The Common Core in Washington

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Skills available for Washington high school math standards

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Common Core State Standards: Algebra 1 Common Core State Standards: Algebra 1
Common Core State Standards: Algebra 2 Common Core State Standards: Algebra 2
Common Core State Standards: All High School Pathways Common Core State Standards: All High School Pathways
Common Core State Standards: Fourth Courses Common Core State Standards: Fourth Courses
Common Core State Standards: Geometry Common Core State Standards: Geometry
Common Core State Standards: Mathematical Practices Common Core State Standards: Mathematical Practices
Common Core State Standards: Mathematics I Common Core State Standards: Mathematics I
Common Core State Standards: Mathematics II Common Core State Standards: Mathematics II
Common Core State Standards: Mathematics III Common Core State Standards: Mathematics III
Common Core State Standards: Precalculus Common Core State Standards: Precalculus

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9-12.HSS Statistics and Probability

9-12.HSS-ID Interpreting Categorical and Quantitative Data
- 9-12.HSS-ID.A Summarize, represent, and interpret data on a single count or measurement variable
  - 9-12.HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  - 9-12.HSS-ID.A.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.HSS-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 (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.HSS-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables
  - 9-12.HSS-ID.B.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.HSS-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    - 9-12.HSS-ID.B.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
    - 9-12.HSS-ID.B.6b Informally assess the fit of a function by plotting and analyzing residuals.
      - Interpret a scatter plot (A1-MM.8)
    - 9-12.HSS-ID.B.6c 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.HSS-ID.C Interpret linear models
  - 9-12.HSS-ID.C.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.HSS-ID.C.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.HSS-ID.C.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-MM.16)
  - Checkpoint opportunity
    - Checkpoint: Linear modeling (A1-MM.18)

The Common Core in Washington

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9-12.HSN Number and Quantity

9-12.HSN-RN The Real Number System

9-12.HSN-RN.A Extend the properties of exponents to rational exponents.

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

9-12.HSN-RN.B Use properties of rational and irrational numbers.

9-12.HSN-RN.B.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.HSN-Q Quantities

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

9-12.HSN-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.

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

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

Checkpoint opportunity

9-12.HSA Algebra

9-12.HSA-SSE Seeing Structure in Expressions

9-12.HSA-SSE.A Interpret the structure of expressions

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

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

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

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

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

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

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

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

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

9-12.HSA-SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

Checkpoint opportunity

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

9-12.HSA-APR.A Perform arithmetic operations on polynomials

9-12.HSA-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

9-12.HSA-CED Creating Equations

9-12.HSA-CED.A Create equations that describe numbers or relationships

9-12.HSA-CED.A.1 Create equations and inequalities in one variable and use them to solve problems.

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

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

Checkpoint opportunity

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

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

9-12.HSA-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.

9-12.HSA-REI.B Solve equations and inequalities in one variable

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

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

9-12.HSA-REI.B.4a 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.HSA-REI.C Solve systems of equations

9-12.HSA-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.

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

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

9-12.HSA-REI.C.8 Represent a system of linear equations as a single matrix equation in a vector variable.

9-12.HSA-REI.C.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

9-12.HSA-REI.D Represent and solve equations and inequalities graphically

9-12.HSA-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).

9-12.HSA-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

9-12.HSF Functions

9-12.HSF-IF Interpreting Functions

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

9-12.HSF-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.

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

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

9-12.HSF-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.

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

9-12.HSF-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

9-12.HSF-IF.C Analyze functions using different representations

9-12.HSF-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.

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

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

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

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

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

9-12.HSF-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