Mathematics Courses 1-3

Transcription

1 A Correlation of Prentice Hall Mathematics Courses 1-3 to for Mathematics (2014) Grades 6-8

2 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) Introduction This document demonstrates how Prentice Hall Mathematics Courses 1-3 meets the Indiana s Academic Standards for Mathematics (2014) Grades 6-8. Correlation page references are to the Student and Teacher s Edition. Prentice Hall Mathematics Courses 1-3 is built especially for middle school students with full alignment to the Common Core State Standards. Prentice Hall Middle Grades Mathematics also offers better technology to engage middle school learners. The Common Core Edition of Prentice Hall Mathematics for Courses 1-3 contains Common Core Lessons created to ensure 100% alignment to the Common Core State Standards. The Lessons are found in the Student Edition and Teacher support and pacing for these lessons can be found in the Teacher Edition. Prentice Hall Mathematics Courses 1-3 maintains quality content with the research-based approach students need. Daily, integrated intervention and powerful test prep help all students master the standards and prepare for high-stakes assessments. Engage Your Middle School Learners Capture students' interest with exciting and easy-to-use technology. Know You Are Effective Feel confident about the program's strong authorship, proven student success, and wide range of built-in opportunities to assess your students' understanding. Build Life Long Learners Students are preparing for algebra and beyond by developing their problem solving skills, improving their conceptual understanding, and providing them with the tools they'll need for ongoing success. This document demonstrates the high degree of success students will achieve by using Prentice Hall Mathematics Courses Pearson Education, Inc. or its affiliate(s). All rights reserved

3 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) Table of Contents Grade 6... Error! Bookmark not defined. Grade 7... Error! Bookmark not defined. Grade 8... Error! Bookmark not defined. Copyright 2014 Pearson Education, Inc. or its affiliate(s). All rights reserved

4 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 Prentice Hall Mathematics Course 1 PROCESS STANDARDS FOR MATHEMATICS PS.1: Make sense of problems and Students are challenged to make sense of persevere in solving them. problems and persevere in solving them throughout the course. In addition to Guided Problem Solving lessons, homework exercises for each lesson include one or more Guided Problem Solving items. SE/TE: 18, 34, 56-57, 63, 68, 72, 91-92, , , , , , 190, 219, 235 PS.2: Reason abstractly and quantitatively. Students are challenged to reason abstractly and creatively throughout the course. Some lessons focus on quantitative reasoning skills, and homework exercises frequently include Number Sense and/or Reasoning problems. SE/TE: 26-30, 60, 69 (#21), 91, 105, , , , , , 148, , 165, 191 (#33), PS.3: Construct viable arguments and critique the reasoning of others. Students are challenged to construct viable arguments and critique the reasoning of others throughout the course. Students are exposed to More Than One Way to do a problem, and are asked to make conjectures and to perform Error Analyses of examples of faulty reasoning. SE/TE: 69 (#26), 155 (#3), 174 (#12), 179 (#31), 191 (#36), 203, 225 (#30), 234, 250 (#26), 268, 274 (#26), 319 (#31), 322, 379 (AL 8.4a), 428 SE = Student Edition 1 TE = Teacher s Edition

5 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 PS.4: Model with mathematics. Prentice Hall Mathematics Course 1 Students are challenged to model problem situations with mathematical expressions and equations throughout the course. In addition to Guided Problem Solving lessons, homework exercises for each lesson include one or more Guided Problem Solving items which frequently incorporate mathematical modeling. SE/TE: 49-50, 81-83, 91, 117, , 132, , , , 241, 244, 277, 283, 286, PS.5: Use appropriate tools strategically. Students are challenged to strategically use a variety of tools, including number lines, algebra tiles, and calculators, throughout the course. Hands On Activity Labs and Technology Activity Labs are incorporated between regular lessons throughout the textbook. SE/TE: 21, 31, 37, 61, 92, 113, 129, 137, 181, 216, 221, 227, 237, 260, 280 PS.6: Attend to precision. Students are challenged to attend to precision in the use of mathematical vocabulary and the performance of computation algorithms, including estimation strategies, throughout the course. In addition to Vocabulary Builders and estimation lessons, homework exercises for each lesson might include Estimation problems. SE/TE: 8-11, 65, 105, , 225, 249, 276, 311, , , , 384, , 420, 437 SE = Student Edition 2 TE = Teacher s Edition

6 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 PS.7: Look for and make use of structure. Prentice Hall Mathematics Course 1 Students are challenged to look for and make use of structure, e.g., by identifying patterns and by applying properties, throughout the course. SE/TE: 4-7, 12-15, 22-25, 42, , 112, 119, 123, 195 (#35), 197, 216, , 352, , 425 PS.8: Look for and express regularity in repeated reasoning. Students are challenged to look for and express regularity in reasoning, e.g., while practicing computation algorithms and identifying repeating geometric patterns, throughout the course. SE/TE: 38-41, 44-47, , , 199, 200 (#29), , , , , 406, , 431, 437, Mathematics Standards for Grade 6 NUMBER SENSE 6.NS.1: Understand that positive and negative numbers are used to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge). Use positive and negative numbers to represent and compare quantities in real-world contexts, explaining the meaning of 0 in each situation. SE/TE: 515, , , 523, , 528, 529, , , , , , 546, 547, 553, SE = Student Edition 3 TE = Teacher s Edition

7 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.NS.2: Understand the integer number system. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself (e.g., ( 3) = 3), and that 0 is its own opposite. Prentice Hall Mathematics Course 1 SE/TE: 515, , , 523, , 528, 529, , , , , , 546, 547, 553, NS.3: Compare and order rational numbers and plot them on a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts. SE/TE: 5, 26-30, 58, 156, , , 288, 304, , 316, 514, , 564, 570, NS.4: Understand that the absolute value of a number is the distance from zero on a number line. Find the absolute value of real numbers and know that the distance between two numbers on the number line is the absolute value of their difference. Interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. SE/TE: , 524 (Check Skills You'll Need), 528, 554 (Check Skills You'll Need), 564, NS.5: Know commonly used fractions (halves, thirds, fourths, fifths, eighths, tenths) and their decimal and percent equivalents. Convert between any two representations (fractions, decimals, percents) of positive rational numbers without the use of a calculator. SE/TE: 175, , 181, , 186, , , 205, 208, , 335, 337, 339 (#36), 342, NS.6: Identify and explain prime and composite numbers. SE/TE: , 170, 171, 177, 185, 188, 189, 190, 195, 204 SE = Student Edition 4 TE = Teacher s Edition

8 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.NS.7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers from 1 to 100, with a common factor as a multiple of a sum of two whole numbers with no common factor. Prentice Hall Mathematics Course 1 SE/TE: , , , 187, , , 201, 205, 210, , , 232, 258, , NS.8: Interpret, model, and use ratios to show the relative sizes of two quantities. Describe how a ratio shows the relationship between two quantities. Use the following notations: a/b, a to b, a:b. SE/TE: 25 (#43), , 310, 311, , , , , 339, 341, , 356, 360, 437, NS.9: Understand the concept of a unit rate and use terms related to rate in the context of a ratio relationship. SE/TE: , 320, 322, 354, NS.10: Use reasoning involving rates and ratios to model real-world and other mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations). SE/TE: 25 (#43), , 311, , , , , 339, 341, , 356, 360, 437, 488 COMPUTATION 6.C.1: Divide multi-digit whole numbers fluently using a standard algorithmic approach. SE/TE: 2, 49, 641, C.2: Compute with positive fractions and positive decimals fluently using a standard algorithmic approach. SE/TE: 32-35, 37, 38-41, 42, 44-47, , , , , 260, , , 271, , SE = Student Edition 5 TE = Teacher s Edition

9 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.C.3: Solve real-world problems with positive fractions and decimals by using one or two operations. Prentice Hall Mathematics Course 1 SE/TE: 34-35, 39-41, 46-47, 50, , , , , , , , , , , C.4: Compute quotients of positive fractions and solve real-world problems involving division of fractions by fractions. Use a visual fraction model and/or equation to represent these calculations. SE/TE: 271, , , 286, , 300, C.5: Evaluate positive rational numbers with whole number exponents. SE/TE: , 169, 170, 204, 206, 426 (Check Skills You'll Need), C.6: Apply the order of operations and properties of operations (identity, inverse, commutative properties of addition and multiplication, associative properties of addition and multiplication, and distributive property) to evaluate numerical expressions with nonnegative rational numbers, including those using grouping symbols, such as parentheses, and involving whole number exponents. Justify each step in the process. SE/TE: 12-15, 16-19, 20, 25, 30, 52-53, 54, 106, 126, , 148, 151, 152, , 201, 348 (Check Skills You'll Need) ALGEBRA AND FUNCTIONS 6.AF.1: Evaluate expressions for specific values of their variables, including expressions with whole-number exponents and those that arise from formulas used in real-world problems. SE/TE: , 118 (Check Skills You'll Need), 150, 152, 165, 264, 270, 275, 344, , 445, 459, , 497, AF.2: Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is substituted into them. SE/TE: CC16-CC17, CC18-CC19 SE = Student Edition 6 TE = Teacher s Edition

10 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.AF.3: Define and use multiple variables when writing expressions to represent realworld and other mathematical problems, and evaluate them for given values. Prentice Hall Mathematics Course 1 SE/TE: , 117, , 150, 152, 165, 267, , , , 445, 459, , 497, AF.4: Understand that solving an equation or inequality is the process of answering the following question: Which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. SE/TE: , 128, 129, , , 137, , 151, 152, , , , 546, , AF.5: Solve equations of the form x + p = q, x - p = q, px = q, and x/p = q fluently for cases in which p, q and x are all nonnegative rational numbers. Represent real world problems using equations of these forms and solve such problems. SE/TE: , 128, 129, , , 137, , , 151, 152, , , , 304, AF.6: Write an inequality of the form x > c, x c, x < c, or x c, where c is a rational number, to represent a constraint or condition in a real-world or other mathematical problem. Recognize inequalities have infinitely many solutions and represent solutions on a number line diagram. SE/TE: , , 598, AF.7: Understand that signs of numbers in ordered pairs indicate the quadrant containing the point; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Graph points with rational number coordinates on a coordinate plane. SE/TE: , 552, 553, , , 565, 566, CC28-CC29, CC30-CC31, CC32-CC33 SE = Student Edition 7 TE = Teacher s Edition

11 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.AF.8: Solve real-world and other mathematical problems by graphing points with rational number coordinates on a coordinate plane. Include the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Prentice Hall Mathematics Course 1 SE/TE: , 552, 553, , , 565, 566, CC28-CC29, CC30-CC31, CC32-CC33 6.AF.9: Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. SE/TE: , 329, CC20-CC21, CC32- CC33 6.AF.10: Use variables to represent two quantities in a proportional relationship in a real-world problem; write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. SE/TE: , CC32-C33 GEOMETRY AND MEASUREMENT 6.GM.1: Convert between measurement systems (English to metric and metric to English) given conversion factors, and use these conversions in solving real-world problems. The opportunity to address this standard can be found on the following pages. Please see: SE/TE: , 414, , 436, CC24-CC25 6.GM.2: Know that the sum of the interior angles of any triangle is 180º and that the sum of the interior angles of any quadrilateral is 360º. Use this information to solve real-world and mathematical problems. SE/TE: 379 (AL 8-4a), , 385 SE = Student Edition 8 TE = Teacher s Edition

12 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.GM.3: Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate; apply these techniques to solve real-world and other mathematical problems. Prentice Hall Mathematics Course 1 SE/TE: 551 (#32), 553, CC30-CC31 6.GM.4: Find the area of complex shapes composed of polygons by composing or decomposing into simple shapes; apply this technique to solve real-world and other mathematical problems. SE/TE: , 431, , 436, , 468, GM.5: Find the volume of a right rectangular prism with fractional edge lengths using unit cubes of the appropriate unit fraction edge lengths (e.g., using technology or concrete materials), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths to solve real-world and other mathematical problems. SE/TE: 457, , 461, 466, 469, 470, CC26-CC27 6.GM.6: Construct right rectangular prisms from nets and use the nets to compute the surface area of prisms; apply this technique to solve real-world and other mathematical problems. SE/TE: , 461, 469, 470 DATA ANALYSIS AND STATISTICS 6.DS.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for the variability in the answers. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. SE/TE: 78, 93-96, 97, CC14-CC15 SE = Student Edition 9 TE = Teacher s Edition

13 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 6 6.DS.2: Select, create, and interpret graphical representations of numerical data, including line plots, histograms, and box plots. Prentice Hall Mathematics Course 1 SE/TE: 70-73, 74-77, 78, 79, 83, 84, 85, 86-90, 92, 93-96, 97, 98, , 102, CC6-CC7, CC8-CC9, CC10-CC13 6.DS.3: Formulate statistical questions; collect and organize the data (e.g., using technology); display and interpret the data with graphical representations (e.g., using technology). SE/TE: 78, 93-96, 97, CC14-CC15 6.DS.4: Summarize numerical data sets in relation to their context in multiple ways, such as: report the number of observations; describe the nature of the attribute under investigation, including how it was measured and its units of measurement; determine quantitative measures of center (mean and/or median) and spread (range and interquartile range), as well as describe any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered; and relate the choice of measures of center and spread to the shape of the data distribution and the context in which the data were gathered. SE/TE: 61-64, 65, 66-69, 71-73, 77, 82-83, 85, 86, 90, 95-96, 98, , 102, CC6-CC7, CC8-CC9, CC10-CC13 SE = Student Edition 10 TE = Teacher s Edition

14 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 Prentice Hall Mathematics Course 2 PROCESS STANDARDS FOR MATHEMATICS PS.1: Make sense of problems and Students are challenged to make sense of persevere in solving them. problems and persevere in solving them throughout the course. In addition to Guided Problem Solving lessons, homework exercises for each lesson include one or more Guided Problem Solving items. SE/TE: 10-11, 16-17, 22-23, 46-47, 50-51, 64-65, , , , , , 152, , , PS.2: Reason abstractly and quantitatively. Students are challenged to reason abstractly and creatively throughout the course. Some lessons focus on quantitative reasoning skills, and homework exercises frequently include Number Sense and/or Reasoning problems. SE/TE: 6-7, 12, 24-25, 33-34, 70-71, 73, 77-78, 82-85, 86, 87-90, , , , 135, 144 PS.3: Construct viable arguments and critique the reasoning of others. Students are challenged to construct viable arguments and critique the reasoning of others throughout the course. Students are exposed to More Than One Way to do a problem, and are asked to make conjectures and to perform Error Analyses of examples of faulty reasoning. SE/TE: 28-29, 135, 143, 144, 151 (#41), 190 (#48), 246, 312, 313 (#30), 327 (#29), 332, 334 (#25), 353 (#29-30), 390, 418 (#24) 11

15 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 PS.4: Model with mathematics. Prentice Hall Mathematics Course 2 Students are challenged to model problem situations with mathematical expressions and equations throughout the course. In addition to Guided Problem Solving lessons, homework exercises for each lesson include one or more Guided Problem Solving items which frequently incorporate mathematical modeling. SE/TE: 24-25, 64-65, 80-81, , 152, , , , 187, , , 247, 249, 253, PS.5: Use appropriate tools strategically. Students are challenged to strategically use a variety of tools, including number lines, algebra tiles, and calculators, throughout the course. Hands On Activity Labs and Technology Activity Labs are incorporated between regular lessons throughout the textbook. SE/TE: 13, 19, 36-37, 38-42, 43, 72, 85, 101, 125, 135, 140, 141, , 173, 179 PS.6: Attend to precision. Students are challenged to attend to precision in the use of mathematical vocabulary and the performance of computation algorithms, including estimation strategies, throughout the course. In addition to Vocabulary Builders and estimation lessons, homework exercises for each lesson might include Estimation problems. SE/TE: 4-7, 26, 96-97, , 124, , , 158, 185, 257, , 299 (Ex 3), 302, ,

16 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 PS.7: Look for and make use of structure. Prentice Hall Mathematics Course 2 Students are challenged to look for and make use of structure, e.g., by identifying patterns and by applying properties, throughout the course. SE/TE: 26-30, 48-51, 52, 68-71, 74-78, 91-94, 95, , , , 158, 168, , , PS.8: Look for and express regularity in repeated reasoning. Students are challenged to look for and express regularity in reasoning, e.g., while practicing computation algorithms and identifying repeating geometric patterns, throughout the course. SE/TE: 8-11, 14-17, 20-23, 38-42, 44-47, , 110, , , , , , , , 251 Mathematics Standards for Grade 7 NUMBER SENSE 7.NS.1: Find the prime factorization of whole numbers and write the results using exponents. SE/TE: 75-78, 79, 112, 114, NS.2: Understand the inverse relationship between squaring and finding the square root of a perfect square integer. Find square roots of perfect square integers. SE/TE: , , 429, 430, 672 (T670) 13

17 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 7.NS.3: Know there are rational and irrational numbers. Identify, compare, and order rational and common irrational numbers ( 2, 3, 5, ) and plot them on a number line. Prentice Hall Mathematics Course 2 SE/TE: 87, 91, 98, , 113, 278, , , 429, 430 COMPUTATION 7.C.1: Understand p + q as the number located a distance q from p, in the positive or negative direction, depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing realworld contexts. SE/TE: 31-34, 36-37, 38-42, 61, 62, CC6- CC7 7.C.2: Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts. SE/TE: 40-41, 61, 62, CC6-CC7 7.C.3: Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 and the rules for multiplying signed numbers. SE/TE: 43, 44-47, 48-51, 52, 61, 62, 66, CC8-CC9 7.C.4: Understand that integers can be divided, provided that the divisor is not zero, and that every quotient of integers (with non-zero divisor) is a rational number. Understand that if p and q are integers, then (p/q) = ( p)/q = p/( q). SE/TE: division of integers: 44-47, 48-51, 52, 61, 62, 66; division of positive and negative rational numbers: CC10-CC11 14

18 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 7.C.5: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. Prentice Hall Mathematics Course 2 SE/TE: , 237, 266, 268, CC18- CC19 7.C.6: Use proportional relationships to solve ratio and percent problems with multiple operations, such as the following: simple interest, tax, markups, markdowns, gratuities, commissions, fees, conversions within and across measurement systems, percent increase and decrease, and percent error. SE/TE: 236, , 243, , , , 258, , 264, , , , 309, , C.7: Compute with rational numbers fluently using a standard algorithmic approach. SE/TE: 8-11, 14-17, 20-23, 38-42, 44-47, 48-51, 69-71, , , , , , CC6-CC7, CC8-CC9, CC10-CC11 7.C.8: Solve real-world problems with rational numbers by using one or two operations. SE/TE: 8-11, 14, 16-17, 20-23, 24-25, 38, 40-42, 44-47, 48-51, 64-65, , , , , CC10-CC11 ALGEBRA AND FUNCTIONS 7.AF.1: Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear expressions, including situations that involve factoring (e.g., given 2x - 10, create an equivalent expression 2(x - 5)). Justify each step in the process. SE/TE: 8-10, 12, 15-17, 48-51, 52, 60, 61, 62, 66, 133, , , , 221, CC12-CC13 7.AF.2: Solve equations of the form px + q= r and p(x + q) = r fluently, where p, q, and r are specific rational numbers. Represent real-world problems using equations of these forms and solve such problems. SE/TE: 52, , 178, 179, , , , , 199, , , 222, 226, 308,

19 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 7.AF.3: Solve inequalities of the form px +q (> or ) r or px + q (< or ) r, where p, q, and r are specific rational numbers. Represent real-world problems using inequalities of these forms and solve such problems. Graph the solution set of the inequality and interpret it in the context of the problem. Prentice Hall Mathematics Course 2 SE/TE: , , , 221, 222, AF.4: Define slope as vertical change for each unit of horizontal change and recognize that a constant rate of change or constant slope describes a linear function. Identify and describe situations with constant or varying rates of change. SE/TE: , 502, 503, 525, AF.5: Graph a line given its slope and a point on the line. Find the slope of a line given its graph. SE/TE: , 502, 503, 525, AF.6: Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin). SE/TE: 27, , 242, , 251, 253, 256, 257, CC24-CC25, CC26-CC27 7.AF.7: Identify the unit rate or constant of proportionality in tables, graphs, equations, and verbal descriptions of proportional relationships. SE/TE: , 236, 237, 242, , 258, , 264, 266, 268, CC18-CC19, CC24-CC25, CC26-CC27 7.AF.8: Explain what the coordinates of a point on the graph of a proportional relationship mean in terms of the situation, with special attention to the points (0, 0) and (1,r), where r is the unit rate. SE/TE: 242, , 258, CC24-CC25, CC26-CC27 16

20 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 7.AF.9: Identify real-world and other mathematical situations that involve proportional relationships. Write equations and draw graphs to represent proportional relationships and recognize that these situations are described by a linear function in the form y = mx, where the unit rate, m, is the slope of the line. GEOMETRY AND MEASUREMENT 7.GM.1: Draw triangles (freehand, with ruler and protractor, and using technology) with given conditions from three measures of angles or sides, and notice when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.GM.2: Identify and describe similarity relationships of polygons including the angle-angle criterion for similar triangles, and solve problems involving similarity. 7.GM.3: Solve real-world and other mathematical problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing. Create a scale drawing by using proportional reasoning. 7.GM.4: Solve real-world and other mathematical problems that involve vertical, adjacent, complementary, and supplementary angles. 7.GM.5: Understand the formulas for area and circumference of a circle and use them to solve real-world and other mathematical problems; give an informal derivation of the relationship between circumference and area of a circle. 7.GM.6: Solve real-world and other mathematical problems involving volume of cylinders and three-dimensional objects composed of right rectangular prisms. Prentice Hall Mathematics Course 2 SE/TE: 27, , 242, , 251, 253, 256, 257, CC24-CC25, CC26-CC27 SE/TE: 335, , 364 (#26), CC20- CC21 SE/TE: 251, , 256, 257, 267, 268 SE/TE: 258, , 264, 267, 268, SE/TE: 329, , 345, 366, 368 SE/TE: 393, , 403, 416, 427, 429, 430, 495 SE/TE: 419, , 426, 429,

21 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 7.GM.7: Construct nets for right rectangular prisms and cylinders and use the nets to compute the surface area; apply this technique to solve real-world and other mathematical problems. Prentice Hall Mathematics Course 2 SE/TE: , 420, 429, 430 DATA ANALYSIS, STATISTICS, AND PROBABILITY 7.DSP.1: Understand that statistics can be SE/TE: , , CC30-CC31 used to gain information about a population by examining a sample of the population and generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.DSP.2: Use data from a random sample to draw inferences about a population. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. SE/TE: , , CC30-CC31 7.DSP.3: Find, use, and interpret measures of center (mean and median) and measures of spread (range, interquartile range, and mean absolute deviation) for numerical data from random samples to draw comparative inferences about two populations. SE/TE: CC28-CC29, CC30-CC31 7.DSP.4: Make observations about the degree of visual overlap of two numerical data distributions represented in line plots or box plots. Describe how data, particularly outliers, added to a data set may affect the mean and/or median. SE/TE: 58, CC28-CC29 18

22 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 7 7.DSP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Understand that a probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. Understand that a probability of 1 indicates an event certain to occur and a probability of 0 indicates an event impossible to occur. Prentice Hall Mathematics Course 2 SE/TE: , 585, , 591, , 597, , , 614, 616, DSP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its relative frequency from a large sample. SE/TE: 585, , 596, 597, CC32- CC33 7.DSP.7: Develop probability models that include the sample space and probabilities of outcomes to represent simple events with equally likely outcomes. Predict the approximate relative frequency of the event based on the model. Compare probabilities from the model to observed frequencies; evaluate the level of agreement and explain possible sources of discrepancy. SE/TE: 585, , 591, , 597, , , 614, 616,

23 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 Prentice Hall Mathematics Course 3 PROCESS STANDARDS FOR MATHEMATICS PS.1: Make sense of problems and Students are challenged to make sense of persevere in solving them. problems and persevere in solving them throughout the course. In addition to Guided Problem Solving lessons, homework exercises for each lesson include one or more Guided Problem Solving items. SE/TE: 55-56, 88-89, , , , , , 278, , 343, , , , , PS.2: Reason abstractly and quantitatively. Students are challenged to reason abstractly and creatively throughout the course. Some lessons focus on quantitative reasoning skills, and homework exercises frequently include Number Sense and/or Reasoning problems. SE/TE: 36, 64, 216 (#16-21), 221 (#33-34), 240, , 333, 339 (#32), 385, 401 (#12), 441 (#15), , 485 (#5), 501, PS.3: Construct viable arguments and critique the reasoning of others. Students are challenged to construct viable arguments and critique the reasoning of others throughout the course. Students are exposed to More Than One Way to do a problem, and are asked to make conjectures and to perform Error Analyses of examples of faulty reasoning. SE/TE: 15, 30 (#40), 39, 42 (#11), 54 (#6), 69 (#39), 74, 110 (#49), 121 (#19), , 148 (#13), 176, 177 (#29), 222 (#43),

24 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 PS.4: Model with mathematics. Prentice Hall Mathematics Course 3 Students are challenged to model problem situations with mathematical expressions and equations throughout the course. In addition to Guided Problem Solving lessons, homework exercises for each lesson include one or more Guided Problem Solving items which frequently incorporate mathematical modeling. SE/TE: 5-8, 34-36, 107, , , , 272, , 278 (#16), , 454, , 560, 568 (#19), 587 PS.5: Use appropriate tools strategically. Students are challenged to strategically use a variety of tools, including number lines, algebra tiles, and calculators, throughout the course. Hands On Activity Labs and Technology Activity Labs are incorporated between regular lessons throughout the textbook. SE/TE: 32, 71, 85, 90, 111, 140, 145, 191, 196, 245, 260, 265, 302, 344, 363 PS.6: Attend to precision. Students are challenged to attend to precision in the use of mathematical vocabulary and the performance of computation algorithms, including estimation strategies, throughout the course. In addition to Vocabulary Builders and estimation lessons, homework exercises for each lesson might include Estimation problems. SE/TE: 80, 77, 107, 109, 116, , , 228, , 286, , , 390 (#12), 402,

25 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 PS.7: Look for and make use of structure. Prentice Hall Mathematics Course 3 Students are challenged to look for and make use of structure, e.g., by identifying patterns and by applying properties, throughout the course. SE/TE: 10-13, 26-30, 33-36, 38-41, 57-60, 96, , , , , , , , 517, PS.8: Look for and express regularity in repeated reasoning. Students are challenged to look for and express regularity in reasoning, e.g., while practicing computation algorithms and identifying repeating geometric patterns, throughout the course. SE/TE: 16-19, 20-23, 24-25, 33-36, 38-41, 61, 66-69, 72-76, 86-89, 91, 150, , , , Mathematics Standards for Grade 8 NUMBER SENSE 8.NS.1: Give examples of rational and irrational numbers and explain the difference between them. Understand that every number has a decimal expansion; for rational numbers, show that the decimal expansion terminates or repeats, and convert a decimal expansion that repeats into a rational number. SE/TE: 57-60, 61, 62-65, 66-69, , 116, 119, 122, 123, 125, 152, 154, 158, , NS.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers. SE/TE: , 116, 119, 122, 123, 125, 152, 154, ,

26 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 8.NS.3: Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions. Prentice Hall Mathematics Course 3 SE/TE: 86-89, 90, 92-95, 99, 100, 110, , , , 125, 337, , 399, , NS.4: Use square root symbols to represent solutions to equations of the form x^2 = p, where p is a positive rational number. COMPUTATION 8.C.1: Solve real-world problems with rational numbers by using multiple operations. SE/TE: , , , 122, 123, 125, 126, , 154, 158 SE/TE: 34-36, 39-41, 82-84, 87-89, , , , , , , , 272, , , C.2: Solve real-world and other mathematical problems involving numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology, such as a scientific calculator, graphing calculator, or excel spreadsheet. SE/TE: 92-95, 96, 99, 100, , 575, 582, , 591, 592, ALGEBRA AND FUNCTIONS 8.AF.1: Solve linear equations with rational number coefficients fluently, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems. 8.AF.2: 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 transforming a 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). SE/TE: 33-36, 38-41, 42, , 260, , 270, , , , , , , 296, SE/TE: 36 (#40), CC10-CC11 23

27 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 8.AF.3: Understand that a function assigns to each x-value (independent variable) exactly one y-value (dependent variable), and that the graph of a function is the set of ordered pairs (x, y). 8.AF.4: Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. Prentice Hall Mathematics Course 3 SE/TE: 513, 516, 517, , 527, , 533, , , , , 550, 553, 554 SE/TE: , 522, 549 (#31), 553, AF.5: 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. Describe similarities and differences between linear and nonlinear functions from tables, graphs, verbal descriptions, and equations. SE/TE: , 517, , 527, , 532, 533, , , , 550, 553, AF.6: Construct a function to model a linear relationship between two quantities given a verbal description, table of values, or graph. Recognize in y = mx + b that m is the slope (rate of change) and b is the y- intercept of the graph, and describe the meaning of each in the context of a problem. SE/TE: , 527, , 532, 533, , , , 553, AF.7: Compare properties of two linear functions given in different forms, such as a table of values, equation, verbal description, and graph (e.g., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed). SE/TE: 550, CC32-CC33 24

28 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 8.AF.8: Understand that solutions to a system of two linear equations correspond to points of intersection of their graphs because points of intersection satisfy both equations simultaneously. Approximate the solution of a system of equations by graphing and interpreting the reasonableness of the approximation. Prentice Hall Mathematics Course 3 SE/TE: CC28-CC31 GEOMETRY AND MEASUREMENT 8.GM.1: Identify, define and describe attributes of three-dimensional geometric objects (right rectangular prisms, cylinders, cones, spheres, and pyramids). Explore the effects of slicing these objects using appropriate technology and describe the two-dimensional figure that results. SE/TE: , , 362, 363, , 367, , 373, , 379, , , 387, , GM.2: Solve real-world and other mathematical problems involving volume of cones, spheres, and pyramids and surface area of spheres. SE/TE: , 392, , 405, GM.3: Verify experimentally the properties of rotations, reflections, and translations, including: lines are mapped to lines, and line segments to line segments of the same length; angles are mapped to angles of the same measure; and parallel lines are mapped to parallel lines. SE/TE: , 140, , 145, , 153, 154, CC12-CC13 8.GM.4: 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. Describe a sequence that exhibits the congruence between two given congruent figures. SE/TE: , 347, 348, CC12-CC13 25

29 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 8.GM.5: 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. Describe a sequence that exhibits the similarity between two given similar figures. 8.GM.6: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Prentice Hall Mathematics Course 3 SE/TE: CC14-CC15 For additional related content, please see: SE/TE: , 185, , , 203, 204, SE/TE: , 140, , , 153, 154, CC12-CC13, CC14-CC15 8.GM.7: Use inductive reasoning to explain the Pythagorean relationship. SE/TE: 111, CC8 8.GM.8: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions. 8.GM.9: Apply the Pythagorean Theorem to find the distance between two points in a coordinate plane. SE/TE: 111, , 117, , 122, 123, , 139 (#24), 153, 154, 158, 200, CC8-CC9, CC16-CC17 SE/TE: DATA ANALYSIS, STATISTICS, AND PROBABILITY 8.DSP.1: Construct and interpret scatter SE/TE: 443, , 448, 449, 453, 455, plots for bivariate measurement data to , 460, 463, 465, 620, 621, CC18- investigate patterns of association between CC19, CC20-CC21 two quantitative variables. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.DSP.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 describe the model fit by judging the closeness of the data points to the line. SE/TE: 443, 445, 446, 447, 448, 449, 453, 463, CC20-CC21 26

30 A Correlation of Prentice Hall Mathematics Courses 1-3 to the for Mathematics (2014) for Mathematics (2014), Grade 8 8.DSP.3: Write and use equations that model linear relationships to make predictions, including interpolation and extrapolation, in real-world situations involving bivariate measurement data; interpret the slope and y-intercept. Prentice Hall Mathematics Course 3 SE/TE: CC20-CC21 For additional related content, please see: SE/TE: 443, 445, 446, 447, DSP.4: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Understand and use appropriate terminology to describe independent, dependent, complementary, and mutually exclusive events. SE/TE: , 253, 474, 479, 485, , , , , 505, DSP.5: Represent sample spaces and find probabilities of compound events (independent and dependent) using methods, such as organized lists, tables, and tree diagrams. SE/TE: , 253, 474, 491, DSP.6: For events with a large number of outcomes, understand the use of the multiplication counting principle. Develop the multiplication counting principle and apply it to situations with a large number of outcomes. SE/TE: , , , , 505,