The Common Core in Maryland

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Skills available for Maryland high school math standards

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Maryland College and Career-Ready Frameworks: Algebra I Maryland College and Career-Ready Frameworks: Algebra I
Maryland College and Career-Ready Frameworks: Algebra II Maryland College and Career-Ready Frameworks: Algebra II
Maryland College and Career-Ready Frameworks: Geometry Maryland College and Career-Ready Frameworks: Geometry
Maryland College and Career-Ready Standards: Algebra 1 Maryland College and Career-Ready Standards: Algebra 1
Maryland College and Career-Ready Standards: Algebra 2 Maryland College and Career-Ready Standards: Algebra 2
Maryland College and Career-Ready Standards: All High School Pathways Maryland College and Career-Ready Standards: All High School Pathways
Maryland College and Career-Ready Standards: Geometry Maryland College and Career-Ready Standards: Geometry
Maryland College and Career-Ready Standards: Mathematical Practices Maryland College and Career-Ready Standards: Mathematical Practices
Maryland College and Career-Ready Standards: Mathematics I Maryland College and Career-Ready Standards: Mathematics I
Maryland College and Career-Ready Standards: Mathematics II Maryland College and Career-Ready Standards: Mathematics II
Maryland College and Career-Ready Standards: Mathematics III Maryland College and Career-Ready Standards: Mathematics III
Maryland College and Career-Ready Standards: Precalculus A Maryland College and Career-Ready Standards: Precalculus A
Maryland College and Career-Ready Standards: Precalculus B Maryland College and Career-Ready Standards: Precalculus B
Maryland College and Career-Ready Standards: Statistics Maryland College and Career-Ready Standards: Statistics

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N Number and Quantity

N.RN The Real Number System
- N.RN.A Use properties of rational and irrational numbers.
  - N.RN.A.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
  - Checkpoint opportunity
    - Checkpoint: Rational and irrational numbers (A1)
N.Q Quantities
- N.Q.A Reason quantitatively and use units to solve problems.
  - N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  - N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
  - N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
  - Checkpoint opportunity
    - Checkpoint: Units and quantities (A1-E.8)

A Algebra

A.SSE Seeing Structure in Expressions
- A.SSE.A Interpret the structure of expressions.
  - A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
    - A.SSE.A.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
    - 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)
  - A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.
- A.SSE.B Write expressions in equivalent forms to solve problems.
  - A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
    - A.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
    - A.SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
    - A.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.
      - Evaluate expressions using exponent rules (A1-R.12)
      - Evaluate an exponential function (A1-V.1)
  - Checkpoint opportunity
    - Checkpoint: Quadratic and exponential expressions (A1-AA.14)
A.APR Arithmetic with Polynomials and Rational Expressions
- A.APR.A Perform arithmetic operations on polynomials.
  - A.APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
  - Checkpoint opportunity
    - Checkpoint: Polynomial operations (A1)
- A.APR.B Understand the relationship between zeros and factors of polynomials.
  - N.APR.B.3 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.
A.CED Creating Equations
- A.CED.A Create equations that describe numbers or relationships.
  - A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  - A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  - A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
  - A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
    - 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: Modeling with linear, quadratic, and exponential equations and inequalities (A1-AA.15)
A.REI Reasoning with Equations and Inequalities
- A.REI.A Understand solving equations as a process of reasoning and explain the reasoning.
  - A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
- A.REI.B Solve equations and inequalities in one variable.
  - A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  - A.REI.B.4 Solve quadratic equations in one variable.
    - A.REI.B.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x − p)² = q that has the same solutions. Derive the quadratic formula from this form.
      - Complete the square (A1-Z.4)
    - A.REI.B.4.b Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
  - Checkpoint opportunity
    - Checkpoint: Solve linear equations and inequalities (A1-F.16)
    - Checkpoint: Quadratic equations (A1)
- A.REI.C Solve systems of equations.
  - A.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
    - Solve a system of equations using elimination (A1-O.10)
    - Solve a system of equations using elimination: word problems (A1-O.11)
  - A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
- A.REI.D Represent and solve equations and inequalities graphically.
  - A.REI.D.10 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).
  - A.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
  - A.REI.D.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 corresponding half planes.
  - Checkpoint opportunity
    - Checkpoint: Solve equations using graphs and tables (A1-M.19)
    - Checkpoint: Systems of equations and inequalities (A1-P.8)

F Functions

F.IF Interpreting Functions
- F.IF.A Understand the concept of a function and use function notation.
  - F.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  - F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  - F.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
- F.IF.B Interpret functions that arise in applications in terms of the context.
  - F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
  - F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  - F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
    - Rate of change: tables (A1-M.15)
    - Rate of change: graphs (A1-M.16)
  - Checkpoint opportunity
    - Checkpoint: Average rate of change (A1-M.18)
    - Checkpoint: Function concepts and sequences (A1)
- F.IF.C Analyze functions using different representations.
  - F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    - F.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
    - F.IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  - F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    - F.IF.C.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  - F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
    - Compare linear functions: graphs and equations (A1-N.11)
    - Compare linear functions: tables, graphs, and equations (A1-N.12)
  - Checkpoint opportunity
    - Checkpoint: Analyze, interpret, and compare functions (A1-BB.7)
    - Checkpoint: Graph and analyze functions (A1-FF.8)
F.BF Building Functions
- F.BF.A Build a function that models a relationship between two quantities.
  - F.BF.A.1 Write a function that describes a relationship between two quantities.
    - F.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
  - Checkpoint opportunity
    - Checkpoint: Write functions (A1)
- F.BF.B Build new functions from existing functions.
  - F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  - Checkpoint opportunity
    - Checkpoint: Function transformations (A1)
F.LE Linear, Quadratic, and Exponential Models
- F.LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
  - F.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
    - F.LE.A.1.a Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
    - F.LE.A.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
    - F.LE.A.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
  - F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  - F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
    - Compare linear and exponential growth (A1-AA.11)
    - Compare linear, exponential, and quadratic growth (A1-AA.12)
- F.LE.B Interpret expressions for functions in terms of the situation they model.
  - F.LE.B.5 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)

S Statistics

S.ID Interpreting Categorical and Quantitative Data
- S.ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.
  - S.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    - S.ID.B.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
    - S.ID.B.6.b Informally assess the fit of a function by plotting and analyzing residuals.
      - Interpret a scatter plot (A1-JJ.1)
    - S.ID.B.6.c Fit a linear function for a scatter plot that suggests a linear association.
      - Write equations for lines of best fit (A1-JJ.5)
- S.ID.C Interpret linear models.
  - S.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
  - S.ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
    - Match correlation coefficients to scatter plots (A1-JJ.3)
    - Calculate correlation coefficients (A1-JJ.4)
  - S.ID.C.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-JJ.11)
  - Checkpoint opportunity
    - Checkpoint: Linear, exponential, and quadratic modeling (A1)

The Common Core in Maryland

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N Number and Quantity

N.RN The Real Number System

N.RN.A Use properties of rational and irrational numbers.

N.RN.A.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Checkpoint opportunity

N.Q Quantities

N.Q.A Reason quantitatively and use units to solve problems.

N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Checkpoint opportunity

A Algebra

A.SSE Seeing Structure in Expressions

A.SSE.A Interpret the structure of expressions.

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

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

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

A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

A.SSE.B Write expressions in equivalent forms to solve problems.

A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.B.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

A.SSE.B.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions.

Checkpoint opportunity

A.APR Arithmetic with Polynomials and Rational Expressions

A.APR.A Perform arithmetic operations on polynomials.

A.APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Checkpoint opportunity

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

N.APR.B.3 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.

A.CED Creating Equations

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

A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Checkpoint opportunity

A.REI Reasoning with Equations and Inequalities

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

A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

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

A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.REI.B.4 Solve quadratic equations in one variable.

A.REI.B.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x − p)2 = q that has the same solutions. Derive the quadratic formula from this form.

Checkpoint opportunity

A.REI.C Solve systems of equations.

A.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

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

A.REI.D.10 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).

A.REI.D.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 corresponding half planes.

Checkpoint opportunity

F Functions

F.IF Interpreting Functions

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

F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

F.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

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

F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Checkpoint opportunity

F.IF.C Analyze functions using different representations.

F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.C.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.C.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Checkpoint opportunity

F.BF Building Functions

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

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

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

Checkpoint opportunity

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

Checkpoint opportunity

F.LE Linear, Quadratic, and Exponential Models

A.REI.B.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x − p)² = q that has the same solutions. Derive the quadratic formula from this form.