# Correlation to the Common Core State Standards

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1 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

2 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

3 Houghton Mifflin Harcourt Go Math! Grade 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, , , , 132, 136, 140, 144, 148, , 162, , , 192, , 214, , 250, , 266, , , , 327A 327B, , 374, 378, , , , , , , 448, 462, , 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, , 107A 107B, , 119A 119B, , 132, 136, 140, 144, 148, 149A 149B, , 162, 163A 163B, , 167A 167B, , 192, 203A 203B, , 214, , 229A 229B, , 250, 259A 259B, , 266, 277A 277B, , 281A 281B, , 285A 285B, , 327A 327B, , 374, 378, 379A 379B, , 399A 399B, , 403A 403B, , 407A 407B, , 413A 413B, , 417A 417B, , 448, 462, 463A 463B, , 492, 518

4 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, , 103A 103B, , , , , , , , , , , , , , , , , , , , , , , , , , 342, , , , , , , , , , , , , , , , , , , , TE: 13A 13B, 13 16, 19A 19B, 19 22, 23A 23B, 23 26, 27A 27B, 27 30, 31A 31B, A 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, , 103A 103B, , 107A 107B, , 111A 111B, 115A 115B, , 129A 129B, , 137A 137B, , 145A 145B, , 149A 149B, , 153A 153B, , 167A 167B, , 177A 177B, , 181A 181B, , 185A 185B, 199A 199B, , 203A 203B, , 211A 211B, , 225A 225B, 233A 233B, , 237A 237B, , 243A 243B, 247A 247B, , 255A 255B, , 259A 259B, , , 291A 291B, , 299A 299B, , 311A 311B, , 342, 345A 345B, 349A 349B, , 371A 371B, , 375A 375B, , 385A 385B, 389A 389B, , 403A 403B, , 429A 429B, , 455A 455B, 463A 463B, 467A 467B, , 477A 477B, , 481A 481B, , 485A 485B, , 489A 489B, , 493A 493B, , 497A 497B, 503A 503B, , 507A 507B, 511A 511B, 515A 515B,

5 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, , 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, , 214, 228, 246, 293, 298, 314, 348, 405, 413, 420, 440, 444, Model with mathematics. SE: 30, 34, 62, 81 84, 85 88, 95 96, , 266 TE: 30, 34, 62, 71B, 81A 81B, 81 84, 85A 85B, 85 88, 95 96, 141A 141B, , Use appropriate tools strategically. SE: 9 12, 22, 41 42, 49 52, 59 62, 83, 88, 93 95, , , , , , 163A 163B, , , , , , , , , , , , , , , , , TE: 9A 9B, 9 12, 22, 41A, 41 42, 49A 49B, 49 52, 59 62, 83, 88, 93 95, , , 133A 133B, , 153A 153B, , 159A 159B, , , 189A 189B, , 195A 195B, , 221A 221B, , 229A 229B, , 251A 251B, , 263A 263B, , 315A 315B, , 319A 319B, , 323A 323B, , 327A 327B, , 341A 341B, , 363A 363B, , 379A 379B, , 417A 417B, , 433A 433B, , 445A 445B,

6 6. Attend to precision. SE: 5A 5B, 5 8, 56, 81 84, 85 88, , , , , , , , , 433A 433B, , 437A 437B, , 441A 441B, , 445A 445B, , 449A 449B, , TE: 5A 5B, 5 8, 56, 81A 81B, 81 84, 85A 85B, 85 88, 99A 99B, , 103A, , , 111A 111B, , 295A 295B, , 333A 333B, , 337A 337B, , 345A 345B, , 353A 353B, , , , , , , 459A 459B, Look for and make use of structure. SE: 5 8, 9 12, 41 44, 45 48, 89 92, 93 96, , , , , 455A 455B, , 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, , 177A 177B, , 233A 233B, , 337A 337B, , , 511A 511B, Look for and express regularity in repeated reasoning. SE: 29, 54 55, 65, 70, 84, 131, 135, 143, 151, , 201, , 234, 245, 262, , 365, 388 TE: 29, 54 55, 59B, 65, 70, 84, 131, 135, 143, 151, , 201, 207A 207B, , 234, 245, 262, , 365, 388 4

7 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: 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: statements of multiplicative comparisons as multiplication equations Edition: 2.1, 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, TE: 71A, 71B, 71 74, PB: P23, P35, P55, P Edition: 2.2 SE: 30, , 152, ,162, 168, , 206, , TE: 30, 119A, 119B, , 152, 153A, 153B, , 162, 168, 185A, 185B, , 206, , 263A, 263B, PB: P59, P74, P77, P131 5

8 Gain familiarity with factors and multiples. 4. Find all factor pairs for a whole number in the range 1 SE: 59 62, Recognize that a whole number is a multiple of TE: 59A, 59B, 59 62, 63A, 63B, each of its factors. Determine whether a given whole PB: P29, P30e P30f, P31, P36a P36b number in the range is a multiple of a given onedigit number. Determine whether a given whole number PG: PG70 PG71, PG72 PG73 in the range is prime or composite 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, TE: 89A, 89B, 89 92, 93A, 93B, 93 97, 515A, 515B, 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 Edition: 5.6, 10.7 SE: 5, 9, 10 TE: 5, 9, Edition: 1.1 SE: 5 8, 9 12, TE: 5A, 5B, 5 8, 9A, 9B, 9 12, 19A, 19B, PB: P3, P5, P Edition: 1.2, 1.5 SE: TE: 23B, PB: P11 6

9 Use place value understanding and properties of operations to perform multi-digit arithmetic. 4. Fluently add and subtract multi-digit whole numbers SE: using the standard algorithm. TE: 27A, 27B, 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, , , , , , , , , , TE: 41A, 41B, 41 44, 53A, 53B, 53 56, 149A, 149B, , 153A, 153B, , 159A, 159B, , 163A, 163B, , 167B, , 181B, , 189A, 189B, , 195A, 195B, , 199A, 199B, , 203A, 203B, PB: P21, P27, P75, P77, P79, P81, P83, P91, P95, P97, P99, P Edition: 2.6, 2.8, 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, , , , , , , , , , , TE: 45A, 45B, 45 48, 49A, 49B, 50 51, 71 74, 221A, 221B, , 225A, 225B, , 229A, 229B, , 233A, 233B, , 237A, 237B, , 243A, 243B, , 247A, 247B, , 251A, 251B, , 255A, 255B, , 259A, 259B, , PB: P23, P25, P111, P113, P115, P117, P119, P121, P123, P125, P127, P129, P130a P130b PG: PG78 PG Edition: 4.1, 4.3, 4.5, 4.7, 4.8, 4.9 7

10 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: , , , 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, , 319A, 319B, , 323A, 323B, , 327A, 327B, 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 PG Edition: 6.1, 6.2, 6.3, 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, , 413 TE: 403A, 404, 407A, , 413 PB: P188a P188d PG: PG88 PG 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: , , , , joining and separating parts referring to the same whole. TE: 399A, 399B, , 403A, 403B, , 407A, 407B, , 413A, 413B, , 417A, 417B, PB: P199, P201, P203, P206, P 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 Edition: 7.2 8

11 c. Add and subtract mixed numbers with like SE: , , 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 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: , , , , TE: , 403B, , 407B, , 413B, , 417A, 417B, PB: P199, P201, P203, P205, P Edition: 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 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 Edition: 8.3, 8.4 PB: P268a P268b PG: PG114 PG Edition: 8.5 9

12 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 Edition: Use decimal notation for fractions with denominators 10 or 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: , , , TE: 333B, , 337A, 337B, , , 353A, 353B, PB: B11, P165, P167 PG: PG120 SE: TE: 371A, 371B, PB: P185 10

13 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: , , , , , , 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, , 433A, 433B, , 437A, 437B, , 441A, , 449A, , 455A, 455B, , 459A, 459B, 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, 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, , 252, , , , , , TE: 1 2, 148, 152, 168, , 252, , , 439, 440, 455A, 455B, , , 467A, 467B, PB: B1 B2, P214a P214b, P215, P217, P279 P280, P281 P282 PG: PG100 PG101, PG124 PG125, PG126 PG Edition: 9.5, Apply the area and perimeter formulas for rectangles in real world and mathematical problems. SE: , TE: , 541A, 541B, PB: P269, P276a P276b PG: PG116 PG Edition: 13.3, 13.4,

14 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 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 Edition: 11.1 b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees Edition: Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. PB: PG: P238e P238h PG106 PG Edition: 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 PG Edition: 11.4,

15 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: acute, obtuse), and perpendicular and parallel lines. TE: 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, 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: TE: 477A, 477B, PB: P Edition: 10.2, 10.4 SE: , TE: 503A, 503B, , 507A, 507B, PB: P249, P251 13

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