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MS.AI.Algebra I
Algebra I
AI.A-APR. Algebra: Arithmetic with Polynomials and Rational Expressions (A-APR)
Perform arithmetic operations on polynomials
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Create equations that describe numbers or relationships
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A-CED.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.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.
AI.A-REI. Algebra: Reasoning with Equations and Inequalities (A-REI)
Solve systems of equations
A-REI.5. Given a system of two equations in two variables, show and explain why the sum of equivalent forms of the equations produces the same solution as the original system.
Understand solving equations as a process of reasoning and explain the reasoning
A-REI.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 a solution method.
Represent and solve equations and inequalities graphically
A-REI.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.12. Graph the solutions to 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 to a system of linear inequalities in two variables as the intersection of the correspondin
AI.A-SSE. Algebra: Seeing Structure in Expressions (A-SSE)
Write expressions in equivalent forms to solve problems
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.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 GuideFunctions
AI.F-BF. Functions: Building Functions (F-BF)
Build a function that models a relationship between two quantities
F-BF.1. Write a function that describes a relationship between two quantities.
F-BF.1.a. Determine an explicit expression or steps for calculation from a context.
F-IF.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.7.a. Graph functions (linear and quadratic) and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Understand the concept of a function and use function notation
F-IF.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 c
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
F-IF.3. Recognize that sequences are functions whose domain is a subset of the integers.
Quiz, Flash Cards, Worksheet, Game & Study GuideSequences
Interpret functions that arise in applications in terms of the context
F-IF.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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
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.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.F-LE. Functions: Linear, Quadratic, and Exponential Models (F-LE)
Construct and compare linear, quadratic, and exponential models and solve problems
F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.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 GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.N-RN. Number and Quantity: The Real Number System (N-RN)
Use properties of rational and irrational numbers
N-RN.3. Explain why: the sum or product of two rational numbers is rational; the sum of a rational number and an irrational number is irrational; and the product of a nonzero rational number and an irrational number is irrational.
AI.S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data (S-ID)
Summarize, represent, and interpret data on two categorical and quantitative variables
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.
Create equations that describe numbers or relationships
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Note this standard appears in previous courses with a slight variation in the standard language.]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A-CED.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.
AII.A-REI. Algebra: Reasoning with Equations and Inequalities (A-REI)
Represent and solve equations and inequalities graphically
A-REI.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
Understand solving equations as a process of reasoning and explain the reasoning
A-REI.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 a solution method.
AII.A-SSE. Algebra: Seeing Structure in Expressions (A-SSE)
Write expressions in equivalent forms to solve problems
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.3.c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t 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 GuideFunctions
AII.F-BF. Functions: Building Functions (F-BF)
Build a function that models a relationship between two quantities
F-BF.1. Write a function that describes a relationship between two quantities.
F-BF.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F-IF.8.b. 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 exponential gro
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Understand the concept of a function and use function notation
F-IF.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 GuideSequences
Interpret functions that arise in applications in terms of the context
F-IF.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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
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.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AII.N-RN. Number and Quantity: The Real Number System (N-RN)
Extend the properties of exponents to rational exponents
N-RN.2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
AII.S-CP. Statistics and Probability: Conditional Probability and the Rules of Probability (S-CP)
Understand independence and conditional probability and use them to interpret data
S-CP.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.
AIII.A.8. Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AIII.F. Functions
Analyze functions using different representations
AIII.F.23. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AIII.G. Geometry
Recognize, sketch, and transform graphs of functions
AIII.G.38. Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AIII.SP. Statistics and Probability
Explore and apply fundamental principles of probability.
AIII.SP.46. Prove statements using mathematical induction.
Demonstrate basic knowledge of functions, including their behavior and characteristics
C.A.4. Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and end behavior).
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
C.NQ. Number and Quantity
Compute and determine the reasonableness of results in mathematical and real world situations
C.NQ.3. Prove statements using mathematical induction.
FAC.EI.10. Graph the solution point of an equation and the solution set of an inequality in one variable on a horizontal number line. For inequalities, be able to interpret and write the solution set in a variety of ways (e.g., set notation).
FAC.EI.7. Fluently solve and check multi-step equations and inequalities with an emphasis on the distributive property, variables on both sides, and rational coefficients. Explain each step when solving a multistep equation and inequality. Justify each step using t
FAC.EI.8. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. (7.EE.4a)
FAC.EI.9. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Solve inequalities of these forms fluently. (7.EE.4b)
FAC.F.12. 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. Use function notation, where appropriate. (F-IF.1, F-IF.2)
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
FAC.F.13. Compare and contrast a function and a relation. Use appropriate strategies to assess whether a given situation represents a function or a relation (e.g,. the vertical line test).
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
FAC.F.15. Determine the rate of change of a linear function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. (8.F.4) Use the rate of change to determine if two lines are parallel, perpendicular, o
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
FAC.F.16. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. (8.F.4)
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
FAC.F.17. Create and graph the equation of a linear function given the rate of change and y-intercept. Compare and contrast up to three linear functions written in a various forms (i.e., point-slope, slope-intercept, standard form).
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
FAC.F.18. Given two points, a graph, a table of values, a mapping, or a real-world context determine the linear function that models this information. Fluently convert between the point-slope, slope-intercept, and standard form of a line.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
FAC.F.21. Describe the following characteristics of linear and quadratic parent functions by inspection: domain/range, increasing/decreasing intervals, intercepts, symmetry, and asymptotic behavior. Identify each characteristic in set notation or words, where appro
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
FAC.F.22. Graph a system of two functions, f(x) and g(x), on the same Coordinate Plane by hand for simple cases, and with technology for complicated cases. Explain the relationship between the point(s) of intersection and the solution to the system. Determine the s
FAC.F.23. With accuracy, graph the solutions to a linear inequality in two variables as a half-plane, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes on the same Coordinate Plane. (
FAC.G.38. Fluently use formulas and/or appropriate measuring tools to find length and angle measures, perimeter, area, volume, and surface area of polygons, circles, spheres, cones, cylinders, pyramids, and composite or irregular figures. Use them to solve real-wor
FAC.S.40. Without technology, fluently calculate the measures of central tendency (mean, median, mode), measures of spread (range, interquartile range), and understand the impact of extreme values (outliers) on each of these values. (6.SP.5, 8.SP.1, S-ID.3) Justify
FAC.S.41. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear associa
FAC.S.43. For scatter plots that suggest a linear association, informally fit a straight line and predict the equation for the line of best fit. (8.SP.2)
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
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.
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
G-CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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.
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.
G-GMD. Geometry: Geometric Measurement and Dimension (G-GMD)
Explain volume formulas and use them to solve problems
G-GMD.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-GPE. Geometry: Expressing Geometric Properties with Equations (G-GPE)
Use coordinates to prove simple geometric theorems algebraically
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).
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G-SRT. Geometry: Similarity, Right Triangles, and Trigonometry (G-SRT)
Understand similarity in terms of similarity transformations
G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor:
G-SRT.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.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
Create equations that describe numbers or relationships
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A-CED.2. Create equations in two variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Note this standard appears in future courses with a slight variation in the standard language.]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A-CED.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.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.
IMI.A-REI. Algebra: Reasoning with Equations and Inequalities (A-REI)
Represent and solve equations and inequalities graphically
A-REI.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.12. Graph the solutions to 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 to a system of linear inequalities in two variables as the intersection of the correspondin
A-REI.5. Given a system of two equations in two variables, show and explain why the sum of equivalent forms of the equations produces the same solution as the original system.
IMI.A-SSE. Algebra: Seeing Structure in Expressions (A-SSE)
Write expressions in equivalent forms to solve problems
A-SSE.3. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A-SSE.3.c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t 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 GuideFunctions
IMI.F-BF. Functions: Building Functions (F-BF)
Build a function that models a relationship between two quantities
F-BF.1. Write a function that describes a relationship between two quantities.
F-BF.1.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-IF.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.7.a. Graph functions (linear and quadratic) and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Understand the concept of a function and use function notation
F-IF.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 c
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
F-IF.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 GuideSequences
Interpret functions that arise in applications in terms of the context
F-IF.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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
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.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
IMI.F-LE. Functions: Linear, Quadratic, and Exponential Models (F-LE)
Construct and compare linear, quadratic, and exponential models and solve problems
F-LE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
F-LE.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 GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
IMI.G-CO. Geometry: Congruence (G-CO)
Prove geometric theorems
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
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.
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
G-CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
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.
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.
IMI.S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data (S-ID)
Summarize, represent, and interpret data on two categorical and quantitative variables
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.
IMII.A-APR. Algebra: Arithmetic with Polynomials and Rational Expressions (A-APR)
Perform arithmetic operations on polynomials
A-APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Create equations that describe numbers or relationships
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Note this standard appears in previous courses with a slight variation in the standard language.]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A-CED.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.
A-CED.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.
IMII.A-REI. Algebra: Reasoning with Equations and Inequalities (A-REI)
Understand solving equations as a process of reasoning and explain the reasoning
A-REI.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 a solution method.
A-REI.6. Solve systems of linear equations algebraically, exactly, approximately, and graphically while focusing on pairs of linear equations in two variables.
Interpret functions that arise in applications in terms of the context
F-IF.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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
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.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Analyze functions using different representations
F-IF.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.7.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F-IF.8.b. 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 exponenti
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
IMII.G-GMD. Geometry: Geometric Measurement and Dimension (G-GMD)
Explain volume formulas and use them to solve problems
G-GMD.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.
IMII.G-SRT. Geometry: Similarity, Right Triangles, and Trigonometry (G-SRT)
Understand similarity in terms of similarity transformations
G-SRT.1. Verify experimentally the properties of dilations given by a center and a scale factor:
G-SRT.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.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
N-RN.3. Explain why: the sum or product of two rational numbers is rational; the sum of a rational number and an irrational number is irrational; and the product of a nonzero rational number and an irrational number is irrational.
IMII.S-CP. Statistics and Probability: Conditional Probability and the Rules of Probability (S-CP)
Understand independence and conditional probability and use them to interpret data
S-CP.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.
Create equations that describe numbers or relationships
A-CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [Note this standard appears in previous courses with a slight variation in the standard language.]
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
IMIII.A-REI. Algebra: Reasoning with Equations and Inequalities (A-REI)
Understand solving equations as a process of reasoning and explain the reasoning
A-REI.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 a solution method.
Represent and solve equations and inequalities graphically
A-REI.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
Interpret functions that arise in applications in terms of the context
F-IF.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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
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.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
IMIII.G-GPE. Geometry: Expressing Geometric Properties with Equations (G-GPE)
Use coordinates to prove simple geometric theorems algebraically
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).
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G-GPE.7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
IMIII.S-ID. Statistics and Probability: Interpreting Categorical and Quantitative Data (S-ID)
Summarize, represent, and interpret data on two categorical and quantitative variables
S-ID.6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S-ID.6.b. Informally assess the fit of a function by plotting and analyzing residuals.