1. Recognize, classify, and use real numbers and their properties. (P, M, N)
a. Describe the real number system using a diagram to show the relationships of
component sets of numbers that compose the set of real numbers.
b. Model properties and equivalence relationships of real numbers.
c. Demonstrate and apply properties of real numbers to algebraic expressions.
d. Perform basic operations on square roots excluding rationalizing denominators.
2. Recognize, create, extend, and apply patterns, relations, and functions and their applications. (P, D, G, N)
a. Analyze relationships between two variables, identify domain and range, and
determine whether a relation is a function.
b. Explain and illustrate how change in one variable may result in a change in another
variable.
c. Determine the rule that describes a pattern and determine the pattern given the
rule.
d. Apply patterns to graphs and use appropriate technology.
3. Simplify algebraic expressions, solve and graph equations, inequalities and systems in one and two variables. (P, D, G, N)
a. Solve, check, and graph linear equations and inequalities in one variable,
including rational coefficients.
b. Graph and check linear equations and inequalities in two variables.
c. Solve and graph absolute value equations and inequalities in one variable.
d. Use algebraic and graphical methods to solve systems of linear equations and
inequalities.
e. Translate problem-solving situations into algebraic sentences and determine
solutions.
4. Explore and communicate the characteristics and operations of polynomials. (P, M, G, N)
a. Classify polynomials and determine the degree.
b. Add, subtract, multiply, and divide polynomial expressions.
c. Factor polynomials using algebraic methods and geometric models.
d. Investigate and apply real-number solutions to quadratic equations algebraically
and graphically.
e. Use convincing arguments to justify unfactorable polynomials.
f. Apply polynomial operations to problems involving perimeter and area.
5. Utilize various formulas in problem-solving situations. (P, D, M, G, N)
a. Evaluate and apply formulas (e.g., circumference, perimeter, area, volume,
Pythagorean Theorem, interest, distance, rate, and time).
b. Reinforce formulas experimentally to verify solutions.
c. Given a literal equation, solve for any variable of degree one.
d. Using the appropriate formula, determine the length, midpoint, and slope of a
segment in a coordinate plane.
e. Use formulas (e.g., point-slope and slope-intercept) to write equations of lines.
6. Communicate using the language of algebra. (P, D, M, G, N)
a. Recognize and demonstrate the appropriate use of terms, symbols, and notations.
b. Distinguish between linear and non-linear equations.
c. Translate between verbal expressions and algebraic expressions.
d. Apply the operations of addition, subtraction, and scalar multiplication to matrices.
e. Use scientific notation to solve problems.
f. Use appropriate algebraic language to justify solutions and processes used in
solving problems.
7. Interpret and apply slope as a rate of change. (P, D, M, G, N)
a. Define slope as a rate of change using algebraic and geometric representations.
b. Interpret and apply slope as a rate of change in problem-solving situations.
c. Use ratio and proportion to solve problems including direct variation .
d. Apply the concept of slope to parallel and perpendicular lines.
8. Analyze data and apply concepts of probability. (P, D, M, G, N)
a. Collect, organize, graph, and interpret data sets, draw conclusions, and make
predictions from the analysis of data.
b. Define event and sample spaces and apply to simple probability problems.
c. Use counting techniques, permutations, and combinations to solve probability
problems.
a. Describe the real number system using a diagram to show the relationships of
component sets of numbers that compose the set of real numbers.
b. Model properties and equivalence relationships of real numbers.
c. Demonstrate and apply properties of real numbers to algebraic expressions.
d. Perform basic operations on square roots excluding rationalizing denominators.
2. Recognize, create, extend, and apply patterns, relations, and functions and their applications. (P, D, G, N)
a. Analyze relationships between two variables, identify domain and range, and
determine whether a relation is a function.
b. Explain and illustrate how change in one variable may result in a change in another
variable.
c. Determine the rule that describes a pattern and determine the pattern given the
rule.
d. Apply patterns to graphs and use appropriate technology.
3. Simplify algebraic expressions, solve and graph equations, inequalities and systems in one and two variables. (P, D, G, N)
a. Solve, check, and graph linear equations and inequalities in one variable,
including rational coefficients.
b. Graph and check linear equations and inequalities in two variables.
c. Solve and graph absolute value equations and inequalities in one variable.
d. Use algebraic and graphical methods to solve systems of linear equations and
inequalities.
e. Translate problem-solving situations into algebraic sentences and determine
solutions.
4. Explore and communicate the characteristics and operations of polynomials. (P, M, G, N)
a. Classify polynomials and determine the degree.
b. Add, subtract, multiply, and divide polynomial expressions.
c. Factor polynomials using algebraic methods and geometric models.
d. Investigate and apply real-number solutions to quadratic equations algebraically
and graphically.
e. Use convincing arguments to justify unfactorable polynomials.
f. Apply polynomial operations to problems involving perimeter and area.
5. Utilize various formulas in problem-solving situations. (P, D, M, G, N)
a. Evaluate and apply formulas (e.g., circumference, perimeter, area, volume,
Pythagorean Theorem, interest, distance, rate, and time).
b. Reinforce formulas experimentally to verify solutions.
c. Given a literal equation, solve for any variable of degree one.
d. Using the appropriate formula, determine the length, midpoint, and slope of a
segment in a coordinate plane.
e. Use formulas (e.g., point-slope and slope-intercept) to write equations of lines.
6. Communicate using the language of algebra. (P, D, M, G, N)
a. Recognize and demonstrate the appropriate use of terms, symbols, and notations.
b. Distinguish between linear and non-linear equations.
c. Translate between verbal expressions and algebraic expressions.
d. Apply the operations of addition, subtraction, and scalar multiplication to matrices.
e. Use scientific notation to solve problems.
f. Use appropriate algebraic language to justify solutions and processes used in
solving problems.
7. Interpret and apply slope as a rate of change. (P, D, M, G, N)
a. Define slope as a rate of change using algebraic and geometric representations.
b. Interpret and apply slope as a rate of change in problem-solving situations.
c. Use ratio and proportion to solve problems including direct variation .
d. Apply the concept of slope to parallel and perpendicular lines.
8. Analyze data and apply concepts of probability. (P, D, M, G, N)
a. Collect, organize, graph, and interpret data sets, draw conclusions, and make
predictions from the analysis of data.
b. Define event and sample spaces and apply to simple probability problems.
c. Use counting techniques, permutations, and combinations to solve probability
problems.