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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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M3.N Number and Quantity

M3.N.Q Quantities
- M3.N.Q.A Reason quantitatively and use units to understand problems.
  - M3.N.Q.A.1 Use units as a way to understand real-world problems.
    - M3.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.
    - M3.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.
    - M3.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.
      - Exponential growth and decay: word problems (PC-K.5)
      - Compound interest: word problems (PC-K.6)
    - M3.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.

M3.A Algebra

M3.A.SSE Seeing Structure in Expressions
- M3.A.SSE.A Interpret the structure of expressions.
  - M3.A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
    - M3.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
      - Polynomial vocabulary (A2-L.1)
      - Interpret parts of quadratic expressions: word problems (A2-N.14)
    - M3.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 (A2-N.14)
M3.A.APR Arithmetic with Polynomials and Rational Expressions
- M3.A.APR.A Understand the relationship between zeros and factors of polynomials.
  - M3.A.APR.A.1 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).
  - M3.A.APR.A.2 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.
M3.A.CED Creating Equations
- M3.A.CED.A Create equations that describe numbers or relationships.
  - M3.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.
    - Solve quadratic equations: word problems (A2-O.7)
    - Write exponential functions: word problems (A2-Z.3)
  - M3.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 and inequalities with two variables on coordinate axes with labels and scales, and use the graphs to make predictions.
  - M3.A.CED.A.3 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.
    - Rearrange multi-variable equations (A2-B.4)
M3.A.REI Reasoning with Equations and Inequalities
- M3.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
  - M3.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.
  - M3.A.REI.A.2 Solve radical equations in one variable and identify extraneous solutions when they exist.
    - Solve radical equations (A2-S.4)

M3.F Functions

M3.F.IF Interpreting Functions
- M3.F.IF.A Understand the concept of a function and use function notation.
  - M3.F.IF.A.1 Use function notation.
    - M3.F.IF.A.1.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.
    - M3.F.IF.A.1.b Interpret statements that use function notation in terms of a context.
      - Interpret functions using everyday language (A2)
  - M3.F.IF.A.2 Understand geometric formulas as functions.
- M3.F.IF.B Interpret functions that arise in applications in terms of the context.
  - M3.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.
  - M3.F.IF.B.4 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.
    - Average rate of change (A2-A.9)
- M3.F.IF.C Analyze functions using different representations.
  - M3.F.IF.C.5 Graph functions expressed algebraically and show key features of the graph by hand and using technology.
  - M3.F.IF.C.6 Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.
    - M3.F.IF.C.6.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.
      - Identify linear and exponential functions (A2-Z.7)
      - Describe linear and exponential growth and decay (A2-Z.8)
    - M3.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 (A2-D.4)
      - Exponential functions over unit intervals (A2-Z.6)
M3.F.BF Building Functions
- M3.F.BF.A Build new functions from existing functions.
  - M3.F.BF.A.1 Build a function that describes a relationship between two quantities.
    - M3.F.BF.A.1.a Combine standard function types using composition.
  - M3.F.BF.A.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.
  - M3.F.BF.A.3 Find the inverse of a function.
    - M3.F.BF.A.3.a Determine whether a function is one-to-one.
      - Identify inverse functions (A2-V.1)
    - M3.F.BF.A.3.b Find the inverse of a function on an appropriate domain.
    - M3.F.BF.A.3.c Given an invertible function on an appropriate domain, identify the domain of the inverse function.
M3.F.LE Linear, Quadratic, and Exponential Models
- M3.F.LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
  - M3.F.LE.A.1 Know that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or cubically.
    - Compare linear, exponential, and quadratic growth (A1-AA.12)
    - Describe linear and exponential growth and decay (A2-Z.8)
  - M3.F.LE.A.2 Know the relationship between exponential functions and logarithmic functions.
    - M3.F.LE.A.2.a Solve exponential equations using a variety of strategies, including logarithms.
    - M3.F.LE.A.2.b Understand that a logarithm is the solution to abct = d, where a, b, c, and d are numbers.
    - M3.F.LE.A.2.c Evaluate logarithms using technology.
      - Evaluate logarithms using a calculator (A2-AA.7)

M3.G Geometry

M3.G.C Circles
- M3.G.C.A Find areas of sectors of circles.
  - M3.G.C.A.1 Use proportional relationships between the area of a circle and the area of a sector within the circle to solve problems and represent solutions in a real-world context.
    - Area of sectors (G-W.7)
M3.G.SRT Similarity, Right Triangles, and Trigonometry
- M3.G.SRT.A Define trigonometric ratios and solve problems involving triangles.
  - M3.G.SRT.A.1 Use side ratios in right triangles to define trigonometric ratios.
    - M3.G.SRT.A.1.a Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    - M3.G.SRT.A.1.b Explain and use the relationship between the sine and cosine of complementary angles.
      - Sine and cosine of complementary angles (G-Q.9)
  - M3.G.SRT.A.2 Solve triangles.
    - M3.G.SRT.A.2.a Know and use the Pythagorean Theorem and trigonometric ratios (sine, cosine, tangent, and their inverses) to solve right triangles in a real-world context.
    - M3.G.SRT.A.2.b Know and use relationships within special right triangles to solve problems in a real-world context.
    - M3.G.SRT.A.2.c Use the Law of Sines and Law of Cosines to solve non-right triangles in a real-world context.
M3.G.MG Modeling with Geometry
- M3.G.MG.A Apply geometric concepts in modeling situations.
  - M3.G.MG.A.1 Use geometric shapes, their measures, and their properties to model objects found in a real-world context for the purpose of approximating solutions to problems.
    - Pythagorean theorem (G-P.1)
M3.G.GMD Geometric Measurement and Dimension
- M3.G.GMD.A Explain volume and surface area formulas and use them to solve problems.
  - M3.G.GMD.A.1 Understand and explain the formulas for the volume and surface area of a cylinder, cone, prism, and pyramid.
  - M3.G.GMD.A.2 Use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems in a real-world context.

M3.S Statistics and Probability

M3.S.ID Interpreting Categorical and Quantitative Data
- M3.S.ID.A Summarize, represent, and interpret data on a single count or measurement variable.
  - M3.S.ID.A.1 Use measures of center to solve real-world and mathematical problems.
    - Box plots (A2)
    - Mean, median, mode, and range (A1-II.2)
  - M3.S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (mean, median, and/or mode) and spread (range, interquartile range, and standard deviation) of two or more different data sets.
    - Choose appropriate measures of center and variation (A1-II.7)
    - Variance and standard deviation (A2-RR.2)
  - M3.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points.
  - M3.S.ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages using the Empirical Rule.
    - Find probabilities using the normal distribution I (A2-QQ.2)
  - M3.S.ID.A.5 Compute, interpret, and compare z-scores for normally distributed data in a real-world context.
    - Find probabilities using the normal distribution II (A2-QQ.3)
    - Find z-values (A2-QQ.4)
- M3.S.ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.
  - M3.S.ID.B.6 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.
M3.S.IC Making Inferences and Justifying Conclusions
- M3.S.IC.A Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
  - M3.S.IC.A.1 Recognize the purposes of and differences among sample surveys, experiments, and observational studies.
    - Experiment design (A2-RR.8)
  - M3.S.IC.A.2 Identify potential sources of bias in statistical studies.
    - Identify biased samples (A2-RR.1)
  - M3.S.IC.A.3 Distinguish between a statistic and a parameter. Evaluate reports based on data and recognize when poor conclusions are drawn from well-collected data.
M3.S.CP Conditional Probability and the Rules of Probability
- M3.S.CP.A Understand independence and conditional probability and use them to create visual representations of data.
  - M3.S.CP.A.1 Use set notation to represent contextual situations.
    - M3.S.CP.A.1.a Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or", "and", "not").
      - Theoretical and experimental probability (G-AA.1)
      - Outcomes of compound events (G-AA.2)
    - M3.S.CP.A.1.b Flexibly move between visual models (Venn diagrams, frequency tables, etc.) and set notation.
      - Find probabilities using two-way frequency tables (A2-OO.5)
  - M3.S.CP.A.2 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Categorize events as independent or dependent.
- M3.S.CP.B Understand and apply basic concepts of probability.
  - M3.S.CP.B.3 Apply statistical counting.
    - M3.S.CP.B.3.a Use the Fundamental Counting Principle to compute probabilities of compound events and solve problems.
      - Counting principle (A2-OO.2)
    - M3.S.CP.B.3.b Use permutations and combinations to compute probabilities of compound events and solve problems.
      - Combinations and permutations (A2-OO.3)
      - Find probabilities using combinations and permutations (A2-OO.4)
  - M3.S.CP.B.4 Use the Law of Large Numbers to assess the validity of a statistical claim.
    - Expected values for a game of chance (A2-PP.9)
    - Choose the better bet (A2-PP.10)
- M3.S.CP.C Use the rules of probability to compute probabilities of compound events in a uniform probability model.
  - M3.S.CP.C.5 Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A and interpret the answer in terms of the given context.
    - Find conditional probabilities (A2-OO.8)
    - Find conditional probabilities using two-way frequency tables (A2-OO.10)
  - M3.S.CP.C.6 Understand and apply the Addition Rule.
    - M3.S.CP.C.6.a Explain the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B) in terms of visual models (Venn diagrams, frequency tables, etc.).
    - M3.S.CP.C.6.b Apply the Addition Rule to solve problems and interpret the answer in terms of the given context.
      - Find probabilities using the addition rule (A2-OO.11)
- M3.S.CP.D Apply geometric concepts to situations involving probability.
  - M3.S.CP.D.7 Calculate probabilities using geometric figures.
    - Geometric probability (G-AA.14)

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M3.N Number and Quantity

M3.N.Q Quantities

M3.N.Q.A Reason quantitatively and use units to understand problems.

M3.N.Q.A.1 Use units as a way to understand real-world problems.

M3.N.Q.A.1.a Choose and interpret the scale and the origin in graphs and data displays.

M3.N.Q.A.1.b Use appropriate quantities in formulas, converting units as necessary.

M3.N.Q.A.1.c Define and justify appropriate quantities within a context for the purpose of modeling.

M3.N.Q.A.1.d Choose an appropriate level of accuracy when reporting quantities.

M3.A Algebra

M3.A.SSE Seeing Structure in Expressions

M3.A.SSE.A Interpret the structure of expressions.

M3.A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

M3.A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

M3.A.SSE.A.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

M3.A.APR Arithmetic with Polynomials and Rational Expressions

M3.A.APR.A Understand the relationship between zeros and factors of polynomials.

M3.A.APR.A.1 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).

M3.A.APR.A.2 Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.

M3.A.CED Creating Equations

M3.A.CED.A Create equations that describe numbers or relationships.

M3.A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems in a real-world context.

M3.A.CED.A.3 Rearrange formulas to isolate a quantity of interest using algebraic reasoning.

M3.A.REI Reasoning with Equations and Inequalities

M3.A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.

M3.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.

M3.A.REI.A.2 Solve radical equations in one variable and identify extraneous solutions when they exist.

M3.F Functions

M3.F.IF Interpreting Functions

M3.F.IF.A Understand the concept of a function and use function notation.

M3.F.IF.A.1 Use function notation.

M3.F.IF.A.1.a Use function notation to evaluate functions for inputs in their domains, including functions of two variables.

M3.F.IF.A.1.b Interpret statements that use function notation in terms of a context.

M3.F.IF.A.2 Understand geometric formulas as functions.

M3.F.IF.B Interpret functions that arise in applications in terms of the context.

M3.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.

M3.F.IF.B.4 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.

M3.F.IF.C Analyze functions using different representations.

M3.F.IF.C.5 Graph functions expressed algebraically and show key features of the graph by hand and using technology.

M3.F.IF.C.6 Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.

M3.F.IF.C.6.a Compare properties of two different functions. Functions may be of different types and/or represented in different ways.

M3.F.IF.C.6.b Compare properties of the same function on two different intervals or represented in two different ways.

M3.F.BF Building Functions

M3.F.BF.A Build new functions from existing functions.

M3.F.BF.A.1 Build a function that describes a relationship between two quantities.

M3.F.BF.A.1.a Combine standard function types using composition.

M3.F.BF.A.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.

M3.F.BF.A.3 Find the inverse of a function.

M3.F.BF.A.3.a Determine whether a function is one-to-one.

M3.F.BF.A.3.b Find the inverse of a function on an appropriate domain.

M3.F.BF.A.3.c Given an invertible function on an appropriate domain, identify the domain of the inverse function.

M3.F.LE Linear, Quadratic, and Exponential Models

M3.F.LE.A Construct and compare linear, quadratic, and exponential models and solve problems.

M3.F.LE.A.1 Know that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or cubically.

M3.F.LE.A.2 Know the relationship between exponential functions and logarithmic functions.

M3.F.LE.A.2.a Solve exponential equations using a variety of strategies, including logarithms.

M3.F.LE.A.2.b Understand that a logarithm is the solution to abct = d, where a, b, c, and d are numbers.

M3.F.LE.A.2.c Evaluate logarithms using technology.

M3.G Geometry

M3.G.C Circles

M3.G.C.A Find areas of sectors of circles.

M3.G.C.A.1 Use proportional relationships between the area of a circle and the area of a sector within the circle to solve problems and represent solutions in a real-world context.

M3.G.SRT Similarity, Right Triangles, and Trigonometry

M3.G.SRT.A Define trigonometric ratios and solve problems involving triangles.

M3.G.SRT.A.1 Use side ratios in right triangles to define trigonometric ratios.

M3.G.SRT.A.1.a Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

M3.G.SRT.A.1.b Explain and use the relationship between the sine and cosine of complementary angles.

M3.G.SRT.A.2 Solve triangles.

M3.G.SRT.A.2.a Know and use the Pythagorean Theorem and trigonometric ratios (sine, cosine, tangent, and their inverses) to solve right triangles in a real-world context.

M3.G.SRT.A.2.b Know and use relationships within special right triangles to solve problems in a real-world context.

M3.G.SRT.A.2.c Use the Law of Sines and Law of Cosines to solve non-right triangles in a real-world context.

M3.G.MG Modeling with Geometry

M3.G.MG.A Apply geometric concepts in modeling situations.

M3.G.MG.A.1 Use geometric shapes, their measures, and their properties to model objects found in a real-world context for the purpose of approximating solutions to problems.

M3.G.GMD Geometric Measurement and Dimension

M3.G.GMD.A Explain volume and surface area formulas and use them to solve problems.

M3.G.GMD.A.1 Understand and explain the formulas for the volume and surface area of a cylinder, cone, prism, and pyramid.

M3.G.GMD.A.2 Use volume and surface area formulas for cylinders, cones, prisms, pyramids, and spheres to solve problems in a real-world context.