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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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M1.N Number and Quantity

M1.N.Q Quantities
- M1.N.Q.A Reason quantitatively and use units to understand problems.
  - M1.N.Q.A.1 Use units as a way to understand real-world problems.
    - M1.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.
    - M1.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.
    - M1.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.
    - M1.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.
  - Checkpoint opportunity
    - Checkpoint: Units and quantities (A1-E.8)
M1.N.M Matrices
- M1.N.M.A Perform operations on matrices and use matrices in applications.
  - M1.N.M.A.1 Use matrices to represent data in a real-world context. Interpret rows, columns, and dimensions of matrices in terms of the context.
    - Matrix vocabulary (A1-LL.1)
  - M1.N.M.A.2 Perform operations on matrices in a real-world context.
    - M1.N.M.A.2.a Multiply a matrix by a scalar to produce a new matrix.
      - Multiply a matrix by a scalar (A1-LL.4)
    - M1.N.M.A.2.b Add and/or subtract matrices by hand and using technology.
      - Add and subtract matrices (A1-LL.3)
      - Add and subtract scalar multiples of matrices (A1-LL.5)
    - M1.N.M.A.2.c Multiply matrices of appropriate dimensions, by hand in simple cases and using technology for more complicated cases.
      - Multiply two matrices (A1-LL.6)
    - M1.N.M.A.2.d Describe the roles that zero matrices and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real number system.
      - Determinant of a matrix (A2-TT.10)
      - Inverse of a matrix (A2-TT.12)
  - M1.N.M.A.3 Create and use augmented matrices to solve systems of linear equations in real-world contexts, by hand and using technology.
    - Solve a system of equations using augmented matrices (A1-O.12)
    - Solve a system of equations using augmented matrices: word problems (A1-O.13)

M1.A Algebra

M1.A.SSE Seeing Structure in Expressions
- M1.A.SSE.A Interpret the structure of expressions.
  - M1.A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
    - M1.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
      - Identify terms and coefficients (8-K.10)
      - Sort factors of variable expressions (A1-B.8)
    - M1.A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.
      - Interpret the slope and y-intercept of a linear function (A1-N.7)
M1.A.CED Creating Equations
- M1.A.CED.A Create equations that describe numbers or relationships.
  - M1.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.
  - M1.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.
  - M1.A.CED.A.3 Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.
  - M1.A.CED.A.4 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.
    - Rearrange multi-variable equations (A1-C.18)
    - Linear equations: solve for y (A1-L.8)
  - Checkpoint opportunity
    - Checkpoint: Modeling with linear equations and inequalities (A1-P.9)
    - Checkpoint: Expressions, equations, and inequalities (A1)
M1.A.REI Reasoning with Equations and Inequalities
- M1.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
  - M1.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.
- M1.A.REI.B Solve equations and inequalities in one variable.
  - M1.A.REI.B.2 Solve linear and absolute value equations and inequalities in one variable.
    - M1.A.REI.B.2.a Solve linear equations and inequalities, including compound inequalities, in one variable. Represent solutions algebraically and graphically.
    - M1.A.REI.B.2.b Solve absolute value equations and inequalities in one variable. Represent solutions algebraically and graphically.
  - Checkpoint opportunity
    - Checkpoint: Solve linear equations and inequalities (A1-F.16)
- M1.A.REI.C Solve systems of equations.
  - M1.A.REI.C.3 Write and solve a system of linear equations in a real-world context.
- M1.A.REI.D Represent and solve equations and inequalities graphically.
  - M1.A.REI.D.4 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
  - M1.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.
  - M1.A.REI.D.6 Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
  - Checkpoint opportunity
    - Checkpoint: Systems of equations and inequalities (A1-P.8)
    - Checkpoint: Solve equations using graphs and tables (A1)

M1.F Functions

M1.F.IF Interpreting Functions
- M1.F.IF.A Understand the concept of a function and use function notation.
  - M1.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 corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  - M1.F.IF.A.2 Use function notation.
    - M1.F.IF.A.2.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.
    - M1.F.IF.A.2.b Interpret statements that use function notation in terms of a context.
      - Interpret functions using everyday language (A1-M.13)
  - M1.F.IF.A.3 Understand geometric formulas as functions.
- M1.F.IF.B Interpret functions that arise in applications in terms of the context.
  - M1.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.
  - M1.F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the context of the function it models.
- M1.F.IF.C Analyze functions using different representations.
  - M1.F.IF.C.6 Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.
    - M1.F.IF.C.6.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.
      - Compare linear functions: graphs and equations (A1-N.11)
      - Compare linear functions: tables, graphs, and equations (A1-N.12)
    - M1.F.IF.C.6.b Compare properties of the same function on two different intervals or represented in two different ways.
      - Linear functions over unit intervals (A1-AA.8)
      - Exponential functions over unit intervals (A1-AA.9)
  - Checkpoint opportunity
M1.F.BF Building Functions
- M1.F.BF.A Build a function that models a relationship between two quantities.
  - M1.F.BF.A.1 Build a function that describes a relationship between two quantities.
    - M1.F.BF.A.1.a Determine steps for calculation, a recursive process, or an explicit expression from a context.
  - M1.F.BF.A.2 Define sequences as functions, including recursive definitions, whose domain is a subset of the integers. Write explicit and recursive formulas for arithmetic and geometric sequences in context and connect them to linear and exponential functions.
M1.F.LE Linear and Exponential Models
- M1.F.LE.A Construct and compare linear and exponential models and solve problems.
  - M1.F.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
    - M1.F.LE.A.1.a Know that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
    - M1.F.LE.A.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
    - M1.F.LE.A.1.c Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another.
  - M1.F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.
- M1.F.LE.B Interpret expressions for functions in terms of the situation they model.
  - M1.F.LE.B.3 Interpret the parameters in a linear or exponential function in terms of a context.
  - Checkpoint opportunity
    - Checkpoint: Compare linear and exponential functions (A1-AA.13)

M1.G Geometry

M1.G.CO Congruence
- M1.G.CO.A Experiment with transformations in the plane.
  - M1.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.
  - M1.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)
  - Checkpoint opportunity
    - Checkpoint: Transformations in the plane (G)
- M1.G.CO.B Use geometric theorems to justify relationships.
  - M1.G.CO.B.3 Use definitions and theorems about lines and angles to solve problems and to justify relationships in geometric figures.
  - M1.G.CO.B.4 Use definitions and theorems about triangles to solve problems and to justify relationships in geometric figures.
    - Proofs involving isosceles triangles (G-L.11)
    - Proofs involving triangles I (G-N.9)
  - Checkpoint opportunity
    - Checkpoint: Line and angle theorems (G-D.10)
- M1.G.CO.C Perform geometric constructions.
  - M1.G.CO.C.5 Perform formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
  - M1.G.CO.C.6 Use geometric constructions to solve geometric problems in context, by hand and using technology.
M1.G.GPE Geometric Properties with Equations
- M1.G.GPE.A Use coordinates to solve problems and justify simple geometric theorems algebraically.
  - M1.G.GPE.A.1 Use coordinates to solve problems and justify geometric relationships algebraically.
    - Classify shapes on the coordinate plane: justify your answer (G-O.13)
  - M1.G.GPE.A.2 Use the slope criteria for parallel and perpendicular lines to solve problems and to justify relationships in geometric figures.
  - M1.G.GPE.A.3 Understand the relationship between the Pythagorean Theorem and the distance formula and use an efficient method to solve problems on the coordinate plane.
  - Checkpoint opportunity
    - Checkpoint: Area and perimeter in the coordinate plane (G-S.16)
    - Checkpoint: Parallel and perpendicular lines (G)

M1.S Statistics and Probability

M1.S.ID Interpreting Categorical and Quantitative Data
- M1.S.ID.A Summarize, represent, and interpret data on two categorical and quantitative variables.
  - M1.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.
- M1.S.ID.B Interpret linear models.
  - M1.S.ID.B.2 Interpret the rate of change and the constant term of a linear model in the context of the data.
  - M1.S.ID.B.3 Use technology to compute the correlation coefficient of a linear model; interpret the correlation coefficient in the context of the data.
    - Match correlation coefficients to scatter plots (A1-JJ.3)
    - Calculate correlation coefficients (A1-JJ.4)
  - M1.S.ID.B.4 Explain the differences between correlation and causation. Recognize situations where an additional factor may be affecting correlated data.
    - Correlation and causation (A1-JJ.11)
  - Checkpoint opportunity
    - Checkpoint: Linear modeling (A1-JJ.12)

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M1.N Number and Quantity

M1.N.Q Quantities

M1.N.Q.A Reason quantitatively and use units to understand problems.

M1.N.Q.A.1 Use units as a way to understand real-world problems.

M1.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.

M1.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.

M1.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.

M1.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.

Checkpoint opportunity

M1.N.M Matrices

M1.N.M.A Perform operations on matrices and use matrices in applications.

M1.N.M.A.1 Use matrices to represent data in a real-world context. Interpret rows, columns, and dimensions of matrices in terms of the context.

M1.N.M.A.2 Perform operations on matrices in a real-world context.

M1.N.M.A.2.a Multiply a matrix by a scalar to produce a new matrix.

M1.N.M.A.2.b Add and/or subtract matrices by hand and using technology.

M1.N.M.A.2.c Multiply matrices of appropriate dimensions, by hand in simple cases and using technology for more complicated cases.

M1.N.M.A.2.d Describe the roles that zero matrices and identity matrices play in matrix addition and multiplication, recognizing that they are similar to the roles of 0 and 1 in the real number system.

M1.N.M.A.3 Create and use augmented matrices to solve systems of linear equations in real-world contexts, by hand and using technology.

M1.A Algebra

M1.A.SSE Seeing Structure in Expressions

M1.A.SSE.A Interpret the structure of expressions.

M1.A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

M1.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

M1.A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

M1.A.CED Creating Equations

M1.A.CED.A Create equations that describe numbers or relationships.

M1.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.

M1.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.

M1.A.CED.A.3 Create individual and systems of equations and/or inequalities to represent constraints in a contextual situation, and interpret solutions as viable or non-viable.

M1.A.CED.A.4 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

Checkpoint opportunity

M1.A.REI Reasoning with Equations and Inequalities

M1.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.

M1.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.

M1.A.REI.B Solve equations and inequalities in one variable.

M1.A.REI.B.2 Solve linear and absolute value equations and inequalities in one variable.

M1.A.REI.B.2.a Solve linear equations and inequalities, including compound inequalities, in one variable. Represent solutions algebraically and graphically.

M1.A.REI.B.2.b Solve absolute value equations and inequalities in one variable. Represent solutions algebraically and graphically.

Checkpoint opportunity

M1.A.REI.C Solve systems of equations.

M1.A.REI.C.3 Write and solve a system of linear equations in a real-world context.

M1.A.REI.D Represent and solve equations and inequalities graphically.

M1.A.REI.D.4 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

M1.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.

M1.A.REI.D.6 Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Checkpoint opportunity

M1.F Functions

M1.F.IF Interpreting Functions

M1.F.IF.A Understand the concept of a function and use function notation.

M1.F.IF.A.2 Use function notation.

M1.F.IF.A.2.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.

M1.F.IF.A.2.b Interpret statements that use function notation in terms of a context.

M1.F.IF.A.3 Understand geometric formulas as functions.

M1.F.IF.B Interpret functions that arise in applications in terms of the context.

M1.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.

M1.F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the context of the function it models.

M1.F.IF.C Analyze functions using different representations.

M1.F.IF.C.6 Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

M1.F.IF.C.6.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.

M1.F.IF.C.6.b Compare properties of the same function on two different intervals or represented in two different ways.

Checkpoint opportunity

M1.F.BF Building Functions

M1.F.BF.A Build a function that models a relationship between two quantities.

M1.F.BF.A.1 Build a function that describes a relationship between two quantities.

M1.F.BF.A.1.a Determine steps for calculation, a recursive process, or an explicit expression from a context.

M1.F.BF.A.2 Define sequences as functions, including recursive definitions, whose domain is a subset of the integers. Write explicit and recursive formulas for arithmetic and geometric sequences in context and connect them to linear and exponential functions.

M1.F.LE Linear and Exponential Models

M1.F.LE.A Construct and compare linear and exponential models and solve problems.

M1.F.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

M1.F.LE.A.1.a Know that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.

M1.F.LE.A.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

M1.F.LE.A.1.c Recognize situations in which a quantity grows or decays by a constant factor per unit interval relative to another.

M1.F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description of a relationship, or input-output pairs.

M1.F.LE.B Interpret expressions for functions in terms of the situation they model.

M1.F.LE.B.3 Interpret the parameters in a linear or exponential function in terms of a context.

Checkpoint opportunity

M1.G Geometry