Correlation to the Common Core State Standards

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1 Correlation to the Common Core State Standards Go Math! 2011 Grade 3 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 MS79524d

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 3 Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. SE: 9 12, 45 48, 49 52, 59 62, 63 66, 67 70, 89 92, 102, , , , , , , , , 168, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , 390, 416, 466, , 488, 506, 519, 520, 550, 558, 562 TE: 9A 9B, 9 12, 45A 45B, 45 48, 49A 49B, 49 52, 59A 59B, 59 62, 63A 63B, 63 66, 67A 67B, 67 70, 89A 89B, 89 92, 102, 107A 107B, , 111A 111B, , 115A 115B, , 133A 133B, , 137A 137B, , 143A 143B, , 147A 147B, , 161A 161B, , 168, 169A 169B, , 173A 173B, , 177A 177B, , 183A 183B, , 191A 191B, , 195A 195B, , 205A 205B, , 209A 209B, , 213A 213B, , 217A 217B, , 221A 221B, , 227A 227B, , 231A 231B, , 235A 235B, , 253A 253B, , 257A 257B, , , 271A 271B, , 275A 275B, , 279A 279B, , 301A 301B, , 305A 305B, , 313A 313B, , , 323A 323B, , 327A 327B, , 331A 331B, , 351A 351B, , 377A 377B, , 390, 416, 466, 467A 467B, , 488, 506, 519, 520, 550

4 2. Reason abstractly and quantitatively. SE: 5 8, 9 10, 13 16, 17 20, 27 30, 31 34, 45 48, 49 52, 55 58, 59 62, 63 66, 89 92, 93 96, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , TE: 5A 5B, 9A 9B, 13A 13B, 17A 17B, 27A 27B, 31A 31B, 41A 41B, 45A 45B, 49A 49B, 55A 55B, 59A 59B, 63A 63B, 89A 89B, 93A 93B, 103A 103B, 107A 107B, 111A 111B, 115A 115B, 151A 151B, 161A 161B, 165A 165B, 169A 169B, 173A 173B, 177A 177B, 187A 187B, 195A 195B, 205A 205B, 209A 209B, 213A 213B, 217A 217B, 221A 221B, 227A 227B, 231A 231B, 235A 235B, 239A 239B, 243A 243B, 253A 253B, 257A 257B, 261A 261B, 265A 265B, 271A 271B, 275A 275B, 283A 283B, 291A 291B, 301A 301B, 305A 305B, 309A 309B, 313A 313B, 319A 319B, 323A 323B, 327A 327B, 365A 365B, 387A 387B, 391A 391B, 395A 395B, 399A 399B, 405A 405B, 425A 425B, 429A 429B, 433A 433B, 437A 437B, 441A 441B, 445A 445B, 451A 451B, 455A 455B, 459A 459B, 463A 463B, 467A 467B, 471A 471B, 481A 481B, 489A 489B, 493A 493B, 499A 499B, 503A 503B, 507A 507B, 541A 541B, 547A 547B, 551A 551B 2

5 3. Construct viable arguments and critique the reasoning of others. SE: 8, 12, 13, 34, 47, 58, 62, 106, 176, 186, 208, 220, 308, 316, 322, 326, 334, 358, 376, 380, 428, 432, 436, 448, 454, 484, 492, 496, 502, 524, 534, 536 TE: 8, 12, 13, 34, 47, 58, 62, 106, 176, 186, 208, 220, 308, 316, 322, 326, 334, 358, 376, 380, 428, 432, 436, 448, 454, 484, 492, 496, 502, 521B, 524, 534, Model with mathematics. SE: 67 70, 113, , , , , , , , 238, 282, 322, , 519, 528 TE: 67A 67B, 67 70, 113, 129B, , 137A 137B, , 143A 143B, , 147A 147B, , 151A 151B, , , 227A 227B, 238, 282, 322, 335A 335B, , 519, Use appropriate tools strategically. SE: 23 26, 27 30, 77 80, 81 84, 85 88, , , , , , , , , , , , , , , , TE: 23A 23B, 23 26, 27A 27B, 27 30, 77A 77B, 77 80, 81A 81B, 81 84, 85A 85B, 85 88, 99A 99B, , , 355A 355B, , , , 399A 399B, , , 429A 429B, , 517A 517B, , 521A 521B, , 525A 525B, , 529A 529B, , 537A 537B, , 555A 555B, , 559A 559B, , 563A 563B,

6 6. Attend to precision. SE: , , , , , , 264, 274, , 322, 338, 368, 372, , , , , TE: 107A 107B, , 187A 187B, , 227A 227B, , 243A 243B, , , 257A 257B, , 264, 274, 275A 275B, , 322, 338, 368, 372, 373A 373B, , 391A 391B, , 409A 409B, , , 537B, Look for and make use of structure. SE: 5 8, 23 26, , , , , , , , , , , , , TE: 5A 5B, 5 8, 23A 23B, 23 26, 191A 191B, , 213A 213B, , 217A 217B, , 239A 239B, , 283A 283B, , 287A 287B, , 347A 347B, , 355A 355B, , 359A 359B, , 369A 369B, , 499A 499B, , 507A 507B, , 529A 529B, Look for and express regularity in repeated reasoning. SE: 43, 47, 50 51, 61, 65, , , 279, , , , 375 TE: 43, 47, 50 51, 61, 65, 110, , , 221B, 279, , , , 375 4

7 Standards for Mathematical Content 3.OA Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. 1. Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. SE: , , , , , , , , , , , , , , , , , TE: 161A 161B, , 165A 165B, , 169A 169B, , 173A 173B, , 177A 177B, , 183A 183B, , 187A 187B, , 191A 191B, , 195A 195B, , 205A 205B, , 209A 209B, , 213A 213B, , 217A 217B, , 221A 221B, , 227A 227B, , 231A 231B, , 235A 235B, , 243A 243B, PB: P81, P83, P85, P87, P89, P91, P93, P95, P97, P103, P105, P107, P109, P111, P113, P115, P117, P Edition: 3.3 5

8 2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. SE: , , , , , , , , , , , , , , , , , , TE: 253A 253B, , B, , 261A 261B, , 265A 265B, , 271A 271B, , 275A 275B, , 279A 279B, , 283A 283B, , 287A 287B, , 291A 291B, , 301A 301B, , 305A 305B, , 309A 309B, , 313A 313B, , 319A 319B, , 323A 323B, , 327A 327B, , 331A 331B, , 335A 335B, PB: P127, P129, P131, P133, P135, P137, P139, P141, P143, P145, P151, P153, P155, P157, P159, P161, P163, P165, P Edition: 6.1, 6.4 6

9 3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. SE: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , TE: 161A 161B, , 165A 165B, , 169A 169B, , 173A 173B, , 177A 177B, , 183A 183B, , 187A 187B, , 191A 191B, , 195A 195B, , 205A 205B, , 209A 209B, , 213A 213B, , 217A 217B, , 221A 221B, , 227A 227B, , 231A 231B, , 235A 235B, , 243A 243B, , 253A 253B, , B, , 261A 261B, , 265A 265B, , 271A 271B, , 275A 275B, , 279A 279B, , 283A 283B, , 287A 287B, , 291A 291B, , 301A 301B, , 305A 305B, , 309A 309B, , 313A 313B, , 319A 319B, , 323A 323B, , 327A 327B, , 331A 331B, , 335A 335B, , 551A 551B, PB: P81, P83, P85, P87, P89, P91, P93, P95, P97, P103, P105, P107, P109, P111, p113, p115, P117, P119, P121, P127, P129, P131, P133, P135, P137, P139, P141, P143, P145, P151, P153, P155, P157, P159, P161, P163, P165, P167, P273, P274a PG: PG Edition: 6.1 7

10 4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. SE: , , , , , , , , , , , TE: 213A 213B, , 217A 217B, , 221A 221B, , 231A 231B, , 235A 235B, , 243A 243B, , 283A 283B, , 291A 291B, , 313A 313B, , 319A 319B, , 323A 323B, , 327A 327B, PB: P107, P109, P111, P115, P117, P121, P141, P145, P157, P159, P161, P163 Understand properties of multiplication and the relationship between multiplication and division. 5. Apply properties of operations as strategies to multiply and divide. SE: , , , , , , , TE: 191A 191B, , 195A 195B, , 213A 213B, , 217A 217B, , 221A 221B, , 231A 231B, , 235A 235B, , 309A 309B, PB: P95, P97, P107, P109, P111, P115, P117, P Edition: Understand division as an unknown-factor problem. SE: , , , , , , , TE: 283A 283B, , 291A 291B, , 301A 301B, , 305A 305B, , 313A 313B, , 319A 319B, , 323A 323B, , 327A 327B, PB: P141, P145, P151, P153, P157, P159, P161, P163 8

11 Multiply and divide within Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. SE: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , TE: 165A 165B, , 169A 169B, , 173A 173B, , 177A 177B, , 183A 183B, , 187A 187B, , 191A 191B, , 195A 195B, , 205A 205B, , 209A 209B, , 221A 221B, , 227A 227B, , 231A 231B, , 235A 235B, , 239A 239B, , 243A 243B, , 261A 261B, , 265A 265B, , 275A 275B, , 287A 287B, , 291A 291B, , 301A 301B, , 305A 305B, , 309A 309B, , 313A 313B, , 319A 319B, , 323A 323B, , 327A 327B, , 331A 331B, , 335A 335B, PB: P83, P85, P87, P89, P91, P93, P95, P97, P103, P105, P111, P113, P115, P117, P119, P121, P131, P133, P137, P143, P145, P151, P153, P155, P157, P159, P161, P163, P165, P167 9

12 Solve problems involving the four operations, and identify and explain patterns in arithmetic. 8. Solve two-step word problems using the four operations. 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: , , , TE: 183A 183B, , 213A 213B, , 227A 227B, , 331A 331B, PB: P91, P107, P113, P165 PG: PG100 PG101, PG108 PG109 Mega Math Additional Coverage: Ice Station Exploration: Arctic Algebra, Level I 2012 Edition: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. SE: 5 8, 9 12, , , , , , , , TE: 5A 5B, 5 8, 9A 9B, 9 12, 173A 173B, , 177A 177B, , 209A 209B, , 221A 221B, , 227A 227B, , 231A 231B, , 239A 239B , 243A 243B, PB: P3, P5, P87, P89, P105, P111, P113, P115, P119, P121. P303 P304, P315 P316 PG: PG110 PG111, PG122 PG Edition: 4.7,

13 3.NBT Number and Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. 1. Use place value understanding to round whole numbers to the nearest 10 or 100. SE: 31 34, TE: 31A 31B, 31 34, 41A 41B, PB: P15, P21 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. SE: 41 44, 45 48, 49 52, 55 58, 59 62, 63 66, TE: 41A 41B, 41 44, 45A 45B, 45 48, 49A 49B, 49 52, 55A 55B, 55 58, 59A 59B, 59 62, 63A 63B, 63 66, 67A 67B, PB: P21, P23, P25, P27, P29, P31, P33, P287 P288, P289 P190 PG: PG96 PG97, PG98 PG Edition: 1.4, 1.5, 1.6, 1.7, 1.9, 1.10, Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. SE: TE: 177A 177B, PB: P303 PG: PG110 PG111 Mega Math Additional Coverage: The Numbers Games: Up, Up and Array, Level I 2012 Edition: 5.4,

14 3.NF Number and Operations Fractions Develop understanding of fractions as numbers. 1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. SE: , , , TE: 345E, 345G, 347A 347B, , 355A 355B, , 359A 359B, , 365A 365B, PB: P173, P177, P179, P181 PG: PG89 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. SE: , , , , TE: 359A 359B, , 365A 365B, , 391A 391B, , , PB: P179, P181, P195, P201, P Edition: 8.5 b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. SE: , , , , TE: 359A 359B, , 365A 365B, , , , PB: P179, P181, P195, P Edition:

15 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. SE: , TE: 409A 409B, , 413A 413B, PB: P203, P205 Mega Math Additional Coverage: Fraction Action: Number Line Mine, Level E 2012 Edition: 8.5 b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. SE: , TE: 409A 409B, , 413A 413B, PB: P203, P205 SE: , , TE: 345E, 359A 359B, , 365A 365B, , 413A 413B, PB: P179, P181, P Edition: 8.9 d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. SE: , , TE: 387A 387B, , 395A 395B, , 399A 399B, PB: P193, P197, P199 PG: PG89 13

16 3.MD Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. 1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. SE: 81 84, 85 88, 89 92, TE: 81A 81B, 81 84, 85A 85B, 85 88, 89A 89B, 89 92, 93A 93B, PB: P41, P45, P47 2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Represent and interpret data. 3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve oneand two-step how many more and how many less problems using information presented in scaled bar graphs. 4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. SE: TE: 563A 563B, PB: P279, P325, P327 PG: PG130 PG131, PG132 PG Edition: 10.7, 10.8, 10.9 SE: , , TE: 137A 137B, , 143A 143B, , 147A 147B, PB: P69, P71, P73, P74a P74d PG: PG64 PG67 SE: , TE: 151A 151B, , 521A 521B, PB: P75, P257, P259, P260a P260b PG: PG68 PG69 14

17 Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 5. Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. SE: TE: 547A 547B, PB: P Edition: 11.3, 11.4 b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. SE: TE: 547A 547B, PB: P Edition: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). SE: , TE: 547A 547B, , 551A 551B, PB: P271, P Edition:

18 7. Relate area to the operations of multiplication and addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. SE: , TE: 547A, 547B, , 551A 551B, PB: P273, P274b, P274c, P274d PG: PG74 PG77 b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent wholenumber products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems Edition: 11.7 SE: , TE: 547A 547B, , 551A 551B, PB: P271, P273, P274a P274d PG: PG74PG Edition: 11.7 SE: TE: 217A 217B, PB: P109, P307 P308 PG: PG114 PG Edition: 11.6 TE: 547B 2012 Edition:

19 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. 8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. SE: , , , TE: 533A 533B, , 537A 537B, , 541A 541B, , 551A 551B, PB: P265, P267, P269, P273, P274a P274d PG: PG74 PG77 3.G Geometry Reason with shapes and their attributes. 1. Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. SE: , , , TE: 425A 425B, , 433A 433B, , 441A 441B, , 445A 445B, PB: P211, P215, P219, P221 PG: PG90 PG91 Mega Math Additional Coverage: Ice Station Exploration: Polar Planes, Level G 2012 Edition: 12.2, 12.4, 12.6, Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. SE: , 453, TE: 347A 347B, , 453, 459A 459B, Edition:

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