Arkansas

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Skills available for Arkansas high school math standards

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Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics Arkansas Curriculum Framework: Advanced Topics and Modeling in Mathematics
Arkansas Curriculum Framework: Algebra I Arkansas Curriculum Framework: Algebra I
Arkansas Curriculum Framework: Algebra I Part A Arkansas Curriculum Framework: Algebra I Part A
Arkansas Curriculum Framework: Algebra I Part B Arkansas Curriculum Framework: Algebra I Part B
Arkansas Curriculum Framework: Algebra II/Advanced Algebra Arkansas Curriculum Framework: Algebra II/Advanced Algebra
Arkansas Curriculum Framework: Algebra III Arkansas Curriculum Framework: Algebra III
Arkansas Curriculum Framework: Bridge to Algebra II Arkansas Curriculum Framework: Bridge to Algebra II
Arkansas Curriculum Framework: Calculus Arkansas Curriculum Framework: Calculus
Arkansas Curriculum Framework: Computer Science and Mathematics Arkansas Curriculum Framework: Computer Science and Mathematics
Arkansas Curriculum Framework: Geometry Arkansas Curriculum Framework: Geometry
Arkansas Curriculum Framework: Geometry A Arkansas Curriculum Framework: Geometry A
Arkansas Curriculum Framework: Geometry B Arkansas Curriculum Framework: Geometry B
Arkansas Curriculum Framework: Mathematical Applications and Algorithms Arkansas Curriculum Framework: Mathematical Applications and Algorithms
Arkansas Curriculum Framework: Precalculus Arkansas Curriculum Framework: Precalculus
Arkansas Curriculum Framework: Statistics Arkansas Curriculum Framework: Statistics

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F Functions

F.1.MAA The student will graphically, numerically, and algebraically evaluate concepts of different types of functions; include recursively defined functions, series, and sequences; and apply them to programming applications
- F.1.MAA.1 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [e.g., the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1]
- F.1.MAA.2 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases: graph exponential and logarithmic functions showing intercepts, end behavior, and trigonometric functions, showing period, midline, and amplitude; graph linear and quadratic functions and show intercepts, maxima, and minima; graph rational functions identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.
- F.1.MAA.3 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- F.1.MAA.4 Compare properties of two functions each represented in a different way: algebraically, graphically, numerically in tables, or by verbal descriptions (e.g., given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum).
  - Compare linear functions: tables, graphs, and equations (A1-T.16)
- F.1.MAA.5 Write a function that describes a relationship between two quantities: compose functions [e.g., if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time]; combine standard function types using arithmetic operations (e.g., build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential and relate these functions to the model); determine an explicit expression, a recursive process, or steps for calculation from a context.
- F.1.MAA.6 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
- F.1.MAA.7 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  - Inverses of trigonometric functions (PC-M.9)
- F.1.MAA.8 Use inverse functions to solve trigonometric equations that arise in modeling contexts, evaluate the solutions using technology, and interpret them in terms of the context.
  - Solve trigonometric equations (PC-M.11)
- F.1.MAA.9 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
  - Introduction to complex numbers (A2-I.1)
- F.1.MAA.10 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  - Multiply complex numbers (A2-I.4)
  - Add and subtract complex numbers (PC-R.1)
- F.1.MAA.11 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

EF Equations and Formulas

EF.2.MAA The student will manipulate formulas and equations and apply them to programming applications
- EF.2.MAA.1 Represent constraints by equations or inequalities and by systems of equations and/or inequalities (two and three variable systems); interpret solutions as viable or nonviable options in a modeling context (e.g., represent inequalities describing nutritional and cost constraints on combinations of different foods).
- EF.2.MAA.2 Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (e.g., rearrange Ohm's law V = IR to highlight resistance R).
  - Solve multi-variable equations (A2-B.6)
- EF.2.MAA.3 Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone; use dissection arguments, Cavalieri's principle, and informal limit arguments.
- EF.2.MAA.4 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
- EF.2.MAA.5 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

SEM Systems of Equations and Matrices

SEM.3.MAA The student will create, manipulate, and solve systems of equations and matrices and apply them to programming arrays
- SEM.3.MAA.1 Represent a system of linear equations as a single matrix equation in a vector variable.
- SEM.3.MAA.2 Find the inverse of a matrix if it exists and use it to solve systems of linear equations; use technology for matrices of dimension 3 × 3 or greater.
- SEM.3.MAA.3 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).
- SEM.3.MAA.4 Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).
  - Multiply a matrix by a scalar (PC-L.4)
- SEM.3.MAA.5 Add, subtract, and multiply matrices of appropriate dimensions.
- SEM.3.MAA.6 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation but still satisfies the associative and distributive properties.
  - Matrix operation rules (PC-L.2)
  - Properties of matrices (PC-L.8)
- SEM.3.MAA.7 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
- SEM.3.MAA.8 Work with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.

PS Problem Solving

PS.4.MAA The student will develop and apply logical reasoning skills to solve real-world problems through the development of mathematical models
- PS.4.MAA.1 Analyze and interpret graphs, charts, and tables in the design and implementation of a computer program.
- PS.4.MAA.2 Write an algorithm to solve mathematical problems using formulas, equations, and functions.
- PS.4.MAA.3 Analyze and interpret truth tables from basic statements using Boolean operators (AND, OR, XOR, and NOT).
- PS.4.MAA.4 Write an algorithm from a mathematical model.

PD Program Design

PD.5.MAA The student will design a step-by-step plan to solve a given problem
- PD.5.MAA.1 Translate a mathematical expression into a computer statement which involves writing assignment statements and using the order of operations.
- PD.5.MAA.2 Implement conditional statements that include if/then, if/then/else, case statements, and Boolean logic.
- PD.5.MAA.3 Define and differentiate Decision (selection) and Sequence (process).
- PD.5.MAA.4 Represent an algorithm representation as a flowchart and in pseudocode.
- PD.5.MAA.5 Use flowchart terminology such as terminals (starts and stops), subroutines, and connectors.
- PD.5.MAA.6 Develop recursive relationships from mathematical models (e.g., arithmetic and geometric sequences).
- PD.5.MAA.7 Define and use variable data types (e.g., integers, real, character).

PI Program Implementation

PI.6.MAA The student will create, edit, and execute programs using a programmable calculator and/or computer spreadsheet application program
- PI.6.MAA.1 Create, edit, and execute a program utilizing an array in a programmable calculator and spreadsheet application.
- PI.6.MAA.2 Create, edit, and execute programs using recursions and loops in a programmable calculator and spreadsheet application.
- PI.6.MAA.3 Create, edit, and execute programs to calculate mathematical formulas (e.g., quadratic formula, volume of a simple solid).
- PI.6.MAA.4 Develop functional programs from algorithms developed from the mathematical models.
- PI.6.MAA.5 Create programs using various display modes including tables and graphs.
- PI.6.MAA.6 Locate, categorize, and implement programming commands.
- PI.6.MAA.7 Use subroutines to reduce keystrokes and memory use.
- PI.6.MAA.8 Use a spreadsheet application to sort data using various methods (e.g., bubble, quick, shell).

DMT Data Manipulation and Testing

DMT.7.MAA The student will manipulate data to adjust and test programs designed using a programmable calculator and/or computer spreadsheet application
- DMT.7.MAA.1 Compare results from mathematical formulas to their program equivalent.
- DMT.7.MAA.2 Identify and eliminate error messages using troubleshooting techniques (debug).
- DMT.7.MAA.3 Understand and differentiate the different error types (e.g., syntax, runtime, logic).
- DMT.7.MAA.4 Design and investigate best-case or worst-case scenarios of a program.
- DMT.7.MAA.5 Name a range, one cell or a group of cells; use the name to select cells.
- DMT.7.MAA.6 Estimate best-case or worst-case scenarios using a spreadsheet application scenario tool.

Arkansas

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F Functions

F.1.MAA The student will graphically, numerically, and algebraically evaluate concepts of different types of functions; include recursively defined functions, series, and sequences; and apply them to programming applications

F.1.MAA.1 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [e.g., the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1]

F.1.MAA.3 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.1.MAA.4 Compare properties of two functions each represented in a different way: algebraically, graphically, numerically in tables, or by verbal descriptions (e.g., given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum).

F.1.MAA.6 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

F.1.MAA.7 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

F.1.MAA.8 Use inverse functions to solve trigonometric equations that arise in modeling contexts, evaluate the solutions using technology, and interpret them in terms of the context.

F.1.MAA.9 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

F.1.MAA.10 Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

F.1.MAA.11 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

EF Equations and Formulas

EF.2.MAA The student will manipulate formulas and equations and apply them to programming applications

EF.2.MAA.2 Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (e.g., rearrange Ohm's law V = IR to highlight resistance R).

EF.2.MAA.3 Give an informal argument for the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone; use dissection arguments, Cavalieri's principle, and informal limit arguments.

EF.2.MAA.4 Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

EF.2.MAA.5 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

SEM Systems of Equations and Matrices

SEM.3.MAA The student will create, manipulate, and solve systems of equations and matrices and apply them to programming arrays

SEM.3.MAA.1 Represent a system of linear equations as a single matrix equation in a vector variable.

SEM.3.MAA.2 Find the inverse of a matrix if it exists and use it to solve systems of linear equations; use technology for matrices of dimension 3 × 3 or greater.

SEM.3.MAA.3 Use matrices to represent and manipulate data (e.g., to represent payoffs or incidence relationships in a network).

SEM.3.MAA.4 Multiply matrices by scalars to produce new matrices (e.g., as when all of the payoffs in a game are doubled).

SEM.3.MAA.5 Add, subtract, and multiply matrices of appropriate dimensions.

SEM.3.MAA.6 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation but still satisfies the associative and distributive properties.

SEM.3.MAA.7 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers; the determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

SEM.3.MAA.8 Work with 2 × 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.

PS Problem Solving

PS.4.MAA The student will develop and apply logical reasoning skills to solve real-world problems through the development of mathematical models

PS.4.MAA.1 Analyze and interpret graphs, charts, and tables in the design and implementation of a computer program.

PS.4.MAA.2 Write an algorithm to solve mathematical problems using formulas, equations, and functions.

PS.4.MAA.3 Analyze and interpret truth tables from basic statements using Boolean operators (AND, OR, XOR, and NOT).

PS.4.MAA.4 Write an algorithm from a mathematical model.

PD Program Design

PD.5.MAA The student will design a step-by-step plan to solve a given problem

PD.5.MAA.1 Translate a mathematical expression into a computer statement which involves writing assignment statements and using the order of operations.

PD.5.MAA.2 Implement conditional statements that include if/then, if/then/else, case statements, and Boolean logic.

PD.5.MAA.3 Define and differentiate Decision (selection) and Sequence (process).

PD.5.MAA.4 Represent an algorithm representation as a flowchart and in pseudocode.

PD.5.MAA.5 Use flowchart terminology such as terminals (starts and stops), subroutines, and connectors.

PD.5.MAA.6 Develop recursive relationships from mathematical models (e.g., arithmetic and geometric sequences).

PD.5.MAA.7 Define and use variable data types (e.g., integers, real, character).

PI Program Implementation

PI.6.MAA The student will create, edit, and execute programs using a programmable calculator and/or computer spreadsheet application program

PI.6.MAA.1 Create, edit, and execute a program utilizing an array in a programmable calculator and spreadsheet application.

PI.6.MAA.2 Create, edit, and execute programs using recursions and loops in a programmable calculator and spreadsheet application.

PI.6.MAA.3 Create, edit, and execute programs to calculate mathematical formulas (e.g., quadratic formula, volume of a simple solid).

PI.6.MAA.4 Develop functional programs from algorithms developed from the mathematical models.

PI.6.MAA.5 Create programs using various display modes including tables and graphs.

PI.6.MAA.6 Locate, categorize, and implement programming commands.

PI.6.MAA.7 Use subroutines to reduce keystrokes and memory use.

PI.6.MAA.8 Use a spreadsheet application to sort data using various methods (e.g., bubble, quick, shell).

DMT Data Manipulation and Testing

DMT.7.MAA The student will manipulate data to adjust and test programs designed using a programmable calculator and/or computer spreadsheet application

DMT.7.MAA.1 Compare results from mathematical formulas to their program equivalent.

DMT.7.MAA.2 Identify and eliminate error messages using troubleshooting techniques (debug).

DMT.7.MAA.3 Understand and differentiate the different error types (e.g., syntax, runtime, logic).

DMT.7.MAA.4 Design and investigate best-case or worst-case scenarios of a program.

DMT.7.MAA.5 Name a range, one cell or a group of cells; use the name to select cells.

DMT.7.MAA.6 Estimate best-case or worst-case scenarios using a spreadsheet application scenario tool.