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Pacing Guide VITAL INFORMATION Teacher Name Subject Area Sanctus Yanni Algebra 1 Date Grade / class Topic: Unit / Chapter / Section Unit 3: Linear Equations and Inequalities. Unit 4: Statistical Models Unit 5: Linear Systems and Piecewise-Defined Functions. Unit 6 Exponential Relationships Unit 7 Polynomial Operations February 2017- June 2017 Grade 8 Q3 W Standard Concept 1W AREI.D.12 A-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. 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. 1W S-ID.B.5 Skills 1) Graphing Linear Inequalities involving ā¤ šš ā„ 2) Graphing Linear Inequalities involving < šš > 3) Creating Models with Linear Inequalities. 1) 2) 3) 4) 5) 6) Categorical Data and Frequencies. Constructing Two-Way Frequency Tables. Reading Two-Way Frequency Tables. Relative frequencies. Two-Way Relative Frequency Tables. Conditional Relative Frequencies. Assessment Content Describe and graph linear inequalities with two variables. Ex: 30 + 5y ā„ 4x Unit 3: Module7: Linear Equations and Inequalities. Count frequency for categorical data. Measure relative frequency and conditional relative frequency. Using decimal, percent and fractions. Unit 4: Statistical Models. Module 8: Multivariable categorical Data. 7.3 Linear Inequalities in Two Variables 8.1 Two-Way Frequency Tables. 8.2 Relative Frequency 2W S-ID.A.1 S-ID.A.2 SID.B.6C S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 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.B.6C Fit a linear function for a scatter plot that suggests a linear association. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 1W 2W AREI.C.5 AREI.C.5 AREI.C.6 Exploring Data. Measures of Center: Mean and Median. Measures of Spread: Range and IQR. Using Dot Plots to display Data. Comparing Data Sets. Comparing Data Distributions. a. Symmetric, Skew-left, Skew-right. Understanding Histograms. Creating Histograms. Estimating from Histograms. Constructing Box Plots. (Box and whiskers) Comparing Box Plots. (two Box plots) Describing How Variables are related in Scatter Plots. (negative, positive, no correlation) Estimating the Correlation Coefficient of a Linear Fit. (describe correlation negative/positive, weak/strong) Fitting Linear Functions to Data. (Line of best fit) Find mean, median, range and IQR for a data set. Describe data distribution. Decide whether a value is an outlier. Plot a line plot. Graph a histogram Make a box plot. Describe a scatter plot. Make a line of best fit. Estimate a correlation coefficient. 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. 1) Types of Systems of Linear Equations. 2) Solving Consistent, Independent Linear systems by graphing. (solving by graphing, consistent/inconsistent, Independent/dependent systems) 3) Solving Special Linear Systems by Graphing. (inconsistent) 4) Estimating solutions of linear systems by graphing. 5) Interpreting Graphs of linear systems to solve problems. (word problems) Graph a system of linear equations. Find the solution of a system by graphing. Estimate the solution from the graph. 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., 1) Exploring the substitution Method of solving Linear systems. 2) Solving consistent, independent Linear systems by substitution. (solving by substitution) 3) Solving Special Linear Systems by substitution. (Proving no solution to parallel lines) 4) Solving Linear System Models by Substitution. (Word Problems) 1) Exploring the Effects of adding Equations. (Elimination) Solve linear systems by substitution. Decide is one solution, infinite solutions, or no solutions. Unit 4: Module 9: OneVariable Data Distributions. 9.1 Measures of center and spread 9.2 Data distributions and outliers. 9.3 Histograms and Box Plots. Unit 4: Module 10: Linear Modeling and Regression. 10.1 Scatter Plots and Trend Lines. Unit 5: Linear Systems and Piecewise-Defined Functions. Module 11: Solving Systems of Linear Equations. 11.1 Solving Linear Systems by Graphing. Solve linear systems by Elimination. Solve linear systems by multiplying first. 11.2 Solving Linear systems by Substitution. 11.3 Solving Linear Systems by adding or subtracting. 11.4 Solving Linear Systems by Multiplying First. with graphs), focusing on pairs of linear equations in two variables. 2W ACED.A.3 AREI.D.12 A-CED.A.3 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 describing nutritional and cost constraints on combinations of different foods. A-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. 2) Solving Special Linear Systems by Adding or Subtracting. 3) Solving Linear System Models by Adding or Subtracting. (Word Problems 1) Understanding Linear Systems and Multiplication. 2) Solving Linear Systems by Multiplying First. 3) Solving Linear system models by multiplying first. (Word Problems) 1) Creating Linear System Models by changing Parameters. 2) Creating Linear System Models from Verbal Descriptions. 3) Creating Linear System Models from Tables. 4) Creating Linear System Models from Graphs. 5) Determining Solutions of Systems of Linear Inequalities. 6) Solving Systems of Linear Inequalities by Graphing. 7) Graphing Systems of Inequalities with Parallel Boundary Lines. 8) Modeling Real-world constraints with Systems. 9) Modeling Real-world constraints with systems of linear equations. 10) Modeling Real-world constraints with systems of Linear inequalities. Interpret word problem to a system of linear equations. Create a system of linear equation from a table or from a graph. Graph a system of linear inequalities and find the solution. Unit 5: Module 12: Modeling with Linear Systems. 12.1 Creating Systems of Linear Equations. 12.2 Graphing Systems of Linear Inequalities. 12.3 Modeling with linear systems. Q4 2W 1.5W AREI.B.3 FIF.C.7B NRN.A.1 NRN.A.2 A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. F-IF.C.7B Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. 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 1) 2) 3) 4) 5) Exploring Piecewise-defined function Models. Evaluating Piecewise-defined functions. Graphing Piecewise-defined functions. Modeling with piecewise-defined functions. Building piecewise-defined functions from graphs. 1) Understanding the Parent Absolute Value Function. 2) Graphing Translations of Absolute Value Functions. (š(š„) = |š„ ā ā| + š) 3) Constructing Functions for Given Graphs of Absolute Value Functions. 4) Solving Absolute Value Equations Graphically. (Disjunction āx= or x=ā) 5) Solving Absolute Value Equations Algebraically. 6) Absolute Value Equations with Fewer than Two Solutions. 7) Visualizing the solution set of an absolute value inequality. 8) Solving Absolute Value Inequalities Graphically. 9) Solving Absolute Value Inequalities Algebraically. 10) Solving a real-world problem with absolute value inequalities. Understanding Integer Exponents. 1) Exploring Rational Exponents. ć(ać^(1/2)) 2) Simplifying Numerical Expressions with n^th roots. 3) Simplifying Numerical Expressions with rational exponents. 1) Exploring Operations with Rational and Irrational Numbers. 2) Simplifying Multivariable Expressions Containing Radicals. (22 ā 22 ) 3) Simplifying Multivariable Expressions Containing Rational Exponents. 4) Simplifying Real-World Expressions with Rational Exponents. Evaluate a piecewise function for a given value. Graph piecewise function. Write and equation for a piecewise graph. Unit 5: module 13: PiecewiseDefined Functions. Graph absolute value function. Write an equation from graph. 13.2 Absolute Value Functions and Transformations. Solve absolute value equations. 13.1 Understanding piecewisedefined functions. 13.3 Solving Absolute Value Equations. 13.4 Solving Absolute Value Inequalities. Solve absolute value inequalities. Evaluate exponential expressions. Simplify exponential expressions. Simplify algebraic exponential expressions. Unit 6: Exponential Relationships. Module 14: Rational Exponents and Radicals. 14.1 Understanding Rational Exponents and Radicals. 14.2 Simplifying Expressions with Rational Exponents and Radicals. 2.5 W 2W ASSE.A.1a AAPR.A.1 AAPR.A.1 using the properties of exponents A-SSE.A.1a Interpret expressions that represent a quantity in terms of its context. A-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. A-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. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) Identifying Monomials Classifying Polynomials Writing Polynomials in Standard Form Simplifying Polynomials Evaluating Polynomials Modeling Polynomial Addition Using Algebra Tiles Adding Polynomials Using a Vertical Format Adding Polynomials Using a Horizontal Format Modeling with Polynomials Modeling Polynomial Subtraction Using Algebra Tiles Subtracting Polynomials Using a Vertical Format Subtracting Polynomials Using a Horizontal Format Modeling with Polynomials Classify polynomials by degree an terms. Simplify polynomials. 1) 2) 3) 4) Modeling Polynomial Multiplication Multiplying Monomials Multiplying a Polynomial by a Monomial Multiplying a Polynomial by a Monomial to Solve a Real-World Problem Modeling Binomial Multiplication Multiplying Binomials Using the Distributive Property Multiplying Binomials Using FOIL Multiplying Polynomials Modeling with Polynomial Multiplication Modeling Special Products Multiplying (a + b)2 Multiplying (a - b)2 Multiplying (a + b) (a - b) Modeling with Special Products Multiply monomials, Multiply binomials, Multiply trinomials. 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) Find sum of polynomials. Find difference of polynomials. Unit 7 Polynomial Operations Module 17 Adding and Subtracting Polynomials Lesson 17.1 Understanding Polynomial Expressions Lesson 17.2 Adding Polynomial Expressions Lesson 17.3 Subtracting Polynomial Expressions Module 18 Multiplying and Dividing Polynomials Lesson 18.1 Multiplying Polynomial Expressions by Monomials Lesson 18.2 Multiplying Polynomial Expressions Lesson 18.3 Special Products of Binomials