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Skills available for Tennessee high school math standards

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Tennessee Academic Standards: Algebra I Tennessee Academic Standards: Algebra I
Tennessee Academic Standards: Algebra II Tennessee Academic Standards: Algebra II
Tennessee Academic Standards: Calculus Tennessee Academic Standards: Calculus
Tennessee Academic Standards: Geometry Tennessee Academic Standards: Geometry
Tennessee Academic Standards: Integrated Mathematics I Tennessee Academic Standards: Integrated Mathematics I
Tennessee Academic Standards: Integrated Mathematics II Tennessee Academic Standards: Integrated Mathematics II
Tennessee Academic Standards: Integrated Mathematics III Tennessee Academic Standards: Integrated Mathematics III
Tennessee Academic Standards: Mathematical Reasoning for Decision Making Tennessee Academic Standards: Mathematical Reasoning for Decision Making
Tennessee Academic Standards: Precalculus Tennessee Academic Standards: Precalculus
Tennessee Academic Standards: Statistics Tennessee Academic Standards: Statistics

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M2.N Number and Quantity

M2.N.RN The Real Number System
- M2.N.RN.A Extend the properties of integer exponents to rational exponents.
  - M2.N.RN.A.1 Extend the properties of integer exponents to rational exponents.
    - M2.N.RN.A.1.a Develop the meaning of rational exponents by applying the properties of integer exponents.
      - Evaluate integers raised to rational exponents (A1-S.2)
    - M2.N.RN.A.1.b Explain why x^1/n can be written as the n^th root of x.
    - M2.N.RN.A.1.c Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- M2.N.Q.A Reason quantitatively and use units to understand problems.
  - M2.N.Q.A.1 Use units as a way to understand real-world problems.
    - M2.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.
    - M2.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.
    - M2.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.
    - M2.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.

M2.A Algebra

M2.A.SSE Seeing Structure in Expressions
- M2.A.SSE.A Interpret the structure of expressions.
  - M2.A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
    - M2.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
    - M2.A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
      - Interpret parts of quadratic expressions: word problems (A1-Y.13)
M2.A.APR Arithmetic with Polynomials and Rational Expressions
- M2.A.APR.A Perform arithmetic operations on polynomials.
  - M2.A.APR.A.1 Add, subtract, and multiply polynomials. Use these operations to demonstrate that polynomials form a closed system that adhere to the same properties of operations as the integers.
  - Checkpoint opportunity
    - Checkpoint: Polynomial operations (A1-W.15)
- M2.A.APR.B Understand the relationship between zeros and factors of polynomials.
  - M2.A.APR.B.2 Know and apply the Factor Theorem: For a polynomial p(x) and a number a, p(a) = 0 if and only if (x – a) is a factor of p(x).
    - Solve a quadratic equation using the zero product property (A1-Z.2)
    - Write a quadratic function from its zeros (A2-N.10)
M2.A.CED Creating Equations
- M2.A.CED.A Create equations that describe numbers or relationships.
  - M2.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.
  - M2.A.CED.A.2 Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.
  - M2.A.CED.A.3 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.
    - Rearrange multi-variable equations (A2-B.4)
M2.A.REI Reasoning with Equations and Inequalities
- M2.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
  - M2.A.REI.A.1 Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.
- M2.A.REI.B Solve equations and inequalities in one variable.
  - M2.A.REI.B.2 Solve quadratic equations and inequalities in one variable.
    - M2.A.REI.B.2.a Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has non-real solutions.
    - M2.A.REI.B.2.b Solve quadratic inequalities using the graph of the related quadratic equation.
      - Graph solutions to quadratic inequalities (A2-O.9)
  - M2.A.REI.B.3 Solve radical equations in one variable and identify extraneous solutions when they exist.
    - Solve radical equations I (A1-FF.6)
    - Solve radical equations II (A1-FF.7)
- M2.A.REI.C Solve systems of equations.
  - M2.A.REI.C.4 Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically, graphically, and using technology.
    - Solve a system of linear and quadratic equations by graphing (A1-Z.9)
    - Solve a system of linear and quadratic equations (A1-Z.10)
- M2.A.REI.D Represent and solve equations and inequalities graphically.
  - M2.A.REI.D.5 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 approximate solutions by graphing the functions or making a table of values, using technology when appropriate.

M2.F Functions

M2.F.IF Interpreting Functions
- M2.F.IF.A Understand the concept of function and use function notation.
  - M2.F.IF.A.1 Use function notation.
    - M2.F.IF.A.1.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.
    - M2.F.IF.A.1.b Interpret statements that use function notation in terms of a context.
      - Interpret functions using everyday language (A1-M.13)
  - M2.F.IF.A.2 Understand geometric formulas as functions.
- M2.F.IF.B Interpret functions that arise in applications in terms of the context.
  - M2.F.IF.B.3 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.
  - M2.F.IF.B.4 Relate the domain of a function to its graph and, where applicable, to the context of the function it models.
  - M2.F.IF.B.5 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.
    - Rate of change: tables (A1-M.15)
    - Rate of change: graphs (A1-M.16)
- M2.F.IF.C Analyze functions using different representation.
  - M2.F.IF.C.6 Graph functions expressed algebraically and show key features of the graph by hand and using technology.
  - M2.F.IF.C.7 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    - M2.F.IF.C.7.a Rewrite quadratic functions to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a real-world context.
    - M2.F.IF.C.7.b Know and use the properties of exponents to interpret expressions for exponential functions in terms of a real-world context.
  - M2.F.IF.C.8 Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.
    - M2.F.IF.C.8.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.
      - Compare linear, exponential, and quadratic growth (A1-AA.12)
    - M2.F.IF.C.8.b Compare properties of the same function on two different intervals or represented in two different ways.
      - Linear functions over unit intervals (A2-D.4)
      - Exponential functions over unit intervals (A2-Z.6)
  - Checkpoint opportunity
    - Checkpoint: Graph and analyze functions (A1)
M2.F.BF Building Functions
- M2.F.BF.A Build a function that models a relationship between two quantities.
  - M2.F.BF.A.1 Build a function that describes a relationship between two quantities.
    - Solve quadratic equations: word problems (A1-Z.7)
    - M2.F.BF.A.1.a Combine standard function types using arithmetic operations.
- M2.F.BF.B Build new functions from existing functions.
  - M2.F.BF.B.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given graphs.
  - Checkpoint opportunity
    - Checkpoint: Function transformations (A1-DD.7)

M2.G Geometry

M2.G.CO Congruence
- M2.G.CO.A Experiment with transformations in the plane.
  - M2.G.CO.A.1 Describe transformations as functions that take points in the plane (pre-image) as inputs and give other points (image) as outputs. Compare transformations that preserve distance and angle measure to those that do not, by hand for basic transformations and using technology for more complex cases.
  - M2.G.CO.A.2 Given a rectangle, parallelogram, trapezoid, or regular polygon, determine the transformations that carry the shape onto itself and describe them in terms of the symmetry of the figure.
    - Transformations that carry a polygon onto itself (G-H.15)
  - M2.G.CO.A.3 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
    - Rotate polygons about a point (G-H.7)
  - M2.G.CO.A.4 Given a geometric figure, draw the image of the figure after a sequence of one or more rigid motions, by hand and using technology. Identify a sequence of rigid motions that will carry a given figure onto another.
  - Checkpoint opportunity
    - Checkpoint: Congruence transformations (G-H.17)
    - Checkpoint: Transformations in the plane (G-I.7)
- M2.G.CO.B Understand congruence in terms of rigid motions.
  - M2.G.CO.B.5 Given two figures, use the definition of congruence in terms of rigid motions to determine informally if they are congruent.
  - M2.G.CO.B.6 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
    - Prove triangles are congruent using rigid motions (G-L.1)
  - M2.G.CO.B.7 Explain how the criteria for triangle congruence (ASA, SAS, AAS, SSS, and HL) follow from the definition of congruence in terms of rigid motions.
  - Checkpoint opportunity
    - Checkpoint: Rigid motion and congruence (G-L.13)
- M2.G.CO.C Use geometric theorems to justify relationships.
  - M2.G.CO.C.8 Use definitions and theorems about triangles to solve problems and to justify relationships in geometric figures.
    - Proofs involving triangles II (G-N.10)
  - M2.G.CO.C.9 Use definitions and theorems about parallelograms to solve problems and to justify relationships in geometric figures.
  - Checkpoint opportunity
    - Checkpoint: Parallelogram theorems (G-O.16)
M2.G.SRT Similarity, Right Triangles, and Trigonometry
- M2.G.SRT.A Understand similarity in terms of similarity transformations.
  - M2.G.SRT.A.1 Use properties of dilations given by a center and a scale factor to solve problems and to justify relationships in geometric figures.
  - M2.G.SRT.A.2 Define similarity in terms of transformations. Use transformations to determine whether two figures are similar.
- M2.G.SRT.B Use similarity to solve problems and justify relationships.
  - M2.G.SRT.B.3 Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.

M2.S Statistics and Probability

M2.S.ID Interpreting Categorical and Quantitative Data
- M2.S.ID.A Summarize, represent, and interpret data on two categorical and quantitative variables.
  - M2.S.ID.A.1 Represent data from two quantitative variables on a scatter plot, and describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

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M2.N Number and Quantity

M2.N.RN The Real Number System

M2.N.RN.A Extend the properties of integer exponents to rational exponents.

M2.N.RN.A.1 Extend the properties of integer exponents to rational exponents.

M2.N.RN.A.1.a Develop the meaning of rational exponents by applying the properties of integer exponents.

M2.N.RN.A.1.b Explain why x1/n can be written as the nth root of x.

M2.N.RN.A.1.c Rewrite expressions involving radicals and rational exponents using the properties of exponents.

M2.N.Q.A Reason quantitatively and use units to understand problems.

M2.N.Q.A.1 Use units as a way to understand real-world problems.

M2.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.

M2.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.

M2.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.

M2.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.

M2.A Algebra

M2.A.SSE Seeing Structure in Expressions

M2.A.SSE.A Interpret the structure of expressions.

M2.A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

M2.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

M2.A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

M2.A.APR Arithmetic with Polynomials and Rational Expressions

M2.A.APR.A Perform arithmetic operations on polynomials.

M2.A.APR.A.1 Add, subtract, and multiply polynomials. Use these operations to demonstrate that polynomials form a closed system that adhere to the same properties of operations as the integers.

Checkpoint opportunity

M2.A.APR.B Understand the relationship between zeros and factors of polynomials.

M2.A.APR.B.2 Know and apply the Factor Theorem: For a polynomial p(x) and a number a, p(a) = 0 if and only if (x – a) is a factor of p(x).

M2.A.CED Creating Equations

M2.A.CED.A Create equations that describe numbers or relationships.

M2.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.

M2.A.CED.A.2 Create equations and inequalities in two variables to represent relationships between quantities and use them to solve problems in a real-world context. Graph equations with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.

M2.A.CED.A.3 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

M2.A.REI Reasoning with Equations and Inequalities

M2.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.

M2.A.REI.A.1 Understand solving equations as a process of reasoning and explain the reasoning. Construct a viable argument to justify a solution method.

M2.A.REI.B Solve equations and inequalities in one variable.

M2.A.REI.B.2 Solve quadratic equations and inequalities in one variable.

M2.A.REI.B.2.a Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has non-real solutions.

M2.A.REI.B.2.b Solve quadratic inequalities using the graph of the related quadratic equation.

M2.A.REI.B.3 Solve radical equations in one variable and identify extraneous solutions when they exist.

M2.A.REI.C Solve systems of equations.

M2.A.REI.C.4 Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically, graphically, and using technology.

M2.A.REI.D Represent and solve equations and inequalities graphically.

M2.A.REI.D.5 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 approximate solutions by graphing the functions or making a table of values, using technology when appropriate.

M2.F Functions

M2.F.IF Interpreting Functions

M2.F.IF.A Understand the concept of function and use function notation.

M2.F.IF.A.1 Use function notation.

M2.F.IF.A.1.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.

M2.F.IF.A.1.b Interpret statements that use function notation in terms of a context.

M2.F.IF.A.2 Understand geometric formulas as functions.

M2.F.IF.B Interpret functions that arise in applications in terms of the context.

M2.F.IF.B.3 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.

M2.F.IF.B.4 Relate the domain of a function to its graph and, where applicable, to the context of the function it models.

M2.F.IF.B.5 Calculate and interpret the average rate of change of a function (presented algebraically or as a table) over a specified interval. Estimate and interpret the rate of change from a graph.

M2.F.IF.C Analyze functions using different representation.

M2.F.IF.C.6 Graph functions expressed algebraically and show key features of the graph by hand and using technology.

M2.F.IF.C.7 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

M2.F.IF.C.7.a Rewrite quadratic functions to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a real-world context.

M2.F.IF.C.7.b Know and use the properties of exponents to interpret expressions for exponential functions in terms of a real-world context.

M2.F.IF.C.8 Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

M2.F.IF.C.8.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.

M2.F.IF.C.8.b Compare properties of the same function on two different intervals or represented in two different ways.

Checkpoint opportunity

M2.F.BF Building Functions

M2.F.BF.A Build a function that models a relationship between two quantities.

M2.F.BF.A.1 Build a function that describes a relationship between two quantities.

M2.F.BF.A.1.a Combine standard function types using arithmetic operations.

M2.F.BF.B Build new functions from existing functions.

M2.F.BF.B.2 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given graphs.

Checkpoint opportunity

M2.G Geometry

M2.G.CO Congruence

M2.G.CO.A Experiment with transformations in the plane.

M2.G.CO.A.2 Given a rectangle, parallelogram, trapezoid, or regular polygon, determine the transformations that carry the shape onto itself and describe them in terms of the symmetry of the figure.

M2.G.CO.A.3 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

M2.G.CO.A.4 Given a geometric figure, draw the image of the figure after a sequence of one or more rigid motions, by hand and using technology. Identify a sequence of rigid motions that will carry a given figure onto another.

Checkpoint opportunity

M2.G.CO.B Understand congruence in terms of rigid motions.

M2.N.RN.A.1.b Explain why x^1/n can be written as the n^th root of x.

M2.A.REI.B.2.a Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, knowing and applying the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when a quadratic equation has non-real solutions.