Correlation to the Common Core State Standards

Correlation to the Common Core State Standards Go Math! 2011 Grade 4 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 MS79524e

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 4 2011 correlated to the Common Core State Standards for Mathematics Grade 4 Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. SE: 27 30, 31 34, 45 48, 49 52, 53 56, 70, 71 74, 81 84, 85 88, 92, 103 106, 107 110, 119 122, 132, 136, 140, 144, 148, 149 152, 162, 163 166, 167 170, 192, 203 206, 214, 229 232, 250, 259 262, 266, 277 280, 281 282, 285 288, 327A 327B, 327 330, 374, 378, 379 380, 399 402, 403 406, 407 410, 413 416, 417 420, 448, 462, 463 466, 492, 518 TE: 27A 27B, 27 30, 31A 31B, 31 34, 45A 45B, 45 48, 49A 49B, 49 52, 53A 53B, 53 56, 70, 71B, 71 74, 81A 81B, 81 84, 85A 85B, 85 88, 92, 103A 103B, 103 106, 107A 107B, 107 110, 119A 119B, 119 122, 132, 136, 140, 144, 148, 149A 149B, 149 152, 162, 163A 163B, 163 166, 167A 167B, 167 170, 192, 203A 203B, 203 206, 214, 225 228, 229A 229B, 229 232, 250, 259A 259B, 259 262, 266, 277A 277B, 277 280, 281A 281B, 281 284, 285A 285B, 285 288, 327A 327B, 327 330, 374, 378, 379A 379B, 379 380, 399A 399B, 399 402, 403A 403B, 403 406, 407A 407B, 407 410, 413A 413B, 413 416, 417A 417B, 417 420, 448, 462, 463A 463B, 463 466, 492, 518

2. Reason abstractly and quantitatively. SE: 13 16, 19 22, 23 26, 27 30, 31 34, 41 44, 45 48, 49 52, 53 56, 59 62, 63 66, 67 70, 71 74, 81 84, 85 88, 89 92, 93 96, 99 102, 103A 103B, 103 106, 111 114, 115 118, 129 132, 137 140, 145 148, 149 152, 153 156, 167 170, 177 180, 181 184, 185 188, 199 202, 203 206, 211 214, 233 236, 237 240, 243 246, 247 250, 255 258, 259 262, 282 284, 291 294, 299 302, 311 314, 342, 345 348, 349 352, 371 374, 375 378, 385 388, 389 392, 403 406, 429 432, 455 458, 463 466, 467 470, 477 480, 481 484, 485 488, 489 492, 493 496, 497 500, 503 506, 507 510, 511 514 TE: 13A 13B, 13 16, 19A 19B, 19 22, 23A 23B, 23 26, 27A 27B, 27 30, 31A 31B, 31 34. 41A 41B, 41 44, 45A 45B, 45 48, 49A 49B, 49 52, 53A 53B, 53 56, 59A 59B, 59 62, 63A 63B, 63 66, 67A 67B, 67 70, 71A 71B, 71 74, 81A 81B, 81 84, 85A 85B, 85 88, 89A 89B, 89 92, 93A 93B, 93 96, 99A 99B, 99 102, 103A 103B, 103 106, 107A 107B, 107 110, 111A 111B, 115A 115B, 115 118, 129A 129B, 129 132, 137A 137B, 137 140, 145A 145B, 145 148, 149A 149B, 149 152, 153A 153B, 153 156, 167A 167B, 167 170, 177A 177B, 177 180, 181A 181B, 181 184, 185A 185B, 199A 199B, 199 202, 203A 203B, 203 206, 211A 211B, 211 214, 225A 225B, 233A 233B, 233 236, 237A 237B, 237 240, 243A 243B, 247A 247B, 247 250, 255A 255B, 255 258, 259A 259B, 259 262, 282 284, 291A 291B, 291 294, 299A 299B, 299 302, 311A 311B, 311 314, 342, 345A 345B, 349A 349B, 349 352, 371A 371B, 371 374, 375A 375B, 375 378, 385A 385B, 389A 389B, 389 392, 403A 403B, 403 406, 429A 429B, 429 432, 455A 455B, 463A 463B, 467A 467B, 467 470, 477A 477B, 477 480, 481A 481B, 481 484, 485A 485B, 485 488, 489A 489B, 489 492, 493A 493B, 493 496, 497A 497B, 503A 503B, 503 506, 507A 507B, 511A 511B, 515A 515B, 515 518 2

3. Construct viable arguments and critique the reasoning of others. SE: 8, 12, 16, 34, 44, 48, 52, 66, 74, 101, 106, 118, 166, 170, 198, 207 210, 214, 228, 246, 293, 298, 314, 348, 405, 413, 420, 440, 444, 480 TE: 8, 12, 16, 34, 44, 48, 52, 66, 74, 101, 106, 118, 166, 170, 198, 207A 207B, 207 210, 214, 228, 246, 293, 298, 314, 348, 405, 413, 420, 440, 444, 480 4. Model with mathematics. SE: 30, 34, 62, 81 84, 85 88, 95 96, 141 144, 266 TE: 30, 34, 62, 71B, 81A 81B, 81 84, 85A 85B, 85 88, 95 96, 141A 141B, 141 144, 266 5. Use appropriate tools strategically. SE: 9 12, 22, 41 42, 49 52, 59 62, 83, 88, 93 95, 111 114, 129 130, 133 136, 153 156, 159 162, 163A 163B, 163 166, 189 192, 195 198, 221 224, 229 232, 251 254, 263 266, 315 318, 319 322, 323 326, 327 330, 341 344, 363 366, 379 380, 417 420, 433 436, 445 448 TE: 9A 9B, 9 12, 22, 41A, 41 42, 49A 49B, 49 52, 59 62, 83, 88, 93 95, 111 114, 129 130, 133A 133B, 133 136, 153A 153B, 153 156, 159A 159B, 159 162, 163 166, 189A 189B, 189 192, 195A 195B, 195 198, 221A 221B, 221 224, 229A 229B, 229 232, 251A 251B, 251 254, 263A 263B, 263 266, 315A 315B, 315 318, 319A 319B, 319 322, 323A 323B, 323 326, 327A 327B, 327 330, 341A 341B, 341 344, 363A 363B, 363 366, 379A 379B, 379 380, 417A 417B, 417 420, 433A 433B, 433 436, 445A 445B, 445 448 3

6. Attend to precision. SE: 5A 5B, 5 8, 56, 81 84, 85 88, 99 102, 103 105, 107 110, 111 114, 333 336, 337 340, 345 348, 353 356, 433A 433B, 433 436, 437A 437B, 437 440, 441A 441B, 441 444, 445A 445B, 445 448, 449A 449B, 449 452, 459 462 TE: 5A 5B, 5 8, 56, 81A 81B, 81 84, 85A 85B, 85 88, 99A 99B, 99 102, 103A, 103 105, 107 110, 111A 111B, 111 114, 295A 295B, 295 298, 333A 333B, 333 336, 337A 337B, 337 340, 345A 345B, 345 348, 353A 353B, 353 356, 433 436, 437 440, 441 444, 445 448, 449 452, 459A 459B, 459 462 7. Look for and make use of structure. SE: 5 8, 9 12, 41 44, 45 48, 89 92, 93 96, 129 132, 177 180, 233 236, 337 340, 455A 455B, 455 458, 511 515 TE: 5A 5B, 5 8, 9A 9B, 9 12, 41A 41B, 41 44, 45A 45B, 45 48, 89A 89B, 89 92, 93A 93B, 93 96, 129A 129B, 129 132, 177A 177B, 177 180, 233A 233B, 233 236, 337A 337B, 337 340, 455 458, 511A 511B, 511 515 8. Look for and express regularity in repeated reasoning. SE: 29, 54 55, 65, 70, 84, 131, 135, 143, 151, 178 179, 201, 207 210, 234, 245, 262, 334 335, 365, 388 TE: 29, 54 55, 59B, 65, 70, 84, 131, 135, 143, 151, 178 179, 201, 207A 207B, 207 210, 234, 245, 262, 334 335, 365, 388 4

Standards for Mathematical Content 4.OA Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. 1. Interpret a multiplication equation as a comparison, e.g., SE: 116 118 interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal TE: 116 118 statements of multiplicative comparisons as multiplication equations. 2012 Edition: 2.1, 2.2 2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. SE: 71 74, 116 118 TE: 71A, 71B, 71 74, 116 118 PB: P23, P35, P55, P57 2012 Edition: 2.2 SE: 30, 119 122, 152, 153-156,162, 168, 185 188, 206, 207 210, 263 266 TE: 30, 119A, 119B, 119 122, 152, 153A, 153B, 153 156, 162, 168, 185A, 185B, 185 188, 206, 207 210, 263A, 263B, 263 266 PB: P59, P74, P77, P131 5

Gain familiarity with factors and multiples. 4. Find all factor pairs for a whole number in the range 1 SE: 59 62, 63 66 100. Recognize that a whole number is a multiple of TE: 59A, 59B, 59 62, 63A, 63B, 63 66 each of its factors. Determine whether a given whole PB: P29, P30e P30f, P31, P36a P36b number in the range 1 100 is a multiple of a given onedigit number. Determine whether a given whole number PG: PG70 PG71, PG72 PG73 in the range 1 100 is prime or composite. 2012 Edition: 5.1, 5.4, 5.5 Generate and analyze patterns. 5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. SE: 89 92, 93 97, 515 518 TE: 89A, 89B, 89 92, 93A, 93B, 93 97, 515A, 515B, 515 518 PB: P45, P47, P255 Mega Math Additional Coverage: The Number Games: Tiny's Think Tank, Level J 4.NBT Number and Operations in Base Ten Generalize place value understanding for multi-digit whole numbers. 1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. 2. Read and write multi-digit whole numbers using baseten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 3. Use place value understanding to round multi-digit whole numbers to any place. 2012 Edition: 5.6, 10.7 SE: 5, 9, 10 TE: 5, 9, 10 2012 Edition: 1.1 SE: 5 8, 9 12, 19 22 TE: 5A, 5B, 5 8, 9A, 9B, 9 12, 19A, 19B, 19 22 PB: P3, P5, P9 2012 Edition: 1.2, 1.5 SE: 23 26 TE: 23B, 23 26 PB: P11 6

Use place value understanding and properties of operations to perform multi-digit arithmetic. 4. Fluently add and subtract multi-digit whole numbers SE: 27 30 using the standard algorithm. TE: 27A, 27B, 27 30 PB: P13 5. Multiply a whole number of up to four digits by a onedigit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. SE: 41 44, 53 56, 149 152, 153 156, 159 162, 163 166, 167 170, 181 184, 189 192, 195 198, 199 202, 203 206 TE: 41A, 41B, 41 44, 53A, 53B, 53 56, 149A, 149B, 149 152, 153A, 153B, 153 156, 159A, 159B, 159 162, 163A, 163B, 163 166, 167B, 167 170, 181B, 181 184, 189A, 189B, 189 192, 195A, 195B, 195 198, 199A, 199B, 199 202, 203A, 203B, 203 206 PB: P21, P27, P75, P77, P79, P81, P83, P91, P95, P97, P99, P101 2012 Edition: 2.6, 2.8, 3.3 6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. SE: 45 48, 50 51, 71 74, 221 224, 225 228, 229 232, 233 236, 237 240, 243 246, 247 250, 251 254, 255 258, 259 262, TE: 45A, 45B, 45 48, 49A, 49B, 50 51, 71 74, 221A, 221B, 221 224, 225A, 225B, 225 228, 229A, 229B, 229 232, 233A, 233B, 233 236, 237A, 237B, 237 240, 243A, 243B, 243 246, 247A, 247B, 247 250, 251A, 251B, 251 254, 255A, 255B, 255 258, 259A, 259B, 259 262, PB: P23, P25, P111, P113, P115, P117, P119, P121, P123, P125, P127, P129, P130a P130b PG: PG78 PG79 2012 Edition: 4.1, 4.3, 4.5, 4.7, 4.8, 4.9 7

4.NF Number and Operations Fractions Extend understanding of fraction equivalence and ordering. 1. Explain why a fraction a/b is equivalent to a fraction (n x SE: 315 318, 319 322, 323 326, 327 330 a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even TE: 315A, 315B, 315 318, 319A, 319B, 319 322, 323A, 323B, 323 326, 327A, 327B, 327 330 though the two fractions themselves are the same size. PB: P157, P159, P161, P162a P162b, P163 Use this principle to recognize and generate equivalent fractions. PG: PG80 PG81 2012 Edition: 6.1, 6.2, 6.3, 6.5 2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. SE: 404, 407 408, 413 TE: 403A, 404, 407A, 407 408, 413 PB: P188a P188d PG: PG88 PG91 2012 Edition: 6.4, 6.6, 6.7, 6.8 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as SE: 399 402, 403 406, 407 410, 413 416, 417 420 joining and separating parts referring to the same whole. TE: 399A, 399B, 399 402, 403A, 403B, 403 406, 407A, 407B, 407 410, 413A, 413B, 413 416, 417A, 417B, 417 420 PB: P199, P201, P203, P206, P207 2012 Edition: 7.1 b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. 2012 Edition: 7.2 8

c. Add and subtract mixed numbers with like SE: 403 405, 408 409, 414 denominators, e.g., by replacing each mixed number TE: 403, 404, 408, 414 with an equivalent fraction, and/or by using properties of operations and the relationship between addition and PB: P201, P203, P205 subtraction. 2012 Edition: 7.6, 7.7, 7.8, 7.9 d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. SE: 399 402, 403 406, 407 410, 413 416, 417 420 TE: 399 402, 403B, 403 406, 407B, 407 410, 413B, 413 416, 417A, 417B, 417 420 PB: P199, P201, P203, P205, P207 2012 Edition: 7.10 4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. 2012 Edition: 8.1, 8.2 b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. 2012 Edition: 8.3, 8.4 PB: P268a P268b PG: PG114 PG115 2012 Edition: 8.5 9

Understand decimal notation for fractions, and compare decimal fractions. 5. Express a fraction with denominator 10 as an equivalent SE: 316, 339 fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and TE: 337A 100. 2012 Edition: 9.6 6. Use decimal notation for fractions with denominators 10 or 100. 7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. SE: 333 336, 337 340, 349 352, 353 356 TE: 333B, 333 336, 337A, 337B, 337 340, 349 352, 353A, 353B, 353 356 PB: B11, P165, P167 PG: PG120 SE: 371 374 TE: 371A, 371B, 371 374 PB: P185 10

4.MD Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; SE: 429 432, 433 436, 437 440, 441 444, 449 452, 455 458, 459 462 hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two TE: 13, 429A, 429 432, 433A, 433B, 433 436, 437A, 437B, 437 440, 441A, 441 444, 449A, 449 452, 455A, 455B, 455 458, 459A, 459B, 459 462 column table. PB: P213, P215, P225 Mega Math Additional Coverage: The Number Games: Tiny's Think Tank, Levels M, N, O, and Q 2012Edition: 12.1, 12.3, 12.4, 12.11 2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. SE: 2, 148, 152, 168, 229 232, 252, 407 410, 419 420, 439 440, 455 458, 464 466, 467 470 TE: 1 2, 148, 152, 168, 229 232, 252, 407 410, 419 420, 439, 440, 455A, 455B, 455 458, 464 466, 467A, 467B, 467 470 PB: B1 B2, P214a P214b, P215, P217, P279 P280, P281 P282 PG: PG100 PG101, PG124 PG125, PG126 PG127 2012 Edition: 9.5, 12.10 3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. SE: 525 528, 541 544 TE: 525 528, 541A, 541B, 541 544 PB: P269, P276a P276b PG: PG116 PG117 2012 Edition: 13.3, 13.4, 13.5 11

Represent and interpret data. 4. Make a line plot to display a data set of measurements in PB: P214a P214b fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using PG: PG100 PG101 information presented in line plots. 2012 Edition: 12.5 Geometric measurement: understand concepts of angle and measure angles. 5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a onedegree angle, and can be used to measure angles. 2012 Edition: 11.1 b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. 2012 Edition: 11.2 6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. PB: PG: P238e P238h PG106 PG109 2012 Edition: 11.3 7. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. PB: P238i P238j PG: PG110 PG111 2012 Edition: 11.4, 11.5 12

4.G Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 1. Draw points, lines, line segments, rays, angles (right, SE: 477 480 acute, obtuse), and perpendicular and parallel lines. TE: 477 480 Identify these in two-dimensional figures. PB: P237, P238a P238d, P238f P238h PG: PG102 PG105, PG107 PG109 Mega Math Additional Coverage: Ice Station Exploration: Polar Planes, Levels B and C 2012 Edition: 10.1, 10.3 2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. 3. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. SE: 477 480 TE: 477A, 477B, 477 480 PB: P237 2012 Edition: 10.2, 10.4 SE: 503 506, 507 510 TE: 503A, 503B, 503 506, 507A, 507B, 507 510 PB: P249, P251 13