The Common Core in California

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Skills available for California high school math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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California Common Core Content Standards: Algebra I California Common Core Content Standards: Algebra I
California Common Core Content Standards: Algebra II California Common Core Content Standards: Algebra II
California Common Core Content Standards: Geometry California Common Core Content Standards: Geometry
California Common Core Content Standards: Mathematics I California Common Core Content Standards: Mathematics I
California Common Core Content Standards: Mathematics II California Common Core Content Standards: Mathematics II
California Common Core Content Standards: Mathematics III California Common Core Content Standards: Mathematics III
California Common Core Content Standards: Calculus California Common Core Content Standards: Calculus
California Common Core Content Standards: Mathematical Practices California Common Core Content Standards: Mathematical Practices

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9-12.S Statistics and Probability

9-12.S-ID Interpreting Categorical and Quantitative Data
- 9-12. Summarize, represent, and interpret data on a single count or measurement variable
  - 9-12.S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  - 9-12.S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  - 9-12.S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
    - Box plots (A1-N.9)
    - Identify an outlier and describe the effect of removing it (A1-MM.5)
  - Checkpoint opportunity
    - Checkpoint: Line plots, histograms, and box plots (A1-N.10)
    - Checkpoint: Compare data sets (A1-MM.17)
- 9-12. Summarize, represent, and interpret data on two categorical and quantitative variables
  - 9-12.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.
    - Find probabilities using two-way frequency tables (A1-LL.3)
    - Find conditional probabilities using two-way frequency tables (A1-LL.4)
  - 9-12.S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    - 9-12.S-ID.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
    - 9-12.S-ID.6.b Informally assess the fit of a function by plotting and analyzing residuals.
      - Interpret a scatter plot (A1-MM.8)
    - 9-12.S-ID.6.c Fit a linear function for a scatter plot that suggests a linear association.
      - Write equations for lines of best fit (A1-MM.12)
  - Checkpoint opportunity
    - Checkpoint: Two-way frequency tables (A1-LL.11)
- 9-12. Interpret linear models
  - 9-12.S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
    - Interpret regression lines (A1-MM.14)
    - Analyze a regression line of a data set (A1-MM.15)
  - 9-12.S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
    - Match correlation coefficients to scatter plots (A1-MM.10)
    - Calculate correlation coefficients (A1-MM.11)
  - 9-12.S-ID.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-MM.16)
  - Checkpoint opportunity
    - Checkpoint: Linear modeling (A1-MM.18)

The Common Core in California

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9-12.N Number and Quantity

9-12.N-RN The Real Number System

9-12. Extend the properties of exponents to rational exponents.

9-12.N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

9-12.N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

9-12. Use properties of rational and irrational numbers.

9-12.N-RN.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

9-12.N-Q Quantities

9-12. Reason quantitatively and use units to solve problems.

9-12.N-Q.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.

9-12.N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.

9-12.N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Checkpoint opportunity

9-12.A. Algebra

9-12.A-SSE Seeing Structure in Expressions

9-12. Interpret the structure of expressions

9-12.A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

9-12.A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

9-12.A-SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity.

9-12.A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

9-12. Write expressions in equivalent forms to solve problems

9-12.A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

9-12.A-SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

9-12.A-SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

9-12.A-SSE.3.c Use the properties of exponents to transform expressions for exponential functions.

Checkpoint opportunity

9-12.A-APR Arithmetic with Polynomials and Rational Expressions

9-12. Perform arithmetic operations on polynomials

9-12.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.

Checkpoint opportunity

9-12.A-CED Creating Equations

9-12. Create equations that describe numbers or relationships

9-12.A-CED.1 Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

9-12.A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

9-12.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.

9-12.A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Checkpoint opportunity

9-12.A-REI Reasoning with Equations and Inequalities

9-12. Understand solving equations as a process of reasoning and explain the reasoning

9-12.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.

9-12. Solve equations and inequalities in one variable

9-12.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

9-12.A-REI.3.1 Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

9-12.A-REI.4 Solve quadratic equations in one variable.

9-12.A-REI.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

9-12. Solve systems of equations

9-12.A-REI.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.

9-12.A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

9-12.A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

9-12. Represent and solve equations and inequalities graphically

9-12.A-REI.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).

9-12.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 corresponding half-planes.

Checkpoint opportunity

9-12.F Functions

9-12.F-IF Interpreting Functions

9-12. Understand the concept of a function and use function notation

9-12.F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

9-12.F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

9-12. Interpret functions that arise in applications in terms of the context

9-12.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.

9-12.F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

9-12.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.

Checkpoint opportunity

9-12. Analyze functions using different representations

9-12.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.

9-12.F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

9-12.F-IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

9-12.F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

9-12.F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

9-12.F-IF.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.

9-12.F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions.

9-12.F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Checkpoint opportunity

9-12.F-BF Building Functions

9-12. Build a function that models a relationship between two quantities