4th Quarter Pacing Guide LESSON PLANNING

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1 Domain: Reasoning with Equations and Inequalities Cluster: Solve equations and inequalities in one variable KCAS: A.REI.4a: Solve quadratic equations in one variable. 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. (1) 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. (2) Solve quadratic equations in one variable. (3) Notes from Appendix A: Students should learn of the existence of the complex number system, but will not solve quadratics with complex solutions until Algebra II. (4) Derive the quadratic formula by completing the square on a quadratic equation in x.

2 Domain: Reasoning with Equations and Inequalities Cluster: Solve equations and inequalities in one variable KCAS: A.REI.4b: Solve quadratic equations in one variable. b. 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. (1) Solve quadratic equations by various methods and justify the method used (2) Understand properties of complex numbers and express complex solutions as a ± bi

3 Domain: Interpreting Functions Cluster: Analyze functions using different representations KCAS: F.IF.7b: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*(modeling standard) b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. (1) Graph square root, cube root, and piecewise- defined functions, including step functions and absolute value functions, by hand in simple cases or using technology for more complicated cases, and show/label key features of the graph.

4 Domain: Interpreting Categorical and Quantitative Data Cluster: Summarize, represent, and interpret data on a single count or measurement variable Standard: S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). (Statistics and Probability is a Modeling Conceptual Category.) (1) Represent data with plots on the real number line using various display types by creating dot plots, histograms and box plots.

5 Domain: Interpreting Categorical and Quantitative Data Cluster: Summarize, represent, and interpret data on a single count or measurement variable Standard: 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. (Statistics and Probability is a Modeling Conceptual Category.) (1) Choose the appropriate measure for center (mean, median) and spread (interquartile range, standard deviation) based on the shape of a data distribution. (2) Use appropriate statistics for center and spread to compare two or more data sets.

6 Domain: Interpreting Categorical and Quantitative Data Cluster: Summarize, represent, and interpret data on a single count or measurement variable Standard: S.ID.3: Interpret differences in shape, center and spread in the context of data sets, accounting for possible effects of extreme data points (outliers). (Statistics and Probability is a Modeling Conceptual Category.) (1) Define the context of data sets as meaning the specific nature of the attributes under investigation. (2) Interpret differences in shape, center and spread in the context of data sets. (3) Describe the possible effects the presence of outliers in a set of data can have on shape, center, and spread in the context of the data sets.

7 Domain: Interpreting Categorical and Quantitative Data Cluster: Summarize, represent, and interpret data on two categorical and quantitative variables Standard: 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. (Statistics and Probability is a Modeling Conceptual Category.) (1) Recognize the differences between joint, marginal and conditional relative frequencies. (2) Calculate relative frequencies including joint, marginal and conditional relative frequencies. (3) Summarize categorical data for two categories in two-way frequency tables. (4) Interpret relative frequencies in the context of the data. (5) Recognize possible associations and trends in the data.

8 Domain: Linear, Quadratic, and Exponential Models *(Modeling Domain) Cluster: Construct and compare linear, quadratic, and exponential models and solve problems Standard: F.LE.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. (1) Fluently compute growth rates for linear, exponential and quadratic functions. (2) Informally define the concept of end behavior. (3) Compare tables and graphs of exponential and other polynomial functions to observe that a quantity increasing exponentially exceeds all others to solve mathematical and real-world problems. (3) Notes from Appendix A: Compare linear and exponential growth to quadratic growth.

9 Domain: Reasoning with Equations and Inequalities Cluster: Solve systems of equations Standard: A.REI.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 x2 + y2 = 3 (1) Transform a simple system consisting of a linear equation and a quadratic equation in 2 variables so that a solution can be found algebraically and graphically. (2) Include systems consisting of one linear and one quadratic equation. Include systems that lead to work with fractions. For example, finding the intersections between x 2 y 2 1 and y = x 1/2 leads to the point (3/5, 4/5) on the unit circle, corresponding to the Pythagorean triple of (3) Explain the correspondence between the algebraic & graphical solutions to a simple system consisting of a linear equation and a quadratic equation in 2 variables.