Integrated Math I: A Common Core Program Software and Textbook Scope & Sequence

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1 Unit 1: Relationships Between Quantities and Reasoning with Equations Chapter Lesson Title Key Math Objective A Picture is Worth a Thousand Words Understanding Quantities and Their Relationships 1.2 A Sort of Sorts Analyzing and Sorting Graphs There Are Many Ways to Represent Functions Function Families for 200 Alex Recognizing Algebraic and Graphical Representations of Functions Recognizing Functions by Characteristics 2.1 The Plane! Modeling Linear Situations 2.2 What Goes UP Must Come Down Problem Solving Using Multiple Methods 2.3 Scouting for Prizes! Modeling Inequalities 2.4 We're Shipping Out 2.5 Play Ball! 2.6 Choose Wisely! Quantities and Relationships Graphs, Equations & Inequalities Solving and Graphing Compound Inequalities Absolute Value Equations and Inequalities Understanding Non-Linear Graphs and Inequalities CCSS N.Q.2 F.LE.1.b F.IF.1 F.IF.5 F.IF.5, F.IF.9, A.REI.10 F.IF.1, F.IF.2, F.IF.7.a F.IF.1, F.IF.4, F.IF.7.a, F.IF.9 F.LE.1.b, F.LE.2 A.CED.2 A.REI.1, A.CED.1 A.CED.2 N.Q.1 A.SSE.1 A.REI.3, A.CED.1, A.CED.2 N.Q.1, A.SSE.1 A.CED.1, A.CED.2, A.CED.3 A.CED.1 A.CED.2 A.REI.3 A.CED.1 A.CED.2 A.CED.3 N.Q.1 A.CED.1 A.CED.2 A.CED.3 Key Terms the dependent quantity, independent quantity Relations and Functions discrete graph, continuous graph, relation, domain, range, function, Vertical Line Test function notation, increasing function, decreasing function, constant function, function family, linear functions, exponential functions, absolute minimum, absolute maximum, quadratic functions, linear absolute value functions, linear piecewise functions Section 1: Recognizing Non-Numeric Functions Section 2: Recognizing Numeric Functions Section 3: Recognizing Graphs of Functions Section 4: Classifying Relations and Functions Graphs of Functions Section 1: Identifying Key Characteristics of Graphs of Functions first differences, solution, point of intersection solve an inequality solution of a compound inequality, conjunction, disjunction opposites; absolute value; linear absolute value equation; linear absolute value inequality; equivalent compound inequality Linear and Four Quadrant Graphs Linear Equation and Inequality Solving with Graphs Linear Inequalities Absolute Value Equations and Inequalities Non-Linear Equation and Inequality Solving with Graphs This chapter introduces non-linear functions, including exponential, quadratic, linear piecewise, and linear absolute value functions. Students will classify each function family using graphing calculators, equations and graphs. Each function family is then defined and graphic organizers are created. The purpose is to review solving linear equations, understand the relationship between the graph and the solution to equations and inequalities, and generalize to all functions. We need to figure out a clever way to address N.Q.3 Section 1: Graphing with Positive Integer Rates of Change Section 2: Graphing with Positive Fractional Rates of Change Section 3: Graphing with Negative Rates of Change Section 1: Solving Linear Equations and Inequalities Graphically Section 1: Graphing Inequalities Section 2: Graphing Compound Inequalities Section 3: Graphing Compound Inequalities with Non-Standard Solutions Section 4: Solving Linear Inequalities Section 5: Solving Compound Linear Inequalities Section 1: Solving Simple Absolute Value Equations Section 2: Solving Absolute Value Equations Section 3: Solving Simple Absolute Value Inequalities Section 4: Solving Simple Absolute Value Inequalities with Non-Standard Solutions Section 5: Solving Absolute Value Inequalities Section 1: Solving Non-Linear Equations and Inequalities Graphically Integrated Math 1: A Common Core Program 1

2 3 Linear Functions Purpose is recall as well as driving to seeing component parts and interpreting appropriately. 3.1 Is it Getting Hot in Here? Modeling Data Using Linear Regression S.ID.6, S.ID.7, N.Q.2, A.REI.3 linear regression, line of best fit, linear regression equation, significant digits, correlation coefficient 3.2 Tickets For Sale 3.3 Cool As a Cucumber or Hot Like a Tamale! Standard Form of Linear Equations Literal Equations in Standard and Slope-Intercept Form 3.4 A Growing Business Combining Linear Equations A.SSE.1 A.CED.2 A.CED.3 A.CED.4 A.REI.3 A.CED.2 A.CED.4 A.REI.1 A.SSE.1 A.CED.2 A.CED.3 A.REI.3 standard form; slope-intercept form Linear in General Form literal equation Literal Equations Linear and the Distributive Property Equations of a Line Linear Function Operations and Composition Section 1: Modeling with Linear Inequalities Section 2: Modeling Linear Equations in General Form Section 1: Solving Literal Equations with Variable Terms on the Same Side (No Type In) Section 2: Solving Literal Equations with Variable Terms on the Same Side (Type In) Section 3: Solving Literal Equations with Variable Terms on Opposite Sides (No Type In) Section 4: Solving Literal Equations with Variable Terms on Opposite Sides (Type In) Section 5: Solving Literal Equations (No Type In) Section 6: Solving Literal Equations (Type In) Section 1: Modeling with Integer Rates of Change Section 2: Modeling with Fractional Rates of Change Section 3: Modeling using the Distributive Property over Division Section 4: Modeling More Complex Equations Section 1: Modeling Given Slope and a Point Section 2: Calculating Slopes Section 3: Modeling Given Two Points Section 4: Modeling Given an Initial Point Section 1: Evaluating Linear Functions Section 2: Adding and Subtracting Linear Functions Section 3: Modeling with Linear Function Composition Section 4: Composing Linear Functions Integrated Math 1: A Common Core Program 2

3 Unit 2: Linear and Exponential Relationships Chapter Lesson Title Key Math Objective CCSS Key Terms the Is There a Pattern Here? The Password Is Operations! The Power of Algebra is a Curious Thing Thank Goodness Descartes Didn't Drink Some Warm Milk! Well, Maybe It IS a Function! Sequences Recognizing Patterns and Sequences Arithmetic and Geometric Sequences Using Formulas to Determine Terms of a Sequence Graphs of Sequences Sequences and Functions Graphs of Linear and Exponential Functions This chapter sequences, and focuses on arithmetic and geometric sequences. Sequences are described using recursive and explicit formulas. The relationship between arithmetic and geometric sequences, and linear and exponential functions is developed. F.LE.1.b F.LE.2 F.BF.1.a F.BF.1, F.BF.1.a F.BF.2, A.SSE.1 A.SSE.1.a F.IF.1, F.IF.4 F.LE.2 F.IF.1, F.IF.2, F.IF.3,F.BF.1, F.BF.2,F.LE.1, F.LE.1.a,F.LE.1.b, F.LE.1.c,F.LE.2, F.LE.5 sequence, term of a sequence, infinite sequence, finite sequence arithmetic sequence, common difference, geometric sequence, common ratio Sequences Sequences and Functions index, explicit formula, recursive formula ` Section 1: Describing Patterns in Sequences Section 2: Writing Recursive Formulas Section 3: Writing Explicit Formulas Section 1: Writing Sequences as Functions This chapter examines the graphical behavior of exponential functions, including domain, range, increasing or decreasing, and asymptotes. Transformations of exponential functions are addressed. The relationship between rational exponents and radical form is introduced. Common bases are used to solve simple exponential equations algebraically. 5.1 Go for the Curve! Downtown and Uptown Let the Transformations Begin! Take Some Time to Reflect Radical! Because It's Cliché! Comparing Linear and Exponental Functions Graphs of Exponential Functions Translations of Linear and Exponential Functions Reflections of Linear and Exponential Functions Properties of Rational Exponents A.SSE.1.a, A.SSE.1.b, A.CED.1, F.IF.3, F.IF.6, F.IF.7.e, F.BF.1.a, F.BF.2, F.LE.1.a, F.LE.1.b, F.LE.1.c, F.LE.2, F.LE.3,F.LE.5 A.SSE.1.a, A.SSE.1.b, A.CED.1, A.REI.11, F.IF.4, F.IF.7.e, F.LE.5 F.BF.3 A.REI.10 F.IF.4 A.REI.10 N.RN.1 N.RN.2 simple interest, compound interest Exponential horizontal asymptote basic function, transformation, vertical translation, horizontal translation, argument of a function reflection, line of reflection cube root, index, nth root, radicand, rational exponent Graphs of Exponential Functions Linear and Exponential Transformations Properties of Exponents Section 1: Modeling Equations with Starting Points of One Section 2: Modeling Equations with Starting Points Other Than One Section 1: Identifying Key Characteristics of Exponential Functions Section 1: Shifting Vertically Section 2: Reflecting and Dilating using Graphs Section 3: Shifting Horizontally Section 4: Transforming using Tables of Values Section 5: Using Multiple Transformations Section 1: Using the Product Rule Section 2: Using the Quotient Rule Section 3: Using the Power to a Power Rule Section 4: Using the Product to a Power Rule Section 5: Using the Quotient to a Power Rule Section 6: Using Properties of Exponents with Whole Number Powers Section 7: Simplifying Expressions with Negative Exponents Section 8: Using Properties of Exponents with Integer Powers A.REI.3, A.CED.1, 5.6 Checkmate! Solving Exponential Functions A.CED.2, N.Q.2, A.REI.10, A.REI.11 Integrated Math 1: A Common Core Program 3

4 Unit 3: Reasoning with Equations Chapter Lesson Title Prepping for the Robot Challenge Systems of Equations Key Math Objective Solving Linear Systems Grpahically and Algebraically CCSS A.REI.5 A.REI.6 A.REI.10 A.REI.11 Key Terms system of linear equations; break-even point; substituion method; consistent systems; inconsistent systems the This chapter focuses on solving systems of linear equations graphically and algebraically using the substitution method or the linear combinations method. Systems of Linear Equations Modeling Section 1: Solving Linear Systems using Integers Section 2: Solving Linear Systems using Decimals 6.2 There's Another Way? Using Linear Combinations to Solve a Linear System A.REI.5 A.REI.6 A.REI.10 A.REI.11 linear combinations method Linear System Solving using Substitution Section 1: Solving Linear Systems using Substitution 6.3 What's For Lunch? Solving More Systems A.REI.5 A.REI.6 A.REI.10 A.REI.11 Linear System Solving using Linear Combinations Section 1: Solving Linear Systems using Linear Combinations Section 2: Solving Linear Systems using Student's Choice 6.4 Which is the Best Method? Using Graphing, Substitution, and Linear Combinations A.REI.6 A.REI.10 A.REI The Playoffs Graphing Inequalities A.REI.12 half-plane 7.2 Working the System Systems of Linear Inequalities A.REI.12 contraints; solution of a linear inequality Our Biggest Sale of the Season! Take it to the Max or Min Systems of Inequalities Systems with More than Two Linear Inequalities This chapter introduces linear inequalities in two variables and then extends to systems of linear inequalities. System of inequalities are used to represent constraints and a maximizing or minimizing function is determined. A.REI.12 Linear Programming A.REI.12 linear programming Graphs of Linear Inequalities in Two Variables Systems of Linear Inequalities Section 1: Graphing Linear Inequalities in Two Variables Section 1: Systems of Linear Inequalities Integrated Math 1: A Common Core Program 4

5 Unit 4: Descriptive Statistics Chapter Lesson Title Key Math Objective CCSS Key Terms Start Your Day the Right Way Which Measure Is Better? Whose Scores Are Better? 8.4 You Are Too Far Away! Analyzing Data Sets for One Variable Putting the Pieces Together Graphically Representing Data S.ID.1, S.ID.3 Determining the Best Measure of Center for a Data Set Calculating and Interpreting Standard Deviation Calculating IQR and Identifying Outliers S.ID.1 S.ID.2, S.ID.3 dot plot, discrete data, distribution of data symmetric, skewed right, skewed left, box plot, five number summary, histogram, continuous data statistic, measure of central tendency, mean, median the S.ID.1 S.ID.2, S.ID.3 standard deviation S.ID.1 S.ID.2, S.ID.3 interquartile range (IQR), outlier, lower fence, upper fence Analyzing and Interpreting Data S.ID.1, S.ID.2, S.ID.3 stem-and-leaf plot side-by-side stem-and-leaf plot Analyzing Data Sets for Two Quantitative Variables 9.1 Like a Glove Least Squares Regression S.ID.6a S.ID.6.c S.ID.7 interpolation extrapolation least squares regression line This chapter focuses on data in one variable through the use of visual displays and summarizing statistics. Emphasis is placed on interpreting data and using appropriate techniques to describe data. Measures of Central Tendency Categorical Data Display Comaprisons Numerical Data Display Comparisons Mean Absolute Deviation Variance and Standard Deviation Lines of Best Fit Section 1: Calculating Mean, Median, Mode, and Range Section 2: Determining Appropriate Measures Section 3: Measuring the Effects of Changing Data Sets Section 4: Calculating a Data Value Given a Mean Section 1: Comparing Displays of Categorical Data Section 1: Comparing Histograms, Dot Plots, and Stem and Leaf Plots Section 2: Comparing Box and Whisker Plots Section 1: Calculating Mean Absolute Deviation Section 2: Using Mean Absolute Deviation Section 1: Computing Variants and Standard Deviation Section 1: Estimating Lines of Best Fit Section 2: Using Lines of Best Fit This chapter focuses on data in two variables through the scatter plots and regression equations. Emphasis is placed on determining the appropriate function to model a set of data and analyzing how well the regression equation fits the data. 9.2 Gotta Keep It Correlatin' Correlation S.ID.7 S.ID.8 S.ID.6a S.ID.6c Line of Best Fit Section 1: Interpreting Lines of Best Fit Section 2: Analyzing Residuals of Lines of Best Fit 9.3 The Residual Effect Creating Residual Plots To Fit or Not To Fit? That Is The Question! Who Are You? Who? Who? Could You Participate in Our Survey? Using Residual Plots Causation vs. Correlation Analyzing Data Sets for Two Categorical Variables Interpreting Frequency Distributions S.ID.6.a S.ID.6.b S.ID.7 S.ID.8 S.ID.6.a S.ID.6.b S.ID.7 S.ID.8 S.ID.9 S.ID.5 residual causation necessary condition sufficient condition common response confounding variable residual plot categorical data, two-way frequency table, frequency distribution, joint frequency, marginal frequency distribution This chapter focuses on categorical data in two variables through the use of visual displays and summarizing statistics. Emphasis is placed on interpreting data and using appropriate techniques to describe data It's So Hot Outside! Relative Frequency Distribution S.ID She Blinded Me with Science! Relative Frequency Conditional Distribution S.ID.5 relative frequency distribution, relative frequency marginal distribution relative frequency, conditional distribution Frequency and Relative Frequency Section 1: Reading Visual Displays of Frequency Tables 10.4 Oh! Switch the Station! Drawing Conclusions from Data S.ID.5 Integrated Math 1: A Common Core Program 5

6 Let's Take a Little Trip Every Graph Tells a Story Whodunit? The Function Family Line- Up People, Tea, and Carbon Dioxide 11.4 BAC is BAD News Mathematical Modeling Modeling Data with Curves of Best Fit Modeling Using Exponential Functions Choosing the Best Function to Model Data This chapter presents opportunities to model real-world data using linear and exponential functions. The focus is on determining the appropriate function or functions for a given data set. F.IF.4 F.IF.5 F.IF.4 F.IF.5 F.LE.1.b F.IF.4, F.IF.5, F.IF.7, F.BF.1, F.BF.4, F.LE.1, F.LE.2 F.IF.4, F.IF.5, F.IF.7, F.BF.1, F.BF.4,F.LE.1, F.LE.2 Curve of Best Fit Linear and Non-Linear Regression Section 1: Interpreting Curves of Best Fit Section 2:Analyzing Residuals of Curves of Best Fit Section 1: Analyzing Lines and Curves of Best Fit Integrated Math 1: A Common Core Program 6

7 Unit 5: Congruence, Proof, and Constructions Chapter Lesson Title Key Math Objective CCSS 12 Geometry on the Key Terms the This chapter uses distance, midpoint, and slope to examine segments and lines in the coordinate plane. Patty paper and constructions are used to duplicate segments and angles, bisect segments and angles, create parallel and perpendicular lines, and create triangles and quadrilaterals Let's Move! Translating and Constructing Line Segments G.CO.1, G.CO.2, G.CO.4, G.CO.5, G.CO.6, G.CO.12, G.CO.13, Distance Formula, transformation, rigid motion, translation, image, preimage, arc, congruent line segments, conrguent, intersection, copy (duplicating) a line segment* Distance and Midpoint Section 1: Finding Distances using the Pythagorean Theorem Section 2: Finding Distances using the Distance Formula Section 3: Finding Midpoints Section 4: Finding Distances and Midpoints 12.2 Treasure Hunt Midpoints and Bisectors 12.3 It's All About Angles Did You Find a Parking Space? Making Copies- Just as Perfect as the Original Slide, Flip, Turn: The Latest Dance Craze? Translating and Constructing Angles and Angle Bisectors Parallel and Perpendicular Lines in the Constructing Perpendicular Lines, Parallel Lines, and Polygons Translating, Rotating, and Reflecting Geometric Figures 13.2 All The Same To You Congruent Triangles 13.3 Side-Side-Side SSS Congruence Theorem 13.4 Side-Angle-Side SAS Congruence Theorem Congruence Through Transformations You Shouldn't Make Assumptions Ahhhhh We're Sorry We Didn't Include You Angle-Side-Angle Congruence Theorem Angle-Angle-Side Congruent Theorem G.CO.12, G.GPE.6,, G.GPE.6 G.CO.1, G.CO.2, G.CO.4, G.CO.5, G.CO.6, G.CO.12 G.CO.1, G.GPE.4, Midpoint, Midpoint Formula, segment bisector, Bisect a Line Segment* angle, angle bisector, Copying (duplicating) an Angle*, Bisecting an Angle* point-slope form, G.CO.12, G.CO.13 G.CO.2 G.CO.4 G.CO.5 G.CO.6 G.CO.7 G.CO.8 G.CO.6, G.CO.7, G.CO.8, G.CO.12 G.CO.6, G.CO.7, G.CO.8, G.CO.12 G.CO.6, G.CO.7, G.CO.8, G.CO.12 G.CO.6, G.CO.7, G.CO.8 rotation, angle of rotation, point of rotation, reflection, line of reflection congruent angles, corresponding sides, corresponding angles theorem, postulate, SSS Congruence Theorem SAS Congruent Theorem, included angles ASA Congruence, included side AAS Congruence Theorem, non-included side Parallel and Perpendicular Lines Translations of Plane Figures Rotations of Plane Figures Reflections of Plane Figures Section 1: Modeling Parallel and Perpendicular Lines This chapter addresses transformations of figures on the coordinate plane, focusing on similarity and congruence, and the effects of transformation on coordinates. Conditions for triangle congruence are explored and congruent triangles are constructed using these conditions. Section 1: Translating Plane Figures Section 1: Rotating Plane Figures Section 1: Reflecting Plane Figures Integrated Math 1: A Common Core Program 7

8 Unit 6: Connecting Algebra and Geometry Through Coordinates Chapter Transforming to a New Level! Looking at Something Familiar in a New Way One Figure, Many Names 14.4 Let's Go Halfsies! Name That Triangle! Lesson Title Key Math Objective CCSS Key Terms Perimeter and Area of Geometric Figures on the Name That Quadrilateral! Is That Point On the Circle? Name That Point on a Circle Using Transformation to Determine Perimeter and Area Area and Perimeter of Triangles on the Area and Perimeter of Parallelograms on the Determining the Perimeter and Area of Trapezoids and Composite Figures Connecting Algebra and Geometry with Polygons A Little Dash of Logic What's Your Conclusion? Classifying Triangles on the Classifying Quadrilaterals on the Determining Points on a Circle G.GPE.4 Circles and Points on the Logic Two Methods of Logical Reasoning Understanding Conditional Statements, Arguments, and Truth Tables bases of a trapezoid, legs of a trapezoid, regular polygon, composite figure the Perimeter and Area of Triangles and Quadrilaterals Section 1: Calculating Perimeter and Area of Squares and Rectangles Section 2: Calculating Perimeter and Area of Parallelograms Section 3: Calculating Perimeter and Area of Triangles Section 4: Calculating Perimeter and Area of Trapezoids Section 5: Calculating Area of Composite Figures G.GPE.4 Triangle Classification Section 1: Classifying Triangles G.GPE.4 Polygon Classification G.GPE.4 induction deduction conditional statement, propositional form, propositional variables, hypothesis, conclusion, truth table, truth value, converse, inverse, contrapositive, logically equivalent, biconditional statement This chapter focuses on using slope and distance to classify triangles and quadrilaterals in the coordinate plane. Given a subset of vertices and a set of conditions, the remaining possible vertices are determined. This chapter introduces methods of reasoning and logical thinking to serve as a preview to formal proofs that will be expected in the next course. This chapter focuses on calculating perimeter and area of figures represented in the coordinate plane, through the use of distance, midpoint, and slope. Circles in the coordinate plane are represented using a standard equation. Section 1: Classifying Quadrilaterals Section 2: Classifying Polygons Proofs Aren't Just for Geometry Your Oldest Likes Spinach? Shoes and Math Scores? Introduction to Direct and Indirect Proof with the Properties of Numbers Using Logic to Solve Problems, Part 1 Using Logice to Solve Problems, Part 2 proof by contradiction Integrated Math 1: A Common Core Program 8