Okla. Admin. Code § 210:15-3-63
Current through Vol. 42, No. 8, January 2, 2025
Section 210:15-3-63 - Standard Two: Algebraic Reasoning and Algebra(a)Statement of the standard. Students will focus on number and operations to develop fluency with an importance of understanding numbers, ways of representing numbers, relationships among numbers, relationships among number systems, and meanings of operations and how they relate to one another. Students will place an emphasis on the development of estimation to determine the reasonableness of solutions and answers and to compute efficiently and proficiently.(b)Standard Two objectives for Pre-Kindergarten. The following objectives apply for students in Pre-Kindergarten:(1) Recognize, duplicate, and extend patterns.(A)Objective 1. Sort and group up to 5 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common.(B)Objective 2. Recognize, duplicate, and extend repeating patterns involving manipulatives, sound, movement, and other contexts.(c)Standard Two objectives for Kindergarten. The following objectives apply for students in Kindergarten:(1) Duplicate patterns in a variety of contexts.(A)Objective 1. Sort and group up to 10 objects into a set based upon characteristics such as color, size, and shape. Explain verbally what the objects have in common.(B)Objective 2. Recognize, duplicate, complete, and extend repeating, increasing, and decreasing patterns in a variety of contexts (i.e., shape, color, size, objects, sounds, movement).(d)Standard Two objectives for Grade 1. The following objectives apply for students in Grade 1: (1) Identify patterns found in real-world and mathematical problems.(A)Objective 1. Identify, create, complete, and extend repeating, increasing, and decreasing patterns in a variety of mathematical contexts (e.g., quantity, numbers, or shapes).(e)Standard Two objectives for Grade 2. The following objectives apply for students in Grade 2: (1) Describe the relationship found in patterns to solve real-world and mathematical problems. (A)Objective 1. Represent, create, describe, complete, and extend increasing and decreasing patterns with quantity and numbers in a variety of contexts.(B)Objective 2. Represent and describe repeating patterns involving shapes in a variety of contexts.(2) Use number sentences involving unknowns to represent and solve real-world and mathematical problems.(A)Objective 1. Use objects and number lines to represent number sentences.(B)Objective 2. Generate models and situations to represent number sentences and vice versa.(C)Objective 3. Apply the commutative property, identity property, and number sense to find values for unknowns that make addition and subtraction number sentences true or false.(f)Standard Two objectives for Grade 3. The following objectives apply for students in Grade 3:(1) Describe and create representations of numerical and geometric patterns. (A)Objective 1. Create, describe, and extend patterns involving addition, subtraction, or multiplication to solve problems in a variety of contexts.(B)Objective 2. Describe the rule (limited to a single operation) for a pattern from an input/output table or function machine involving addition, subtraction, or multiplication..(C)Objective 3. Explore and develop visual representations of increasing and decreasing geometric patterns and construct the next steps.(2) Use number sentences involving multiplication and unknowns to represent and solve real-world and mathematical problems.(A)Objective 1. Use number sense with the properties of addition, subtraction, and multiplication, to find unknowns (represented by symbols) in one-step equations. Generate real-world situations to represent number sentences.(B)Objective 2. Identify, represent and apply the number properties (commutative, identity, and associative properties of addition and multiplication) using models and manipulatives to solve problems.(g)Standard Two objectives for Grade 4. The following objectives apply for students in Grade 4: (1) Describe, create, and analyze multiple representations of patterns to solve real-world and mathematical problems. (A)Objective 1. Create an input/output chart or table to represent or extend a numerical pattern.(B)Objective 2. Describe the single operation rule for a pattern from an input/output table or function machine involving any operation of a whole number.(C)Objective 3. Construct models to show growth patterns involving geometric shapes and define the single operation rule of the pattern.(2) Use multiplication and division with variables to create number sentences representing a given mathematical situation.(A)Objective 1. Use the relationships between multiplication and division with the properties of multiplication to solve problems and find values for variables that make number sentences true.(B)Objective 2. Solve for a variable in an equation involving addition, subtraction, multiplication, or division with whole numbers. Analyze models to represent number sentences and vice versa.(C)Objective 3. Determine the unknown addend or factor in equivalent and non-equivalent expressions. (e.g., 5 + 6 = 4 + [], 3 x 8 < 3 x []).(h)Standard Two objectives for Grade 5. The following objectives apply for students in Grade 5: (1) Describe and graph patterns of change created through numerical patterns.(A)Objective 1. Use tables and rules of up to two operations to describe patterns of change and make predictions and generalizations about various mathematical situations.(B)Objective 2. Use a rule or table to represent ordered pairs of whole numbers and graph these ordered pairs on a coordinate plane, identifying the origin and axes in relation to the coordinates.(2) Understand and interpret expressions, equations, and inequalities involving variables and whole numbers, and use them to represent and evaluate real-world and mathematical problems.(A)Objective 1. Generate equivalent numerical expressions and solve problems using number sense involving whole numbers by applying the commutative property, associative property, distributive property, and order of operations (excluding exponents).(B)Objective 2. Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.(C)Objective 3. Evaluate expressions involving variables when values for the variables are given.(i)Standard Two objectives for Grade 6. The following objectives apply for students in Grade 6:(1) Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs, and rules to model and solve mathematical problems.(A)Objective 1. Plot integer- and rational-valued (limited to halves and fourths) ordered pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs.(B)Objective 2. Represent relationships between two varying positive quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.(C)Objective 3. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.(2) Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers. (A)Objective 1. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems.(3) Use equations and inequalities to model and solve mathematical problems and use the idea of maintaining equality to solve equations. Interpret solutions in the original context. (A)Objective 1. Model mathematical situations using expressions, equations, and inequalities involving variables and rational numbers.(B)Objective 2. Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x+p=q and px=q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.(j)Standard Two objectives for Grade 7. The following objectives apply for students in Grade 7:(1) Explain the concept of proportionality in mathematical models and situations and distinguish between proportional and non-proportional relationships. (A)Objective 1. Identify a relationship between two varying quantities, x and y, as proportional if it can be expressed in the form y/x=k or y = kx; distinguish proportional relationships from non-proportional relationships.(B)Objective 2. Recognize that the graph of a proportional relationship is a line through the origin and the coordinate (1, r), where r is the slope and the unit rate (constant of proportionality, k).(2) Identify and justify proportional relationships using mathematical models and situations; solve problems involving proportional relationships and interpret results in the original context.(A)Objective 1. Represent proportional relationships with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. Determine and compare the unit rate (constant of proportionality, slope, or rate of change) given any of these representations.(B)Objective 2. Solve multi-step problems with proportional relationships (e.g., distance-time, percent increase or decrease, discounts, tips, unit pricing, mixtures and concentrations, similar figures, other mathematical situations).(C)Objective 3. Use proportional reasoning to solve problems involving ratios.(D)Objective 4. Use proportional reasoning to assess the reasonableness of solutions.(3) Represent mathematical situations using equations and inequalities involving variables and rational numbers.(A)Objective 1. Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers.(B)Objective 2. Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form x + p > q and x + p < q, where p and q are nonnegative rational numbers.(4) Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions.(A)Objective 1. Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.(B)Objective 2. Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols.(k)Standard Two objectives for Pre-Algebra. The following objectives apply for students in Pre-Algebra:(1) Explain the concept of function in mathematical situations and distinguish between the concepts of linear and nonlinear functions.(A)Objective 1. Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable.(B)Objective 2. Use linear functions to represent and model mathematical situations.(C)Objective 3. Identify a function as linear if it can be expressed in the form y=mx + b or if its graph is a non-vertical straight line.(2) Identify and justify linear functions using mathematical models and situations; solve problems involving linear functions and interpret results in the original context. (A)Objective 1. Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.(B)Objective 2. Identify, describe, and analyze linear relationships between two variables.(C)Objective 3. Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.(D)Objective 4. Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects.(E)Objective 5. Solve problems involving linear functions and interpret results in the original context.(3) Generate equivalent numerical and algebraic expressions and use algebraic expressions and use algebraic properties to evaluate expressions. (A)Objective 1. Use substitution to simplify and evaluate algebraic expressions.(B)Objective 2. Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive).(4) Represent and solve problems using mathematical models and situations with equations and inequalities involving linear expressions. (A)Objective 1. Solve mathematical problems using linear equations with one variable where there could be one, infinitely many, or no solutions. Represent situations using linear equations and interpret solutions in the original context.(B)Objective 2. Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form px+q>r and px+q<r, where p,q, and r are rational numbers.(C)Objective 3. Represent real-world situations using equations and inequalities involving one variable.(l)Standard Two objectives for Algebra 1. The following objectives apply for students in Algebra 1: (1) Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context. (A)Objective 1. Use knowledge of solving equations with rational values to represent, use and apply mathematical models (e.g., angle measures, geometric formulas, dimensional analysis, Pythagorean theorem, science, or statistics) and interpret the solutions in the original context.(B)Objective 2. Solve absolute value equations and interpret the solutions in the original context.(C)Objective 3. Analyze, use and apply mathematical models to solve problems involving systems of linear equations with a maximum of two variables by graphing, substitution, and elimination. Graphing calculators or other appropriate technology may be utilized. Interpret the solutions in the original context.(2) Represent and solve real-world and mathematical problems using linear inequalities and compound inequalities; interpret solutions in the original context. (A)Objective 1. Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions.(B)Objective 2. Represent relationships using mathematical models with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.(3) Create and evaluate equivalent algebraic expressions and equations using algebraic properties. (A)Objective 1. Solve equations involving several variables for one variable in terms of the others.(B)Objective 2. Simplify polynomial expressions by adding, subtracting, or multiplying.(C)Objective 3. Factor common monomial factors from polynomial expressions and factor quadratic expressions with a leading coefficient of 1.(D)Objective 4. Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x [CIRCLED DOT OPERATOR] y=2x+y(4) Analyze real-world and mathematical problems involving linear equations. (A)Objective 1. Analyze, use and apply mathematical models and other data sets (e.g., graphs, equations, two points, a set of data points) to calculate and interpret the slope and the x- and y-intercepts of a line.(B)Objective 2. Analyze and interpret mathematical models involving lines that are parallel, perpendicular, horizontal, and vertical.(C)Objective 3. Write the equation of the line given its slope and y-intercept, slope and one point, two points, x- and y-intercepts, or a set of data points.(D)Objective 4. Express linear equations in slope-intercept, point-slope, and standard forms. Convert between these forms.(E)Objective 5. Analyze and interpret associations between graphical representations and written scenarios.(5)Functions. Understand functions as descriptions of covariation (how related quantities vary together) in real-world and mathematical problems.(A)Objective 1. Distinguish between relations and functions.(B)Objective 2. Identify the dependent variable, independent variable, domain and range given a function, equation, or graph. Identify restrictions on the domain and range in mathematical models.(C)Objective 3. Write linear functions, using function notation, to represent mathematical models.(D)Objective 4. Read and interpret the linear piecewise function, given a graph modeling a situation.(E)Objective 5. Interpret graphs as being discrete or continuous.(6)Functions. Recognize and understand that families of functions are defined by their characteristics.(A)Objective 1. Distinguish between linear and nonlinear (including exponential) functions Understand that linear functions grow by equal intervals (arithmetic) and that exponential functions grow by equal factors over equal intervals (geometric).(B)Objective 2. Recognize the parent functions f(x) = x and f(x) = |x|. Predict the effects of vertical and horizontal transformations [ f(x + c) and f(x) + c, algebraically and graphically.(7)Functions. Represent functions in multiple ways and use the representation to interpret real-world and mathematical problems.(A)Objective 1. Identify and generate equivalent representations of linear functions, graphs, tables, and real-world situations.(B)Objective 2. Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of the original context.(C)Objective 3. Add, subtract, and multiply functions using function notation.(m)Standard Two objectives for Algebra 2. The following objectives apply for students in Algebra 2:(1) Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context.(A)Objective 1. Use mathematical models to represent quadratic relationships and solve using factoring, completing the square, the quadratic formula, and various methods (including graphing calculator or other appropriate technology). Find non-real roots when they exist.(B)Objective 2. Use mathematical models to represent exponential relationships, such as compound interest, depreciation, and population growth. Solve these equations algebraically or graphically (including graphing calculator or other appropriate technology).(C)Objective 3. Solve one-variable rational equations and check for extraneous solutions.(D)Objective 4. Solve polynomial equations with real roots using various methods (e.g. polynomial division, synthetic division, using graphing calculators or other appropriate technology).(E)Objective 5. Solve square and cube root equations with one variable and check for extraneous solutions.(F)Objective 6. Solve common and natural logarithmic equations using the properties of logarithms.(G)Objective 7. Represent and evaluate mathematical models using systems of linear equations with a maximum of three variables. Graphing calculators or other appropriate technology may be used.(H)Objective 8. Use tools to solve systems of equations containing one linear equation and one quadratic equation. Graphing calculators or other appropriate technology may be used.(I)Objective 9. Solve systems of linear inequalities in two variables, with a maximum of three inequalities; graph and interpret the solutions on a coordinate plane. Graphing calculators or other appropriate technology may be used.(2) Generate and evaluate equivalent algebraic expressions and equations using various strategies. (A)Objective 1. Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping using a variety of tools and strategies.(B)Objective 2. Add, subtract, multiply, divide, and simplify polynomial expressions.(C)Objective 3. Add, subtract, multiply, divide, and simplify rational expressions.(D)Objective 4. Recognize that a quadratic function has different equivalent representations [f(x) = ax2 + bx + c, f(x) = a(x - h)2 + k, and f(x) = a(x - p)(x - q)]. Identify and use the mathematical model that is most appropriate to solve problems.(E)Objective 5. Rewrite algebraic expressions involving radicals and rational exponents using the properties of exponents.(3) Represent and solve mathematical and real-world problems involving arithmetic and geometric sequences and series. (A)Objective 1. Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Using the pattern, find the next term.(B)Objective 2. Recognize that geometric sequences are exponential using equations, tables, graphs, and verbal descriptions. Given the formula f(x) = a(r)x, find the next term and define the meaning of a and r within the context of the problem..(C)Objective 3. Solve problems that can be modeled using arithmetic sequences or series given the nth terms and sum formulas. Graphing calculators or other appropriate technology may be used.(D)Objective 4. Solve problems that can be modeled using finite geometric sequences or series given the nth terms and sum formulas. Graphing calculators or other appropriate technology may be used.(4)Functions. Understand functions as descriptions of covariation (how related quantities vary together).(A)Objective 1. Use algebraic, interval, and set notations to specify the domain and range of various types of functions and evaluate a function at a given point in its domain. (B) Objective 2. Identify the parent forms of exponential, radical (square root and cube root only), quadratic, and logarithmic functions. Predict the effects of transformations [f(x + c), f(x) + c, f(cx), and cf(x)] algebraically and graphically.(C)Objective 3. Graph a quadratic function. Identify the domain, range, x- and y-intercepts, maximum or minimum value, axis of symmetry, and vertex using various methods and tools that may include a graphing calculator or appropriate technology.(D)Objective 4. Graph exponential and logarithmic functions. Identify the domain, range, asymptotes, and x- and y-intercepts using various methods and tools that may include graphing calculators or other appropriate technology. Recognize exponential decay and growth graphically and algebraically.(E)Objective 5. Analyze the graph of a polynomial function by identifying the domain, range, intercepts, zeros, relative maxima, relative minima, and intervals of increase and decrease.(F)Objective 6. Graph a rational function. Identify the domain (including holes), range, x- and y-intercepts, vertical and horizontal asymptotes, using various methods and tools that may include a graphing calculator or other appropriate technology. (excluding slant or oblique asymptotes).(G)Objective 7. Graph a radical function (square root and cube root only). Identify the domain, range, and x- and y-intercepts using various methods and tools that may include a graphing calculator or other appropriate technology.(H)Objective 8. Graph piecewise functions with no more than three branches (i.e., linear, quadratic, or exponential branches). Analyze the function by identifying the domain, range, intercepts, and intervals for which it is increasing, decreasing, and constant using various methods and tools (e.g., graphing calculator, other appropriate technology).(I)Objective 9. Recognize whether a discrete or continuous graphical representation is appropriate to create the graph based on a mathematical model.(5)Functions. Analyze functions through algebraic combinations, compositions, and inverses, if they exist.(A)Objective 1. Add, subtract, multiply, and divide functions using function notation and recognize domain restrictions.(B)Objective 2. Combine functions by composition and recognize that g(x) = f-1(x), the inverse function of f(x), if and only if f(g(x)) = g(f(x)) = x.(C)Objective 3. Find and graph the inverse of a function, if it exists, in mathematical models. Know that the domain of a function f is the range of the inverse function f-1, and the range of the function f is the domain of the inverse function f-1.(D)Objective 4. Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.(n)Standard Two objectives for Pre Calculus and Trigonometry. The following objectives apply for students in Pre Calculus and Trigonometry:(1) Analyze functions and relations.(A)Objective 1. Interpret characteristics of a function defined by an expression in the context of the situation.(B)Objective 2. Sketch the graph of a function that models a relationship between two quantities, identifying key features.(C)Objective 3. Interpret characteristics of graphs and tables for a function that models a relationship between two quantities in terms of the quantities.(D)Objective 4. Describe end behavior, asymptotic behavior, and points of discontinuity.(E)Objective 5. Determine if a function has an inverse. Algebraically and graphically find the inverse or define any restrictions on the domain that meet the requirement for invertibility, and find the inverse on the restricted domain.(2) Build functions to model and validate relationships among functions.(A)Objective 1. Model relationships through composition, and attend to the restrictions of the domain.(B)Objective 2. Rewrite a function as a composition of functions.(C)Objective 3. Interpret the meanings of quantities involving functions and their inverses.(D)Objective 4. Verify by analytical methods that one function is the inverse of another.(3) Predict and verify solutions involving functions.(A)Objective 1. Predict solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.(B)Objective 2. Graphically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.(C)Objective 3. Algebraically verify solutions involving functions that are quadratic, polynomial of higher order, rational, exponential, and logarithmic.Okla. Admin. Code § 210:15-3-63
Adopted by Oklahoma Register, Volume 40, Issue 5, November 15, 2022, eff. 12/11/2022