Common Core State Standards with California Additions 1 Standards Map. Algebra I

Transcription

1 Common Core State s with California Additions 1 s Map Algebra I *Indicates a modeling standard linking mathematics to everyday life, work, and decision-making N-RN 1. N-RN 2. Publisher Language 2 Primary Supporting NUMBER AND QUANTITY THE REAL NUMBER SYSTEM. Extend the properties of exponents to rational exponents. 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. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5 (1/3)3 to hold, so (5 1/3 ) 3 must equal 5. Rewrite expressions involving radicals and rational exponents Topic 13: Laws of exponents: Exploring 1, "Special exponents" pages Topic 13: Laws of exponents: Exploring 4, "Other laws for 1 These standards were originally produced by the Common Core State s Initiative, a state-led effort coordinated by the National Governors Association Center for Best Practices and the Council of Chief State School Officers. California additions were made by the State Board of Education when it adopted the Common Core on August 2, 2010 and modified pursuant to Senate Bill 1200 located at (Outside Source) on January 16, Additions are marked in bold and underlined. 2 For some standards that appear in multiple courses (e.g., Algebra I and Algebra II), some examples included in the language of the standard that did not apply to this standards map were removed. California Department of Education Common Core State s Map January 16, 2013 Page 1

2 Publisher Language 2 Primary Supporting using the properties of exponents. exponents" pp 3-4, page 7 N-RN 3. N-Q 1. N-Q 2. N-Q 3. Use properties of rational and irrational numbers. 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. QUANTITIES Reason quantitatively and use units to solve problems. [Foundation for work with expressions, equations and functions.] 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.* Define appropriate quantities for the purpose of descriptive modeling.* Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.* Topic 1: Constructing graphs: Exploring 1, "Representing data" Topic 7: Creating linear models for data: Overview, page 2 Topic 4: Exploring rate of change in motion problems: Exploring 4, "What's my rate" p 3 California Department of Education Common Core State s Map January 16, 2013 Page 2

3 Publisher Language 2 Primary Supporting A-SSE 1a. A-SSE 1b. A-SSE 2. ALGEBRA SEEING STRUCTURE IN EXPRESSIONS Interpret the structure of expressions [Linear, exponential, quadratic.] Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and coefficients.* Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P and a factor not depending on P.* Use the structure of an expression to identify ways to rewrite it. Topic 2: Multiple representations in the real world: Exploring 1, "Tiling square pools" page 5; Exploring 2, "What's in a rule" and equations: Exploring 2, "Growth and decay" pp 5-10 Topic 18: Operations on polynomials: Exploring 3, "Factoring" page 3 Topic 2: Multiple representations in the real world: Exploring 2, "What's in a rule" and equations: Exploring 3, "Modeling with exponential functions" and equations: Exploring 3, "Modeling with exponential functions" page 11 California Department of Education Common Core State s Map January 16, 2013 Page 3

4 A-SSE 3a. A-SSE 3b. A-SSE 3c. Publisher Language 2 Primary Supporting Topic 18: Operations on polynomials: Exploring 3, "Factoring" Topic 19: Modeling with quadratic functions: Exploring 3, "Completing the square" Topic 21: The quadratic formula: Exploring 2, "The algebra of square roots" pages 2 and 4-7 Write expressions in equivalent forms to solve problems. [Quadratic and exponential.] Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines.* Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.* Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. Use the properties of exponents to Topic 18: Operations on polynomials: Exploring 3, "Factoring" Topic 19: Modeling with quadratic functions: Exploring 3, "Completing the square" and equations: Exploring 3, "Modeling with exponential functions" page 11 California Department of Education Common Core State s Map January 16, 2013 Page 4

5 Publisher Language 2 Primary Supporting transform expressions for exponential functions. For example, the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.* A-APR 1. A-CED 1. ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONS Perform arithmetic operations on polynomials. [Linear and quadratic.] 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. CREATING EQUATIONS Create equations that describe numbers or relationships. [Linear, quadratic, and exponential (integer inputs only); for A.CED.3 linear only.] Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and Topic 18 Operations on Polynomials: Exploring 1, "Multiplying polynomials" and Exploring 2 "Finding sums and differences" Topic 3: Functions: Exploring 2, "Modeling with functions" pp 9-10; Topic 8: Solving linear equations and inequalities: Overview page 1 Topic 9: Absolute value California Department of Education Common Core State s Map January 16, 2013 Page 5

6 A-CED 2. A-CED 3. Publisher Language 2 Primary Supporting exponential functions.* equations and piecewise functions: Exploring 1, The definitions of absolute value pages 9-11; Exploring 2, Solving with graphs and tables pages 1-7 and equations: Exploring 2, "Growth and decay" pg 4 Topic 20: Solving quadratic equations: Exploring 1, "Solving by graphing" pp 1-3 Create equations in two or more Topic 3: Functions: Exploring 2, variables to represent relationships "Modeling with functions" pg 5 between quantities; graph equations and page 8 on coordinate axes with labels and Topic 6: Moving beyond slopeintercept: scales.* Exploring 1, pp Topic 8: Solving linear equations and inequalities: Overview page 1 Topic 12: Other nonlinear relationships: Exploring 1, "Building blocks" pp 1-7 and Exploring 2, "Too many triangles" pg 5 and pg 8 Topic 17: Graphs of quadratic functions: Exploring 1, "y = ax 2 " pp 1-6 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. For example, represent inequalities Topic 8: Solving linear equations and inequalities: Exploring 1, "Solving linear equations" pp 6-8 and Exploring 3, "Linear inequalities in one variable" pp 1-4 California Department of Education Common Core State s Map January 16, 2013 Page 6

7 A-CED 4. A-REI 1. A-REI 3. Publisher Language 2 Primary Supporting describing nutritional and cost constraints on combinations of different foods. * Rearrange formulas to highlight a Topic 8: Solving linear quantity of interest, using the same equations and inequalities: reasoning as in solving equations. Exploring 2, "More solving linear For example, rearrange Ohm s law V equations" pages 7-8 = IR to highlight resistance R. * REASONING WITH EQUATIONS AND INEQUALITIES Understand solving equations as a process of reasoning and explain the reasoning. [Master linear; learn as general principle.] 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. Solve equations and inequalities in one variable. [Linear inequalities; literal that are linear in the variables being solved for; quadratics with real solutions.] Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Topic 8: Solving linear equations and inequalities: Exploring 1, "Solving linear equations" page 1, page 3, page 5 and Exploring 2, "More solving linear equations" page 1 Topic 8: Solving linear equations and inequalities: Exploring 1, "Solving linear equations" and Exploring 2, "More solving linear equations" California Department of Education Common Core State s Map January 16, 2013 Page 7

8 Publisher Language 2 Primary Supporting A-REI 3.1. A-REI 4a. A-REI 4b. A-REI 5. Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. Solve quadratic equations in one variable. 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. Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x 2 = 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. Solve Systems of Equations. [Linear-linear and linear-quadratic.] 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 Topic 9: Absolute value equations and piecewise functions: Exploring 1, The definitions of absolute value pages 9-11; Exploring 2, Solving with graphs and tables pages 1-7; Exploring 3, Solving analytically pages 1-5 Topic 20: Solving quadratic equations: Exploring 4, "Completing the square" Topic 21: The quadratic formula: Exploring 3, "Using the quadratic formula" pp 3-11 Topic 20: Solving quadratic equations: Exploring 4, "Completing the square" Topic 21: The quadratic formula: Exploring 3, "Using the quadratic formula" pp 3-11 Topic 11: Other methods for solving systems: Exploring 2, "Linear combination method" page 2; Exploring 3, "Why linear California Department of Education Common Core State s Map January 16, 2013 Page 8

9 Publisher Language 2 Primary Supporting produces a system with the same combination works"; Guided solutions. assessment A-REI 6. A-REI 7. A-REI 10. A-REI 11. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.] 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). Explain why the x-coordinates of the points where the graphs of the Topic 10: Systems of linear equations and inequalites: Exploring 1, "Solving systems of equations in slope-intercept form"; Exploring 2, "Solving systems of equations in standard form" (Note: This topic is being revised Summer 2013, and the revised content will be available after August 1, 2013.) Topic 11: Other methods for solving systems: Constructed response Topic 8: Solving linear equations and inequalities: Overview 1; Exploring 1, "Solving linear equations" pp 6-8 Topic 8: Solving linear equations and inequalities: California Department of Education Common Core State s Map January 16, 2013 Page 9

10 A-REI 12. Publisher Language 2 Primary Supporting equations y = f(x) and y = g(x) Overview 1; Exploring 1, "Solving intersect are the solutions of the linear equations" page 8; equation f(x) = g(x); find the Exploring 2, "More solving linear solutions approximately, e.g., using equations, page 3 and page 6 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.* Graph the solutions to a linear inequality in two variables as a halfplane (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. FUNCTIONS INTERPRETING FUNCTIONS Understand the concept of a function and use function notation. [Learn as general principle; focus on linear and exponential and on arithmetic and geometric sequences] Topic 8: Solving linear equations and inequalities: Exploring 4, "Linear inequalities in two variables" Topic 10: Solving systems of linear equations and inequalities: Exploring 3, "Systems of inequalities" (Note: This topic is being revised Summer 2013, and the revised content will be available after August 1, 2013.) California Department of Education Common Core State s Map January 16, 2013 Page 10

11 F-IF 1. F-IF 2. F-IF 3. F-IF 4. Publisher Language 2 Primary Supporting Understand that a function from one Topic 1: Constructing graphs: set (called the domain) to another Exploring 3, "Domain and range" set (called the range) assigns to Topic 3: Functions: Exploring 3, each element of the domain exactly "Graphs" pp 3-5 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). Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 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. Interpret functions that arise in applications in terms of the context. [Linear, exponential, and quadratic.] 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: Topic 3: Functions: Exploring 1, "Function notation" pp 5-6; Exploring 2, "Modeling with functions" pp 9-10 Topic 3: Functions: Exploring 1, "Function notation" pp 7-13 Topic 3: Functions: Exploring 3, "Graphs" pp 6-8 Topic 4: Exploring rate of change in motion problems: Overview page 3; Exploring 2, "More graph matching" page 9; Student Activity Sheet 2 question California Department of Education Common Core State s Map January 16, 2013 Page 11

12 F-IF 5. F-IF 6. Publisher Language 2 Primary Supporting intercepts; intervals where the 13; Student Activity Sheet 3, function is increasing, decreasing, question 8 positive, or negative; relative Topic 6: Moving beyond slopeintercept: maximums and minimums; Exploring 1, "Using symmetries; end behavior; and slope-intercept form" page 11; periodicity.* Exploring 3, "Intercepts and standard form" pages 2 and 4 and equations: Exploring 2, "Growth and decay" pp 8-10 Topic 19: Modeling with quadratic functions: Exploring 2, "Quadratic forms" pp Topic 20: Solving quadratic equations: Exploring 1, "Solving by graphing" page 2, pp 4-5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* 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.* Topic 1: Constructing graphs: Exploring 3, "Domain and range" Topic 3: Functions: Exploring 3, "Graphs" pp 3-5 Topic 12: Other nonlinear relationships: Exploring 1, "Building blocks" page 12 Topic 4: Exploring rate of change in motion problems: Exploring 4, "What's my rate" pp 3-7; pp 9-11 Topic 5: Exploring rate of change in other situations: Exploring 1, "Constant rates" pp 2-7; EX 3, "Rates that are not California Department of Education Common Core State s Map January 16, 2013 Page 12

13 Publisher Language 2 Primary Supporting constant" pages 3, 6, and 9 F-IF 7a. F-IF 7b. F-IF 7e. Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined.] Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph linear and quadratic functions and show intercepts, maxima, and minima.* Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.* Graph functions expressed symbolically and show key features of the graph, by hand in simple Topic 6: Moving beyond slopeintercept: Exploring 1, "Using slope-intercept form" page 10; EX 3, "Intercepts and standard form" pp 6-8; Topic 19: Modeling with quadratic functions: Exploring 4, "Using y = ax 2 + bx + c to model data" pages 3-6 Topic 9: Absolute value and piecewise functions: Exploring 1, "The definitions of absolute value" pp 5-6; Exploring 4, "Other piecewise functions" pages 2, 5, and 11 Topic 12: Other nonlinear relationships: Exploring 1, Building blocks pages 12-15; EX 3, Cubic and cube root functions (Note: This topic is being revised Summer 2013, and the revised content will be available after August 1, 2013.) and equations: Exploring 1, "Comparing linear and California Department of Education Common Core State s Map January 16, 2013 Page 13

14 F-IF 8a. cases and using technology for more complicated cases. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. * Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 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. Publisher Language 2 Primary Supporting exponential growth" page 4 Topic 19: Modeling with quadratic functions: Exploring 4, "Using y = ax 2 + bx + c to model data" pages 3-6 Topic 19: Modeling with quadratic functions: Exploring 3, "Completing the square" pages 2, 5, and 7 Topic 20: Solving quadratic equations: Exploring 2, "Solving by factoring" page 3; Exploring 3, "Connecting solution methods" page 3 F-IF 8b. F-IF 9. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01) 12t, and y = (1.2) t/10, and classify them as representing exponential growth or decay. Compare properties of two functions each represented in a different way and equations: Guided assessment, pages 5 and 7 Topic 3: Functions: Exploring 3, "Graphs" page 9 California Department of Education Common Core State s Map January 16, 2013 Page 14

15 Publisher Language 2 Primary Supporting (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. BUILDING FUNCTIONS F-BF 1a. Build a function that models a relationship between two quantities. [For F.BF.1, 2, linear, exponential, and quadratic.] Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context.* Topic 2: Multiple representations in the real world: Exploring 1 "Tiling square pools" page 6 Topic 6: Moving beyond slopeintercept: Exploring 1, "Using slope-intercept form" pages 2, 6, 10 Topic 12: Other nonlinear relationships: Exploring 1, "Building blocks" page 4; Exploring 2, "Too many triangles" page 5 and equations: Exploring 3, "Modeling with exponential functions" page 2 Topic 17: Graphs of quadratic functions: Exploring 2, "y = x 2 + c" pages 1-4 California Department of Education Common Core State s Map January 16, 2013 Page 15

16 F-BF 1b. Publisher Language 2 Primary Supporting Write a function that describes a Topic 2: Multiple relationship between two quantities. representations in the real Combine standard function types world: Exploring 1 "Tiling square using arithmetic operations. For pools" page 6 example, build a function that Topic 6: Moving beyond slopeintercept: models the temperature of a cooling Exploring 1, "Using body by adding a constant function slope-intercept form" pages 2, 6, to a decaying exponential, and 10 relate these functions to the model.* Topic 12: Other nonlinear relationships: Exploring 1, "Building blocks" page 4; Exploring 2, "Too many triangles" page 5 and equations: Exploring 3, "Modeling with exponential functions" page 2 Topic 17: Graphs of quadratic functions: Exploring 2, "y = x 2 + c" pages 1-4 F-BF 2. F-BF 3. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. * Build new functions from existing functions. [Linear, exponential, quadratic, and absolute value; for F.BF.4a, linear only.] 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 T15. Arithmetic and geometric sequences Entire topic Topic 6: Moving beyond slopeintercept: Exploring, "m, b, and the graph of y = mx + b" pp 1-2 California Department of Education Common Core State s Map January 16, 2013 Page 16

17 Publisher Language 2 Primary Supporting (both positive and negative); find the Topic 7: Creating linear models value of k given the graphs. for data: Exploring 3, Experiment with cases and illustrate "Transformations on linear an explanation of the effects on the functions" graph using technology. Include recognizing even and odd functions and equations: Exploring 1, from their graphs and algebraic "Comparing exponential and expressions for them. linear growth" page 6 Topic 17: Graphs of quadratic functions: Exploring 3, "Changes to the parent function" pp 4-5 and pp 7- Topic 19: Modeling with quadratic functions: Exploring 2, "Quadatic forms" pp 5-7 F-BF 4a. F-LE 1a. Find inverse functions. 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. LINEAR, QUADRATIC, AND EXPONENTIAL MODELS Construct and compare linear, quadratic, and exponential models and solve problems. Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over T8: Solving linear equations and inequalities: Exploring 3 The inverse of a linear function Topic 6: Moving beyond slopeintercept: Exploring 1, Using slope-intercept form page 12 California Department of Education Common Core State s Map January 16, 2013 Page 17

18 F-LE 1b. F-LE 1c. F-LE 2. Publisher Language 2 Primary Supporting equal intervals.* Distinguish between situations that Topic 4: Exploring rate of can be modeled with linear functions change in motion problems: and with exponential functions. Exploring 4, What s my rate Recognize situations in which one Topic 5: Exploring rate of quantity changes at a constant rate change in other situations: per unit interval relative to another.* Exploring 1, Constant rates Topic 6: Moving beyond slopeintercept: Overview; Exploring 1, Using slope-intercept form ; Exploring 3, Point-slope form ; and equations: Exploring 1 Comparing exponential and linear growth Distinguish between situations that can be modeled with linear functions and with exponential functions. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.* 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).* and equations: Exploring 3 Modeling with exponential functions Topic 6: Moving beyond slopeintercept: Overview, pp 1-3; Exploring 1, "Using slopeintercept form" page 2, pp 6-7 and page 10; Exploring 4, "Pointslope form" pages 5 and 7; Topic 7: Creating linear models for data: Exploring 2, "Rate of change" page 5 and equations: Exploring 1, California Department of Education Common Core State s Map January 16, 2013 Page 18

19 Publisher Language 2 Primary Supporting "Comparing linear and exponential growth" pp 3-4; F-LE 3. F-LE 5. F-LE 6. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* Interpret expressions for functions in terms of the situation they model. Interpret the parameters in a linear or exponential function in terms of a context.* [Linear and exponential of form f(x)=b x +k.] Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.* STATISTICS AND PROBABILITY INTERPRETING CATEGORICAL AND QUANTITATIVE DATA Summarize, represent, and interpret data on a single count or measurement variable. and equations: Exploring 1, "Comparing linear and exponential growth" pages 4 and 7 Topic 2: Multiple representations in the real world: Constructed response and equations: Exploring 1, "Comparing linear and exponential growth" pp 4-5 Topic 20: Solving quadratic equations: Exploring 1, "Solving by graphing" California Department of Education Common Core State s Map January 16, 2013 Page 19

20 S-ID 1. S-ID 2. S-ID 3. S-ID 5. Publisher Language 2 Primary Supporting Represent data with plots on the Topic 16: Descriptive statistics: real number line (dot plots, Exploring 1, "Univariate data" histograms, and box plots).* (Note: This topic is being developed Summer 2013, and the revised content will be available after August 1, 2013.) 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.* Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* Summarize, represent, and interpret data on two categorical and quantitative variables. [Linear focus, discuss general principle.] 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.* Topic 16: Descriptive statistics, Exploring 2, "Comparing univariate data sets" (Note: This topic is being developed Summer 2013, and the revised content will be available after August 1, 2013.) Topic 16: Descriptive statistics, Exploring 2, "Comparing univariate data sets" (Note: This topic is being developed Summer 2013, and the revised content will be available after August 1, 2013.) Topic 16: Descriptive statistics, Exploring 3, "Bivariate categorical data" (Note: This topic is being developed Summer 2013, and the revised content will be available after August 1, 2013.) California Department of Education Common Core State s Map January 16, 2013 Page 20

21 S-ID 6a. S-ID 6b. S-ID 6c. S-ID 7. Publisher Language 2 Primary Supporting Represent data on 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. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models * Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Informally assess the fit of a function by plotting and analyzing residuals.* Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Fit a linear function for a scatter plot that suggests a linear association.* Interpret linear models. Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* Topic 7: Creating linear models for data: Exploring 1, "Trend lines" pp 1-2; Exploring 4, "Line of best fit" and equations: Constructed response Topic 19: Modeling with quadratic functions: Exploring 4, Using y = ax 2 + bx + c to model data Topic 7: Creating linear models for data: Exploring 4, "Line of best fit" pp 7-8 Topic 7: Creating linear models for data: Exploring 1, "Trend lines" pp 1-2; Exploring 2, Rate of change ; Exploring 4, "Line of best fit" Topic 6: Moving beyond slopeintercept: More practice, pages 4 and 7 Topic 7: Creating linear models for data: Exploring 2, "Rate of change" page 6; Exploring 4, "Line of best fit" page 2 (panel 4) S-ID 8. Compute (using technology) and Topic 7: Creating linear models California Department of Education Common Core State s Map January 16, 2013 Page 21

22 S-ID 9. MP 1. MP 2. Publisher Language 2 Primary Supporting interpret the correlation coefficient of for data: Exploring 4, "Line of a linear fit.* best fit" pp 2-3 Distinguish between correlation and Topic 7: Creating linear models causation.* for data: Exploring 2, "Rate of change" pp MATHEMATICAL PRACTICES Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Topic 5: Exploring rate of change in other situations: MARS Task: "Differences"; Advice for Instruction, Deliver Instruction, Block 5 Topic 10: Systems of linear equations and inequalities: MARS Task: "Pathways"; Advice for Instruction, Deliver Instruction, Block 5 Topic 12: Other nonlinear relationships: MARS Task: "Patchwork"; Advice for Instruction, Deliver Instruction, Block 2 Topic 10: Systems of linear equations and inequalities: MARS Task: "Pathways"; Advice for Instruction, Deliver Instruction, Block 5 Topic 12: Other nonlinear relationships: MARS Task: "Patchwork"; Advice for Instruction, Deliver Instruction, Block 2 California Department of Education Common Core State s Map January 16, 2013 Page 22

23 MP 3. Publisher Language 2 Primary Supporting Construct viable arguments and critique the reasoning of others. Topic 5: Exploring rate of change in other situations: MARS Task: "Differences"; Advice for Instruction, Deliver Instruction, Block 5 Topic 10: Systems of linear equations and inequalities: MARS Task: "Pathways"; Advice for Instruction, Deliver Instruction, Block 5 MP 4. Model with mathematics. Topic 7: Creating linear models for data: EX 2, "Rate of change" Topic 10: Systems of linear equations and inequalities: MARS Task: "Pathways"; Advice for Instruction, Deliver Instruction, Block 5 and equations: EX 1, "Comparing linear and exponential growth" MP 5. Use appropriate tools strategically. Topic 12: Other nonlinear relationships: MARS Task: "Patchwork"; Advice for Instruction, Deliver Instruction, Block 2 Topic 19: Modeling with quadratic functions: EX 1, "Using y = ax 2 + c to model data" and Exploring 3, "Completing the square," pages 1, 4, and 6 California Department of Education Common Core State s Map January 16, 2013 Page 23

24 Publisher Language 2 Primary Supporting MP 6. Attend to precision. Topic 1: Constructing graphs: Exploring 1, "Representing data" and Exploring 2 "Focus on the action," pg 4 Topic 4: Exploring rate of change in motion problems: Exploring 4, "What's my rate," page 3 MP 7. Look for and make use of structure. Topic 5: Exploring rate of change in other situations: MARS Task: "Differences"; Advice for Instruction, Deliver Instruction, Block 5 Topic 18: Operations on polynomials: Exploring 3, "Factoring" MP 8. Appendix Look for and express regularity in repeated reasoning. Topic 12: Other nonlinear relationships: MARS Task: "Patchwork"; Advice for Instruction, Deliver Instruction, Block 2 California Department of Education Posted March 2013 California Department of Education Common Core State s Map January 16, 2013 Page 24