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GA.AAGBAA.Accelerated Analytic Geometry B/Advanced Algebra
Accelerated Analytic Geometry B/Advanced Algebra
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions.
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a circle formula A = π r^2 to highlight the radius r.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.SSE. Seeing Structure in Expressions Write expressions in equivalent forms to solve problemsMGSE9-12.A.SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.MGSE9-12.A.SSE.3c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t, where t is in years, can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate i
MGSE9-12.F.BF. Building Functions Build a function that models a relationship between two quantitiesMGSE9-12.F.BF.1. Write a function that describes a relationship between two quantities.MGSE9-12.F.BF.1a. Determine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MGSE9-12.F.IF. Interpreting Functions Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7a. Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.F.IF.7e. Graph exponential and logarithmic functions, showing intercepts and end behavior.
MGSE9-12.F.IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.MGSE9-12.F.IF.8b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponen
MGSE9-12.N.RN. The Real Number System Extend the properties of exponents to rational exponents.MGSE9-12.N.RN.1. Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 beca
MGSE9-12.N.RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
MGSE9-12.S.CP. Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret dataMGSE9-12.S.CP.2. Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two
GA.MAAIGA.Accelerated Algebra I/Geometry A
Accelerated Algebra I/Geometry A
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions (integer inputs only).
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a circle formula A = π r^2 to highlight the radius r.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoningMGSE9-12.A.REI.1. Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next u
Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.REI.12. Graph the solution set to a linear inequality in two variables.
Solve equations and inequalities in one variableMGSE9-12.A.REI.3. Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax + 3 = 7, solve for x.
Solve systems of equationsMGSE9-12.A.REI.5. Show and explain why the elimination method works to solve a system of two-variable equations.
MGSE9-12.A.REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
MGSE9-12.F.BF. Building Functions Build a function that models a relationship between two quantitiesMGSE9-12.F.BF.1. Write a function that describes a relationship between two quantities.MGSE9-12.F.BF.1a. Determine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MGSE9-12.F.IF. Interpreting Functions Understand the concept of a function and use function notationMGSE9-12.F.IF.1. Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.F.IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, studQuiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7a. Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.F.IF.7e. Graph exponential functions, showing intercepts and end behavior.
MGSE9-12.F.LE. Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic, and exponential models and solve problemsMGSE9-12.F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.MGSE9-12.F.LE.1a. Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates oQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.G.CO. Congruence Experiment with transformations in the planeMGSE9-12.G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MGSE9-12.G.CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
MGSE9-12.G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MGSE9-12.G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MGSE9-12.G.CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motionsMGSE9-12.G.CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Prove geometric theoremsMGSE9-12.G.CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
MGSE9-12.G.SRT. Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformationsMGSE9-12.G.SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor.MGSE9-12.G.SRT.1a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.
MGSE9-12.G.SRT.1b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.
MGSE9-12.G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angl
Prove theorems involving similarityMGSE9-12.G.SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MGSE9-12.N.RN. The Real Number System Use properties of rational and irrational numbers.MGSE9-12.N.RN.3. Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.
MGSE9-12.S.ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variablesMGSE9-12.S.ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
MGSE9-12.S.ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MGSE9-12.S.ID.6c. Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.
GA.MACAAGA.Accelerated Coordinate Algebra/Analytic Geometry A
Accelerated Coordinate Algebra/Analytic Geometry A
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, and exponential functions (integer inputs only).
MGSE9-12.A.CED.2. Create linear, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interes
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoningMGSE9-12.A.REI.1. Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next u
Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.REI.12. Graph the solution set to a linear inequality in two variables.
Solve equations and inequalities in one variableMGSE9-12.A.REI.3. Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax + 3 = 7, solve for x.
Solve systems of equationsMGSE9-12.A.REI.5. Show and explain why the elimination method works to solve a system of two-variable equations.
MGSE9-12.A.REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
MGSE9-12.F.BF. Building Functions Build a function that models a relationship between two quantitiesMGSE9-12.F.BF.1. Write a function that describes a relationship between two quantities.MGSE9-12.F.BF.1a. Determine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MGSE9-12.F.IF. Interpreting Functions Understand the concept of a function and use function notationMGSE9-12.F.IF.1. Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.F.IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, studQuiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7a. Graph linear functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.F.IF.7e. Graph exponential functions, showing intercepts and end behavior.
MGSE9-12.F.LE. Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic, and exponential models and solve problemsMGSE9-12.F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.MGSE9-12.F.LE.1a. Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates oQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.G.CO. Congruence Experiment with transformations in the planeMGSE9-12.G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MGSE9-12.G.CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
MGSE9-12.G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MGSE9-12.G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MGSE9-12.G.CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motionsMGSE9-12.G.CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Prove geometric theoremsMGSE9-12.G.CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
MGSE9-12.G.GMD. Geometric Measurement and Dimension Explain volume formulas and use them to solve problemsMGSE9-12.G.GMD.1. Give informal arguments for geometric formulas.MGSE9-12.G.GMD.1a. Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.
MGSE9-12.G.GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MGSE9-12.G.GPE. Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraicallyMGSE9-12.G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MGSE9-12.G.GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
MGSE9-12.G.SRT. Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformationsMGSE9-12.G.SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor.MGSE9-12.G.SRT.1a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.
MGSE9-12.G.SRT.1b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.
MGSE9-12.G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angl
Prove theorems involving similarityMGSE9-12.G.SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MGSE9-12.S.ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variablesMGSE9-12.S.ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
MGSE9-12.S.ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MGSE9-12.S.ID.6c. Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.
MGSE9–12.N.RN. The Real Number System Use properties of rational and irrational numbers.MGSE9–12.N.RN.3. Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.
GA.MAFM.Advanced Finite Mathematics
Advanced Finite Mathematics
MAFM.LR. Logical Reasoning Represent and interpret statements using logical symbolism.MAFM.LR.3. Determine whether a logical argument is valid or invalid, and determine whether a logical argument is a tautology or a contradiction.
MAFM.MP. Methods of ProofMAFM.MP.2. Prove statements directly from definitions and previously proved statements. For example, using the definition of “rational number”, prove that every integer is rational; using the definition of “divides”, prove that if a divides b and b divides a, then a
MAFM.MP.5. Use the method of mathematical induction to prove statements involving the positive integers. For example, prove that 3 divides 2^(2n) – 1 for all positive integers n; prove that 1 + 2 + 3 + … + n = n (n + 1)/2; prove that a given recursive sequence has a
MAFM.NT. Number Theory Prove statements in number theory.MAFM.NT.5. Prove statements involving properties of numbers. For example, prove that the sum of two rational numbers is rational; prove that if a is even and b is odd, then (a^2 + b^2 + 1)/2 is an integer; prove that any odd number squared is of the form 8k + 1 for
MAFM.NT.6. Prove statements involving the floor and ceiling functions. For example, for every integer n, prove that the floor of n/2 is equal to n/2 if n is even and equal to (n – 1)/2 if n is odd.
MAFM.NT.7. Prove the Fundamental Theorem of Arithmetic, the Euclidean algorithm, and Fermat’s Little Theorem.
MAFM.PC. Probability and Combinatorics Calculate the probability of events.MAFM.PC.2. Apply the axioms of probability to determine the probability of dependent and independent events, including use of the multiplication rule for independent events.
Use methods of counting.MAFM.PC.5. Calculate the number of permutations of a set with n elements. Calculate the number of permutations of r elements taken from a set of n elements.
MAFM.PC.6. Calculate the number of subsets of size r that can be chosen from a set of n elements. Recognize this number as the number of combinations “n choose r”.
MAFM.PC.7. Calculate the number of combinations with repetitions of r elements from a set of n elements as n + r – 1 choose r.
Prove statements involving combinatorics.MAFM.PC.10. Use the pigeonhole principle to prove statements about counting.
MAFM.PC.8. Prove combinatorial identities. For example, prove that n + 1 choose r is equal to n choose r – 1 plus n choose r; prove that the sum of the entries in the kth row of Pascal’s triangle is 2^k (where the first row is row 0).
MAFM.PC.9. Apply a combinatorial argument to prove the binomial theorem.
MAFM.ST. Set Theory Use set theoretic operations.MAFM.ST.4. Given a relation on two sets, determine whether the relation is a function and determine the relation’s inverse relation, if it exists.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MTCR.GF. Graphs and Functions Students will identify and analyze functions using mappings, relations, graphs, and real-world applications.MTCR.GF.1. Students will use the definition of functions to identify functions in various forms. (MGSE9-12.F.IF.5)Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MTCR.LEI. Linear Equations and Inequalities Students will solve equations and inequalities in one variable and then, extend this knowledge to two-variable linear equations and inequalities.MTCR.LEI.1. Students will solve multi-step equations and inequalities, using all forms of rational numbers as coefficients. (MGSE9-12.A.REI.l, MGSE9-12.A.CED.1)
MTCR.LEI.2. Students will set-up and solve application problems including direct and inverse variations and proportions. (MGSE9-12.A.CED.1)Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MTCR.LEI.3. Students will graph linear equations and inequalities using intercepts, slope and y-intercept, and tables of values. (MGSE9-12.N.Q.1)
MTCR.LEI.4. Students will determine and identify relationships between lines using slope. (MGSE9-12.G.GPE.5)
MTCR.LEI.5. Students will solve systems of linear equations using graphing, substitution, and elimination, and then, apply these methods to set-up and solve application problems involving systems. (MGSE9-12.A.CED.3)
MTCR.MG. Measurement and Geometry Students will classify basic geometric shapes and then, calculate the perimeters, areas, volumes, and surface areas of figures extending this work into contextual problems.MTCR.MG.4. Students will use formulas to isolate unknowns and then calculate the perimeters, areas, volumes, and surface areas of the shapes including setting-up and solving contextual problems. (MGSE9-12.A.REI.3, MGSE9-12.A.CED.4, MGSE9-12.G.GMD.1, MGSE9-12.G.GMD.3
MTCR.NLR. Non-Linear Relationships Students will simplify square roots, rational expressions, and polynomial expressions, and then, solve equations involving these expressions.MTCR.NLR.3. Students will perform basic operations with polynomial expressions including the use of order of operations, substitution of rational numbers for variables, operations with exponents, and binomial expansion. (MGSE9-12A.SSE.l, MGSE9-12.A.SSE.2, MGSE9-12A.S
MTCR.NS. Number Sense Students will analyze rational numbers using place value and will perform all basic operations using these numbers without the use of a calculator.MTCR.NS.1. Students will use place value to analyze whole numbers, numbers in scientific notation, and decimals. (MFANSQ1)
MTCR.NS.2. Students will perform mathematical operations involving all forms of positive, rational numbers, including the use of order of operations. (MFANSQ4)
MTCR.NS.3. Students will be able to convert fractions to decimals to percents from any given representation. (MFANSQ4)
MTCR.NS.4. Students will extend their knowledge of positive, rational numbers to negative values, including comparisons and absolute values. (MFANSQ2)
GA.MAFM.Technical College Readiness Mathematics
Technical College Readiness Mathematics
MAFM.LR. Logical Reasoning Represent and interpret statements using logical symbolism.MAFM.LR.3. Determine whether a logical argument is valid or invalid, and determine whether a logical argument is a tautology or a contradiction.
MAFM.MP. Methods of ProofMAFM.MP.2. Prove statements directly from definitions and previously proved statements. For example, using the definition of “rational number”, prove that every integer is rational; using the definition of “divides”, prove that if a divides b and b divides a, then a
MAFM.MP.5. Use the method of mathematical induction to prove statements involving the positive integers. For example, prove that 3 divides 2^(2n) – 1 for all positive integers n; prove that 1 + 2 + 3 + … + n = n (n + 1)/2; prove that a given recursive sequence has a
MAFM.NT. Number Theory Prove statements in number theory.MAFM.NT.5. Prove statements involving properties of numbers. For example, prove that the sum of two rational numbers is rational; prove that if a is even and b is odd, then (a^2 + b^2 + 1)/2 is an integer; prove that any odd number squared is of the form 8k + 1 for
MAFM.NT.6. Prove statements involving the floor and ceiling functions. For example, for every integer n, prove that the floor of n/2 is equal to n/2 if n is even and equal to (n – 1)/2 if n is odd.
MAFM.NT.7. Prove the Fundamental Theorem of Arithmetic, the Euclidean algorithm, and Fermat’s Little Theorem.
MAFM.PC. Probability and Combinatorics Calculate the probability of events.MAFM.PC.2. Apply the axioms of probability to determine the probability of dependent and independent events, including use of the multiplication rule for independent events.
Use methods of counting.MAFM.PC.5. Calculate the number of permutations of a set with n elements. Calculate the number of permutations of r elements taken from a set of n elements.
MAFM.PC.6. Calculate the number of subsets of size r that can be chosen from a set of n elements. Recognize this number as the number of combinations “n choose r”.
MAFM.PC.7. Calculate the number of combinations with repetitions of r elements from a set of n elements as n + r – 1 choose r.
Prove statements involving combinatorics.MAFM.PC.10. Use the pigeonhole principle to prove statements about counting.
MAFM.PC.8. Prove combinatorial identities. For example, prove that n + 1 choose r is equal to n choose r – 1 plus n choose r; prove that the sum of the entries in the kth row of Pascal’s triangle is 2^k (where the first row is row 0).
MAFM.PC.9. Apply a combinatorial argument to prove the binomial theorem.
MAFM.ST. Set Theory Use set theoretic operations.MAFM.ST.4. Given a relation on two sets, determine whether the relation is a function and determine the relation’s inverse relation, if it exists.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MTCR.GF. Graphs and Functions Students will identify and analyze functions using mappings, relations, graphs, and real-world applications.MTCR.GF.1. Students will use the definition of functions to identify functions in various forms. (MGSE9-12.F.IF.5)Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MTCR.LEI. Linear Equations and Inequalities Students will solve equations and inequalities in one variable and then, extend this knowledge to two-variable linear equations and inequalities.MTCR.LEI.1. Students will solve multi-step equations and inequalities, using all forms of rational numbers as coefficients. (MGSE9-12.A.REI.l, MGSE9-12.A.CED.1)
MTCR.LEI.2. Students will set-up and solve application problems including direct and inverse variations and proportions. (MGSE9-12.A.CED.1)Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MTCR.LEI.3. Students will graph linear equations and inequalities using intercepts, slope and y-intercept, and tables of values. (MGSE9-12.N.Q.1)
MTCR.LEI.4. Students will determine and identify relationships between lines using slope. (MGSE9-12.G.GPE.5)
MTCR.LEI.5. Students will solve systems of linear equations using graphing, substitution, and elimination, and then, apply these methods to set-up and solve application problems involving systems. (MGSE9-12.A.CED.3)
MTCR.MG. Measurement and Geometry Students will classify basic geometric shapes and then, calculate the perimeters, areas, volumes, and surface areas of figures extending this work into contextual problems.MTCR.MG.4. Students will use formulas to isolate unknowns and then calculate the perimeters, areas, volumes, and surface areas of the shapes including setting-up and solving contextual problems. (MGSE9-12.A.REI.3, MGSE9-12.A.CED.4, MGSE9-12.G.GMD.1, MGSE9-12.G.GMD.3
MTCR.NLR. Non-Linear Relationships Students will simplify square roots, rational expressions, and polynomial expressions, and then, solve equations involving these expressions.MTCR.NLR.3. Students will perform basic operations with polynomial expressions including the use of order of operations, substitution of rational numbers for variables, operations with exponents, and binomial expansion. (MGSE9-12A.SSE.l, MGSE9-12.A.SSE.2, MGSE9-12A.S
MTCR.NS. Number Sense Students will analyze rational numbers using place value and will perform all basic operations using these numbers without the use of a calculator.MTCR.NS.1. Students will use place value to analyze whole numbers, numbers in scientific notation, and decimals. (MFANSQ1)
MTCR.NS.2. Students will perform mathematical operations involving all forms of positive, rational numbers, including the use of order of operations. (MFANSQ4)
MTCR.NS.3. Students will be able to convert fractions to decimals to percents from any given representation. (MFANSQ4)
MTCR.NS.4. Students will extend their knowledge of positive, rational numbers to negative values, including comparisons and absolute values. (MFANSQ2)
GA.MAG.Analytic Geometry
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic, functions.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a circle formula A = π r^2 to highlight the radius r.
MGSE9-12.F.BF. Building Functions Build a function that models a relationship between two quantitiesMGSE9-12.F.BF.1. Write a function that describes a relationship between two quantities.MGSE9-12.F.BF.1a. Determine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MGSE9-12.F.IF. Interpreting Functions Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7a. Graph quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.G.CO. Congruence Understand congruence in terms of rigid motionsMGSE9-12.G.CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Prove geometric theoremsMGSE9-12.G.CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
MGSE9-12.G.GMD. Geometric Measurement and Dimension Explain volume formulas and use them to solve problemsMGSE9-12.G.GMD.1. Give informal arguments for geometric formulas.MGSE9-12.G.GMD.1a. Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.
MGSE9-12.G.GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MGSE9-12.G.SRT. Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformationsMGSE9-12.G.SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor.MGSE9-12.G.SRT.1a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.
MGSE9-12.G.SRT.1b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.
MGSE9-12.G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angl
Prove theorems involving similarityMGSE9-12.G.SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MGSE9-12.S.CP. Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret dataMGSE9-12.S.CP.2. Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two
MGSE9–12.N.RN. The Real Number System Use properties of rational and irrational numbers.MGSE9–12.N.RN.3. Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.
GA.MAGBA.Accelerated Geometry B/Algebra II
Accelerated Geometry B/Algebra II
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions.
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a circle formula A = π r^2 to highlight the radius r.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.SSE. Seeing Structure in Expressions Write expressions in equivalent forms to solve problemsMGSE9-12.A.SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.MGSE9-12.A.SSE.3c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t, where t is in years, can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate i
MGSE9-12.F.IF. Interpreting Functions Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7e. Graph exponential and logarithmic functions, showing intercepts and end behavior.
MGSE9-12.F.IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.MGSE9-12.F.IF.8b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponen
MGSE9-12.G.GMD. Geometric Measurement and Dimension Explain volume formulas and use them to solve problemsMGSE9-12.G.GMD.1. Give informal arguments for geometric formulas.MGSE9-12.G.GMD.1a. Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.
MGSE9-12.G.GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MGSE9-12.G.GPE. Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraicallyMGSE9-12.G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MGSE9-12.G.GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
MGSE9-12.N.RN. The Real Number System Extend the properties of exponents to rational exponents.MGSE9-12.N.RN.1. Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 beca
MGSE9-12.N.RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
MGSE9-12.S.CP. Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret dataMGSE9-12.S.CP.2. Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two
GA.MAI.Algebra I
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions (integer inputs only).
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a circle formula A = π r^2 to highlight the radius r.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoningMGSE9-12.A.REI.1. Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next u
Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.REI.12. Graph the solution set to a linear inequality in two variables.
Solve equations and inequalities in one variableMGSE9-12.A.REI.3. Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax + 3 = 7, solve for x.
Solve systems of equationsMGSE9-12.A.REI.5. Show and explain why the elimination method works to solve a system of two-variable equations.
MGSE9-12.A.REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
MGSE9-12.F.BF. Building Functions Build a function that models a relationship between two quantitiesMGSE9-12.F.BF.1. Write a function that describes a relationship between two quantities.MGSE9-12.F.BF.1a. Determine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MGSE9-12.F.IF. Interpreting Functions Understand the concept of a function and use function notationMGSE9-12.F.IF.1. Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.F.IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, studQuiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7a. Graph linear and quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.F.IF.7e. Graph exponential functions, showing intercepts and end behavior.
MGSE9-12.F.LE. Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic, and exponential models and solve problemsMGSE9-12.F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.MGSE9-12.F.LE.1a. Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates oQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.N.RN. The Real Number System Use properties of rational and irrational numbers.MGSE9-12.N.RN.3. Explain why the sum or product of rational numbers is rational; why the sum of a rational number and an irrational number is irrational; and why the product of a nonzero rational number and an irrational number is irrational.
MGSE9-12.S.ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variablesMGSE9-12.S.ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
MGSE9-12.S.ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MGSE9-12.S.ID.6c. Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.
GA.MAIIAA.Algebra II/Advanced Algebra
Algebra II/Advanced Algebra
MGSE9-12.A.APR. Arithmetic with Polynomials and Rational Expressions Perform arithmetic operations on polynomialsMGSE9-12.A.APR.1. Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions.
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R; Rearrange area of a circle formula A = π r^2 to highlight the radius r.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.SSE. Seeing Structure in Expressions Write expressions in equivalent forms to solve problemsMGSE9-12.A.SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.MGSE9-12.A.SSE.3c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t, where t is in years, can be rewritten as [1.15^(1/12)]^(12t) ≈ 1.012^(12t) to reveal the approximate equivalent monthly interest rate i
MGSE9-12.F.IF. Interpreting Functions Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7e. Graph exponential and logarithmic functions, showing intercepts and end behavior.
MGSE9-12.F.IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.MGSE9-12.F.IF.8b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as representing exponen
MGSE9-12.N.RN. The Real Number System Extend the properties of exponents to rational exponents.MGSE9-12.N.RN.1. Explain how the meaning of rational exponents follows from extending the properties of integer exponents to rational numbers, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 beca
MGSE9-12.N.RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
MGSE9-12.S.IC. Making Inferences and Justifying Conclusions Make inferences and justify conclusions from sample surveys, experiments, and observational studiesMGSE9-12.S.IC.5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
MGSE9-12.S.ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variableMGSE9-12.S.ID.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to est
GA.MAMDM.Advanced Mathematical Decision Making
Advanced Mathematical Decision Making
MAMDMA. ALGEBRA - Students will explore the applications of functions, their characteristics and their use in modeling. Vectors and matrices are employed for solving problems.MAMDMA1. Students will use vectors and matrices to organize and describe problem situations.MAMDMA1b. Represent geometric transformations and solve problems using matrices in fields such as computer animations.
MAMDMD. DATA ANAYLSIS AND PROBABILITY - Students will explore representations of data and models of data as tools in the decision making.MAMDMD3. Students will apply statistical methods to design, conduct, and analyze statistical studies.
MAMDMD4. Students will use functions to model problem situations in both discrete and continuous relationships.MAMDMD4b. Use linear, exponential, logistic, piecewise and sine functions to construct a model.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MAMDMG. GEOMETRY - Students apply tools to model geometric situations and solve problems. Students extend their knowledge of right triangle trigonometry.MAMDMG1. Students will create and use two- and three-dimensional representations of authentic situations.
MAMDMN. NUMBER AND OPERATIONS - Students will extend their understanding and use of ratios, proportions to solve problems involving in decision making.MAMDMN1. Students will extend the understanding of proportional reasoning, ratios, rates, and percents by applying them to various settings to include business, media, and consumerism.MAMDMN1a. Use proportional reasoning to solve problems involving ratios.
MAMDMN1c. Solve problems involving large quantities that are not easily measured.
MM1P. Process Standards - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.MM1P1. Students will solve problems (using appropriate technology).MM1P1a. Build new mathematical knowledge through problem solving.
MM1P1b. Solve problems that arise in mathematics and in other contexts.
MM1P1c. Apply and adapt a variety of appropriate strategies to solve problems.
MM1P1d. Monitor and reflect on the process of mathematical problem solving.
MM1P2. Students will reason and evaluate mathematical arguments.MM1P2a. Recognize reasoning and proof as fundamental aspects of mathematics.
MM1P2b. Make and investigate mathematical conjecture.
MM1P2c. Develop and evaluate mathematical arguments and proofs.
MM1P2d. Select and use various types of reasoning and methods of proof.
MM1P3. Students will communicate mathematically.MM1P3d. Use the language of mathematics to express mathematical ideas precisely.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
GA.MAMT.Advanced Mathematical Topics
Advanced Mathematical Topics
MAMTDM. DISCRETE MATHEMATICS - Students will demonstrate knowledge of discrete mathematics in the areas of graph theory, combinatorics, and game theory.MAMTDM2. Students will explore counting principles such as: recurrence relations, Polya’s Enumeration Theorem, inclusion-exclusion, and the Pigeonhole principle.
MAMTPR. PROOFS - Students will apply various proof techniques.MAMTPR1. Students will utilize appropriate methods of proof such as: direct proof, proof by mathematical induction, proof by transposition, and proof by contradiction.
MAMTPR4. Students will prove previously recognized mathematical theorems, such as but not limited to the Pythagorean Theorem, the Minimax Theorem, the Binomial Theorem, and Cantor’s Theorem.
GA.MAPC.Accelerated Pre-Calculus
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Solve systems of equationsMGSE9-12.A.REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.
MGSE9-12.F.IF. Interpreting Functions Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.S.CP. Conditional Probability and the Rules of Probability Use the rules of probability to compute probabilities of compound events in a uniform probability modelMGSE9-12.S.CP.9. Use permutations and combinations to compute probabilities of compound events and solve problems.
MGSE9-12.S.IC. Making Inferences and Justifying Conclusions Make inferences and justify conclusions from sample surveys, experiments, and observational studiesMGSE9-12.S.IC.5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
MGSE9-12.S.ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variableMGSE9-12.S.ID.4. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to est
MGSE9-12.S.MD. Use Probability to Make Decisions Calculate expected values and use them to solve problemsMGSE9-12.S.MD.3. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers
MGSE9-12.S.MD.4. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the Unite
GA.MCA.Coordinate Algebra
MGSE9-12.A.CED. Creating Equations Create equations that describe numbers or relationshipsMGSE9-12.A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, and exponential functions (integer inputs only).
MGSE9-12.A.CED.2. Create linear, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interes
MGSE9-12.A.CED.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.
MGSE9-12.A.CED.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight resistance R.
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Understand solving equations as a process of reasoning and explain the reasoningMGSE9-12.A.REI.1. Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next u
Represent and solve equations and inequalities graphicallyMGSE9-12.A.REI.11. Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.
MGSE9-12.A.REI.12. Graph the solution set to a linear inequality in two variables.
Solve equations and inequalities in one variableMGSE9-12.A.REI.3. Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. For example, given ax + 3 = 7, solve for x.
Solve systems of equationsMGSE9-12.A.REI.5. Show and explain why the elimination method works to solve a system of two-variable equations.
MGSE9-12.A.REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
MGSE9-12.F.BF. Building Functions Build a function that models a relationship between two quantitiesMGSE9-12.F.BF.1. Write a function that describes a relationship between two quantities.MGSE9-12.F.BF.1a. Determine an explicit expression and the recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the explicit expression “2x+15” can be described recursively (either in writing or verbally) as Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MGSE9-12.F.IF. Interpreting Functions Understand the concept of a function and use function notationMGSE9-12.F.IF.1. Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.F.IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, studQuiz, Flash Cards, Worksheet, Game & Study Guide Sequences
Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.F.IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Analyze functions using different representationsMGSE9-12.F.IF.7. Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.MGSE9-12.F.IF.7a. Graph linear functions and show intercepts, maxima, and minima (as determined by the function or by context).
MGSE9-12.F.IF.7e. Graph exponential functions, showing intercepts and end behavior.
MGSE9-12.F.LE. Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic, and exponential models and solve problemsMGSE9-12.F.LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.MGSE9-12.F.LE.1a. Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be shown by algebraic proof, with a table showing differences, or by calculating average rates oQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
MGSE9-12.G.CO. Congruence Experiment with transformations in the planeMGSE9-12.G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MGSE9-12.G.CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
MGSE9-12.G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MGSE9-12.G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MGSE9-12.G.CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
MGSE9-12.G.GPE. Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraicallyMGSE9-12.G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MGSE9-12.G.GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
MGSE9-12.S.ID. Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on two categorical and quantitative variablesMGSE9-12.S.ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
MGSE9-12.S.ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MGSE9-12.S.ID.6c. Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.
GA.MEC.Engineering Calculus
MECPS. PROCESS STANDARDS - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.MECPS1. Students will solve engineering-based calculus problems (using appropriate technology).MECPS1a. Build new mathematical knowledge through problem solving.
MECPS1b. Solve problems that arise in mathematics and in other contexts.
MECPS1c. Apply and adapt a variety of appropriate strategies to solve problems, such as considering realistic constraints relevant to the design of a system, component, or process.
MECPS1d. Monitor and reflect on the process of mathematical problem solving and interpret problem solutions.
MECPS2. Students will use visual and written communication to express basic design elements and will communicate mathematically.MECPS2a. Organize and consolidate their mathematical thinking through communication.
MECPS2b. Communicate and use the language of mathematics to articulate their mathematical thinking coherently.
MECPS2c. Present a technical design, using computer-generated model, for an assigned design project.
MECPS3. Students will describe the history of technological advancement and make connections among mathematical ideas and to other disciplines.MECPS3a. Recognize and use connections among mathematical and engineering ideas.
MECPS4. Students will represent mathematics in multiple ways.MECPS4a. Create and use representations to organize, record, and communicate mathematical ideas.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
GA.MFA.Foundations of Algebra
MFAAA. Arithmetic to Algebra Students will extend arithmetic operations to algebraic modeling.MFAAA1. Students will generate and interpret equivalent numeric and algebraic expressions.MFAAA1a. Apply properties of operations emphasizing when the commutative property applies. (MGSE7.EE.1)
MFAAA1b. Use area models to represent the distributive property and develop understandings of addition and multiplication (all positive rational numbers should be included in the models). (MGSE3.MD.7)
MFAAA2. Students will interpret and use the properties of exponents.MFAAA2b. Use properties of integer exponents to find equivalent numerical expressions. For example, 3^2 x 3^(-5) = 3^(-3) = 1/(3^3) = 1/27. (MGSE8.EE.1)
MFAAA2c. Evaluate square roots of perfect squares and cube roots of perfect cubes (MGSE8.EE.2)Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
MFAAA2d. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. (MGSE8.EE.2)Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
MFAEI. Equations and Inequalities Students will solve, interpret, and create linear models using equations and inequalities.MFAEI1. Students will create and solve equations and inequalities in one variable.MFAEI1a. Use variables to represent an unknown number in a specified set. (MGSE.6.EE2,5,6)
MFAEI1b. Explain each step in solving simple equations and inequalities using the equality properties of numbers. (MGSE9-12.A.REI.1)
MFAEI1d. Represent and find solutions graphically.
MFAEI1e. Use variables to solve real-world and mathematical problems. (MGSE6.EE.7,MGSE7.EE.4)
MFAEI2. Students will use units as a way to understand problems and guide the solutions of multi-step problems.MFAEI2c. Graph points in all four quadrants of the coordinate plane. (MGSE6.NS.8)
MFAEI3. Students will create algebraic models in two variables.MFAEI3c. Represent solutions to systems of equations graphically or by using a table of values. (MGSE6.EE.5; MGSE7.EE3; MGSE8.EE.8; MGSE9-12.A.CED.2)
MFAEI3d. Analyze the reasonableness of the solutions of systems of equations within a given context. (MGSE6.EE.5,6,MGSE7.EE4)
MFAEI4. Students will solve literal equations.MFAEI4a. Solve for any variable in a multi-variable equation. (MGSE6.EE.9,MGSE9-12.A.REI.3)
MFAEI4b. Rearrange formulas to highlight a particular variable using the same reasoning as in solving equations. For example, solve for the base in A = 1/2 bh. (MGSE9-12.A.CED.4)
MFANSQ. Number Sense and Quantity Students will compare different representations of numbers (i.e. fractions, decimals, radicals, etc.) and perform basic operations using these different representations.MFANSQ1. Students will analyze number relationships.MFANSQ1b. Understand a fraction a/b as a multiple of 1/b. (MGSE4.NF.4)
MFANSQ2. Students will conceptualize positive and negative numbers (including decimals and fractions).MFANSQ2c. Explain meanings of real numbers in a real world context. (MGSE6.NS.5)Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
MFANSQ3. Students will recognize that there are numbers that are not rational, and approximate them with rational numbers.MFANSQ3a. Find an estimated decimal expansion of an irrational number locating the approximations on a number line. For example, for √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue this pattern in order to obtain better ap
MFANSQ3b. Explain the results of adding and multiplying with rational and irrational numbers. (MGSE9-12.N.RN.3)
MFANSQ4. Students will apply and extend previous understanding of addition, subtraction, multiplication, and division.MFANSQ4b. Find sums, differences, products, and quotients of all forms of rational numbers, stressing the conceptual understanding of these operations. (MGSE7.NS.1,2)
MFANSQ4d. Illustrate and explain calculations using models and line diagrams. (MGSE7.NS.1,2)
MFAPR. Proportional Reasoning Students will use ratios to solve real-world and mathematical problems.MFAPR1. Students will explain equivalent ratios by using a variety of models. For example, tables of values, tape diagrams, bar models, double number line diagrams, and equations. (MGSE6.RP.3)
MFAPR2. Students will recognize and represent proportional relationships between quantities.MFAPR2a. Relate proportionality to fraction equivalence and division. For example, 3/6 is equal to 4/8 because both yield a quotient of 1/2 and, in both cases, the denominator is double the value of the numerator. (MGSE4.NF.1)
MFAPR2b. Understand real-world rate/ratio/percent problems by finding the whole given a part and find a part given the whole. (MGSE6.RP.1,2,3; MGSE7.RP.1,2)
MFAPR2c. Use proportional relationships to solve multistep ratio and percent problems. (MGSE7.RP.2,3)
MFAPR3. Students will graph proportional relationships.MFAPR3a. Interpret unit rates as slopes of graphs. (MGSE8.EE.5)
MFAPR3b. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. (MGSE8.EE.6)
MFAQR. Quantitative Reasoning with Functions Students will create function statements and analyze relationships among pairs of variables using graphs, tables, and equations.MFAQR1. Students will understand characteristics of functions.MFAQR1a. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. (MGSE9-12.F.IF.1)Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MFAQR1c. Graph functions using sets of ordered pairs consisting of an input and the corresponding output. (MGSE8.F.1, 2)
MFAQR2. Students will compare and graph functions.MFAQR2b. Graph by hand simple functions expressed symbolically (use all four quadrants). (MGSE9-12.F.IF.7)
MFAQR2e. Analyze graphs of functions for key features (intercepts, intervals of increase/decrease, maximums/minimums, symmetries, and end behavior) based on context. (MGSE9-12.F.IF.4,7)
MFAQR3. Students will construct and interpret functions.MFAQR3a. Write a function that describes a relationship between two quantities. (MGSE8.F.4, MGSE9-12.F.BF.1)
MFAQR3b. Use variables to represent two quantities in a real-world problem that change in relationship to one another (conceptual understanding of a variable). (MGSE6.EE.9)
GA.MG.Geometry
MGSE9-12.G.CO. Congruence Experiment with transformations in the planeMGSE9-12.G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MGSE9-12.G.CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
MGSE9-12.G.CO.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MGSE9-12.G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MGSE9-12.G.CO.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Understand congruence in terms of rigid motionsMGSE9-12.G.CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Prove geometric theoremsMGSE9-12.G.CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line
MGSE9-12.G.GMD. Geometric Measurement and Dimension Explain volume formulas and use them to solve problemsMGSE9-12.G.GMD.1. Give informal arguments for geometric formulas.MGSE9-12.G.GMD.1a. Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.
MGSE9-12.G.GMD.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MGSE9-12.G.GPE. Expressing Geometric Properties with Equations Use coordinates to prove simple geometric theorems algebraicallyMGSE9-12.G.GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
MGSE9-12.G.GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
MGSE9-12.G.SRT. Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformationsMGSE9-12.G.SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor.MGSE9-12.G.SRT.1a. The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.
MGSE9-12.G.SRT.1b. The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.
MGSE9-12.G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angl
Prove theorems involving similarityMGSE9-12.G.SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MGSE9-12.S.CP. Conditional Probability and the Rules of Probability Understand independence and conditional probability and use them to interpret dataMGSE9-12.S.CP.2. Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two
GA.MHM.History of Mathematics
MHMA. ALGEBRA - Students will investigate historical equation solving techniques in both algebraic and geometric form; understand and use the axiomatic method of abstract algebra; compute defined products on sets of complex numbers; solve linear congruences; deMHMA1. Students will explore and use historical methods for expressing and solving equations.MHMA1d. Translate into modern notation problems appearing in ancient and medieval texts that involve linear, quadratic, or cubic equations and solve them.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MHMP. Process Standards - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.MHMP1. Students will solve problems (using appropriate technology).MHMP1a. Build new mathematical knowledge through problem solving.
MHMP1b. Solve problems that arise in mathematics and in other contexts.
MHMP1c. Apply and adapt a variety of appropriate strategies to solve problems.
MHMP1d. Monitor and reflect on the process of mathematical problem solving.
MHMP2. Students will reason and evaluate mathematical arguments.MHMP2a. Recognize reasoning and proof as fundamental aspects of mathematics.
MHMP2b. Make and investigate mathematical conjectures.
MHMP2c. Develop and evaluate mathematical arguments and proofs.
MHMP2d. Select and use various types of reasoning and methods of proof.
MHMP3. Students will communicate mathematically.MHMP3d. Use the language of mathematics to express mathematical ideas precisely.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
GA.MMC.Multivariable Calculus
MMCP. Process Standards - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.MMCP1. Students will solve problems (using appropriate technology).MMCP1a. Build new mathematical knowledge through problem solving.
MMCP1b. Solve problems that arise in mathematics and in other contexts.
MMCP1c. Apply and adapt a variety of appropriate strategies to solve problems.
MMCP1d. Monitor and reflect on the process of mathematical problem solving.
MMCP2. Students will reason and evaluate mathematical arguments.MMCP2a. Recognize reasoning and proof as fundamental aspects of mathematics.
MMCP2b. Make and investigate mathematical conjectures.
MMCP2c. Develop and evaluate mathematical arguments and proofs.
MMCP2d. Select and use various types of reasoning and methods of proof.
MMCP3. Students will communicate mathematically.MMCP3d. Use the language of mathematics to express mathematical ideas precisely.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
GA.MMF.Mathematics of Finance
MMFA. ALGEBRA - Students will explore the applications of functions, their characteristics, their use in modeling and matrices for solving problems in financial situations.MMFA1. Students will use basic functions to solve and model problems related to stock transactions, banking and credit, employment and taxes, rent and mortgages, retirement planning, and other related finance applications.MMFA1d. Apply exponential and logarithmic functions.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MMFA3. Students will use formulas to investigate investments in banking and retirement planning.MMFA3a. Apply simple and compound interest formulas.
MMFD. DATA ANALYSIS AND STATISTICS - Students will explore representations and models of data as tools in the decision making process of finance.MMFD1. Students will use measures of central tendency to investigate data found in the stock market, retirement planning, transportation, budgeting, and home rental or ownership.
MMFD2. Students will use data displays including bar graphs, line graphs, stock bar charts, candlestick charts, box and whisker plots, stem and leaf plots, circle graphs, and scatterplots to recognize and interpret trends related to the stock market, retirement
MMFD3. Students will use linear, quadratic, and cubic regressions as well as the correlation coefficient to move supply and demand, revenue, profit, and other financial problem situations.
MMFG. GEOMETRY - Students will use geometry to explore real-world applications including, but not limited to, floor plans, square footage, models of furniture arrangements, trip planning, and accident investigations.MMFG1. Students will apply the concepts of area, volume, scale factors, and scale drawings to planning for housing.
MMFP. PROCESS STANDARDS - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.MMFP1. Students will solve problems (using appropriate technology).MMFP1a. Build new mathematical knowledge through problem solving.
MMFP1b. Solve problems that arise in mathematics and in other contexts.
MMFP1c. Apply and adapt a variety of appropriate strategies to solve problems.
MMFP1d. Monitor and reflect on the process of mathematical problem solving.
MMFP2. Students will reason and evaluate mathematical arguments.MMFP2a. Recognize reasoning and proof as fundamental aspects of mathematics.
MMFP2b. Make and investigate mathematical conjecture.
MMFP2c. Develop and evaluate mathematical arguments and proofs.
MMFP2d. Select and use various types of reasoning and methods of proof.
MMFP3. Students will communicate mathematically.MMFP3d. Use the language of mathematics to express mathematical ideas precisely.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
GA.MMIG.Mathematics of Industry and Government
Mathematics of Industry and Government
MMIGP. PROCESS STANDARDS - The following process standards are essential to mastering each of the mathematics content standards. They emphasize critical dimensions of the mathematical proficiency that all students need.MMIGP1. Students will solve problems (using appropriate technology).MMIGP1a. Build new mathematical knowledge through problem solving.
MMIGP1b. Solve problems that arise in mathematics and in other contexts.
MMIGP1c. Apply and adapt a variety of appropriate strategies to solve problems.
MMIGP1d. Monitor and reflect on the process of mathematical problem solving.
MMIGP2. Students will reason and evaluate mathematical arguments.MMIGP2a. Recognize reasoning and proof as fundamental aspects of mathematics.
MMIGP2b. Make and investigate mathematical conjecture.
MMIGP2c. Develop and evaluate mathematical arguments and proofs.
MMIGP2d. Select and use various types of reasoning and methods of proof.
MMIGP3. Students will communicate mathematically.MMIGP3d. Use the language of mathematics to express mathematical ideas precisely.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MMIGPD. PROBABILISTIC DECISION MAKING - Students will use normal and other (e.g., binomial, geometric, and Poisson) distributions as well as simulations to make appropriate decisions.MMIGPD1. Students will use properties of normal distributions to make decisions about optimization and efficiency.MMIGPD1a. Calculate theoretical and empirical probabilities using standardized and non-standardized data.
MMIGPD2. Students will use properties of other distributions (e.g. binomial, geometric, Poisson) to make decisions about optimization and efficiency.MMIGPD2a. Calculate theoretical and empirical probabilities using standardized and non-standardized data.
GA.MPC.Pre-Calculus
MGSE9-12.A.REI. Reasoning with Equations and Inequalities Solve systems of equationsMGSE9-12.A.REI.7. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x^2 + y^2 = 3.
MGSE9-12.F.IF. Interpreting Functions Interpret functions that arise in applications in terms of the contextMGSE9-12.F.IF.4. Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decr
MGSE9-12.S.CP. Conditional Probability and the Rules of Probability Use the rules of probability to compute probabilities of compound events in a uniform probability modelMGSE9-12.S.CP.9. Use permutations and combinations to compute probabilities of compound events and solve problems.
MGSE9-12.S.MD. Use Probability to Make Decisions Calculate expected values and use them to solve problemsMGSE9-12.S.MD.3. Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers
MGSE9-12.S.MD.4. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the Unite
GA.MPGS.Standards for Mathematical Practice
Standards for Mathematical Practice
MPGS.1. Make sense of problems and persevere in solving them.
MPGS.2. Reason abstractly and quantitatively.
GA.MSR.Statistical Reasoning
MSRAD. Analyze Data - Students will select appropriate graphical and numerical methods and use these methods to analyze the data.MSRAD1. Students will use distributions to identify the key features of the data collected. Students will describe the distribution for quantitative and categorical data.MSRAD1a. Describe the distribution for quantitative data.MSRAD1a.iv. Describe and interpret any outliers or gaps in the distribution.
MSRAD2. Students will use distributions to compare two or more groups. Students will compare two or more groups by analyzing distributions.MSRAD2a. Construct appropriate graphical displays of distributions.
MSRAD3. Students will determine if an association exists between two variables (pattern or trend in bivariate data) and use values of one variable to predict values of another variable. Students will analyze associations between variables and make predictions froMSRAD3a. Analyze associations between two variables.MSRAD3a.ii. Create two-way tables for two-variable categorical data.
MSRAD3a.iii. Analyze patterns and trends in data displays.
MSRAD3b. Make predictions and draw conclusions from two-variable data based on data displays.
MSRCD. Collect Data - Students will design and implement a plan to collect the appropriate data to answer the statistical question.MSRCD2. Students will understand that randomness should be incorporated into a sampling or experimental procedure. Students will be able to implement a reasonable random method for selecting a sample or for assigning treatments in an experiment.MSRCD2a. Implement a simple random sample.
MSRFQ. Formulate Questions - Students will formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data.MSRFQ1. Students will apply the statistical method to real-world situations.MSRFQ1b. Collect data by designing a plan to collect appropriate data and employ the plan to collect the data.
MSRFQ1c. Analyze data by selecting appropriate graphical and numerical methods and using these methods to analyze the data.
MSRFQ1d. Interpret results by interpreting the analysis and relating the interpretation to the original question.
MSRFQ2. Students will identify whether the data are categorical or quantitative (numerical). Students will be able to identify the difference between categorical and quantitative (numerical) data.MSRFQ2a. Determine the appropriate graphical display for each type of data.