ARKANSAS DEPARTMENT OF EDUCATION MATHEMATICS ADOPTION Correlation and Comparison with Correlation Grade 8
ARKANSAS DEPARTMENT OF EDUCATION MATHEMATICS ADOPTION Two Pearson s digits 2012 Grade 8 correlations have been provided within this document. Part 1: A Correlation of digits Grade 8 to the (CCSS) Part 1 pages 1-7 Part 2: A Correlation of digits Grade 8 to the Comparison with. Part 2 pages 8-35 The correlation in Part 2 is included at the request of the Arkansas Department of Education and shows how both sets of criteria intersect and align to common content. Please note the CCSS introduces some content at different grade levels and, as a result, several grade levels of the Arkansas Curriculum Framework were aligned to and were included at a single grade level. Consequently, the correlation reflects this shift to other levels. Thank you in advance for your time and consideration of digits for Arkansas middle school students.
Part 1 to the Table of Contents The Number System 8.NS...2 Expressions and Equations 8.EE...2 Functions 8.F...5 Geometry 8.G...6 Statistics and Probability 8.SP...7 1
Part 1 to the Grade 8 digits Topics & Lessons Grade 8 The Number System 8.NS Know that there are numbers that are not rational, and approximate them by rational numbers. 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. 1-1: Expressing Rational Numbers with Decimal Expansions, 1-2: Exploring Irrational Numbers, 1-5: Problem 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., π2). 1-3: Approximating Irrational Numbers, 1-4: Comparing and Ordering Rational and Irrational Numbers, 1-5: Problem Expressions and Equations 8.EE Work with radicals and integer exponents. 1. Know and apply the properties of integer 3-3: Exponents and Multiplication, 3-4: exponents to generate equivalent numerical Exponents and Division, 3-5: Zero and expressions. Negative Exponents, 3-6: Comparing Expressions with Exponents, 3-7: Problem, 4-5: Problem 2. Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = 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. 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. 3-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p, 3-2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p 4-1: Exploring Scientific Notation, 4-2: Using Scientific Notation to Describe Very Large Quantities, 4-3: Using Scientific Notation to Describe Very Small Quantities, 4-4: Operating with Numbers Expressed in Scientific Notation 2
Part 1 to the Grade 8 4. 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. Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 6. 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. Analyze and solve linear equations and pairs of simultaneous linear equations. digits Topics & Lessons Grade 8 4-1: Exploring Scientific Notation, 4-4: Operating with Numbers Expressed in Scientific Notation, 4-5: Problem 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y = mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-7: Problem 5-2: Linear Equations: y = mx, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y = mx = b, 5-7: Problem, 10-3: Relating Similar Triangles and Slope 7. Solve linear equations in one variable. 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem a. 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). b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property 3
Part 1 to the Grade 8 8. Analyze and solve pairs of simultaneous linear equations. a. 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. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. c. Solve real-world and mathematical problems leading to two linear equations in two variables. digits Topics & Lessons Grade 8 6-1: What is a System of Linear Equations in Two Variables?, 6-2: Estimating Solutions of Linear Systems by Inspection, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 6-1: What is a System of Linear Equations in Two Variables?, 6-3: Systems of Linear Equations by Graphing, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction 6-2: Estimating Solutions of Linear Systems by Inspection, 6-3: Systems of Linear Equations by Graphing, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 6-1: What is a System of Linear Equations in Two Variables?, 6-3: Systems of Linear Equations by Graphing, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 4
Part 1 to the Grade 8 digits Topics & Lessons Grade 8 Functions 8.F Define, evaluate, and compare functions. 1. Understand that a function is a rule that 7-1: Recognizing a Function, 7-2: assigns to each input exactly one output. Representing a Function, 7-4: Nonlinear The graph of a function is the set of ordered Functions, 8-1: Defining a Linear Function pairs consisting of an input and the Rule corresponding output. 1 2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 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. 8-4: Comparing Two Linear Functions 7-3: Linear Functions, 7-4: Nonlinear Functions, 8-1: Defining a Linear Function Rule, 8-3: Initial Value Use functions to model relationships between quantities. 4. Construct a function to model a linear 8-1: Defining a Linear Function Rule, 8-2: relationship between two quantities. Rate of Change, 8-3: Initial Value, 8-5: Determine the rate of change and initial Constructing a Function to Model a Linear value of the function from a description of a Relationship, 8-6: Problem 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. 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. 7-3: Linear Functions, 7-4: Nonlinear Functions, 7-5: Increasing and Decreasing Intervals, 7-6: Sketching a Function Graph, 7-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value 5
Part 1 to the Grade 8 digits Topics & Lessons Grade 8 Geometry 8.G Understand congruence and similarity using physical models, transparencies, or geometry software. 1. Verify experimentally the properties of rotations, reflections, and translations: 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 10-1: Dilations a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. 9-1: Translations, 9-2: Reflections, 9-3: Rotations 9-1: Translations, 9-2: Reflections, 9-3: Rotations c. Parallel lines are taken to parallel lines. 9-1: Translations, 9-2: Reflections, 9-3: Rotations 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. 3. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 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. 9-4: Congruent Figures, 9-5: Problem 10-1: Dilations, 10-2: Similar Figures, 10-3: Relating Similar Triangles and Slope, 10-4: Problem 10-2: Similar Figures, 10-3: Relating Similar Triangles and Slope, 10-4: Problem, 11-5: Angle-Angle Triangle Similarity 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. 11-1: Angles, Lines, and Transversals, 11-2: Reasoning and Parallel Lines, 11-3: Interior Angles of Triangles, 11-4: Exterior Angles of Triangles, 11-5: Angle-Angle Triangle Similarity, 11-6: Problem Understand and apply the Pythagorean Theorem. 6. Explain a proof of the Pythagorean 12-1: Reasoning and Proof, 12-2: The Theorem and its converse. Pythagorean Theorem, 12-4: The Converse of the Pythagorean Theorem 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 12-2: The Pythagorean Theorem, 12-3: Finding Unknown Leg Lengths, 12-6: Problem 6
Part 1 to the Grade 8 8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. digits Topics & Lessons Grade 8 12-5: Distance in the Coordinate Plane, 12-6: Problem 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. 13-1: Surface Areas of Cylinders, 13-2: Volumes of Cylinders, 13-3: Surface Areas of Cones, 13-4: Volumes of Cones, 13-5: Surface Areas of Spheres, 13-6: Volumes of Spheres, 13-7: Problem Statistics and Probability 8.SP Investigate patterns of association in bivariate data. 1. Construct and interpret scatter plots for 14-1: Interpreting a Scatter Plot, 14-2: bivariate measurement data to investigate Constructing a Scatter Plot, 14-3: patterns of association between two Investigating Patterns Clustering and quantities. Describe patterns such as Outliers, 14-4: Investigating Patterns clustering, outliers, positive or negative Association association, linear association, and nonlinear association. 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. 3. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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 two-way 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. 14-5: Linear Models Fitting a Straight Line, 14-6: Using the Equation of a Linear Model, 14-7: Problem 14-6: Using the Equation of a Linear Model 15-1: Bivariate Categorical Data, 15-2: Constructing Two-Way Frequency Tables, 15-3: Interpreting Two-Way Frequency Tables, 15-4: Constructing Two-Way Relative Frequency Tables, 15-5: Interpreting Two-Way Relative Frequency Tables, 15-6: Choosing a Measure of Frequency, 15-7: Problem 7
Table of Contents The Number System... 9 Expressions and Equations... 10 Functions... 18 Geometry... 25 Statistics and Probability... 32 8
The Number System CC.8.NS.1. Know that there are numbers that are not rational, and approximate them by rational numbers. 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. CC.8.NS.2 Know that there are numbers that are not rational, and approximate them by rational numbers. 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 (square root 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. AR.8.NO.1.4 (NO.1.8.4) Rational Numbers: Understand and justify classifications of numbers in the real number system AR.7.NO.1.6 (NO.1.7.6) Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers) AR.8.NO.3.5 (NO.3.8.5) Application of Computation: Calculate and find approximations of square roots with appropriate technology AR.9-12.LA.AI.1.1 (LA.1.AI.1) Evaluate algebraic expressions, including radicals, by applying the order of operations 1-1: Expressing Rational Numbers with Decimal Expansions, 1-2: Exploring Irrational Numbers 1-2: Exploring Irrational Numbers, 1-5: Problem 1-2: Exploring Irrational Numbers, 1-3: Approximating Irrational Numbers, 1-4: Comparing and Ordering Rational and Irrational Numbers, 1-5: Problem, 3-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p 3-3: Exponents and Multiplication, 3-4: Exponents and Division, 3-5: Zero and Negative Exponents, 3-7: Problem 9
Expressions and Equations CC.8.EE.1 Work with radicals and integer exponents. 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. CC.8.EE.2 Work with radicals and integer exponents. 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. AR.9-12.LA.AI.1.3 (LA.1.AI.3) Apply the laws of (integral) exponents and roots. AR.7.NO.1.6 (NO.1.7.6) Rational Numbers: Recognize subsets of the real number system (natural, whole, integers, rational, and irrational numbers) AR.8.NO.3.4 (NO.3.8.4) Application of Computation: Apply factorization to find LCM and GCF of algebraic expressions AR.9-12.LA.AI.1.3 (LA.1.AI.3) Apply the laws of (integral) exponents and roots. 3-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p, Lesson 3-2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p, 3-3: Exponents and Multiplication, 3-4: Exponents and Division, 3-5: Zero and Negative Exponents, 3-6: Comparing Expressions with Exponents, 3-7: Problem, 4-5: Problem 1-2: Exploring Irrational Numbers 3-4: Exponents and Division 3-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p, Lesson 3-2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p, 3-3: Exponents and Multiplication, 3-4: Exponents and Division, 3-5: Zero and Negative Exponents, 3-6: Comparing Expressions with Exponents, 3-7: Problem 10
CC.8.EE.3 Work with radicals and integer exponents. 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 10^8 and the population of the world as 7 10^9, and determine that the world population is more than 20 times larger. CC.8.EE.4 Work with radicals and integer exponents. 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. AR.9-12.LA.AI.1.4 (LA.1.AI.4) *Solve problems involving scientific notation, including multiplication and division. AR.8.NO.1.1 (NO.1.8.1) Rational Numbers: Read, write, compare and solve problems, with and without appropriate technology, including numbers less than 1 in scientific notation AR.8.NO.1.2 (NO.1.8.2) Rational Numbers: Convert between scientific notation and standard notation, including numbers from zero to one. AR.9-12.LA.AI.1.4 (LA.1.AI.4) *Solve problems involving scientific notation, including multiplication and division. 4-1: Exploring Scientific Notation, 4-2: Using Scientific Notation to Describe Very Large Quantities, 4-3: Using Scientific Notation to Describe Very Small Quantities, 4-4: Operating with Numbers Expressed in Scientific Notation, 4-5: Problem 4-1: Exploring Scientific Notation, 4-2: Using Scientific Notation to Describe Very Large Quantities, 4-3: Using Scientific Notation to Describe Very Small Quantities, 4-4: Operating with Numbers Expressed in Scientific Notation, 4-5: Problem 4-1: Exploring Scientific Notation, 4-2: Using Scientific Notation to Describe Very Large Quantities, 4-3: Using Scientific Notation to Describe Very Small Quantities, 4-4: Operating with Numbers Expressed in Scientific Notation, 4-5: Problem 4-1: Exploring Scientific Notation, 4-2: Using Scientific Notation to Describe Very Large Quantities, 4-3: Using Scientific Notation to Describe Very Small Quantities, 4-4: Operating with Numbers Expressed in Scientific Notation, 4-5: Problem 11
CC.8.EE.5 Understand the connections between proportional relationships, lines, and linear equations. 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 distance-time equation to determine which of two moving objects has greater speed. AR.8.A.4.3 (A.4.8.3) Patterns, Relations and Functions: Interpret and represent a two operation function as an algebraic equation AR.8.A.6.1 (A.6.8.1) Algebraic Models and Relationships: Describe, with and without appropriate technology, the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change (rise/run) and y-intercept in real world problems 5-6: Linear Equations: y=mx + b, 7-2: Representing a Function, 7-4: Nonlinear Functions, 7-7: Problem, 8-2: Rate of Change, 8-3: Initial Value, 8-5: Constructing a Function to Model a Linear Relationship 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y= mx+ b, 5-7: Problem, 7-4: Nonlinear Functions, 7-5: Increasing and Decreasing Intervals, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-5: Constructing a Function to Model a Linear Relationship AR.9-12.LF.AI.3.9 (LF.3.AI.9) Describe the effects of parameter changes, slope and/or y- intercept, on graphs of linear functions and vice versa 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 5-6: Linear Equations: y= mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship 12
CC.8.EE.6 Understand the connections between proportional relationships, lines, and linear equations. 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. AR.9-12.LF.AI.3.6 (LF.3.AI.6) Calculate the slope given: -- two points, -- the graph of a line, -- the equation of a line AR.9-12.LF.AI.3.7 (LF.3.AI.7) Determine by using slope whether a pair of lines are parallel, perpendicular, or neither AR.9-12.LF.AI.3.8 (LF.3.AI.8) *Write an equation in slopeintercept, point-slope, and standard forms given: -- two points, -- a point and y-intercept, -- x-intercept and y- intercept, -- a point and slope, -- a table of data, -- the graph of a line AR.9-12.LF.AC.2.5 (LF.2.AC.5) Calculate the slope given: -- two points, -- a graph of a line, -- an equation of a line 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 5-6: Linear Equations: y= mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, Lesson 10-3: Relating Similar Triangles and Slope 8-4: Comparing Two Linear Functions 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y= mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y= mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship 13
CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable. AR.9-12.SEI.AI.2.8 (SEI.2.AI.8) Communicate real world problems graphically, algebraically, numerically and verbally AR.9-12.SEI.AI.2.1 (SEI.2.AI.1) Solve multistep equations and inequalities with rational coefficients: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically AR.8.A.5.1 (A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology 1-1: Expressing Rational Numbers with Decimal Expansions, 1-3: Approximating Irrational Numbers, 1-4: Comparing and Ordering Rational and Irrational Numbers, 2-2: Equations with Variables on Both Sides, 2-5: Problem, 3-3: Exponents and Multiplication, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 6-1: What is a System of Linear Equations in Two Variables?, 7-1: Recognizing a Function 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 14
CC.8.EE.7a 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). CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. AR.9-12.SEI.AI.2.1 (SEI.2.AI.1) Solve multistep equations and inequalities with rational coefficients: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically AR.9-12.SEI.AI.2.8 (SEI.2.AI.8) Communicate real world problems graphically, algebraically, numerically and verbally AR.8.A.5.1 (A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology AR.9-12.SEI.AI.2.1 (SEI.2.AI.1) Solve multistep equations and inequalities with rational coefficients: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 1-1: Expressing Rational Numbers with Decimal Expansions, 1-3: Approximating Irrational Numbers, 1-4: Comparing and Ordering Rational and Irrational Numbers, 2-2: Equations with Variables on Both Sides, 2-5: Problem, 3-3: Exponents and Multiplication, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 6-1: What is a System of Linear Equations in Two Variables?, 7-1: Recognizing a Function 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 15
(Continued) CC.8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. CC.8.EE.8 Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve pairs of simultaneous linear equations. CC.8.EE.8a 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. AR.8.NO.2.1 (NO.2.8.1) Number theory: Apply the addition, subtraction, multiplication and division properties of equality to two-step equations AR.9-12.SEI.AI.2.2 (SEI.2.AI.2) Solve systems of two linear equations: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically AR.9-12.SEI.AI.2.8 (SEI.2.AI.8) Communicate real world problems graphically, algebraically, numerically and verbally AR.9-12.SEI.AI.2.2 (SEI.2.AI.2) Solve systems of two linear equations: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem 6-2: Estimating Solutions of Linear Systems by Inspection, 6-3: Systems of Linear Equations by Graphing, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 1-1: Expressing Rational Numbers with Decimal Expansions, 1-3: Approximating Irrational Numbers, 1-4: Comparing and Ordering Rational and Irrational Numbers, 2-2: Equations with Variables on Both Sides, 2-5: Problem, 3-3: Exponents and Multiplication, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 6-1: What is a System of Linear Equations in Two Variables?, 7-1: Recognizing a Function 6-2: Estimating Solutions of Linear Systems by Inspection, 6-3: Systems of Linear Equations by Graphing, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 16
CC.8.EE.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. CC.8.EE.8c Solve realworld 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. AR.9-12.SEI.AI.2.2 (SEI.2.AI.2) Solve systems of two linear equations: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically AR.9-12.SEI.AI.2.2 (SEI.2.AI.2) Solve systems of two linear equations: -- numerically (from a table or guess and check), -- algebraically (including the use of manipulatives), -- graphically, -- technologically AR.9-12.SEI.AI.2.8 (SEI.2.AI.8) Communicate real world problems graphically, algebraically, numerically and verbally 6-2: Estimating Solutions of Linear Systems by Inspection, 6-3: Systems of Linear Equations by Graphing, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 6-2: Estimating Solutions of Linear Systems by Inspection, 6-3: Systems of Linear Equations by Graphing, 6-4: Systems of Linear Equations Using Substitution, 6-5: Systems of Linear Equations Using Addition, 6-6: Systems of Linear Equations Using Subtraction, 6-7: Problem 1-1: Expressing Rational Numbers with Decimal Expansions, 1-3: Approximating Irrational Numbers, 1-4: Comparing and Ordering Rational and Irrational Numbers, 2-2: Equations with Variables on Both Sides, 2-5: Problem, 3-3: Exponents and Multiplication, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 6-1: What is a System of Linear Equations in Two Variables?, 7-1: Recognizing a Function 17
Functions CC.8.F.1 Define, evaluate, and compare functions. 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. (Function notation is not required in Grade 8.) AR.7.A.4.1 (A.4.7.1) Patterns, Relations and Functions: Create and complete a function table (input/output) using a given rule with two operations AR.8.A.4.3 (A.4.8.3) Patterns, Relations and Functions: Interpret and represent a two operation function as an algebraic equation AR.9-12.LF.AI.3.1 (LF.3.AI.1) Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data 5-7: Problem, 7-2: Representing a Function, 7-4: Nonlinear Functions, 7-7: Problem 5-6: Linear Equations: y= mx + b 7-2: Representing a Function, 7-4: Nonlinear Functions, 7-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-5: Constructing a Function to Model a Linear Relationship 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions 18
(Continued) CC.8.F.1 Define, evaluate, and compare functions. 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. (Function notation is not required in Grade 8.) AR.9-12.LF.AI.3.2 (LF.3.AI.2) Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data AR.3.A.6.1 (A.6.3.1) Algebraic Models and Relationships: Complete a chart or table to organize given information and to understand relationships and explain the results AR.7.A.6.3 (A.6.7.3) Algebraic Models and Relationships: Create and complete a function table (input/output) using a given rule with two operations in real world situations 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem, 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions, 7-5: Increasing and Decreasing Intervals, 7-6: Sketching a Function Graph, 7-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem 2-4: Solutions One, None, or Infinitely Many, 3-5: Zero and Negative Exponents, 3-7: Problem, 4-3: Using Scientific Notation to Describe Very Small Quantities, 5-6: Linear Equations: y =mx + b, 7-2: Representing a Function, 7-4: Nonlinear Functions, 7-7: Problem 5-7: Problem, 7-2: Representing a Function, 7-4: Nonlinear Functions, 7-7: Problem 19
(Continued) CC.8.F.1 Define, evaluate, and compare functions. 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. (Function notation is not required in Grade 8.) AR.8.A.4.1 (A.4.8.1) Patterns, Relations and Functions: Find the nth term in a pattern or a function table AR.8.A.4.2 (A.4.8.2) Patterns, Relations and Functions: Using real world situations, describe patterns in words, tables, pictures, and symbolic representations 3-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p, 3-2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p, 3-3: Exponents and Multiplication, 3-4: Exponents and Division, 3-5: Zero and Negative Exponents, 3-6: Comparing Expressions with Exponents, 3-7: Problem, 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions, 7-5: Increasing and Decreasing Intervals, 7-6: Sketching a Function Graph, 7-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem 14-4: Investigating Patterns - Association, 14-3: Investigating Patterns - Clustering and Outliers 20
CC.8.F.2 Define, evaluate, and compare functions. 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. AR.9-12.LF.AI.3.8 (LF.3.AI.8) *Write an equation in slopeintercept, point-slope, and standard forms given: -- two points, -- a point and y-intercept, -- x-intercept and y- intercept, -- a point and slope, -- a table of data, -- the graph of a line AR.9-12.LF.AI.3.9 (LF.3.AI.9) Describe the effects of parameter changes, slope and/or y- intercept, on graphs of linear functions and vice versa AR.9-12.LF.AI.3.1 (LF.3.AI.1) Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx + b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions 21
(Continued) CC.8.F.2 Define, evaluate, and compare functions. 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. AR.9-12.LF.AI.3.2 (LF.3.AI.2) Determine domain and range of a relation from an algebraic expression, graphs, set of ordered pairs, or table of data AR.8.A.6.4 (A.6.8.4) Algebraic Models and Relationships: Represent, with and without appropriate technology, simple exponential and/or quadratic functions using verbal descriptions, tables, graphs and formulas and translate among these representations 2-1: Two-Step Equations, 2-2: Equations with Variables on Both Sides, 2-3: Equations Using the Distributive Property, 2-4: Solutions One, None, or Infinitely Many, 2-5: Problem, 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y-intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions, 7-5: Increasing and Decreasing Intervals, 7-6: Sketching a Function Graph, 7-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem 3-1: Perfect Squares, Square Roots, and Equations of the form x 2 = p, 3-2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p, 3-3: Exponents and Multiplication, 3-4: Exponents and Division, 3-5: Zero and Negative Exponents, 3-6: Comparing Expressions with Exponents, 3-7: Problem, 7-3: Linear Functions, 7-4: Nonlinear Functions 22
CC.8.F.3 Define, evaluate, and compare functions. 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. CC.8.F.4 Use functions to model relationships between quantities. 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. AR.9-12.LF.AI.3.1 (LF.3.AI.1) Distinguish between functions and non-functions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data AR.9-12.LF.AI.3.5 (LF.3.AI.5) Interpret the rate of change/slope and intercepts within the context of everyday life AR.9-12.LF.AI.3.6 (LF.3.AI.6) Calculate the slope given: -- two points, -- the graph of a line, -- the equation of a line 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 7-1: Recognizing a Function, 7-2: Representing a Function, 7-3: Linear Functions, 7-4: Nonlinear Functions, 7-5: Increasing and Decreasing Intervals, 7-6: Sketching a Function Graph, 7-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship 23
(Continued) CC.8.F.4 Use functions to model relationships between quantities. 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. AR.9-12.LF.AI.3.7 (LF.3.AI.7) Determine by using slope whether a pair of lines are parallel, perpendicular, or neither AR.9-12.LF.AI.3.9 (LF.3.AI.9) Describe the effects of parameter changes, slope and/or y- intercept, on graphs of linear functions and vice versa AR.8.A.5.2 (A.5.8.2) Expressions, Equations and Inequalities: Solve and graph linear equations (in the form y=mx+b) 8-4: Comparing Two Linear Functions 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem 5-5: The y-intercept of a Line, 5-6: Linear Equations: y=mx+b, 5-7: Problem, 7-3: Linear Functions, 8-1: Defining a Linear Function Rule, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship AR.7.A.6.3 (A.6.7.3) Algebraic Models and Relationships: Create and complete a function table (input/output) using a given rule with two operations in real world situations 5-7: Problem, 7-2: Representing a Function, 7-4: Nonlinear Functions, 7-7: Problem 24
CC.8.F.5 Use functions to model relationships between quantities. 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. Geometry CC.8.G.1 Understand congruence and similarity using physical models, transparencies, or geometry software. Verify experimentally the properties of rotations, reflections, and translations: -- a. Lines are taken to lines, and line segments to line segments of the same length. -- b. Angles are taken to angles of the same measure. -- c. Parallel lines are taken to parallel lines. AR.9-12.LF.AI.3.9 (LF.3.AI.9) Describe the effects of parameter changes, slope and/or y- intercept, on graphs of linear functions and vice versa AR.7.G.9.2 (G.9.7.2) Symmetry and Transformations: Perform translations and reflections of twodimensional figures using a variety of methods (paper folding, tracing, graph paper) AR.5.G.9.1 (G.9.5.1) Symmetry and Transformations: Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged AR.6.G.8.5 (G.8.6.5) Characteristics of Geometric Shapes: Identify similar figures and explore their properties 5-1: Graphing Proportional Relationships, 5-2: Linear Equations: y=mx, 5-3: The Slope of a Line, 5-4: Unit Rates and Slope, 5-5: The y- intercept of a Line, 5-6: Linear Equations: y=mx+ b, 5-7: Problem, 8-1: Defining a Linear Function Rule, 8-2: Rate of Change, 8-3: Initial Value, 8-4: Comparing Two Linear Functions, 8-5: Constructing a Function to Model a Linear Relationship, 8-6: Problem Unit E: 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem Unit E: 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem Unit E: 10-1: Dilations, 10-2: Similar Figures, 10-3: Relating Similar Triangles and Slope, 10-4: Problem, 11-5: Angle-Angle Triangle Similarity 25
CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a twodimensional 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. AR.K.G.9.2 (G.9.K.2) Symmetry and Transformations: Explore slides, flips and turns AR.1.G.9.2 (G.9.1.2) Symmetry and Transformations: Manipulate twodimensional figures through slides, flips and turns AR.2.G.9.2 (G.9.2.2) Symmetry and Transformations: Demonstrate the motion of a single transformation AR.5.G.9.1 (G.9.5.1) Symmetry and Transformations: Predict and describe the results of translation (slide), reflection (flip), rotation (turn), showing that the transformed shape remains unchanged AR.9-12.CGT.G.5.7 (CGT.5.G.7) Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane: -- translations, -- reflections, -- rotations (90, 180, clockwise and counterclockwise about the origin), -- dilations (scale factor) AR.5.G.8.4 (G.8.5.4) Characteristics of Geometric Shapes: Model and identify the properties of congruent figures 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem, 10-1: Dilations, 10-2: Similar Figures 9-4: Congruent Figures 26
(Continued) CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a twodimensional 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. AR.4.G.9.1 (G.9.4.1) Symmetry and Transformations: Determine the result of a transformation of a twodimensional figure as a slide (translation), flip (reflection) or turn (rotation) and justify the answer 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem CC.8.G.3 Understand congruence and similarity using physical models, transparencies, or geometry software. Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. AR.8.G.9.2 (G.9.8.2) Symmetry and Transformations: Draw the results of translations and reflections about the x- and y-axis and rotations of objects about the origin 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem, 10-2: Similar Figures 27
CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. Understand that a twodimensional 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. AR.9-12.CGT.G.5.7 (CGT.5.G.7) Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane: -- translations, -- reflections, -- rotations (90, 180, clockwise and counterclockwise about the origin), -- dilations (scale factor) AR.7.G.9.1 (G.9.7.1) Symmetry and Transformations: Examine the congruence, similarity, and line or rotational symmetry of objects using transformations AR.3.G.9.2 (G.9.3.2) Symmetry and Transformations: Describe the motion (transformation) of a two-dimensional figure as a flip (reflection), slide (translation) or turn (rotation) 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem, 10-1: Dilations, 10-2: Similar Figures, 10-4: Problem 9-4: Congruent Figures, 9-5: Problem, 10-1: Dilations, 10-2: Similar Figures, 10-3: Relating Similar Triangles and Slope 9-1: Translations, 9-2: Reflections, 9-3: Rotations, 9-4: Congruent Figures, 9-5: Problem 28