writes inequalities in equivalent forms.
     8.Writes relations in equivalent forms.
     9.Understands the meanings of terms of an equation.
     10.Understands the meanings of terms of an expression.
     11.Understands the meanings of terms of an inequality.
     12.Understands the meanings of terms of a relation.
     13.Understands the meanings of factors of an equation.
     14.Understands the meanings of factors of an expression.
     15.Understands the meanings of factors of an inequality.
     16.Understands the meanings of factors of a relation.
     17.Understands the meanings of coefficient of an equation.
     18.Understands the meanings of coefficient of an expression.
     19.Understands the meanings of coefficient of an inequality.
     20.Understands the meanings of coefficient of a relation.
   Benchmark 15.Models and solves real world problems using polynomial equations, with and without the use of technology.
    Knowledge/skill statements
     1.Models real world problems using polynomial equations with the use of technology.
     2.Models real world problems using polynomial equations without the use of technology.
     3.Solves real world problems using polynomial equations with the use of technology.
     4.Solves real world problems using polynomial equations without the use of technology.
   Benchmark 16.Solves quadratic equations in one variable(e.g. using quadratic formula, by completing the square)
    Knowledge/skill statements
     1.Understands the concept of quadratic equations
     2.Knows the quadratic formula
     3.Knows how completing the square can be used to solve a quadratic equation
  Level V (Grade (College Readiness))
   Benchmark 1.Solves equations and inequalities involving absolute value
    Knowledge/skill statements
     1.Solves equations involving absolute value
     2.Solves inequalities involving absolute value
   Benchmark 2.Understands graphs of solution sets of quadratic inequalities
    Knowledge/skill statements
     1. Understands the concept of solution sets
     2.Identifies solution sets of quadratic inequalities
     3.Interprets graphs of solution sets of quadratic inequalities
   Benchmark 3.Factors polynomials using a variety of methods (e.g., difference of squares, perfect square trinomials)
    Knowledge/skill statements
     1.Factors polynomials using the difference of squares
     2.Factors polynomials using perfect square trinomials
   Benchmark 5.Solves problem situations that require linear, quadratic, or exponential modeling
    Knowledge/skill statements
     1.Understands the concept of modeling a situation using equations
     2.Solves problem situations that require linear modeling
     3. Solves problem situations that require quadratic modeling
     4. Solves problem situations that require exponential modeling