SADLIER New York Progress Mathematics Correlated to the New York State Common Core Mathematics Curriculum Contents Grade 8 2 Module 1: Integer Exponents and Scientific Notation 4 Module 2: The Concept of Congruence 7 Module 3: Similarity 9 Module 4: Linear Equations 13 Module 5: Examples of Functions from Geometry 15 Module 6: Linear Functions 18 Module 7: Introduction to Irrational Numbers Using Geometry William H. Sadlier, Inc. www.sadlierschool.com 800-221-5175
Module 1 Integer Exponents and Scientific Notation Topic A: Exponential Notation and Properties of Integer Exponents Instructional Days: 6 Lesson 1: Exponential Notation (S) Lesson 2: Multiplication and Division of Numbers in Exponential Form (S) 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 3 5 = 3 3 = 1/3 3 = 1/27. Lesson 3 Understand Zero and Negative Exponent pp. 32 39 Lesson 4 Learn Properties of Exponents pp. 40 47 Lesson 3: Numbers in Exponential Form Raised to a Power (S) Lesson 5 Use Properties of Exponents Generate Equivalent Expressions pp. 48 55 Lesson 4: Numbers Raised to the Zeroth Power (E) Lesson 5: Negative Exponents and the Laws of Exponents (S) Lesson 6: Proofs of Laws of Exponents (S) Mid Module Assessment and Rubric Topic A (assessment 1 day, return 1 day, remediation or further applications 1 day) Topic B: Magnitude and Scientific Notation Instructional Days: 7 Lesson 7: Magnitude (P) Lesson 8: Estimating Quantities (P) Lesson 9: Scientific Notation (P) Lesson 10: Operations with Numbers in Scientific Notation (P) 8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 10 8 and the continued on next page Lesson 8 Estimate and Compare Large or Small Quantities pp. 72 79 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 2
Module 1 Integer Exponents and Scientific Notation Lesson 11: Efficacy of Scientific Notation (S) continued from previous page Lesson 12: Choice of Unit (E) Lesson 13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology (E) 8.EE.A.4 population of the world as 7 times 10 9, and determine that the world population is more than 20 times larger. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Lesson 9 Calculate with Numbers in Scientific Notation pp. 80 87 End of Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 3
Module 2 The Concept of Congruence Topic A: Definitions and Properties of the Basic Rigid Motions Instructional Days: 6 Lesson 1: Why Move Things Around? (E) Lesson 2: Definition of Translation and Three Basic Properties (P) Lesson 3: Translating Lines (S) Lesson 4: Definition of Reflection and Basic Properties (P) Lesson 5: Definition of Rotation and Basic Properties (S) Lesson 6: Rotations of 180 Degrees (P) 8.G.A.1 8.G.A.1a Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length. Lesson 23 Verify Properties of Reflections and Translations pp. 204 211 Lesson 24 Verify Properties of Rotations pp. 212 219 8.G.A.1b Angles are taken to angles of the same measure. Lesson 23 Verify Properties of Reflections and Translations pp. 204 211 Lesson 24 Verify Properties of Rotations pp. 212 219 8.G.A.1c Parallel lines are taken to parallel lines. Lesson 23 Verify Properties of Reflections and Translations pp. 204 211 Lesson 24 Verify Properties of Rotations pp. 212 219 Topic B: Sequencing the Basic Rigid Motions Instructional Days: 4 Lesson 7: Sequencing Translations (E) Lesson 8: Sequencing Reflections and Translations (S) Lesson 9: Sequencing Rotations (E) Lesson 10: Sequences of Rigid Motions (P) 8.G.A.2 Understand that a two dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Lesson 25 Understand and Identify Congruent Figures pp. 220 227 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 4
Module 2 The Concept of Congruence Mid Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days) Topic C: Congruence and Angle Relationships Instructional Days: 4 Lesson 11: Definition of Congruence and Some Basic Properties (S) Lesson 12: Angles Associated with Parallel Lines (E) Lesson 13: Angle Sum of a Triangle (E) Lesson 14: More on the Angles of a Triangle (S) 8.G.A.2 8.G.A.5 Understand that a two dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Lesson 25 Lesson 30 Lesson 31 Understand and Identify Congruent Figures pp. 220 227 Establish Facts about Parallel Lines and Angles pp. 260 265 Establish Facts about Triangles and Angles pp. 266 275 End of Module Assessment and Rubric Topics A through C (assessment 1 day, return 1 day, remediation or further applications 3 days) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 5
Module 2 The Concept of Congruence OPTIONAL Topic D: The Pythagorean Theorem Instructional Days: 2 Lesson 15: Informal Proof of the Pythagorean Theorem (S) 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. Lesson 32 Understand the Pythagorean Theorem pp. 276 283 Lesson 16: Applications of the Pythagorean Theorem (P) Lesson 33 Understand the Converse of the Pythagorean Theorem pp. 284 291 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. Lesson 34 Problem Solving: The Pythagorean Theorem pp. 292 299 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 6
Module 3 Similarity Topic A: Dilation Instructional Days: 7 Lesson 1: What Lies Behind Same Shape? (E) Lesson 2: Properties of Dilations (P) Lesson 3: Examples of Dilations (P) 8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two dimensional figures using coordinates. Lesson 26 Lesson 27 Reflect and Translate Figures on the Coordinate Plane pp. 228 235 Rotate Figures on the Coordinate Plane pp. 236 243 Lesson 4: Fundamental Theorem of Similarity (FTS) (S) Lesson 5: First Consequences of FTS (P) Lesson 28 Dilate Figures on the Coordinate Plane pp. 244 251 Lesson 6: Dilations on the Coordinate Plane (P) Lesson 7: Informal Proofs of Properties of Dilations (Optional) (S) Mid Module Assessment and Rubric Topic A (assessment 1 day, return 1 day, remediation or further applications 3 days) Topic B: Similar Figures Instructional Days: 5 Lesson 8: Similarity (P) Lesson 9: Basic Properties of Similarity (E) Lesson 10: Informal Proof of AA Criterion for Similarity (S) Lesson 11: More About Similar Triangles (P) 8.G.A.4 Understand that a two dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. Lesson 29 Identify Similar Figures pp. 252 259 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 7
Module 3 Similarity Lesson 12: Modeling Using Similarity (M) 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Lesson 30 Lesson 31 Establish Facts about Parallel Lines and Angles pp. 260 265 Establish Facts about Triangles and Angles pp. 266 275 End of Module Assessment and Rubric Topics A through C (assessment 1 day, return 1 day, remediation or further applications 4 days) Topic D: The Pythagorean Theorem Instructional Days: 2 Lesson 15: Proof of the Pythagorean Theorem (S) Lesson 16: The Converse of the Pythagorean Theorem (P) 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. Lesson 32 Lesson 33 Understand the Pythagorean Theorem pp. 276 283 Understand the Converse of the Pythagorean Theorem pp. 284 291 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. Lesson 34 Problem Solving: The Pythagorean Theorem pp. 292 299 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 8
Module 4 Linear Equations Topic A: Writing and Solving Linear Equations Instructional Days: 9 Lesson 1: Writing Equations Using Symbols (P) 8.EE.C.7 Solve linear equations in one variable. Lesson 2: Linear and Nonlinear Expressions in (P) Lesson 3: Linear Equations in (P) Lesson 4: Solving a Linear Equation (P) Lesson 5: Writing and Solving Linear Equations (P) Lesson 6: Solutions of a Linear Equation (P) Lesson 7: Classification of Solutions (S) Lesson 8: Linear Equations in Disguise (P) Lesson 9: An Application of Linear Equations (S) 8.EE.C.7a 8.EE.C.7b Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Lesson 13 Solve Linear Equations pp. 112 119 Lesson 13 Solve Linear Equations pp. 112 119 Topic B: Linear Equations in Two Variables and Their Graphs Instructional Days: 5 Lesson 10: A Critical Look at Proportional Relationships (S) Lesson 11: Constant Rate (P) Lesson 12: Linear Equations in Two Variables (E) Lesson 13: The Graph of a Linear Equation in Two Variables (S) 8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance time graph to a distancetime equation to determine which of two moving objects has greater speed. Lesson 10 Understand Proportional Relationships and Slope pp. 88 95 Lesson 14: The Graph of a Linear Equa on Horizontal and Vertical Lines (S) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 9
Module 4 Linear Equations Mid Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days) Topic C: Slope and Equations of Lines Instructional Days: 9 Lesson 15: The Slope of a Non Vertical Line (P) Lesson 16: The Computation of the Slope of a Non Vertical Line (S) Lesson 17: The Line Joining Two Distinct Points of the Graph = x + has Slope (S) Lesson 18: There Is Only One Line Passing Through a Given Point with a Given Slope (P) Lesson 19: The Graph of a Linear Equation in Two Variables Is a Line (S) Lesson 20: Every Line Is a Graph of a Linear Equation (P) 8.EE.B.5 8.EE.B.6 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance time graph to a distancetime equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. Lesson 10 Understand Proportional Relationships and Slope pp. 88 95 Lesson 11 Understand Slope pp. 96 103 Lesson 12 Write Equations for Lines pp. 104 111 Lesson 21: Some Facts about Graphs of Linear Equations in Two Variables (P) Lesson 22: Constant Rates Revisited (P) Lesson 23: The Defining Equation of a Line (E) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 10
Module 4 Linear Equations Topic D: Systems of Linear Equations and Their Solutions Instructional Days: 7 Lesson 24: Introduction to Simultaneous Equations (P) Lesson 25: Geometric Interpretation of the Solutions of a Linear System (E) Lesson 26: Characterization of Parallel Lines (S) Lesson 27: Nature of Solutions of a System of Linear Equations (P) Lesson 28: Another Computational Method of Solving a Linear System (P) Lesson 29: Word Problems (P) Lesson 30: Conversion Between Celsius and Fahrenheit (M) 8.EE.B.5 8.EE.C.8 8.EE.C.8a Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance time graph to a distancetime equation to determine which of two moving objects has greater speed. Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Lesson 10 Understand Proportional Relationships and Slope pp. 88 95 Lesson 14 Solve Systems of Equations pp. 120 127 8.EE.C.8b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Lesson 14 Solve Systems of Equations pp. 120 127 8.EE.C.8c Solve real world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Lesson 15 Problem Solving: Systems of Equations pp. 128 135 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 11
Module 4 Linear Equations OPTIONAL Topic E: Pythagorean Theorem Instructional Days: 1 Lesson 31: System of Equations Leading to Pythagorean Triples (S) 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. Lesson 34 Problem Solving: The Pythagorean Theorem pp. 292 299 8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. 8.EE.C.8a 8.EE.C.8b Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. Lesson 14 Solve Systems of Equations pp. 120 127 Lesson 14 Solve Systems of Equations pp. 120 127 8.EE.C.8c Solve real world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Lesson 15 Problem Solving: Systems of Equations pp. 128 135 End of Module Assessment and Rubric Topics C through D (assessment 1 day, return 1 day, remediation or further applications 3 days) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 12
Module 5 Examples of Functions from Geometry Topic A: Functions Instructional Days: 8 Lesson 1: The Concept of a Function (P) Lesson 2: Formal Definition of a Function (S) Lesson 3: Linear Functions and Proportionality (P) Lesson 4: More Examples of Functions (P) Lesson 5: Graphs of Functions and Equations (E) Lesson 6: Graphs of Linear Functions and Rate of Change (S) Lesson 7: Comparing Linear Functions and Graphs (E) Lesson 8: Graphs of Simple Nonlinear Functions (E) 8.F.A.1 8.F.A.2 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 3 3 Function notation is not required in Grade 8. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Lesson 16 Understand Functions pp. 142 149 Lesson 17 Represent Functions pp. 150 157 Lesson 17 Represent Functions pp. 150 157 Lesson 18 Compare Functions pp. 158 165 8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Lesson 19 Investigate Linear and Non Linear Functions pp. 166 173 Topic B: Volume Instructional Days: 3 Lesson 9: Examples of Functions from Geometry (E) Lesson 10: Volumes of Familiar Solids Cones and Cylinders (S) Lesson 11: Volume of a Sphere (P) 8.G.C.9 4 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real world and mathematical problems. 4 Solutions that introduce irrational numbers are not introduced until Module 7. Lesson 36 Learn and Apply Volume Formulas pp. 308 315 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 13
Module 5 Examples of Functions from Geometry End of Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 14
Module 6 Linear Functions Topic A: Linear Functions Instructional Days: 5 Lesson 1: Modeling Linear Relationships (P) Lesson 2: Interpreting Rate of Change and Initial Value (P) Lesson 3: Representations of a Line (P) Lessons 4 5: Increasing and Decreasing Functions (P, P) 8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Lesson 20 Use Functions to Model Relationships pp. 174 181 Lesson 21 Problem Solving: Use Linear Models pp. 182 189 8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Lesson 22 Analyze Graphs of Functions pp. 190 197 Topic B: Bivariate Numerical Data Instructional Days: 4 Lesson 6: Scatter Plots (P) Lesson 7: Patterns in Scatter Plots (P) Lesson 8: Informally Fitting a Line (P) Lesson 9: Determining the Equation of a Line Fit to Data (P) 8.SP.A.1 8.SP.A.2 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear continued on next page Lesson 37 Construct and Interpret Scatter Plots pp. 322 329 Lesson 38 Fit Linear Models to Data pp. 330 337 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 15
Module 6 Linear Functions continued from previous page association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Mid Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 1 day) Topic C: Linear and Nonlinear Models Instructional Days: 3 Lesson 10: Linear Models (P) Lesson 11: Using Linear Models in a Data Context (P) Lesson 12: Nonlinear Models in a Data Context (Optional) (P) 8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Lesson 37 Construct and Interpret Scatter Plots pp. 322 329 8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Lesson 38 Fit Linear Models to Data pp. 330 337 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr continued on next page Lesson 39 Problem Solving: Use Linear Models pp. 338 345 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 16
Module 6 Linear Functions continued from previous page as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Topic D: Bivariate Categorical Data Instructional Days: 2 Lesson 13: Summarizing Bivariate Categorical Data in a Two Way Table (P) Lesson 14: Association Between Categorical Variables (P) 8.SP.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two way table. Construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Lesson 40 Analyze Data in Two Way Tables pp. 346 353 End of Module Assessment and Rubric Topics A through D (assessment 1 day, return 1 day, remediation or further applications 1 day) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 17
Module 7 Introduction to Irrational Numbers Using Geometry Topic A: Square and Cube Roots Instructional Days: 5 Lesson 1: The Pythagorean Theorem (P) Lesson 2: Square Roots (S) Lesson 3: Existence and Uniqueness of Square and Cube Roots (S) Lesson 4: Simplifying Square Roots (optional) (P) 8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Lesson 1 Understand Rational and Irrational Numbers pp. 10 17 Lesson 5: Solving Radical Equations (P) 8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Lesson 2 Use Rational Approximations of Irrational Numbers pp. 18 25 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. Lesson 6 Lesson 7 Evaluate Square Roots and Cube Roots pp. 56 63 Solve Simple Equations Involving Squares and Cubes pp. 64 71 Topic B: Decimal Expansions of Numbers Instructional Days: 9 Lesson 6: Finite and Infinite Decimals (P) Lesson 7: Infinite Decimals (S) Lesson 8: The Long Division Algorithm (E) 8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for continued on next page Lesson 1 Understand Rational and Irrational Numbers pp. 10 17 Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 18
Module 7 Introduction to Irrational Numbers Using Geometry Lesson 9: Decimal Expansions of Fractions, Part 1 (P) Lesson 10: Converting Repeating Decimals to Fractions (P) Lesson 11: The Decimal Expansion of Some Irrational Numbers (S) Lesson 12: Decimal Expansion of Fractions, Part 2 (S) Lesson 13: Comparing Irrational Numbers (E) Lesson 14: Decimal Expansion of (S) 8.NS.A.2 continued from previous page rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π 2 ). For example, by truncating the decimal expansion of 2, show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Lesson 2 Use Rational Approximations of Irrational Numbers pp. 18 25 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that 2 is irrational. Lesson 6 Lesson 7 Evaluate Square Roots and Cube Roots pp. 56 63 Solve Simple Equations Involving Squares and Cubes pp. 64 71 Mid Module Assessment and Rubric Topics A through B (assessment 2 days, return 1 day, remediation or further applications 3 days) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 19
Module 7 Introduction to Irrational Numbers Using Geometry Topic C: The Pythagorean Theorem Instructional Days: 4 Lesson 15: Pythagorean Theorem, Revisited (S) Lesson 16: Converse of the Pythagorean Theorem (S) Lesson 17: Distance on the Coordinate Plane (P) 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse. Lesson 32 Lesson 33 Understand the Pythagorean Theorem pp. 276 283 Understand the Converse of the Pythagorean Theorem pp. 284 291 Lesson 18: Applications of the Pythagorean Theorem (E) 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. Lesson 35 Calculate Distances in the Coordinate Plane pp. 300 307 8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Lesson 34 Problem Solving: The Pythagorean Theorem pp. 292 299 Topic D: Applications of Radicals and Roots Instructional Days: 5 Lesson 19: Cones and Spheres (P) Lesson 20: Truncated Cones (P) Lesson 21: Volume of Composite Solids (E) 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. Lesson 35 Calculate Distances in the Coordinate Plane pp. 300 307 Lesson 22: Average Rate of Change (S) Lesson 23: Nonlinear Motion (M) 8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real world and mathematical problems. Lesson 36 Learn and Apply Volume Formulas pp. 308 315 End of Module Assessment and Rubric Topics A through D (assessment 2 days, return 1 day, remediation or further applications 3 days) Lesson Structure Key: P Problem Set Lesson, M Modeling Cycle Lesson, E Explorations Lesson, S Socratic Lesson Copyright William H. Sadlier, Inc. All rights reserved. 20