# Arkansas State Standards for Mathematics: Grade 9

Currently Perma-Bound only has suggested titles for grades K-8 in the Science and Social Studies areas. We are working on expanding this.

AR.LA.1. Algebra I: Language of Algebra: Students will develop the language of algebra including specialized vocabulary, symbols, and operations.

LA.1.AI.1. Evaluate algebraic expressions, including radicals, by applying the order of operations

LA.1.AI.2. Translate word phrases and sentences into expressions, equations, and inequalities, and vice versa

LA.1.AI.3. Apply the laws of (integral) exponents and roots

LA.1.AI.4. Solve problems involving scientific notation, including multiplication and division.

LA.1.AI.5. Perform polynomial operations (addition, subtraction, multiplication) with and without manipulatives

LA.1.AI.6. Simplify algebraic fractions by factoring

LA.1.AI.7. Recognize when an expression is undefined

LA.1.AI.8. Simplify radical expressions such as 3 / the square root of 7

LA.1.AI.9. Add, subtract, and multiply simple radical expressions like three times the square root of 20 + 7 times the square root of 5 and 4 times the square root of 5 multiplied by 2 times the square root of 3

AR.SEI.2. Algebra I: Solving Equation and Inequalities: Students will write, with and without appropriate technology, equivalent forms of equations, inequalities and systems or equations and solve with fluency.

SEI.2.AI.1. Solve multi-step equations and inequalities with rational coefficients: Numerically (from a table or guess and check); algebraically (including the use of manipulatives); graphically; technologically

SEI.2.AI.2. Solve systems of two linear equations: Numerically (from a table or guess and check); algebraically (including the use of manipulatives); graphically; technologically

SEI.2.AI.3. Solve linear formulas and literal equations for a specified variable (Ex. Solve for p in I = prt.)

SEI.2.AI.4. Solve and graph simple absolute value equations and inequalities Ex. |x| = 5, |x| is less than or equal to 5, |x| is greater than 5

SEI.2.AI.5. Solve real world problems that involve a combination of rates, proportions and percents

SEI.2.AI.6. Solve problems involving direct variation and indirect (inverse) variation to model rates of change

SEI.2.AI.7. Use coordinate geometry to represent and/or solve problems (midpoint, length of a line segment, and Pythagorean Theorem)

SEI.2.AI.8. Communicate real world problems graphically, algebraically, numerically and verbally

AR.LF.3. Algebra I: Linear Functions: Students will analyze functions by investigating rates of change, intercepts, and zeros.

LF.3.AI.1. Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data

LF.3.AI.2. Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data

LF.3.AI.3. Know and/or use function notation, including evaluating functions for given values in their domain

LF.3.AI.4. Identify independent variables and dependent variables in various representational modes: words, symbols, and/or graphs

LF.3.AI.5. Interpret the rate of change/slope and intercepts within the context of everyday life (Ex. telephone charges based on base rate (y-intercept) plus rate per minute (slope))

LF.3.AI.6. Calculate the slope given two points; the graph of a line, and the equation of a line

LF.3.AI.7. Determine by using slope whether a pair of lines are parallel, perpendicular, or neither

LF.3.AI.8. Write an equation in slope-intercept, point-slope, and standard forms given two points, a point and y-intercept, x-intercept and y-intercept, a point and slope, a table of data, and the graph of a line

LF.3.AI.9. Describe the effects of parameter changes, slope and/or y-intercept, on graphs of linear functions and vice versa

AR.NLF.4. Algebra I: Non-linear Functions: Students will compare the properties in the family of functions.

NLF.4.AI.1. Factoring polynomials: Greatest common factor; binomials (difference of squares); trinomials

NLF.4.AI.2. Determine minimum, maximum, vertex, and zeros, given the graph

NLF.4.AI.3. Solve quadratic equations using the appropriate methods with and without technology (factoring; quadratic formula with real number solutions

NLF.4.AI.4. Recognize function families and their connections including vertical shift and reflection over the x-axis (quadratics, absolute value, and exponential functions

NLF.4.AI.5. Communicate real world problems graphically, algebraically, numerically and verbally

AR.DIP.5. Algebra I: Data Interpretation and Probability: Students will compare various methods of reporting data to make inferences or predictions.

DIP.5.AI.1. Construct and use scatter plots and line of best fit to make inferences in real life situations

DIP.5.AI.2. Use simple matrices in addition, subtraction, and scalar multiplication

DIP.5.A1.3. Construct simple matrices for real life situations

DIP.5.AI.4. Determine the effects of changes in the data set on the measures of central tendency

DIP.5.AI.5. Use two or more graphs (i.e., box-and- whisker, histograms, scatter plots) to compare data sets

DIP.5.AI.6. Construct and interpret a cumulative frequency histogram in real life situations

DIP.5.AI.7. Recognize linear functions and non-linear functions by using a table or a graph

DIP.5.AI.8. Compute simple probability with and without replacement

DIP.5.AI.9. Recognize patterns using explicitly defined and recursively defined linear functions

DIP.5.AI.10. Communicate real world problems graphically, algebraically, numerically and verbally

DIP.5.AI.11. Explain how sampling methods, bias, and phrasing of questions in data collection impact the conclusions.

DIP.5.AI.12. Recognize when arguments based on data confuse correlation with causation.

AR.DIP.4. Algebra A: Data Interpretation and Probability: Students will compare the properties in the family of functions.

DIP.4.AI.1. TAUGHT IN ALGEBRA B

DIP.5.AI.3. Construct simple matrices for real life situations

AR.NLF.3. Algebra B: Linear Function: Students will analyze functions by investigating rates of change, intercepts, and zeros.

NLF.3.AI.1. TAUGHT IN ALGEBRA A

AR.LG.1.1. Geometry: Language of Geometry: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

LG.1.G.1. Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations: venn diagrams; matrix logic; conditional statements (statement, inverse, converse, and contrapositive), figural patterns

LG.1.G.2. Represent points, lines, and planes pictorially with proper identification, as well as basic concepts derived from these undefined terms, such as segments, rays, and angles

LG.1.G.3. Describe relationships derived from geometric figures or figural patterns

LG.1.G.4. Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines

LG.1.G.5. Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

LG.1.G.6. Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180 degrees, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it's length

AR.T.1. Geometry: Triangles: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.

T.2.G.1 Apply congruence (SSS...) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

T.2.G.2. Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

T.2.G.3. Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems

T.2.G.4. Apply the Pythagorean Theorem and its converse in solving practical problems

T.2.G.5. Use the special right triangle relationships (30 degrees -60 degrees -90 degrees and 45 degrees -45 degrees -90 degrees) to solve problems

T.2.G.6. Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression

T.2.G.7. Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given lengths of sides

AR.M.3. Geometry: Measurement: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.

M.3.G.1. Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular ring on a dartboard.)

M.3.G.2. Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms

M.3.G.3. Relate changes in the measurement of one attribute of an object to changes in other attributes (Ex. How does changing the radius or height of a cylinder affect its surface area or volume?)

M.3.G.4. Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)

M.3.G.5. Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions

AR.R.4. Geometry: Relationships between two- and three- dimensions: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

R.4.G.1. Explore and verify the properties of quadrilaterals

R.4.G.2. Solve problems using properties of polygons: sum of the measures of the interior angles of a polygon; interior and exterior angle measure of a regular polygon or irregular polygon; number of sides or angles of a polygon

R.4.G.3. Identify and explain why figures tessellate

R.4.G.4. Identify the attributes of the five Platonic Solids

R.4.G.5. Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

R.4.G.6. Solve problems using inscribed and circumscribed figures

R.4.G.7. Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects

R.4.G.8. Draw, examine, and classify cross-sections of three-dimensional objects

R.4.G.9. Explore non-Euclidean geometries, such as spherical geometry and identify its unique properties which result from a change in the parallel postulate

AR.CGT.5. Geometry: Coordinate Geometry and Transformations: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

CGT.5.G.1. Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

CGT.5.G.2. Write the equation of a line parallel to a line through a given point not on the line

CGT.5.G.3. Write the equation of a line perpendicular to a line through a given point

CGT.5.G.4. Write the equation of the perpendicular bisector of a line segment

CGT.5.G.5. Determine, given a set of points, the type of figure based on its properties (parallelogram, isosceles triangle, trapezoid)

CGT.5.G.6. Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

CGT.5.G.7. Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane: translations; reflections; rotations (90 degrees, 180 degrees, clockwise and counterclockwise about the origin); dilations (scale factor)

AR.LG.1. Geometry A: Language of Geometry: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

AR.T.2. Geometry A: Triangles: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.

T.2.G.1. Apply congruence (SSS...) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

AR.G.4. Geometry A: Relationships between two and three-dimensions: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

CG.T.5.G.1. Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

CG.T.5.G.2. Write the equation of a line parallel to a line through a given point not on the line

CG.T.5.G.3. Write the equation of a line perpendicular to a line through a given point

AR.PS.1. Algebraic Connections: Probability and Statistics: Students will evaluate and interpret data, make predictions based on data, and apply basic understanding of probability to solve real-world problems.

PS.1.AC.1. Apply counting techniques to determine the number of outcomes: tree diagram, fundamental Counting Principle, permutations (with and without repetition), combinations

PS.1.AC.2. Conduct and interpret simple probability experiments using manipulatives (spinners, dice, cards, coins) and simulations (using random number tables, graphing calculators, or computer software)

PS.1.AC.3. Compute and display theoretical and experimental probability including the use of Venn diagrams: simple, complementary, compound (mutually exclusive, inclusive, independent and dependent events)

PS.1.AC.4. Apply probability to real-world situations such as weather prediction, game theory, fair division, insurance tables, and election theory.

PS.1.AC.5. Interpret and evaluate, with and without appropriate technology, graphical and tabular data displays for consistency with the data, appropriateness of type of graph or data display, scale, overall message

AR.LF.2. Algebraic Connections: Linear Functions: Students will analyze linear functions by investigating rates of change, intercepts, and zeros.

LF.2.AC.1. Create, given a graph without an explicit formula, a written or oral interpretation of the relationship between the independent and dependent variables

LF.2.AC.2. Create, given a situation, a graph that models the relationship between the independent and dependent variables

LF.2.AC.3. Determine the independent and dependent variables, domain and range of a relation from an algebraic expression, graph, set of ordered pairs, or table of data

LF.2.AC.4. Interpret the rate of change (slope) and intercepts within the context of everyday life (Ex. telephone charges based on base rate (y-intercept) plus rate per minute (slope))

LF.2.AC.5. Calculate the slope given: two points; a graph of a line; an equation of a line

LF.2.AC.6. Determine, using slope, whether a pair of lines are parallel, perpendicular, or neither

LF.2.AC.7. Write an equation given two points, a point and y-intercept, an x-intercept and y-intercept; a point and slope; a table of data, and the graph of a line

LF.2.AC.8. Graph, with and without appropriate technology, functions defined as piece-wise and step

AR.SEI.3. Algebraic Connections: Solving Equations and Inequalities: Students will write and solve, with and without appropriate technology, equations, inequalities, systems of equations and systems of inequalities.

SEI.3.AC.1. Solve, with and without appropriate technology, multi-step equations and inequalities with rational coefficients numerically, algebraically and graphically

SEI.3.AC.2. Solve, with and without appropriate technology, systems of two linear equations and systems of two inequalities numerically, algebraically and graphically

SEI.3.AC.3. Solve linear formulas and literal equations for a specified variable

SEI.3.AC.4. Use, with and without appropriate technology, coordinate geometry to represent and solve problems including midpoint, length of a line segment and Pythagorean Theorem

SEI.3.AC.5. Determine and describe, with and without appropriate technology, the resulting change in the perimeter, area, and volume when one or more dimensions change (apply this idea in solving real world problems)

SEI.3.AC.6. Apply linear, piece-wise and step functions to real world situations that involve a combination of rates, proportions and percents such as sales tax, simple interest, social security, constant depreciation and appreciation, arithmetic sequences, constant rate of change, income taxes, postage, utility bills, commission, and traffic tickets

AR.NF.4. Algebraic Connections: Nonlinear Functions: Students will use algebraic, graphical and numerical methods to analyze, compare, transform, and solve nonlinear equations (absolute value, quadratic, and exponential).

NF.4.AC.1. Factor polynomials: greatest common factor; binominals (difference of squares); trinomials; combinations of the above

NF.4.AC.3. Solve, with and without appropriate technology, quadratic equations with real number solutions using factoring and the quadratic formula

NF.4.AC.4. Determine the independent and dependent variables, domain and range of a relation from algebraic equations, graphs, sets of ordered pairs, or tables of data

NF.4.AC.5. Identify and apply nonlinear functions to real world situations such as acceleration, area, volume, population, bacteria, compound interest, percent depreciation and appreciation, amortization, geometric sequences, etc.

NF.4.AC.6. Recognize function families including vertical shifts, horizontal shifts and reflections over the x-axis

AR.RF.1. Algebra II: Relations and Functions: Students will represent and analyze mathematical situations and properties using patterns, relations, functions and algebraic symbols.

RF.1.AII.1. Determine, with or without technology, the domain and range of a relation defined by a graph, a table of values, or a symbolic equation including those with restricted domains and whether a relation is a function

RF.1.AII.2. Evaluate, add, subtract, multiply, divide and compose functions and give appropriate domain and range restrictions

RF.1.AII.3. Determine the inverse of a function (Graph, with and without appropriate technology, functions and their inverses)

RF.1.AII.4. Analyze and report, with and without appropriate technology, the effect of changing coefficients, exponents, and other parameters on functions and their graphs (linear, quadratic, and higher degree polynomial)

RF.1.AII.5. Graph, with and without appropriate technology, funtions defined as piece-wise and step

RF.1.AII.6. Recognize periodic phenomena (sine or cosine functions such as sound waves, length of daylight, circular motion)

RF.1.AII.7. Investigate and identify key characteristics of period functions and their graphs (period, amplitude, maximum, and minimum)

RF.1.AII.8. Use basic properties of frequency and amplitude to solve problems

RF.1.AII.9. Apply the concepts of functions to real world situations

AR.LEI.2. Algebra II: Linear and Absolute Value Equations and Inequalities: Students will analyze and apply various methods to model, graph and solve linear and absolute value equations and inequalities.

LEI.2.AII.1 Solve, with and without appropriate technology, absolute value equations and inequalities written in one or two variables, and graph solutions

LEI.2.AII.2. Solve, with and without appropriate technology, systems of linear equations with two variables and graph the solution set

LEI.2.AII.3 Develop and apply, with and without appropriate technology, the basic operations and properties of matrices (associative, commutative, identity, and inverse)

LEI.2.AII.4. Solve, with and without appropriate technology, systems of linear equations with three variables using algebraic methods, including matrices

LEI.2.AII.5. Apply, with and without technology, the concepts of linear and absolute value equations and inequalities and systems of linear equations and inequalities to model real world situations including linear programming

AR.QEF.3. Algebra II: Quadratic Equations and Functions: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve quadratic equations.

QEF.3.AII.2. Extend the number system to include the complex numbers: evaluate powers of; add, subtract, multiply, and divide complex numbers; rationalize denominators

QEF.3.AII.3. Analyze and solve quadratic equations with and without appropriate technology by factoring, graphing, extracting the square root, completing the square, and using the quadratic formula

QEF.3.AII.4. Derive the quadratic formula and use it to solve equations

QEF.3.AII.5. Develop and analyze, with and without appropriate technology, quadratic relations: graph a parabolic relationship when given its equation; write an equation when given its roots (zeros or solutions) or graph; determine the nature of the solutions graphically and by evaluating the discriminant; determine the maximum or minimum values and the axis of symmetry both graphically and algebraically

QEF.3.AII.6. Apply the concepts of quadratic equations and functions to model real world situations by using appropriate technology when needed

AR.PRF.4. Algebra II: Polynomial and Rational Functions: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve polynomial and rational equations.

PRF.4.AII.1. Determine the factors of polynomials by using factoring techniques including grouping and the sum or difference of two cubes; using long division; using synthetic division

PRF.4.AII.2. Analyze and sketch, with and without appropriate technology, the graph of a given polynomial function, determining the characteristics of domain and range, maximum and minimum points, end behavior, zeros, multiplicity of zeros, y-intercept, and symmetry

PRF.4.AII.3. Write the equation of a polynomial function given its roots

PRF.4.AII.4. Identify the equation of a polynomial function given its graph or table

PRF.4.AII.5. Identify the characteristics of graphs of power functions of the form f(x) = ax^n, for negative integral values of n, including domain, range, end behavior, and behavior at x = 0, and compare these characteristics to the graphs of related positive integral power functions

PRF.4.AII.6. Simplify, add, subtract, multiply, and divide with rational expressions

PRF.4.AII.7. Establish the relationship between radical expressions and expressions containing rational exponents

PRF.4.AII.8. Simplify variable expressions containing rational exponents using the laws of exponents

AR.ELF.5. Algebra II: Exponential and Logarithmic Functions: Students will graph exponential functions and relate them to logarithms. They will solve real world problems using exponential functions.

ELF.5.AII.1. Recognize the graphs of exponential functions distinguishing between growth and decay

ELF.5.AII.2. Graph exponential functions and identify key characteristics: domain, range, intercepts, asymptotes, and end behavior

ELF.5.AII.3. Identify the effect that changes in the parameters of the base have on the graph of the exponential function

ELF.5.AII.4. Recognize and solve problems that can be modeled using exponential functions

ELF.5.AII.5. Establish the relationship between exponential and logarithmic functions

ELF.5.AII.6. Evaluate simple logarithms using the definition (Ex. log base 3 of 81)

ELF.5.AII.7. Use properties of logarithms to manipulate logarithmic expressions

AR.DAP.6. Algebra II: Data Analysis and Probability: Students will evaluate and interpret data, make predictions based on data, and apply basic understanding of probability to solve real world problems.

DAP.6.AII.1. Find regression line for scatter plot, using appropriate technology, and interpret the correlation coefficient

DAP.6.AII.2. Interpret and use the correlation coefficient to assess the strength of the linear relationship between two variables

DAP.6.AII.3. Find the quadratic curve of best fit using appropriate technology

DAP.6.AII.4. Identify strengths and weaknesses of using regression equations to approximate data

DAP.6.AII.5. Compute and explain measures of spread (range, percentiles, variance, standard deviation)

DAP.6.AII.6. Describe the characteristics of a Gaussian normal distribution

AR.LQF.1. Algebra III: Linear and Quadratic Functions: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve linear and quadratic equations.

LQF.1.AIII.1. Evaluate, add, subtract, multiply, divide and compose functions and determine appropriate domain and range restrictions

LQF.1.AIII.2. Develop, write, and graph, with and without appropriate technology, equations of lines in slope-intercept, point-slope, and standard forms given: a point and the slope; two points; real world data

LQF.1.AIII.3. Develop, write, and graph, given a point and the slope, two points, or a point and a line, the equation of a parallel line; a perpendicular line; the perpendicular bisector of a line segment

LQF.1.AIII.5. Solve, with and without appropriate technology, quadratic equations by extracting the square root; graphing; factoring; completing the square; using the quadratic formula

LQF.1.AIII.6. Graph, with and without appropriate technology, functions defined as piece-wise and step

LQF.1.AIII.7. Solve, with and without appropriate technology, systems of linear and quadratic equations and inequalities with two or more variables

LQF.1.AIII.8. Apply, with and without appropriate technology the concepts of functions to real world situations including linear programming

AR.PRF.2. Algebra III: Polynomial and Rational Functions: Students will use algebraic, graphical, and numerical methods to analyze, compare, translate, and solve polynomial and rational equations.

PRF.2.AIII.1. Determine the factors of polynomials by using factoring techniques including grouping, the difference of two squares, and the sum or difference of two cubes; using synthetic division

PRF.2.AIII.2. Investigate and sketch the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multiplicity of zeros, y-intercepts, and symmetry with and without appropriate technology

PRF.2.AIII.3. Simplify, add, subtract, multiply, and divide with rational expressions

PRF.2.AIII.4. Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes)

PRF.2.AIII.5. Establish the relationship between radical expressions and expressions containing rational exponents, and simplify variable expressions containing rational exponents using the laws of exponents

PRF.2.AIII.6. Apply, with and without appropriate technology, the concepts of polynomial and rational functions to model real world situations

AR.ELF.3. Algebra III: Exponential and Logarithmetic Functions: Students will solve real world problems involving logarithmic and exponential functions. They will draw and analyze graphs and find inverse functions.

ELF.3.AIII.1. Establish the inverse relationship between exponential and logarithmic functions

ELF.3.AIII.2. Develop and apply, with and without appropriate technology, the laws of logarithms and the change-of-base formula to simplify and evaluate expressions

ELF.3.AIII.3. Solve, with and without appropriate technology, equations and real world problems involving exponential and logarithmic expressions graphically, algebraically and numerically

ELF.3.AIII.4. Find, with and without appropriate technology, the domain, range, intercepts, and asymptotes of logarithmic and exponential functions

ELF.3.AIII.5. Draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functions

AR.SS.4. Algebra III: Sequences and Series: Students will use sequences and series to represent and analyze mathematical situations.

SS.4.AIII.1. Develop, with and without appropriate technology, a representation of sequences recursively and explicitly

SS.4.AIII.2. Define and discriminate, with and without appropriate technology, between arithmetic and geometric sequences and series

SS.4.AIII.3. Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series

SS.4.AIII.4. Determine, with and without appropriate technology, the nth term of a sequence given a rule or specific terms

SS.4.AIII.5. Use, with and without appropriate technology, sequences and series to solve real world problems

AR.TF.5. Algebra III: Trigonometric Functions: Students will identify, create, and solve real world problems involving right triangles and oblique triangles.

TF.5.AIII.1. Define sine, cosine, and tangent as ratios of sides of right triangles

TF.5.AIII.2. Develop and use, with and without appropriate technology, the Law of Sines and the Law of Cosines to solve oblique triangles

TF.5.AIII.3. Determine (by using an appropriate formula), with and without technology, the area of an oblique triangle

TF.5.AIII.4. Solve, with and without appropriate technology, real world problems involving applications of trigonometric functions; law of Sines; law of Cosines; area of oblique triangles

AR.LF.1. Transition to College Mathematics: Linear Functions: will extend their knowledge of linear equations by using student-generated data to represent constant rates of change. Appropriate technology is essential.

LF.1.TM.1. Identify a linear relationship represented by a table, by a graph, and by symbolic forms

LF.1.TM.2. Determine the initial condition and the rate of change in real-world situations described by y= mx + b

LF.1.TM.3. Make inferences and predictions using recursion on the table; inspection on the graph; algebraic manipulation on the model

LF.1.TM.4. Explain, conjecture, summarize, and defend results orally, in writing and through the use of appropriate technology

AR.EF.2. Transition to College Mathematics: Exponential Functions: Students will enhance their knowledge of exponential functions by exploring the nature of multiplicative change.

EF.2.TM.1. Identify exponential growth or decay by creating tables, graphs, and mathematical models

EF.2.TM.2. Compare exponential models

EF.2.TM.3. Compare and contrast linear and exponential models

EF.2.TM.4. Make inferences and predictions using recursion on the table; inspection of the graph; algebraic manipulation on the model

EF.2.TM.5. Develop, with appropriate technology, an algebraic model through the regression process

EF.2.TM.6. Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technology

AR.MM.3. Transition to College Mathematics: Mathematical Models: Students will expand their use of mathematical models to describe continuous, discontinuous, and discrete phenomena.

MM.3.TM.1. Establish connections between tables and graphs and the symbolic form using geometric and algebraic models (quadratic, rational, etc.)

MM.3.TM.2. Apply, with appropriate technology, matrices to real world problems and decision making

MM.3.TM.3. Make inferences and predictions using recursion on the table; inspection of the graph; algebraic manipulation on the model

MM.3.TM.4. Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technology

AR.PS.4. Transition to College Mathematics: Probability and Statistics: Students will develop strategies that will enable them to make decisions based upon appropriate analysis of data.

PS.4.TM.1. Formulate questions that can be addressed with data and, with appropriate technology, collect, organize, and display relevant data to answer the questions

PS.4.TM.2. Describe and summarize data numerically using central tendency variation, position statistics, and distributions

PS.4.TM.3. Use counting methods, permutations, and combinations to evaluate the likelihood of events occurring

PS.4.TM.4. Make inferences and predictions using recursion on the table; inspection of the graph; algebraic manipulation on the model

PS.4.TM.5. Explain, conjecture, summarize, and defend results orally, in writing, and through the use of appropriate technology

AR.DS.1. Statistics: Descriptive Statistics: Students will create, compare, and evaluate data displays using such methods as histograms, cumulative distribution functions, and scatter plots. For these data, they calculate measures of central tendency (various kinds of means, the median, and the mode) and their derivatives (range, variance, and standard deviation).

DS.1.S.1. Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative distribution functions, pie charts, scatter plots, stem-and-leaf plots, and box-and-whisker plots and draw these by hand or use a computer spread sheet program (Ex: Gather data to answer the question: Which area of the country has the highest school dropout rate? Display your dropout data in various forms.)

DS.1.S.2. Compute and use mean, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation (Ex: Use spreadsheet formulas to compute measures that summarize your dropout data by state.)

AR.DS.2. Statistics: Data Collection: Students will describe the method of data collection in a census, sample survey, experiment, and observational study, and identify an appropriate method of solution for a given familiar or unfamiliar contextual problem. Students will plan and conduct a survey. The plan will address sampling techniques (simple random and stratified) and methods to reduce bias.

DC.2.S.1. Compare and contrast controlled experiments and observational studies and the conclusions one can draw from each

DC.2.S.2. Compare and contrast population and sample, and parameter and statistic

DC.2.S.3. Identify biased sampling methods

DC.2.S.4. Describe simple random sampling

DC.2.S.5. Select a data collection method appropriate for a given context

DC.2.S.6. Investigate and describe sampling techniques, such as simple random sampling, stratified sampling, and cluster sampling

DC.2.S.7. Determine which sampling technique is best, given a particular context

DC.2.S.8. Plan and conduct a survey to answer a question or address an issue, identify possible sources of bias, and describe ways to reduce bias

AR.DS.3. Statistics: Data Collection: Students will construct and interpret display of data to solve problems.

DC.3.S.1. Analyze categorical data

DC.3.S.2. Use and compare methods of data collection

DC.3.S.3. Apply statistical principles and methods in sample surveys; identify difficulties

DC.3.S.4. Apply concepts of probability to solve familiar and unfamiliar contextual problems

DC.3.S.5. Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significance

DC.3.S.6. Recognize, construct and interpret results using confidence intervals in the context of a problem

AR.DS.4. Statistics: Data Analysis: Students will collect and analyze data to solve problems

DA.4.S.1. Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplot, and effects of changing units on summary measures.

DA.4.S.2. Analyze distribution of continuous univariate data (both normal and non-normal)

DA.4.S.3. Construct and interpret graphical display of data

DA.4.S.4. Compare distributions among sets of data.

AR.DS.5. Statistics: Data Analysis: Students will use statistical models to describe and analyze sets of data.

DA.5.S.1. Investigate and solve relevant problems, using technology to collect, organize, display, and analyze data in tabular, graphical, and symbolic forms

DA.5.S.2. Use linear and nonlinear models to formulate predictions from data

DA.5.S.3. Recognize the limitations of mathematical models based on sample data as representations of real world situations

DA.5.S.4. Identify possible correlations between variables in a data set

DA.5.S.5. Develop, use, and explain application and limitations of linear models and line of best fit (linear regression) in a variety of contexts

DA.5.S.6. Use data from samples to make inferences about a population and determine whether claims are reasonable or unreasonable

DA.5.S.7. Determine and use measures of central tendency and dispersion to describe and compare sets of data

DA.5.S.8. Design, conduct, interpret, and justify the results of a probability experiment, sample, or statistical simulation

AR.P.6. Statistics: Probability: Students will compute and distinguish between permutations and combinations and use technology for application.

P.6.S.1. Understand the counting principle, permutations and combinations and use them to solve problems

P.6.S.2. Compare and contrast permutations and combinations

P.6.S.3. Calculate the number of permutations of n objects taken r at a time

P.6.S.4. Calculate the number of combinations of n objects taken r at a time

P.6.S.5. Calculate relative frequency and expected frequency

P.6.S.6. Find conditional probabilities for dependent, independent, and mutually exclusive events

AR.P.7. Statistics: Probability: Students will identify random variables as independent or dependent and find mean and standard deviations for sums and differences of independent random variables.

P.7.S.1. Compare and contrast independent and dependent random variables

P.7.S.2. Find the standard deviation for sums and differences of independent random variables

AR.P.8. Statistics: Probability: Students will find probabilities, including conditional probabilities for events that are either dependent or independent, by applying the law of large numbers, the addition rule, and the multiplication rule.

P.8.S.1. Understand and use the addition rule to calculate probabilities for mutually exclusive and other events

P.8.S.2. Understand and use the multiplication rule to calculate probabilities for independent and dependent events

P.8.S.3. Develop the binomial distribution within a real world context

P.8.S.4. Calculate the mean and standard deviation for a binomial variable

P.8.S.5. Use the binomial distribution to calculate probabilities associated with experiments for which there are only two possible outcomes

AR.P.9. Statistics: Probability: Students will develop, interpret, and apply the binomial probability distribution for discrete random variable, including computing the mean and standard deviation for the binomial variable.

P.9.S.1. Design and conduct an experiment that simulates a binomial distribution.

P.9.S.2. Design and conduct an experiment that simulates a geometric distribution.

P.9.S.3. Simulate probability distributions, including binomial and geometric.

AR.SI.10. Statistics: Statistical Inference: Students will use probability distributions to make statistical inferences.

SI.10.S.1. Explore the characteristics and applications of the normal distribution and standardized scores

SI.10.S.2. Explore a variety of statistical tests such as chi-squares and t-tests and understand the meaning of hypothesis testing

SI.10.S.3. Use relative frequency and expected values to represent and solve problems involving uncertainty

AR.SI.11. Statistics: Statistical Inference: Students will use confidence intervals and hypothesis tests, fit curves to data, and calculate correlation coefficients.

SI.11.S.1. Compute and use confidence intervals to make an estimate

SI.11.S.2. Understand hypothesis tests of means and differences between means and use them to reach a conclusion

SI.11.S.3. Use the principle of least squares to find the curve of best fit for a set of data

SI.11.S.4. Calculate and interpret the correlation coefficient of a set of data

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

PS.1.CM.2 Write an algorithm to solve mathematical problems using formulas, equations, and functions.

PS.1.CM.3 Analyze and interpret truth tables from basic statements using Boolean operators (AND, OR, XOR, and NOT).

PS.1.CM.4 Write an algorithm from a mathematical model.

AR.PD.2. Computer Mathematics: Program Design: The student will design a step-by-step plan to solve a given problem.

PD.2.CM.1 Translate a mathematical expression into a computer statement, which involves writing assignment statements and using the order of operations.

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

PD.2.CM.3 Define and differentiate Decision (selection) and Sequence (process).

PD.2.CM.4 The student will represent an algorithm representation as a flowchart and in pseudocode.

PD.2.CM.5 Use flowchart terminology, such as terminals (starts and stops), subroutines, and connectors.

PD.2.CM.6 Develop recursive relationships from mathematical models (e.g. arithmetic and geometric sequences).

PD.2.CM.7 Define and use variable data types (integers, real, character).

AR.PI.3. Computer Mathematics: Program Implementation: The student will use worksheet functions to program using a computer spreadsheet application program.

PI.3.CM.1 Using a spreadsheet program, create an array.

PI.3.CM.2 Create functions using recursions and loops.

PI.3.CM.3 Locate, categorize, and implement worksheet functions.

PI.3.CM.4 Create constraints to validate cell entries.

PI.3.CM.5 Using a spreadsheet program, sort data using various methods (e.g. bubble, quick, and shell).

AR.PI.4. Computer Mathematics: Program Implementation: The student will use the programming tool to create programs using a programmable calculator.

PI.4.CM.1 Create, edit, and execute a program utilizing an array.

PI.4.CM.2 Create, edit, and execute programs using loops.

PI.4.CM.3 Create, edit, and execute programs to calculate mathematical formulas, such as the quadratic formula, and volume of a simple solid.

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

PI.4.CM.5 Create programs using various display modes (including tables and graphs).

PI.4.CM.6 Locate, categorize, and implement programming commands.

PI.4.CM.7 Use subroutines to reduce keystrokes and memory use.

AR.DMT.5. Computer Mathematics: Data Manipulation and Testing: The student will manipulate data to adjust and test programs designed in a computer spreadsheet application.

DMT.5.CM.1 Name a range (one cell or a group of cells), and use the name to select cells.

DMT.5.CM.2 Using the Scenario tool, estimate best-case or worst-case scenarios.

AR.DMT.6. Computer Mathematics: Data Manipulation and Testing: The student will manipulate data to adjust and test programs designed in a programmable calculator.

DMT.6.CM.1 Compare results from mathematical formulas to their program equivalent.

DMT.6.CM.2 Identify and eliminate error messages using troubleshooting techniques (debug).

DMT.6.CM.3 Understand and differentiate the different error types (syntax, runtime, and logic).

DMT.6.CM.4 Design and investigate best-case or worst-case scenarios of a program.

AR.PRF.1. Pre-Calculus including Trigonometry: Polynomial and Rational Functions: Students will analyze polynomial and rational functions graphically and algebraically.

PRF.1.PCT.1 Investigate and sketch, with and without appropriate technology, the graphs of polynomial and rational functions using the characteristics of domain and range, upper and lower bounds, maximum and minimum points, asymptotes and end behavior, zeros, multiplicity of zeros, y-intercepts, and symmetry

PRF.1.PCT.2 Solve, with and without appropriate technology, polynomial equations utilizing techniques such as Descartes' Rule of Signs, upper and lower bounds, Intermediate Value Theorem and Rational Root Theorem

PRF.1.PCT.3 Describe, with and without appropriate technology, the fundamental characteristics of rational functions: zeros, discontinuities (including vertical asymptotes), and end behavior (including horizontal asymptotes)

PRF.1.PCT.4 Apply the concepts of polynomial and rational functions to model real world situations using appropriate technology when needed

AR.ELF.2. Pre-Calculus including Trigonometry: Exponential and Logarithmic Functions: Students will solve real world problems involving logarithmic and exponential functions. Draw and analyze graphs and find inverse functions.

ELF.2.PCT.1 Establish the inverse relationship between exponential and logarithmic functions

ELF.2.PCT.2 Develop and apply the laws of logarithms and the change-of-base formula to simplify and evaluate expressions

ELF.2.PCT.3 Solve graphically, algebraically and numerically, with and without appropriate technology, equations and real world problems involving exponential and logarithmic expressions

ELF.2.PCT.4 Find, with and without appropriate technology, the domain, range, intercepts, and asymptotes of logarithmic and exponential functions

ELF.2.PCT.5 Draw and analyze, with and without appropriate technology, graphs of logarithmic and exponential functions

AR.C.3. Pre-Calculus including Trigonometry: Conics: Students will identify, analyze and sketch the graphs of the conic sections and relate their equations and graphs.

C.3.PCT.1 Identify, graph, write, and analyze equations of conic sections, using properties such as symmetry, intercepts, foci, asymptotes, and eccentricity, and when appropriate, use technology

C.3.PCT.2 Solve, with and without appropriate technology, systems of equations and inequalities involving conics and other types of equations

C.3.PCT.3 Solve, with and without appropriate technology, real world problems involving conic sections

SS.4.PCT.1 Develop, with and without appropriate technology, a representation of sequences recursively

SS.4.PCT.2 Define and discriminate between arithmetic and geometric sequences and series and use appropriate technology when needed

SS.4.PCT.3 Solve, with and without appropriate technology, problems involving the sum (including Sigma notation) of finite and infinite sequences and series

SS.4.PCT.4 Determine the nth term of a sequence given a rule or specific terms and use appropriate technology when needed

SS.4.PCT.5 Use, with and without appropriate technology, sequences and series to solve real world problems

TF.5.PCT.1 Define the six trigonometric functions as: circular functions; ratios of sides of right triangles; functions of an angle in standard position when given a point on the terminal side of the angle

TF.5.PCT.2 Use degrees and radians interchangeably to represent angle measure

TF.5.PCT.3 Sketch an angle in standard position and determine the reference angle and coterminal angles

TF.5.PCT.4 Find the values of the trigonometric functions given the value of one trigonometric function and an additional piece of qualifying information or given the coordinates of a point on the terminal side of an angle

TF.5.PCT.5 Develop and become fluent in the recall of the exact values of the trigonometric functions for special angles

TF.5.PCT.6 Solve, with and without appropriate technology, real world problems involving applications of trigonometric functions

TF.5.PCT.7 Graph the six trigonometric functions, identify domain, range, intercepts, period, amplitude, and asymptotes as applicable and use symmetry to determine whether the function is even or odd through appropriate technology when needed

TF.5.PCT.8 Determine, with and without appropriate technology, the amplitude, period, phase shift, and vertical shift, and sketch the graph of transformations of the trigonometric functions

TF.5.PCT.9 Identify and graph, with and without appropriate technology, the inverse of trigonometric functions including the restrictions on the domain

AR.OT.6. Pre-Calculus including Trigonometry: Oblique Triangles: Students will identify, create, and solve real world problems involving oblique triangles and vectors.

OT.6.PCT.1 Develop and use the Law of Sines and the Law of Cosines to solve oblique triangles and use appropriate technology when needed

OT.6.PCT.2 Solve real world problems applying the Law of Sines and the Law of Cosines and appropriate technology when needed

OT.6.PCT.3 Determine the area of an oblique triangle by using an appropriate formula and appropriate technology when needed

OT.6.PCT.4 Use vectors to solve problems and describe addition of vectors and multiplication of a vector by a scalar, both symbolically and geometrically

OT.6.PCT.5 Use vectors to model situations defined by magnitude and direction and analyze and solve real world problems by using appropriate technology when needed

AR.TEI.7. Pre-Calculus including Trigonometry: Trigonometric Equations and Identities: Students will verify trigonometric identities and solve trigonometric equations.

TEI.7.PCT.1 Develop the Pythagorean Identities and use to verify other identities and simplify expressions

TEI.7.PCT.2 Develop and use trigonometric formulas including sum and difference formulas and multiple-angle formulas

TEI.7.PCT.3 Solve trigonometric equations algebraically and graphically and use appropriate technology when needed

AR.PC.8. Pre-Calculus including Trigonometry: Polar Coordinates: Students will define polar coordinates and relate them to rectangular coordinates.

PC.8.PCT.1 Convert polar coordinates to rectangular coordinates and rectangular coordinates to polar coordinates

PC.8.PCT.2 Represent equations given in rectangular coordinates in terms of polar coordinates

PC.8.PCT.3 Graph polar equations and use appropriate technology when needed

PC.8.PCT.4 Apply polar coordinates to real world situations and use appropriate technology when needed

AR.MA.1. Topics in Discrete Mathematics: Matrices: Students will use matrices to analyze data to solve real-world problems.

MA.1.TDM.1 Collect and interpret data in a matrix and perform operations to solve real-world problems, with and without technology

MA.1.TDM.2 Solve real-world problems involving systems of linear equations using matrices (e.g., inverses, augmented, Cramer's rule)

MA.1.TDM.3 Find and use the inverse of a matrix to solve real-world problems (e.g., cryptology)

MA.1.TDM.4 Organize and use transition matrices to solve probability problems that link present events to future events, with or without technology (e.g., consumer trends, polling trends, board games, weather trends)

AR.OP.2. Topics in Discrete Mathematics: Optimization: Students will use various techniques to solve optimization problems.

OP.2.TDM.1 Graph systems of linear inequalities with multiple constraints and identify vertices of the feasible region

OP.2.TDM.2 Model and solve real-world problems using linear programming (e.g., maximum profit/minimal cost, investments, agriculture, manufacturing, banking)

OP.2.TDM.3 Interpret the meaning of the minimum or maximum value in terms of the objective function

OP.2.TDM.4 Model and solve real-world problems involving optimization of area and volume

AR.ME.3. Topics in Discrete Mathematics: Measurement: Students will apply various measurement techniques to solve real-world problems.

ME.3.TDM.1 Solve problems using dimensional analysis (factor-label method) (e.g., construction, medical, metric, standard to metric, rate conversions)

ME.3.TDM.2 Use sine, cosine, and tangent ratios to determine lengths of sides and angle measures of right triangles for real-world problems (e.g., angles of elevation and depression and various distances)

ME.3.TDM.3 Use laws of sine and cosine to determine lengths of sides, measures of angles, and area of triangles for real- world problems (e.g., Heron's formula)

ME.3.TDM.4 Calculate the area of two-dimensional composite figures

ME.3.TDM.5 Calculate the surface area and volume of three-dimensional composite figures

AR.EF.4. Topics in Discrete Mathematics: Exponential Functions: Students will extend algebraic skills to solve real-world problems involving exponential/logarithmic functions.

EF.4.TDM.1 Draw and recognize the graphs of logarithmic and exponential functions, with and without appropriate technology

EF.4.TDM.2 Apply properties of logarithms to convert and solve logarithmic (common and natural) and exponential equations

EF.4.TDM.3 Use the change of base formula to simplify and evaluate logarithmic expressions, using technology

EF.4.TDM.4 Recognize and apply properties of exponential functions to solve real-world problems (e.g., compound interest, amortization, annuities, appreciation, depreciation)

EF.4.TDM.5 Recognize and apply properties of logarithmic functions to solve real-world problems (e.g., Richter scale pH, decibel scale, bacterial growth, radioactive decay, Newton's Law of Cooling)

AR.DA.5. Topics in Discrete Mathematics: Data Analysis: Students will analyze data using various statistical tools.

DA.5.TDM.1 Read, interpret, and analyze graphical representations of data used in various contexts (e.g., science reasoning, newspaper graphs)

DA.5.TDM.2 Identify biases that affect the validity of a data set

DA.5.TDM.3 Collect, analyze, and compare data sets using five-number summary

DA.5.TDM.4 Investigate and analyze the characteristics of normal and skewed distributions

DA.5.TDM.5 Determine and interpret the measures of spread of a data set (e.g., standard deviation, range, percentiles, variance)

AR.LSM.1. Topics in Finite Mathematics: Linear Systems and Matrices: Students will examine linear systems and matrices and their applications.

LSM.1.TFM.1 Use matrices (e.g., row-echelon form, Gauss-Jordan method, inverses) to solve systems of linear equations, with or without technology

LSM.1.TFM.2 Find and use the inverse of a matrix to solve real-world problems (e.g., cryptology)

LSM.1.TFM.3 Graph systems of linear inequalities with multiple constraints and identify vertices of the feasible region

LSM.1.TFM.4 Model and solve real-world problems using linear programming (e.g., maximum profit/minimal cost, investments, agriculture, manufacturing, banking)

LSM.1.TFM.5 Interpret the meaning of the minimum or maximum value in terms of the objective function

AR.ST.2. Topics in Finite Mathematics: Set Theory: Students will operate with sets and use set theory to solve problems.

ST.2.TFM.1 Define sets using set-builder notation

ST.2.TFM.2 Use correct terminology to describe relationships between sets in various contexts

ST.2.TFM.3 Perform set operations such as union and intersection, complement, and Cartesian product

ST.2.TFM.4 Use Venn diagrams to explore relationships and patterns and to make arguments about relationships between sets, including real-world situations

ST.2.TFM.5 Use a truth table to draw conclusions about a statement

ST.2.TFM.6 Judge the validity of arguments and give counterexamples to disprove statements

AR.CT.3. Topics in Finite Mathematics: Counting Techniques: Students will use combinatorial reasoning to find numbers of outcomes and related probabilities.

CT.3.TFM.1 Use fundamental counting principles of addition and multiplication to solve problems

CT.3.TFM.2 Evaluate expressions indicating permutations or combinations, with and without technology

CT.3.TFM.3 Evaluate expressions involving distinguishable permutations

CT.3.TFM.4 Distinguish between and use permutations and combinations to solve problems

CT.3.TFM.5 Calculate probabilities of mutually exclusive events, independent events, and dependent events

CT.3.TFM.6 Construct and examine Pascal's triangle

CT.3.TFM.7 Develop and use the binomial theorem

CT.3.TFM.8 Use combinations to find a specified term in a binomial expansion

AR.S.4. Topics in Finite Mathematics: Statistics: Students will compute and analyze data using various statistical tools, with appropriate technology.

S.4.TFM.1 Collect data using random sampling

S.4.TFM.2 Calculate and interpret statistical problems using measures of central tendencies and graphs (histograms, normal curve)

S.4.TFM.3 Analyze and compare data sets using five-number summary, graphically and numerically

S.4.TFM.4 Investigate and analyze the characteristics of normal and skewed distributions

S.4.TFM.5 Determine and interpret measures of variation of a data set, with or without technology: standard deviation; range; percentiles ; variance

AR.F.5. Topics in Finite Mathematics: Finance: Students will solve real-world problems involving financial decision making.

F.5.TFM.1 Read and interpret graphs related to finance

F.5.TFM.2 Apply properties of logarithms to convert and solve logarithmic (common and natural) and exponential equations

F.5.TFM.3 Solve real-world problems involving: compound interest; amortization; annuities; appreciation; depreciation; investments

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