Correlation to the Common Core State Standards

Correlation to the Common Core State Standards Go Math! 2011 Grade 6 Common Core is a trademark of the National Governors Association Center for Best Practices and the Council of Chief State School Officers. Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 07/13 MS79524g

Explanation Of Correlation The following document is a reverse correlation of Go Math! to the Common Core State Standards for Mathematics. The format for this correlation follows the same basic format established by the State Standards, modified to accommodate the addition of page references. The correlation provides a cross-reference between the skills in the State Standards and representative page numbers where those skills are taught or assessed. The references contained in this correlation reflect Houghton Mifflin Harcourt s interpretation of the Mathematic objectives outlined in the Common Core State Standards. Key to References SE Student s Edition TE Teacher s Edition PG Practice Guide PB Practice Book

Houghton Mifflin Harcourt Go Math! Grade 6 2011 correlated to the Common Core State Standards for Mathematics Grade 6 Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. SE: 12, 13 16, 21 24, 49 52, 55, 57 60, 63 66, 71 74, 75 78, 85 88, 93 96, 97 100, 103 106, 107 110, 117 120, 125 128, 129 132, 143 146, 147 150, 154, 167 170, 171 174, 175 178, 179 182, 183 186, 196, 201 204, 208, 215 218, 230, 241 244, 251 254, 255 258, 262, 263 266, 269 272, 273 276, 280, 291 294, 295 298, 328, 329 332, 333 336, 337 340, 346, 347 350, 351 354, 355 358, 359 362, 369 372, 376, 377 380, 381 384, 385 388, 389 392, 399 402, 403 406, 407 410, 411 414, 415 418, 444, 447 450, 451 454, 469 472, 485 488, 491 494, 499 502, 503 506, 510, 521 524, 528, 535 538 TE: 13A 13B, 21A 21B, 49A 49B, 57A 57B, 63A 63B, 71A 71B, 75A 75B, 85A 85B, 93A 93B, 93 96, 97A 97B, 103A 103B, 107A 107B, 117A 117B, 125A 125B, 129A 129B, 143A 143B, 147A 147B, 167A 167B, 171A 171B, 175A 175B, 179A 179B, 183A 183B, 201A 201B, 215A 215B, 241A 241B, 251A 251B, 255A 255B, 263A 263B, 269A 269B, 273A 273B, 291A 291B, 295A 295B, 329A 329B, 333A 333B, 337A 337B, 347A 347B, 351A 351B, 355A 355B, 359A 359B, 369A 369B, 377A 377B, 381A 381B, 385A 385B, 389A 389B, 399A 399B, 403A 403B, 407A 407B, 411A 411B, 415A 415A, 447A 447B, 451A 451B, 469A 469B, 485A 485B, 491A 491B, 499A 499B, 503A 503B, 521A 521B, 535A 535B

2. Reason abstractly and quantitatively. SE: 9 12, 17 20, 27 30, 35 38, 39 42, 49 52, 63 66, 71 74, 75 78, 89 92, 93 96, 97 100, 103 106, 107 110, 118, 121 124, 139 142, 167 170, 175 178, 183 186, 197 200, 251 254, 255 258, 259 262, 277 280, 281 284, 301 304, 321 324, 389 392, 395 398, 407 410, 429 432, 469 472, 473 476, 485 488, 507 510, 517 520, 531 534, 535 538 TE: 9A 9B, 9 12, 17A 17B, 17 20, 27A 27B, 27 30, 35A 35B, 35 38, 39A 39B, 39 42, 49A 49B, 49 52, 63A 63B, 63 66, 71A 71B, 71 74, 75A 75B, 75 78, 89A 89B, 89 92, 93A 93B, 93 96, 97A 97B, 97 100, 103A 103B, 103 106, 107A 107B, 107 110, 118, 121A 121B, 121 124, 139A 139B, 139 142, 167A 167B, 167 170, 175A 175B, 175 178, 183A 183B, 183 186, 197A 197B, 197 200, 251A 251B, 251 254, 255A 255B, 255 258, 259A 259B, 259 262, 277A 277B, 277 280, 281A 281B, 281 284, 301A 301B, 301 304, 321A 321B, 321 324, 389A 389B, 389 392, 395A 395B, 395 398, 407A 407B, 407 410, 429A 429B, 429 432, 469A 469B, 469 472, 473A 473B, 473 476, 485A 485B, 485 488, 507A 507B, 507 510, 517A 517B, 517 520, 531A 531B, 531 534, 535A 535B, 535 538 3. Construct viable arguments and critique the reasoning of others. SE: 38, 42, 78, 88, 138, 192, 244, 304, 305 308, 346, 384, 392, 406, 414, 450, 458, 462, 480 TE: 38, 42, 78, 88, 138, 192, 244, 304, 305 308, 346, 384, 392, 406, 414, 450, 458, 462, 480 2

4. Model with mathematics. SE: 31 34, 53 56, 67 70, 135 138, 151 154, 179 182, 219 222, 241 244, 325 328, 355 358, 369 372, 477 480, 481 484, 491 494, 495 498, 525 528, 531 534, 535 538 TE: 31A 31B, 31 34, 53A 53B, 53 56, 67A 67B, 67 70, 135A 135B, 135 138, 151A 151B, 151 154, 179A 179B, 179 182, 219A 219B, 241A 241B, 241 244, 325A 325B, 325 328, 343A 343B, 343 346, 355A 355B, 355 358, 369A 369B, 369 372, 477A 477B, 477 480, 481A 481B, 481 484, 491A 491B, 491 494, 495A 495B, 495 498, 525A 525B, 525 528, 531A 531B, 531 534, 535A 535B, 535 538 5. Use appropriate tools strategically. SE: 53 56, 67 70, 117 120, 155 158, 205 208, 222, 236, 309 312, 373 376, 381 384, 425 428 TE: 53A 53B, 53 56, 67A 67B, 67 70, 117A 117B, 117 120, 155A 155B, 155 158, 205A 205B, 205 208, 222, 236, 309A 309B, 309 312, 373A 373B, 373 376, 381A 381B, 381 384, 425A 425B, 425 428 6. Attend to precision. SE: 5 8, 17 20, 49 52, 57 60, 63 66, 71 74, 85 88, 89 92, 93 96, 97 100, 107 110, 143 146, 147 150, 171 174, 201 204, 237 240, 259 262, 337 340, 347 350, 351 354, 359 362, 377 380, 385 388, 415 418 TE: 5A 5B, 5 8, 17A 17B, 17 20, 49A 49B, 49 52, 57A 57B, 57 60, 63A 63B, 63 66, 71B, 71 74, 85A 85B, 85 88, 89A 89B, 89 92, 93A 93B, 93 96, 97A 97B, 97 100, 103A 103B, 103 106, 107A 107B, 107 110, 143A 143B, 143 146, 147A 147B, 147 150 171A 171B, 171 174, 201A 201B, 201 204, 237A 237B, 237 240, 259A 259B, 259 262, 329A 329B, 329 332, 333A 333B, 333 336, 337A 337B, 337 340, 347A 347B, 347 350, 351A 351B, 351 354, 359A 359B, 359 362, 377A 377B, 377 380, 385A 385B, 385 388, 415A 415B, 415 418 3

7. Look for and make use of structure. SE: 5 8, 35 38, 189 192, 193 196, 223 226, 227 230, 233 236, 395 398, 399 402, 433 436, 437 440 TE: 5A 5B, 5 8, 35A 35B, 35 38, 189A 189B, 189 192, 193A 193B, 193 196, 223A 223B, 223 226, 227A 227B, 227 230, 233A 233B, 233 236, 395A 395B, 395 398, 399A 399B, 399 402, 433A 433B, 433 436, 437A 437B, 437 440, 441A 441B, 441 444 8. Look for and express regularity in repeated reasoning. SE: 19, 29, 41, 52, 65, 95, 99, 105, 127, 131, 173, 181, 185, 191, 217, 331, 339, 353, 361, 375, 379, 409, 471, 483, 501 TE: 19, 29, 41, 52, 65, 95, 99, 105, 127, 131, 173, 181, 185, 191, 217, 331, 339, 353, 361, 375, 379, 409, 471, 483, 501 4

Standards for Mathematical Content 6.RP Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. SE: 167 170, 175 178, 179 182 TE: 167A 167B, 167 170, 171B, 175B, 175 178, 179A 179B, 179 182 PB: P83, P84a P84d, P87 PG: PG68 PG71, PG100 PG101 2012 Edition: 4.1 2. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. SE: 171 174, 183 186 TE: 171A 171B, 171 174, 183A 183B, 183 186 PB: P85, P91, P204a P204d PG: PG82 PG85, PG100 PG101 3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. 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. Use tables to compare ratios. SE: 168 170, 179 182 TE: 168 170, 179 182 PB: P83, P84a P84d, P204a P204d PG: PG68 PG71, PG82 PG85 2012 Edition: 4.3, 4.4, 4.8 b. Solve unit rate problems including those involving unit pricing and constant speed. SE: 171 174, 183 186 TE: 171A 171B, 171 174, 183A 183B, 183 186 PB: P85, P91, PG100 PG101 2012 Edition: 4.6 5

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. SE: 201 204, 205 208 TE: 201A 201B, 201 204, 205A 205B, 205 208 PB: P99, P100a P100d, P101 PG: PG72 PG75 2012 Edition: 5.1, 5.6 d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. SE: 223 226, 227 230, 233 236 TE: 223A 223B, 223 226, 227A 227B, 227 230, 233A 233B, 233 236 PB: P111, P113, P115 PG: PG100 PG101 2012 Edition: 6.4 6

6.NS The Number System Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. SE: 135 138, 139 142, 143 146, 147 150, 151 154 TE: 135A 135B, 135 138, 139A 139B, 139 142, 143A 143B 143 146, 147A 147B, 147 150, 151 154 PB: P67, P69, P71, P73, P75 PG: PG98 PG99 2012 Edition: 2.8 Compute fluently with multi-digit numbers and find common factors and multiples. 2. Fluently divide multi-digit numbers using the standard algorithm. SE: 64 66, 71 74 TE: 64 66, 71A, 71 74 PB: P31, P35 Mega Math Additional Coverage: The Number Games: Up, Up and Array, Levels L S 2012 Edition: 1.1 3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. 4. 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 1 100 with a common factor as a multiple of a sum of two whole numbers with no common factor. SE: 2, 49 52, 53 56, 57 60, 63 66, 67 70, 71 74, 75 78 TE: 1 2, 49A 49B, 49 52, 53A 53B, 53 56, 57A 57B, 57 60, 63A 63B, 63 66, 67A 67B, 67 70, 71A 71B, 71 74, 75 78 PB: P25, P27, P29, P31, P33, P35, P37 PG: PG98 PG99 SE: 85, 93 96, 97 100, 103 106, 126 TE: 85, 93B, 94 95, 97 100, 126 2012 Edition: 1.3, 1.4, 1.5, 2.4 7

Apply and extend previous understandings of numbers to the system of rational numbers. 5. Understand that positive and negative numbers are used together 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 quantities in real-world contexts, explaining the meaning of 0 in each situation. SE: 321 324 TE: 321A 321B, 321 324 PB: P159, P160a P160d PG: PG78 PG81 6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. a. 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 SE: 321 324 TE: 321A 321B, 321 324 PB: P159 opposite. 2012 Edition: 3.3 b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. SE: 403 406, 407 410, 411 414 TE 403A 403B, 403 406, 407B, 407 410, 411A 411B, 411 414 PB: P199, P201, P203 2012 Edition: 3.8 SE: 321 323, 326 328, 334 336, 343, 345, 355 358 403 406, 407 410, 411 413 TE: 321B, 321 324, 325A 325B, 326 328, 334 336, 343A 343B, 343, 345, 355B, 355 358, 403A 403B, 403 406, 407B, 407 410, 411A 411B, 411 414 PB: P159, P160b, P199, P201, P203 PG: PG78 PG79, PG81 2012 Edition: 3.3 8

7. Understand ordering and absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. SE: 90 91, 322 323 TE: 89A 89B, 90, 321B, 322 323 PB: P159, P160b PG: PG78 PG79, PG81 2012 edition: 3.3 b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. SE: 89, 92, 164, 321, 324 TE: 89, 92, 163 164, 321B, 324 PB: P45, P159, P160a, P160d PG: PG81 2012 Edition: 3.2, 3.4 c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. d. Distinguish comparisons of absolute value from statements about order. 8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. SE: 321, 323 324, 329 332, 337 TE: 321, 323 324 PB: P159 2012 Edition: 3.5 SE: 321 324 TE: 321B, 321 324 2012 Edition: 3.6 SE: 403 406, 451 454 TE: 403A 403B, 403 406, 451A 451B, 451 454 PB: P199, P223 2012 Edition: 3.7, 3.9, 3.10 9

6.EE Expressions and Equations Apply and extend previous understandings of arithmetic to algebraic expressions. 1. Write and evaluate numerical expressions involving whole-number exponents. SE: 5 8, 17 19 TE: 5A 5B, 5 8, 17A, 17 20 PB: P3, P9 2012 Edition: 7.2 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. SE: 31 34 TE: 31A 31B, 31 34 b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. PB: P15 SE: 32 33 TE: 31B, 32 33 PB: P15, P74a PG: PG66 c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). 3. Apply the properties of operations to generate equivalent expressions. 4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). 2012 Edition: 7.4 SE: 35 38, 50 51, 58 59, 94 95, 105, 126 127, 219 222, 241 244 TE: 35A 35B, 35 38, 50, 94, 219B, 219 222, 241A 241B, 241 244 PB: P17, P25, P29, P47, P63, P109, P119 2012 Edition: 7.6 SE: 39 42 TE: 39A 39B, 39 42 PB: P19, P74a P74b PG: PG66 PG67 2012 Edition: 7.7, 7.8 SE: 40 42 TE: 39B, 40 42 PB: P19 2012 Edition: 7.9 10

Reason about and solve one-variable equations and inequalities. 5. Understand solving an equation or inequality as a process of answering a 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 SE: 373 376, 377, 379, 385, 387, 415 418 TE: 373 376, 377B, 377, 379, 385, 415A 415B, 415 418 PB: P187, P191 specified set makes an equation or inequality true. 2012 Edition: 8.1, 8.8 6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. SE: 31 34, 378 380, 386 387, 399 402 TE: 31A 31B, 31 34, 386 387, 399B, 399 402 PB: P15, P187, P191, P197 2012 Edition: 8.7 SE: 369 372, 373 376, 377 380, 381 384, 385 388 TE: 369A 369B, 369 372, 373A 373B, 373 376, 377A 377B, 377 380, 381A 381B, 381 384, 385A 385B, 385 388 PB: P183, P185, P187, P189, P191 2012 Edition: 8.2 8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. SE: 415 418 TE: 415A 415B, 415 418 PB: P205 2012 Edition: 8.9, 8.10 Represent and analyze quantitative relationships between dependent and independent variables. 9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using SE: 399 402, 407 410, 411 414 TE: 399A 399B, 399 402, 407A 407B, 407 410, 411A 411B, 411 414 PB: P197, P203 PG: PG102 PG103 graphs and tables, and relate these to the equation. 2012 Edition: 9.1, 9.2, 9.3, 9.4, 9.5 11

6.G Geometry Solve real-world and mathematical problems involving area, surface area, and volume. 1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. SE: 318, 481 484, 491 494, 503 506 TE: 317 318, 481A 481B, 481 484, 491A 491B, 491 494, 503A 503B, 503 506 PB: P239, P243, P244a P244b, P249 PG: PG86 PG87 2012 Edition: 10.2, 10.4, 10.6 2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving realworld and mathematical problems. 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 in the context of solving real-world and mathematical problems. 4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. SE: 525 528, 535, 537 TE: 525A 525B, 525 528, 535B, 535, 537 PB: P261, P265 Mega Math Additional Coverage: Ice Station Exploration: Arctic Algebra, Level DD 2012 Edition: 11.5 SE: 451 454 TE: 451A 451B, 451 454 PB: P223 2012 Edition: 10.7 SE: 517 520, 521 524 TE: 517A 517B, 517 520, 521A 521B, 521 524 PB: P257, P259, P260a P206b PG: PG88 PG89 2012 Edition: 11.2, 11.4 12

6.SP Statistics and Probability Develop understanding of statistical variability. 1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. SE: 281 TE: 281B, 281 2012 Edition: 12.1 2. 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. 3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. SE: 259 262 TE: 259A 259B, 259 262 PB: P129 2012 Edition: 12.2 SE: 259 262 TE: 259A 259B, 259 262 PB: P129, P130a P130b PG: PG76 PG77 2012 Edition: 12.6, 13.4 13

Summarize and describe distributions. 4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. SE: 263, 265, 270 272, 274 TE: 263A 263B, 263, 265 266, 269A 269B, 270 272, 273B, 274 PB: P131, P133 2012 Edition: 13.2 5. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. SE: 259 262 TE: 259 260, 262 PB: P129 b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. 2012 Edition: 12.2 SE: 251 253, 274, 282 283 TE: 251 253, 269B, 273B PB: P125, P139 2012 Edition: 13.7 c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. SE: 259 262, 263, 265, 270 271, 281 TE: 259A 259B, 259 262, 263A, 263, 265, 269A, 270, 281 PB: P129, P130a P130b, P131, P133 PG: PG76 PG77 2012 Edition: 12.5, 13.1, 13.3, 13.8 SE: 260 262 TE: 260 262 PB: P129 2012 Edition: 13.5, 13.6 14