Pearson Connected Mathematics 2 - Common Core Additional Investigations

Transcription

1 ARKANSAS DEPARTMENT OF EDUCATION MATHEMATICS ADOPTION Pearson - Additional Correlation and Comparison with Correlation Grade 8

2 ARKANSAS DEPARTMENT OF EDUCATION MATHEMATICS ADOPTION Two Pearson (CMP2) with Additional correlations have been provided within this document. Part 1: A correlation of Pearson with Additional to the for Mathematics. Part 1 pages 1-8 Part 2: A correlation of Pearson with Additional to the Comparison with. Part 2 pages 9-32 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, 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 CMP2 for Arkansas middle school students.

3 Part 1 Pearson Additional Correlated to the Grade 8 Units : Additional Thinking with Mathematical Models: Linear and Inverse Relationships Looking for Pythagoras: The Pythagorean Theorem Growing, Growing, Growing: Exponential Relationships Frogs, Fleas, and Painted Cubes: Quadratic Relationships Kaleidoscopes, Hubcaps, and Mirrors: Symmetry and Transformations Say it with Symbols: Making Sense of Symbols The Shapes of Algebra: Linear Systems and Inequalities Samples and Populations: Data and Statistics Table of Contents The Number System 8.NS...2 Expressions and Equations 8.EE...2 Functions 8.F...4 Geometry 8.G...5 Statistics and Probability 8.SP...7 1

4 Part 1 Pearson Additional Correlated to the Grade 8 Pearson with Additional (CMP2) 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 Looking For Pythagoras (Inv. 4) 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. 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). 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. Looking For Pythagoras (Inv. 4) Expressions and Equations 8.EE Work with radicals and integer exponents. 1. Know and apply the properties of integer Growing, Growing, Growing (Inv. 5) exponents to generate equivalent numerical CCSS Investigation 1: Exponents expressions. For example, = 3 3 = 1/33 = 1/ 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. For example, estimate the population of the United States as and the population of the world as 7 109, and determine that the world population is more than 20 times larger. Looking For Pythagoras (Inv. 2, 3, 4) CCSS Investigation 1: Exponents Growing, Growing, Growing (Inv. 1 ACE 39 40, Inv. 2 ACE 15 17, Inv. 4 ACE 8, Inv. 5 ACE 56 60) 2 Key: Inv. = Investigation; ACE = Applications Connections Extensions

5 Part 1 A Correlation of with 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. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 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. Pearson with Additional (CMP2) Grade 8 Growing, Growing, Growing (Inv. 5 ACE 56, 57, 60) Models (Inv. 2) CCSS Investigation 2: Functions Models (Inv. 2) CCSS Investigation 2: Functions 7. Solve linear equations in one variable. Models (Inv. 2) Say It With Symbols (Inv. 1, 2, 3) 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). CCSS Investigation 2: Functions 3 Key: Inv. = Investigation; ACE = Applications Connections Extensions

6 Part 1 A Correlation of with to the Grade 8 b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. 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. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. 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. Pearson with Additional (CMP2) Grade 8 Models (Inv. 2) Say It With Symbols (Inv. 1, 2, 3, 4) The Shapes of Algebra (Inv. 2, 3, 4) The Shapes of Algebra (Inv. 2, 3, 4) The Shapes of Algebra (Inv. 1 ACE 56 57, Inv. 2, 3, 4) The Shapes of Algebra (Inv. 2, 3, 4) Functions 8.F Define, evaluate, and compare functions. 1. Understand that a function is a rule that CCSS Investigation 2: Functions 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. 2. 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. Models (Inv. 1) Growing, Growing, Growing (Inv. 1 ACE 25 26, 38, 47) Frogs, Fleas and Painted Cubes (Inv. 2, 3, 4) Say It With Symbols (Inv. 2) 4 Key: Inv. = Investigation; ACE = Applications Connections Extensions

7 Part 1 A Correlation of with to the Grade 8 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 = s2 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. Pearson with Additional (CMP2) Grade 8 Models (Inv. 2, 3) Growing, Growing, Growing (Inv. 5) The Shapes of Algebra (Inv. 3, 4) Say It With Symbols (Inv. 4) Use functions to model relationships between quantities. 4. Construct a function to model a linear Models (Inv. 1, relationship between two quantities. 2) Determine the rate of change and initial The Shapes of Algebra (Inv. 3, 4) value of the function from a description of a Say It With Symbols (Inv. 4) 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. Models (Inv. 2) Growing, Growing, Growing (Inv. 1, 2, 3, 4) Frogs, Fleas and Painted Cubes (Inv. 1, 2, 3, 4) Say It With Symbols (Inv. 4) Geometry 8.G Understand congruence and similarity using physical models, transparencies, or geometry software. 1. Verify experimentally the properties of rotations, reflections, and translations: Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1, 2, 3, 4, 5) CCSS Investigation 3: Transformations 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. Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1, 2, 3, 4, 5) CCSS Investigation 3: Transformations Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1, 2, 3, 4, 5) CCSS Investigation 3: Transformations c. Parallel lines are taken to parallel lines. Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1, 2, 3, 4, 5) CCSS Investigation 3: Transformations 5 Key: Inv. = Investigation; ACE = Applications Connections Extensions

8 Part 1 A Correlation of with to the Grade 8 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. 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. Pearson with Additional (CMP2) Grade 8 Kaleidoscopes, Hubcaps, and Mirrors (Inv. 3) Kaleidoscopes, Hubcaps, and Mirrors (Inv. 2 ACE 24 25, 32, Inv. 5) CCSS Investigation 3: Transformations CCSS Investigation 4: Geometry Topics CCSS Investigation 4: Geometry Topics Understand and apply the Pythagorean Theorem. 6. Explain a proof of the Pythagorean Looking For Pythagoras (Inv. 3) Theorem and its converse. 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 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. Looking For Pythagoras (Inv. 3, 4) Looking For Pythagoras (Inv. 2, 3) 6 Key: Inv. = Investigation; ACE = Applications Connections Extensions

9 Part 1 A Correlation of with to the Grade 8 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Pearson with Additional (CMP2) Grade 8 Kaleidoscopes, Hubcaps, and Mirrors (Inv. 1 ACE 47 49, Inv. 2 ACE 28, Inv. 3 ACE 24) Looking For Pythagoras (Inv. 3 ACE 18 22, 25, 26, Inv. 4 ACE 57 58) Say It With Symbols (Inv. 1 ACE 55, Inv. 3 ACE 41, Inv. 4 ACE 39) CCSS Investigation 4: Geometry Topics Statistics and Probability 8.SP Investigate patterns of association in bivariate data. 1. Construct and interpret scatter plots for Samples and Populations (Inv. 4) 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. 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. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Samples and Populations (Inv. 4) Models (Inv. 2) The Shapes of Algebra (Inv. 2, 3) Models (Inv. 1, 2) 7 Key: Inv. = Investigation; ACE = Applications Connections Extensions

10 Part 1 A Correlation of with to the Grade 8 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. 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? Pearson with Additional (CMP2) Grade 8 CCSS Investigation 5: Categorical Data 8 Key: Inv. = Investigation; ACE = Applications Connections Extensions

11 A Correlation of with to the Comparison with Grade 8 Units : Additional Thinking with Mathematical Models: Linear and Inverse Relationships Looking for Pythagoras: The Pythagorean Theorem Growing, Growing, Growing: Exponential Relationships Frogs, Fleas, and Painted Cubes: Quadratic Relationships Kaleidoscopes, Hubcaps, and Mirrors: Symmetry and Transformations Say it with Symbols: Making Sense of Symbols The Shapes of Algebra: Linear Systems and Inequalities Samples and Populations: Data and Statistics Table of Contents The Number System...10 Expressions and Equations...11 Functions...18 Geometry...23 Statistics and Probability

12 A Correlation of with to the Comparison with 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 with Looking for Pythagoras Inv. 4: SE: 48, 58, TE: 90 Looking for Pythagoras Inv. 4: SE: 48, 58, TE: 90 Looking for Pythagoras Inv. 2: SE: 20-21, TE: Inv. 3: SE: 31-32, TE: See related content: Frogs, Fleas, and Painted Cubes Inv. 2: SE: 22-25; TE:

13 A Correlation of with to the Comparison with 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. 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) with Inv. 1: SE: 1-4, TE: 8 Looking for Pythagoras Inv. 4: SE: 48, 58, TE: 90 AR.8.NO.3.4 (NO.3.8.4) Application of Computation: Apply factorization to find LCM and GCF of algebraic expressions Frogs, Fleas, and Painted Cubes Inv. 2: SE: 25-26, TE: 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. Inv. 1: SE: 1-4, TE: 8 11

14 A Correlation of with to the Comparison with 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. with Growing, Growing, Growing Inv. 4: SE: 55, TE: 92 Inv. 5: SE: 70-72, TE: 112 Growing, Growing, Growing Inv. 4: SE: 55, TE: 92 Inv. 5: SE: 70-72, TE: 112 Growing, Growing, Growing Inv. 4: SE: 55, TE: 92 Inv. 5: SE: 70-72, TE: 112 Growing, Growing, Growing Inv. 4: SE: 55, TE: 92 Inv. 5: SE: 70-72, TE:

15 A Correlation of with to the Comparison with 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 with Models Inv. 2: SE: 24-31, TE: Say It With Symbols Inv. 4: SE: 59, 61-66, TE: 106 Models Inv. 2: SE: 46, TE: 54 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 Models Inv. 3: SE: 48, 52-58, TE: 74 13

16 A Correlation of with to the Comparison with 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 nonvertical 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 with Models Inv. 2: SE: 34-39, TE: 54 Inv. 2: SE: 7, TE: 18 AR.9-12.LF.AI.3.8 (LF.3.AI.8) *Write an equation in slope-intercept, 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 Models Inv. 2: SE: 34-39, TE: 54 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 Models Inv. 2: SE: 34-39, TE: 54 14

17 A Correlation of with to the Comparison with CC.8.EE.7 Analyze and solve linear equations and pairs of simultaneous linear equations. Solve linear equations in one variable. 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). 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 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 with Models Inv. 2: SE: 24-31, TE: Inv. 2: SE: 5-12, TE: 9-18 Inv. 2: SE: 5-12, TE: 9-18 Inv. 2: SE: 5-12, TE:

18 A Correlation of with to the Comparison with (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. 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 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 with Models Inv. 2: SE: 24-31, TE: Inv. 2: SE: 5-12, TE: 9-18 Inv. 2: SE: 5-12, TE: 9-18 Models Inv. 2: SE: 30-31, TE: The Shapes of Algebra Inv. 3: SE: 38-50, TE: Inv. 4: SE: 54-67, TE:

19 A Correlation of with to the Comparison with (Continued) 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. 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 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. (Continued) 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 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 with The Shapes of Algebra Inv. 3: SE: 42-50, TE: 68 Inv. 4: SE: 59-67, TE: 94 The Shapes of Algebra Inv. 3: SE: 38-50, TE: Inv. 4: SE: 54-67, TE: The Shapes of Algebra Inv. 3: SE: 38-50, TE: Inv. 4: SE: 54-67, TE: The Shapes of Algebra Inv. 3: SE: 38-50, TE: Inv. 4: SE: 54-67, TE: The Shapes of Algebra Inv. 3: SE: 42-50, TE: 68 Inv. 4: SE: 59-67, TE: 94 17

20 A Correlation of with to the Comparison with 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 nonfunctions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data with Inv. 2: SE: 8, TE: 18 Models Inv. 2: SE: 24-31, TE: See Grade 7: Moving Straight Ahead Inv. 1: SE: 5-11, 12-22, TE: 15-34, 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 See related content: Frogs, Fleas, and Painted Cubes Inv. 1: SE: 7-8, TE: Inv. 4: SE: 56, TE: Inv. 2: SE: 8, TE: 18 18

21 A Correlation of with to the Comparison with (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.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 with Inv. 2: SE: 8, TE: 18 AR.8.A.4.1 (A.4.8.1) Patterns, Relations and Functions: Find the nth term in a pattern or a function table Models Inv. 1: SE: 8-11, TE: 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 Models Inv. 1: SE: 5-22, TE:

22 A Correlation of with to the Comparison with 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 slope-intercept, 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 nonfunctions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data 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 with ModelsInv. 2: SE: 34-39, TE: 54 Models Inv. 3: SE: 48, 52-58, TE: 74 Covered in Grade 7: Moving Straight Ahead Inv. 1: SE: 5-11, 12-22, TE: 15-34, See related content: Frogs, Fleas, and Painted Cubes Inv. 1: SE: 7-8, TE: Inv. 4: SE: 56, TE: Growing, Growing, Growing Inv. 1: SE: 6-9, TE:

23 A Correlation of with to the Comparison with 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. AR.9-12.LF.AI.3.1 (LF.3.AI.1) Distinguish between functions and nonfunctions/relations by inspecting graphs, ordered pairs, mapping diagrams and/or tables of data with Covered in Grade 7: Moving Straight Ahead Inv. 1: SE: 5-11, 12-22, TE: 15-34, 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.3.5 (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 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 Models Inv. 2: SE: 34-39, TE: 54 Models Inv. 2: SE: 34-39, TE: 54 Inv. 2: SE: 7, TE: 18 Models Inv. 3: SE: 48, 52-58, TE: 74 21

24 A Correlation of with to the Comparison with (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.8.A.5.2 (A.5.8.2) Expressions, Equations and Inequalities: Solve and graph linear equations (in the form y=mx+b) 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 with Models Inv. 2: SE: 30-31, TE: Inv. 2: SE: 8, TE: 18 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. 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 Models Inv. 3: SE: 48, 52-58, TE: 74 22

25 A Correlation of with to the Comparison with 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. CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. 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. (Continued) AR.7.G.9.2 (G.9.7.2) Symmetry and Transformations: Perform translations and reflections of two-dimensional 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 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 two-dimensional 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 with Kaleidoscopes, Hubcaps, and Mirrors Inv. 1: SE: 6-7, 12-14; TE: 19-22, Kaleidoscopes, Hubcaps, and Mirrors Inv. 1: SE: 6-7, 12-14; TE: 19-22, Looking for Pythagoras Inv. 2: SE: 28, TE: 56 Inv. 4: SE: 56, 58; TE: 65, 98 Kaleidoscopes, Hubcaps, and Mirrors Inv. 1: SE: 6-25; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 1: SE: 6-25; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2: SE: 28-33; TE:

26 A Correlation of with to the Comparison with CC.8.G.2 Understand congruence and similarity using physical models, transparencies, or geometry software. 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. 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 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 with Kaleidoscopes, Hubcaps, and Mirrors Inv. 2: SE: 28-46; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2: SE: 28-46; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 3: SE: 48-53; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2: SE: 28-46; TE:

27 A Correlation of with to the Comparison with 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 twodimensional figures using coordinates. CC.8.G.4 Understand congruence and similarity using physical models, transparencies, or geometry software. 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 twodimensional figures, describe a sequence that exhibits the similarity between them. 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 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) with Kaleidoscopes, Hubcaps, and Mirrors Inv. 5: SE: 79-94; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2: SE: 28-46; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 1: SE: 6-25; TE: Inv. 2: SE: 28-46; TE: Inv. 3: SE: 48-53; TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 2: SE: 28-33; TE:

28 A Correlation of with to the Comparison with CC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. 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 three angles appear to form a line, and give an argument in terms of transversals why this is so. AR.7.G.8.3 (G.8.7.3) Characteristics of Geometric Shapes: Recognize the pairs of angles formed and the relationship between the angles including two intersecting lines and parallel lines cut by a transversal (vertical, supplementary, complementary, corresponding, alternate interior, alternate exterior angles and linear pair) AR.7.G.8.4 (G.8.7.4) Characteristics of Geometric Shapes: Use paper or physical models to determine the sum of the measures of interior angles of triangles and quadrilaterals AR.9-12.LG.G.1.5 (LG.1.G.5) Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel AR.9-12.LG.G.1.6 (LG.1.G.6) Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180, and the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length with Inv. 4: SE: 23-26, TE: Inv. 4: SE: 26-34, TE: 40 Inv. 4: SE: 23-26, TE: Looking for Pythagoras Inv. 3: SE: 33-34, TE:

29 A Correlation of with to the Comparison with (Continued) CC.8.G.5 Understand congruence and similarity using physical models, transparencies, or geometry software. 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 three angles appear to form a line, and give an argument in terms of transversals why this is so. AR.9-12.R.G.4.2 (R.4.G.2) Solve problems using properties of polygons: -- sum of the measures of the interior angles of a polygon, -- interior and exterior angle measure of a regular polygon or irregular polygon, -- number of sides or angles of a polygon with Inv. 4: SE: 26-34, TE: 40 CC.8.G.6 Understand and apply the Pythagorean Theorem. Explain a proof of the Pythagorean Theorem and its converse. AR.9-12.T.G.2.4 (T.2.G.4) Apply the Pythagorean Theorem and its converse in solving practical problems AR.8.G.8.3 (G.8.8.3) Characteristics of Geometric Shapes: Determine appropriate application of geometric ideas and relationships, such as congruence, similarity, and the Pythagorean theorem, with and without appropriate technology Looking for Pythagoras Inv. 4: SE: 46-63, TE: Kaleidoscopes, Hubcaps, and Mirrors Inv. 1: SE: 6-25; TE: Inv. 2: SE: 28-46; TE: Inv. 3: SE: 48-53; TE:

30 A Correlation of with to the Comparison with CC.8.G.7 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. CC.8.G.8 Understand and apply the Pythagorean Theorem. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. CC.8.G.9 Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. AR.9-12.T.G.2.4 (T.2.G.4) Apply the Pythagorean Theorem and its converse in solving practical problems AR.8.M.13.4 (M ) Applications: Find the distance between two points on a coordinate plane using with the Pythagorean theorem AR.9-12.T.G.2.4 (T.2.G.4) Apply the Pythagorean Theorem and its converse in solving practical problems AR.8.M.13.2 (M ) Applications: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology AR.8.M.12.1 (M ) Attributes and Tools: Understand, select and use, with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area and volume to solve real world problems with Looking for Pythagoras Inv. 4: SE: 46-63, TE: Looking for Pythagoras Inv. 1: SE: 8-9, TE: Inv. 3: SE: 35, TE: Looking for Pythagoras Inv. 4: SE: 46-63, TE: Inv. 4: SE: 27, 35; TE: 40 Inv. 4: SE: 27, 35; TE: 40 28

31 A Correlation of with to the Comparison with (Continued) CC.8.G.9 Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. AR.7.M.13.4 (M ) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials with Inv. 4: SE: 27, 35; TE: 40 AR.9-12.M.G.3.2 (M.3.G.2) Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms Inv. 4: SE: 27, 35; TE: 40 29

32 A Correlation of with to the Comparison with Statistics and Probability CC.8.SP.1 Investigate patterns of association in bivariate data. 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. AR.8.DAP.14.3 (DAP ) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, doublebar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs AR.7.DAP.14.3 (DAP ) Collect, organize and display data: Construct and interpret circle graphs, boxand-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology AR.8.DAP.15.4 (DAP ) Data Analysis: Describe how the inclusion of outliers affects those measures with Samples and Populations Inv. 1: SE: 7-24, TE: Inv. 4: SE: 62, TE: Samples and Populations Inv. 1: SE: 7-24, TE: Inv. 4: SE: 62, TE: Samples and Populations Inv. 1: SE: 15, 19; TE: 46 Inv. 4: SE: 67, 75: TE:

33 A Correlation of with to the Comparison with CC.8.SP.2 Investigate patterns of association in bivariate data. 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. AR.8.DAP.14.2 (DAP ) Collect, organize and display data: Explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit) with Samples and Populations Inv. 4: SE: 78, TE: 106 CC.8.SP.3 Investigate patterns of association in bivariate data. 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 as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. AR.8.DAP.14.3 (DAP ) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, doublebar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs Samples and Populations Inv. 1: SE: 7-24, TE: Inv. 4: SE: 62, TE: AR.8.A.7.1 (A.7.8.1) Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost) Models Inv. 2: SE: 34-39, TE: 54 31

34 A Correlation of with to the Comparison with CC.8.SP.4 Investigate patterns of association in bivariate data. 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. 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? AR.8.DAP.14.3 (DAP ) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, doublebar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs AR.9-12.DIP.AI.5 Data Interpretation and Probability: Content Standard 5. Students will compare various methods of reporting data to make inferences or predictions. with Samples and Populations Inv. 1: SE: 7-24, TE: Inv. 4: SE: 62, TE: Samples and Populations Inv. 1: SE: 16, TE: Inv. 3: SE: 47-50, TE: