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MA.AI.Model Algebra I Content Standards [AI]
Model Algebra I Content Standards [AI]
AI.A-APR. Algebra - Arithmetic with Polynomials and Rational ExpressionsAI.A-APR.A. Perform arithmetic operations on polynomials.AI.A-APR.A.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.AI.A-APR.A.1.a. Perform operations on polynomial expressions (addition, subtraction, multiplication), and compare the system of polynomials to the system of integers when performing operations.
AI.A-APR.A.1.b. Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive property.
AI.A-CED. Algebra - Creating EquationsAI.A-CED.A. Create equations that describe numbers or relationships.AI.A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
AI.A-CED.A.3. Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional an
AI.A-CED.A.4. Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (Properties of equality). For example, rearrange Ohm’s law R = V^2/P to solve for voltage, V. Manipulate variables in formulas used in financial contex
AI.A-REI. Algebra - Reasoning with Equations and InequalitiesAI.A-REI.A. Understand solving equations as a process of reasoning and explain the reasoning.AI.A-REI.A.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solution met
AI.A-REI.C. Solve systems of equations.AI.A-REI.C.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
AI.A-REI.C.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
AI.A-REI.D. Represent and solve equations and inequalities graphically.AI.A-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions and make tables of
AI.A-REI.D.12. Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the correspondin
AI.A-SSE. Algebra - Seeing Structure in ExpressionsAI.A-SSE.B. Write expressions in equivalent forms to solve problems.AI.A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.AI.A-SSE.B.3.c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
AI.F-BF. Building FunctionsAI.F-BF.A. Build a function that models a relationship between two quantities.AI.F-BF.A.1. Write linear, quadratic, and exponential functions that describe a relationship between two quantities.AI.F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
AI.F-IF. Functions - Interpreting FunctionsAI.F-IF.A. Understand the concept of a function and use function notation.AI.F-IF.A.1. 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. If f is a function and x is an element of its domain, then f(x) denotes the output (rangeQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
AI.F-IF.A.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n ≥ 1.Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
AI.F-IF.B. Interpret linear, quadratic, and exponential functions with integer exponents that arise in applications in terms of the context.AI.F-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
AI.F-IF.B.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.
AI.F-IF.C. Analyze functions using different representations.AI.F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.AI.F-IF.C.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
AI.F-IF.C.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.AI.F-IF.C.8.b. Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as identifying appreciation and depreciation rate for the value of a house or car some time after its initial purchase: V_n = P(1+r)^n. Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
AI.F-LE. Linear, Quadratic, and Exponential ModelsAI.F-LE.A. Construct and compare linear, quadratic, and exponential models and solve problems.AI.F-LE.A.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.AI.F-LE.A.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
AI.N-RN. Number and Quantity - The Real Number SystemAI.N-RN.A. Extend the properties of exponents to rational exponents.AI.N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
AI.N-RN.B. Use properties of rational and irrational numbers.AI.N-RN.B.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
AI.S-ID. Statistics and Probability - Interpreting Categorical and Quantitative DataAI.S-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.AI.S-ID.B.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.
AI.S-ID.B.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.AI.S-ID.B.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
AI.S-ID.B.6.c. Fit a linear function for a scatter plot that suggests a linear association.
MA.AII.Model Algebra II Content Standards [AII]
Model Algebra II Content Standards [AII]
AII.A-APR. Arithmetic with Polynomials and Rational ExpressionsAII.A-APR.A. Perform arithmetic operations on polynomials.AII.A-APR.A.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.AII.A-APR.A.1.a. Perform operations on polynomial expressions (addition, subtraction, multiplication, and division), and compare the system of polynomials to the system of integers when performing operations.
AII.A-CED. Creating EquationsAII.A-CED.A. Create equations that describe numbers or relationships.AII.A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from simple root and rational functions and exponential functions.
AII.A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
AII.A-CED.A.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent equations describing satellites orbiting Earth and c
AII.A-REI. Reasoning with Equations and InequalitiesAII.A-REI.D. Represent and solve equations and inequalities graphically.AII.A-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
AII.F-IF. Functions - Interpreting FunctionsAII.F-IF.B. Interpret functions that arise in applications in terms of the context (polynomial, rational, square root and cube root, trigonometric, and logarithmic functions).AII.F-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
AII.F-IF.B.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.
MA.CC.High School Content Standards by Conceptual Categories
High School Content Standards by Conceptual Categories
A-APR. Algebra Content Standards - Arithmetic with Polynomials and Rational ExpressionsA-APR.A. Perform arithmetic operations on polynomials.A-APR.A.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.A-APR.A.1.a. Perform operations on polynomial expressions (addition, subtraction, multiplication, division) and compare the system of polynomials to the system of integers when performing operations.
A-APR.A.1.b. Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive property.
A-CED. Algebra Content Standards - Creating EquationsA-CED.A. Create equations that describe numbers or relationships.A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. (Include equations arising from linear and quadratic functions, and simple root and rational functions and exponential functions.)
A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-CED.A.3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constra
A-CED.A.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance, R.
A-REI. Algebra Content Standards - Reasoning with Equations and InequalitiesA-REI.A. Understand solving equations as a process of reasoning and explain the reasoning.A-REI.A.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solution met
A-REI.C. Solve systems of equations.A-REI.C.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
A-REI.C.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A-REI.D. Represent and solve equations and inequalities graphically.A-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
A-REI.D.12. Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the correspondin
A-SSE. Algebra Content Standards - Seeing Structure in ExpressionsA-SSE.B. Write expressions in equivalent forms to solve problems.A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.A-SSE.B.3.c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-BF. Functions Overview - Building FunctionsF-BF.A. Build a function that models a relationship between two quantities.F-BF.A.1. Write a function (linear, quadratic, exponential, simple rational, radical, logarithmic, and trigonometric) that describes a relationship between two quantities.F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-IF. Functions Overview - Interpreting FunctionsF-IF.A. Understand the concept of a function and use function notation.F-IF.A.1. 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f cQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-IF.A.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n ≥ 1.Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
F-IF.B. Interpret functions that arise in applications in terms of the context (linear, quadratic, exponential, rational, polynomial, square root, cube root, trigonometric, logarithmic).F-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
F-IF.B.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.
F-IF.C. Analyze functions using different representations.F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.F-IF.C.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
F-IF.C.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.F-IF.C.8.b. Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as identifying appreciation and depreciation rate for the value of a house or car some time after its initial purchase. For example, ideQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
F-LE. Functions Overview - Linear, Quadratic, and Exponential ModelsF-LE.A. Construct and compare linear, quadratic, and exponential models and solve problems.F-LE.A.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.F-LE.A.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
G-CO. Geometry Content Standards - CongruenceG-CO.A. Experiment with transformations in the plane.G-CO.A.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.
G-CO.A.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
G-CO.A.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G-CO.A.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G-CO.A.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.
G-CO.B. Understand congruence in terms of rigid motions.G-CO.B.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.
G-CO.C. Prove geometric theorems and, when appropriate, the converse of theorems.G-CO.C.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, and conversely prove lines are parallel; poi
G-GMD. Geometry Content Standards - Geometric Measurement and DimensionG-GMD.A. Explain volume formulas and use them to solve problems.G-GMD.A.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
G-GMD.A.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G-GPE. Geometry Content Standards - Expressing Geometric Properties with EquationsG-GPE.B. Use coordinates to prove simple geometric theorems algebraically.G-GPE.B.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).
G-GPE.B.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles (e.g., using the distance formula).
G-SRT. Geometry Content Standards - Similarity, Right Triangles, and TrigonometryG-SRT.A. Understand similarity in terms of similarity transformations.G-SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:G-SRT.A.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G-SRT.A.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G-SRT.A.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 angles
G-SRT.B. Prove theorems involving similarity.G-SRT.B.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
N-RN. Number and Quantity Content Standards - The Real Number SystemN-RN.A. Extend the properties of exponents to rational exponents.N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
N-RN.B. Use properties of rational and irrational numbers.N-RN.B.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
S-CP. Statistics and Probability Content Standards - Conditional Probability and the Rules of ProbabilityS-CP.A. Understand independence and conditional probability and use them to interpret data from simulations or experiments.S-CP.A.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S-ID. Statistics and Probability Content Standards - Interpreting Categorical and Quantitative DataS-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.S-ID.B.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.
S-ID.B.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.S-ID.B.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
S-ID.B.6.c. Fit a linear function for a scatter plot that suggests a linear association.
MA.GEO.Model Geometry Content Standards [GEO]
Model Geometry Content Standards [GEO]
GEO.G-CO. Geometry - CongruenceGEO.G-CO.A. Experiment with transformations in the plane.GEO.G-CO.A.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.
GEO.G-CO.A.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
GEO.G-CO.A.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
GEO.G-CO.A.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
GEO.G-CO.A.5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
GEO.G-CO.B. Understand congruence in terms of rigid motions.GEO.G-CO.B.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.
GEO.G-CO.C. Prove geometric theorems and, when appropriate, the converse of theorems.GEO.G-CO.C.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, and conversely prove lines are parallel; poi
GEO.G-GMD. Geometric Measurement and DimensionGEO.G-GMD.A. Explain volume formulas and use them to solve problems.GEO.G-GMD.A.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
GEO.G-GMD.A.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
GEO.G-GPE. Expressing Geometric Properties with EquationsGEO.G-GPE.B. Use coordinates to prove simple geometric theorems algebraically.GEO.G-GPE.B.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).
GEO.G-SRT. Similarity, Right Triangles, and TrigonometryGEO.G-SRT.A. Understand similarity in terms of similarity transformations.GEO.G-SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:GEO.G-SRT.A.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
GEO.G-SRT.A.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
GEO.G-SRT.A.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 angles
GEO.G-SRT.B. Prove theorems involving similarity.GEO.G-SRT.B.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
GEO.S-CP. Statistics and Probability - Conditional Probability and the Rules of ProbabilityGEO.S-CP.A. Understand independence and conditional probability and use them to interpret data from simulations or experiments.GEO.S-CP.A.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
MA.MI.Model Mathematics I Content Standards [MI]
Model Mathematics I Content Standards [MI]
MI.A-CED. Creating EquationsMI.A-CED.A. Create equations that describe numbers or relationships.MI.A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions with integer exponents.
MI.A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
MI.A-CED.A.3. Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional an
MI.A-CED.A.4. Rearrange formulas to highlight a quantity of interest, using the same reasoning (Properties of equality) as in solving equations. For example, rearrange Ohm’s law, V = IR, to solve for resistance, R. Manipulate variables in formulas used in financial con
MI.A-REI. Reasoning with Equations and InequalitiesMI.A-REI.A. Understand solving equations as a process of reasoning and explain the reasoning.MI.A-REI.A.1. Explain each step in solving a simple linear equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solut
MI.A-REI.C. Solve systems of equations.MI.A-REI.C.5. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
MI.A-REI.C.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
MI.A-REI.D. Represent and solve equations and inequalities graphically.MI.A-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions and/or make tables
MI.A-REI.D.12. Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the correspondin
MI.F-BF. Building FunctionsMI.F-BF.A. Build a function that models a relationship between two quantities.MI.F-BF.A.1. Write linear and exponential functions that describe a relationship between two quantities.MI.F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
MI.F-IF. Functions - Interpreting FunctionsMI.F-IF.A. Understand the concept of a function and use function notation.MI.F-IF.A.1. 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f cQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
MI.F-IF.A.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n - 1) for n ≥ 1.Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
MI.F-IF.B. Interpret linear and exponential functions having integer exponents that arise in applications in terms of the context.MI.F-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
MI.F-IF.B.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.
MI.F-IF.C. Analyze functions using different representations.MI.F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.MI.F-IF.C.7.a. Graph linear functions and show intercepts.
MI.F-LE. Linear, Quadratic, and Exponential ModelsMI.F-LE.A. Construct and compare linear and exponential models and solve problems.MI.F-LE.A.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.MI.F-LE.A.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MI.G-CO. Geometry - CongruenceMI.G-CO.A. Experiment with transformations in the plane.MI.G-CO.A.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.
MI.G-CO.A.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
MI.G-CO.A.3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
MI.G-CO.A.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
MI.G-CO.A.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.
MI.G-CO.B. Understand congruence in terms of rigid motions.MI.G-CO.B.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.
MI.G-GPE. Expressing Geometric Properties with EquationsMI.G-GPE.B. Use coordinates to prove simple geometric theorems algebraically.MI.G-GPE.B.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).
MI.S-ID. Statistics and Probability - Interpreting Categorical and Quantitative DataMI.S-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.MI.S-ID.B.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.
MI.S-ID.B.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.MI.S-ID.B.6.b. Informally assess the fit of a function by plotting and analyzing residuals.
MI.S-ID.B.6.c. Fit a linear function for a scatter plot that suggests a linear association.
MA.MII.Model Mathematics II Content Standards [MII]
Model Mathematics II Content Standards [MII]
MII.A-APR. Arithmetic with Polynomials and Rational ExpressionsMII.A-APR.A. Perform arithmetic operations on polynomials.MII.A-APR.A.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.MII.A-APR.A.1.a. Perform operations on polynomial expressions (addition, subtraction, multiplication), and compare the system of polynomials to the system of integers when performing operations.
MII.A-APR.A.1.b. Factor and/or expand polynomial expressions; identify and combine like terms; and apply the Distributive property.
MII.A-CED. Creating EquationsMII.A-CED.A. Create equations that describe numbers or relationships.MII.A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from quadratic and exponential functions.
MII.A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
MII.A-CED.A.4. Rearrange formulas, including formulas with quadratic terms, to highlight a quantity of interest using the same reasoning as in solving equations (Properties of equality). For example, rearrange Ohm’s law R = V^2/p to solve for voltage, V.
MII.A-SSE. Algebra - Seeing Structure in ExpressionsMII.A-SSE.B. Write quadratic and exponential expressions in equivalent forms to solve problems.MII.A-SSE.B.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.MII.A-SSE.B.3.c. Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.Quiz, Flash Cards, Worksheet, Game & Study Guide Functions
MII.F-BF. Building FunctionsMII.F-BF.A. Build a function that models a relationship between two quantities.MII.F-BF.A.1. Write linear, quadratic, and exponential functions that describe relationships between two quantities.MII.F-BF.A.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
MII.F-IF. Functions - Interpreting FunctionsMII.F-IF.B. Interpret quadratic and exponential functions with integer exponents that arise in applications in terms of the context.MII.F-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
MII.F-IF.B.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.
MII.F-IF.C. Analyze functions using different representations.MII.F-IF.C.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.MII.F-IF.C.7.a. Graph quadratic functions and show intercepts, maxima, and minima.
MII.F-IF.C.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.MII.F-IF.C.8.b. Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as Identifying appreciation/depreciation rate for the value of a house or car some time after its initial purchase:. For example, identiQuiz, Flash Cards, Worksheet, Game & Study Guide Functions
MII.G-CO. Geometry - CongruenceMII.G-CO.C. Prove geometric theorems and, when appropriate, the converse of theorems.MII.G-CO.C.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, and conversely prove lines are parallel; poi
MII.G-GMD. Geometric Measurement and DimensionMII.G-GMD.A. Explain volume formulas and use them to solve problems.MII.G-GMD.A.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
MII.G-GMD.A.3. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MII.G-SRT. Similarity, Right Triangles, and TrigonometryMII.G-SRT.A. Understand similarity in terms of similarity transformations.MII.G-SRT.A.1. Verify experimentally the properties of dilations given by a center and a scale factor:MII.G-SRT.A.1.a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
MII.G-SRT.A.1.b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
MII.G-SRT.A.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 angles
MII.G-SRT.B. Prove theorems involving similarity using a variety of ways of writing proofs, showing validity of underlying reasoning.MII.G-SRT.B.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MII.N-RN. Number and Quantity - The Real Number SystemMII.N-RN.A. Extend the properties of exponents to rational exponents.MII.N-RN.A.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
MII.N-RN.B. Use properties of rational and irrational numbers.MII.N-RN.B.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
MII.S-CP. Statistics and Probability - Conditional Probability and the Rules of ProbabilityMII.S-CP.A. Understand independence and conditional probability and use them to interpret data from simulations or experiments.MII.S-CP.A.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
MA.MIII.Model Mathematics III Content Standards [MIII]
Model Mathematics III Content Standards [MIII]
MIII.A-APR. Arithmetic with Polynomials and Rational ExpressionsMIII.A-APR.A. Perform arithmetic operations on polynomials.MIII.A-APR.A.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.MIII.A-APR.A.1.a. Perform operations on polynomial expressions (addition, subtraction, multiplication, and division), and compare the system of polynomials to the system of integers when performing operations.
MIII.A-CED. Creating EquationsMIII.A-CED.A. Create equations that describe numbers or relationships.MIII.A-CED.A.1. Create equations and inequalities in one variable and use them to solve problems. (Include equations arising from simple root and rational functions.)
MIII.A-CED.A.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
MIII.A-CED.A.3. Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent equations describing satellites orbiting earth and c
MIII.A-REI. Reasoning with Equations and InequalitiesMIII.A-REI.D. Represent and solve equations and inequalities graphically.MIII.A-REI.D.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
MIII.F-IF. Functions - Interpreting FunctionsMIII.F-IF.B. Interpret functions that arise in applications in terms of the context (rational, polynomial, square root, cube root, trigonometric, logarithmic).MIII.F-IF.B.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
MIII.F-IF.B.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.
MA.MP.Mathematical Practice
MP.1. Make sense of problems and persevere in solving them.
MP.2. Reason abstractly and quantitatively.