The Common Core in Rhode Island

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Skills available for Rhode Island high school math standards

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Rhode Island Core Standards: Algebra 1 Rhode Island Core Standards: Algebra 1
Rhode Island Core Standards: Algebra 2 Rhode Island Core Standards: Algebra 2
Rhode Island Core Standards: All High School Pathways Rhode Island Core Standards: All High School Pathways
Rhode Island Core Standards: Geometry Rhode Island Core Standards: Geometry
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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S Statistics and Probability

S-ID Interpreting Categorical and Quantitative Data
- S-ID.A Summarize, represent, and interpret data on a single count or measurement variable. Use calculators, spreadsheets, and other technology as appropriate.
  - S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and boxplots).
  - S-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.
  - 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(outliers).
    - Box plots (A1-N.9)
    - Identify an outlier and describe the effect of removing it (A1-MM.5)
- S-ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.
  - S-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)
  - 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 linear function to the data and use the fitted function to solve problems in the context of the data. Use functions fitted to data or choose a function suggested by the context. Emphasize linear 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-MM.8)
    - 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-MM.12)
- 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.
    - Interpret regression lines (A1-MM.14)
    - Analyze a regression line of a data set (A1-MM.15)
  - S-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)
  - S-ID.C.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-MM.16)

The Common Core in Rhode Island

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N Number and Quantity

N-RN The Real Number System

N-RN.A Extend the properties of exponents to rational exponents.

N-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.

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

N-RN.B Use properties of rational and irrational numbers.

N-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.

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.

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

N-Q.A.3.a Describe the effects of approximate error in measurement and rounding on measurements and on computed values from measurements. Identify significant figures in recorded measures and computed values based on the context given and the precision of the tools used to measure.

A Algebra Content

A-SSE Seeing Structure in Expressions

A-SSE.A Interpret the structure of linear, quadratic, exponential, polynomial, and rational 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. For example, see x4 – y4 as (x ²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

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. For example, the expression 1.15t can be rewritten as (1.15 1/12)12t≈ 1.012112t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

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 certain operations.

A-APR.A.1.a Perform operations on polynomial expressions (addition, subtraction, multiplication, division) and compare the system of polynomials to the system of integers when performing operations.

A-APR.A.1.b Factor and/or expand polynomial expressions, identify and combine like terms, and apply the Distributive property.

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 root and rational functions 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 non-viable 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.

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 or refute 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.3.a Solve linear equations and inequalities in one variable involving absolute value.

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.

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.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x ² + y ² = 3.

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). Show that any point on the graph of an equation in two variables is a solution to the equation.

A-REI.D.12 Graph the solutions of 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 of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

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. For example, given a function representing a car loan, determine the balance of the loan at different points in time.

F-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n −1) for n ≥ 1.

F-IF.B Interpret functions that arise in applications in terms of the context (linear, quadratic,exponential, rational, polynomial, square root, cube root, trigonometric, logarithmic).

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.

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.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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/or completing the square in quadratic and polynomial functions, where appropriate, to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F-IF.C.10 Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial, rational, logarithmic, exponential, or trigonometric.

F-BF Building Functions

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

F-BF.A.1 Write a function (linear, quadratic, exponential, simple rational, radical, logarithmic, and trigonometric) 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.

F-BF.A.1.b Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

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

F-BF.B.4 Find inverse functions algebraically and graphically.

F-BF.B.4.a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. (Include linear and simple polynomial, rational, and exponential functions.)

F-LE Linear, Quadratic, and Exponential Models

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

A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x⁴ – y⁴ as (x ²)² – (y²)², thus recognizing it as a difference of squares that can be factored as (x² – y²)(x² + y²).

A-SSE.B.3.c Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15 ^1/12)^12t≈ 1.0121^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

F-LE.B.5 Interpret the parameters in a linear or exponential function (of the form f(^x) = bx + k) in terms of a context.