common core - pausd

Includes Complete Common Core Correlation Grades K–6

GO Math! is built for the COMMON CORE

Children record, represent, solve, and explain as they discover and build new understandings right in their student books.

Every lesson is four pages to ensure students are learning mathematics at a deeper level of understanding.

It’s New!

NEW Write-in Student Edition

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Since GO Math! was built for the Common Core, all the Mathematical Practices are completely embedded in the lessons.

NEW Ways to Engage

It’s COMMON CORE!

MATHEMATICALPRACTICES

COMMON CORE

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NEW Color Coding for Critical Areas

NEW Common Core State Standards Practice Book

NEW MathBoards

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Read the Problem Lee el problema

Solve the Problem Resuelve el problema

What do I need to find?¿Qué debo hallar?

What information do I need to use?¿Qué información necesito usar?

How will I use the information?¿De qué manera usaré la información?

Show how to solve the problem.Muestra la manera de resolver el problema.

Soluciona el problema

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It’s Built for Student Success

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NEW Common Core State Standards Practice Book

Review the following pages to see for yourself how GO Math!, built from scratch, completely addresses the Common Core State Standards.

Correlations

Common Core State Standards Correlations PG131

Number and Operations in Base Ten Student Edition and Teacher Edition Pages

Use place value understanding and properties of operations to perform multi-digit arithmetic.

CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

9A–9B, 9–12, 13A–13B, 13–16, 35A–35B, 35–38 See Also: 25A–25B, 25–28, 29A–29B, 29–32, 43A–43B, 43–46, 47A–47B, 47–50

CC.3.NBT.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.

17A–17B, 17–20, 21A–21B, 21–24, 25A–25B, 25–28, 29A–29B, 29–32, 39A–39B, 39–42, 43A–43B, 43–46, 47A–47B, 47–50 See Also: 13A–13B, 13–16, 35A–35B, 35–38, 51A–51B, 51–54, 61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–72, 75A–75B, 75–78, 79A–79B, 79–82, 83A–83B, 83–86, 87A–87B, 87–90, 101A–101B, 101–104, 401A–401B, 401–404, 405A–405B, 405–408, 423A–423B, 423–426, 437A–437B, 437–440, 441A–441B, 441–444, 453A–453B, 453–456, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

CC.3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 3 80, 5 3 60) using strategies based on place value and properties of operations.

191A–191B, 191–194, 195A–195B, 195–198, 199A–199B, 199–202

Number and Operations—Fractions Student Edition and Teacher Edition Pages

Develop understanding of fractions as numbers.

CC.3.NF.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.

307A–307B, 307–310, 311A–311B, 311–314, 315A–315B, 315–318, 319A–319B, 319–322, 333A–333B, 333–336, 337A–337B, 337–340, 341A–341B, 341–344 See Also: 351A–351B, 351–354, 355A–355B, 355–358, 359A–359B, 359–362, 363A–363B, 363–366, 369A–369B, 369–372, 373A–373B, 373–376, 377A–377B, 377–380, 517A–517B, 517–520

CC.3.NF.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.

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.

323A–323B, 323–326, 329A–329B, 329–332

323A–323B, 323–326 See Also: 329A–329B, 329–332, 373A–373B, 373–376

323A–323B, 323–326 See Also: 329A–329B, 329–332, 355A–355B, 355–358, 371, 373A–373B, 373–376

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[Head] [bold] Common Core State Standards [Text] The grade-level correlation charts for Grades K-6 on the following pages show how lessons in GO Math! are completely aligned to the Common Core State Standards (CCSS) for Mathematics.

Every CCSS is covered in the lessons.

Standards define what students should understand and should be able to do.

Clusters are groups of related standards.

Domains are larger groups of related standards.

It’s Built for Student Success It’s All Here

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Kindergarten

PG126 Planning Guide

COMMON CORE STATE STANDARDS FOR MATHEMATICS

Standards for Mathematical Practices Teacher Edition and Student Edition Pages

CC.K–12.MP.1 Make sense of problems and persevere in solving them.

In most Teacher Edition lessons. Some examples are: 245A, 473A

In most Student Edition lessons. Some examples are: 48, 68, 124, 160, 188, 228, 232, 244, 252, 480, 484

CC.K–12.MP.2 Reason abstractly and quantitatively. In most Teacher Edition lessons. Some examples are: 205A, 251, 513A

In most Student Edition lessons. Some examples are: 176, 180, 192, 200, 240, 248, 496, 508, 516

CC.K–12.MP.3 Construct viable arguments and critique the reasoning of others.

In most Teacher Edition lessons. Some examples are: 41A, 403, 439, 511

In most Student Edition lessons. Some examples are: 16, 24, 32, 360, 368, 420, 428, 440, 444

CC.K–12.MP.4 Model with mathematics. In most Teacher Edition lessons. Some examples are: 179, 273A, 335

In most Student Edition lessons. Some examples are: 47, 73, 150, 322, 474, 508

CC.K–12.MP.5 Use appropriate tools strategically. In most Teacher Edition lessons. Some examples are: 39, 105A, 325A

In most Student Edition lessons. Some examples are: 48, 96, 112, 120, 124, 312, 316, 320, 328, 332, 336, 340

CC.K–12.MP.6 Attend to precision. In most Teacher Edition lessons. Some examples are: 63, 153A, 483

In most Student Edition lessons. Some examples are: 68, 144, 180, 188, 192, 196, 204, 236, 244, 248

CC.K–12.MP.7 Look for and make use of structure. In most Teacher Edition lessons. Some examples are: 77A, 143, 397A, 433A

In most Student Edition lessons. Some examples are: 252, 364, 372, 388, 396, 400, 416, 420, 424, 428, 436

CC.K–12.MP.8 Look for and express regularity in repeated reasoning.

In most Teacher Edition lessons. Some examples are: 111, 157, 299, 321


Correlations

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Kindergarten

Correlations


Domain: Counting and Cardinality Teacher Edition and Student Edition Pages

Know number names and the count sequence.

CC.K.CC.1 Count to 100 by ones and by tens. 325A–325B, 325–328, 329A–329B, 329–332, 333A–333B, 333–336, 337A–337B, 337–340

CC.K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

145A–145B, 145–147, 317A–317B, 317–320 See Also: 325A–325B, 325–328, 329A–329B, 329–332

CC.K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0–20 (with 0 representing a count of no objects).

17A–17B, 17–20, 25A–25B, 25–27, 45A–45B, 45–48, 49A–49B, 49–52, 93A–93B, 101A–101B, 101–103, 109A–109B, 109–112, 117A–117B, 117–120, 137A–137B, 137–140, 265A–265B, 265–268, 273A–273B, 273–276, 281A–281B, 281–283, 289A–289B, 289–292, 297A–297B, 297–300, 313A–313B, 313–316See Also: 13A–13B, 13–16, 21A–21B, 21–24, 29A–29B, 29–32, 33A–33B, 33–36, 41A–41B, 41–44, 61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–71, 73A–73B, 73–76, 77A–77B, 77–80, 89A–89B, 89–92, 93–96, 97A–97B, 97–100, 105A–105B, 105–108,113A–113B, 113–116, 121A–121B, 121–124, 133A–133B, 133–136, 149A–149B, 149–152, 153A–153B, 153–156, 261A–261B, 261–264, 269A–269B, 269–272, 277A–277B, 277–280, 285A–285B, 285–288, 293A–293B, 293–296, 309A–309B, 309–312, 321A–321B, 321–323

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Kindergarten


Domain: Counting and Cardinality (continued) Teacher Edition and Student Edition Pages

Count to tell the number of objects.

CC.K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

13A–13B, 13–16, 21A–21B, 21–24, 29A–29B, 29–32 See Also: 17A–17B, 17–20, 25A–25B, 25–27, 33A–33B, 33–36, 45A–45B, 45–48, 49A–49B, 49–52, 89A–89B, 89–92, 93A–93B, 93–96, 97A–97B, 97–100, 101A–101B, 101–103, 105A–105B, 105–108, 109A–109B, 109–112, 113A–113B, 113–116, 117A–117B, 117–120, 133A–133B, 133–136, 137A–137B, 137–140, 261A–261B, 261–264, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 277A–277B, 277–280, 281A–281B, 281–283, 285A–285B, 285–288, 289A–289B, 289–292, 293A–293B, 293–296, 297A–297B, 297–300, 309A–309B, 309–312, 313A–313B, 313–316

b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

33A–33B, 33–36See Also: 13A–13B, 13–16, 17A–17B, 17–20, 21A–21B, 21–24, 25A–25B, 25–27, 29A–29B, 29–32, 45A–45B, 45–48, 49A–49B, 49–52, 89A–89B, 89–92, 93A–93B, 93–96, 97A–97B, 97–100, 101A–101B, 101–103, 105A–105B, 105–108, 109A–109B, 109–112, 113A–113B, 113–116, 117A–117B, 117–120, 133A–133B, 133–136, 137A–137B, 137–140, 261A–261B, 261–264, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 277A–277B, 277–280, 281A–281B, 281–283, 285A–285B, 285–288, 289A–289B, 289–292, 293A–293B, 293–296, 297A–297B, 297–300, 309A–309B, 309–312, 313A–313B, 313–316

c. Understand that each successive number name refers to a quantity that is one larger.

41A–41B, 41–44 See Also: 17A–17B, 17–20, 25A–25B, 25–27, 89A–89B, 89–92, 97A–97B, 97–100, 105A–105B, 105–108, 113A–113B, 113–116, 137A–137B, 137–140, 145A–145B, 145–147, 265A–265B, 265–268, 273A–273B, 273–276, 281A–281B, 281–283, 289A–289B, 289–292, 297A–297B, 297–300, 317A–317B, 317–320

Domain continued on next page

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Kindergarten

Correlations


Domain: Counting and Cardinality (continued) Teacher Edition and Student Edition Pages

CC.K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

89A–89B, 89–92, 97A–97B, 97–100, 105A–105B, 105–108, 113A–113B, 113–116, 133A–133B, 133–136, 309A–309B, 309–312See Also: 13A–13B, 13–16, 17A–17B, 17–20, 21A–21B, 21–24, 25A–25B, 25–27, 29A–29B, 29–32, 33A–33B, 33–36, 37A–37B, 37–40, 41A–41B, 41–44, 77A–77B, 77–80, 93A–93B, 93–96, 101A–101B, 101–103, 109A–109B, 109–112, 117A–117B, 117–120, 121A–121B, 121–124, 137A–137B, 137–140, 141A–141B, 141–144, 153A–153B, 153–156, 261A–261B, 261–264, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 277A–277B, 277–280, 281A–281B, 281–283, 285A–285B, 285–288, 289A–289B, 289–292, 293A–293B, 293–296, 297A–297B, 297–300, 313A–313B, 313–316

Compare numbers.

CC.K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.

61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–71, 73A–73B, 73–76, 77A–77B, 77–80, 121A–121B, 121–124, 149A–149B, 149–152, 153A–153B, 153–156, 321A–321B, 321–323

CC.K.CC.7 Compare two numbers between 1 and 10 presented as written numerals.

157A–157B, 157–160 See Also: 61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–71, 73A–73B, 73–76, 77A–77B, 77–80, 121A–121B, 121–124, 149A–149B, 149–152, 153A–153B, 153–156

Domain: Operations and Algebraic Thinking Teacher Edition and Student Edition Pages

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

CC.K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

169A–169B, 169–172, 173A–173B, 173–176, 177A–177B, 177–180, 225A–225B, 225–228, 229A–229B, 229–232, 233A–233B, 233–236See Also: 181A–181B, 181–183, 185A–185B, 185–188, 189A–189B, 189–192, 193A–193B, 193–196, 197A–197B, 197–200, 201A–201B, 201–204, 205A–205B, 205–208, 209A–209B, 209–212, 213A–213B, 213–216, 237A–237B, 237–239, 241A–241B, 241–244, 245A–245B, 245–248, 249A–249B, 249–252

CC.K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

193A–193B, 193–196, 245A–245B, 245–248, 249A–249B, 249–252See Also: 177A–177B, 177–180, 181A–181B, 181–183, 185A–185B, 185–188, 189A–189B, 189–192, 197A–197B, 197–200, 201A–201B, 201–204, 205A–205B, 205–208, 209A–209B, 209–212, 213A–213B, 213–216, 233A–233B, 233–236, 237A–237B, 237–239, 241A–241B, 241–244


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Kindergarten


Domain: Number and Operations in Base Ten Teacher Edition and Student Edition Pages

Work with numbers 11–19 to gain foundations for place value.

CC.K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 5 10 1 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

261A–261B, 261–264, 269A–269B, 269–272, 277A–277B, 277–280, 285A–285B, 285–288, 293A–293B, 293–296See Also: 265A–265B, 265–268, 273A–273B, 273–276, 281A–281B, 281–283, 289A–289B, 289–292, 297A–297B, 297–300

Domain: Operations and Algebraic Thinking (continued) Teacher Edition and Student Edition Pages

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

CC.K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 5 2 1 3 and 5 5 4 1 1).

37A–37B, 37–40, 197A–197B, 197–200, 201A–201B, 201–204, 205A–205B, 205–208, 209A–209B, 209–212, 213A–213B, 213–216

CC.K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

141A–141B, 141–144, 185A–185B, 185–188

CC.K.OA.5 Fluently add and subtract within 5. 181A–181B, 181–183, 189A–189B, 189–192, 237A–237B, 237–239, 241A–241B, 241–244See Also: 177A–177B, 177–180, 233A–233B, 233–236

Domain: Measurement and Data Teacher Edition and Student Edition Pages

Describe and compare measurable attributes.

CC.K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.

481A–481B, 481–484 See Also: 465A–465B, 465–468, 469A–469B, 469–472, 473A–473B, 473–475, 477A–477B, 477–480

CC.K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/ “less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/ shorter.

465A–465B, 465–468, 469A–469B, 469–472, 473A–473B, 473–475, 477A–477B, 477–480

Classify objects and count the number of objects in each category.

CC.K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

493A–493B, 493–496, 497A–497B, 497–500, 501A–501B, 501–503, 505A–505B, 505–508, 509A–509B, 509–512, 513A–513B, 513–516

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Kindergarten

Correlations


Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Domain: Geometry Teacher Edition and Student Edition Pages

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

CC.K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

437A–437B, 437–440, 441A–441B, 441–444, 445A–445B, 445–448

CC.K.G.2 Correctly name shapes regardless of their orientations or overall size.

357A–357B, 357–360, 365A–365B, 365–368, 373A–373B, 373–376, 381A–381B, 381–384, 389A–389B, 389–392, 417A–417B, 417–420, 421A–421B, 421–424, 425A–425B, 425–428, 429A–429B, 429–431 See Also: 361A–361B, 361–364, 369A–369B, 369–372, 377A–377B, 377–379, 385A–385B, 385–388, 393A–393B, 393–396, 397A–397B, 397–400

CC.K.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

433A–433B, 433–436See Also: 357A–357B, 357–360, 365A–365B, 365–368, 373A–373B, 373–376, 381A–381B, 381–384, 389A–389B, 389–392, 417A–417B, 417–420, 421A–421B, 421–424, 425A–425B, 425–428, 429A–429B, 429–431

Analyze, compare, create, and compose shapes.

CC.K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices / “corners”) and other attributes (e.g., having sides of equal length).

361A–361B, 361–364, 369A–369B, 369–372, 377A–377B, 377–380, 385A–385B, 385–388, 393A–393B, 393–396, 397A–397B, 397–400, 413A–413B, 413–416See Also: 417A–417B, 417–420, 421A–421B, 421–424, 425A–425B, 425–428, 429A–429B, 429–431

CC.K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

See Also: 421A–421B, 421–424

CC.K.G.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”

401A–401B, 401–404

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Grade 1





In most Teacher Edition lessons. Some examples are: 317A, 324, 325A, 333, 336, 347, 457A, 468, 469, 472

In most Student Edition lessons. Some examples are: 209, 212, 317, 320, 325, 333, 336, 341, 344, 457, 460, 461, 464, 465, 469, 472

CC.K–12.MP.2 Reason abstractly and quantitatively. In most Teacher Edition lessons. Some examples are: 53A, 57, 67, 103, 133A, 141A, 153A, 157, 161A, 369A, 373, 375, 386

In most Student Edition lessons. Some examples are: 25, 65, 68, 69, 72, 77, 80, 97, 100, 141, 153, 156, 157, 160, 161, 165, 369, 373, 377, 385, 386, 387, 389, 392


In most Teacher Edition lessons. Some examples are: 155, 185A, 186, 189, 209A, 331, 343, 415, 431, 451

In most Student Edition lessons. Some examples are: 103, 124, 185, 189, 192, 196, 321, 324, 329, 332, 337, 340, 345, 346, 347, 348, 417, 420, 421, 424, 425, 429, 432

CC.K–12.MP.4 Model with mathematics. In most Teacher Edition lessons. Some examples are: 17, 21, 37A, 83, 171, 185A, 191, 333, 335, 457, 461, 511

In most Student Edition lessons. Some examples are: 17, 20, 25, 33, 36, 57, 60, 81, 84, 185, 188, 189, 192, 485, 488, 489, 492, 493, 496, 497, 500

CC.K–12.MP.5 Use appropriate tools strategically. In most Teacher Edition lessons. Some examples are: 29, 57A, 125, 201, 263, 265, 401, 425, 469, 509


CC.K–12.MP.6 Attend to precision. In most Teacher Edition lessons. Some examples are: 97A, 103, 129A, 203, 289A, 290, 291, 293, 295, 303, 413A, 417, 431A, 437A


CC.K–12.MP.7 Look for and make use of structure. In most Teacher Edition lessons. Some examples are: 35, 457A, 458, 485A, 487, 489A, 489, 491, 499, 501A, 511

In most Student Edition lessons. Some examples are: 37, 40, 81, 84, 117, 241, 244, 245, 248, 249, 252, 253, 256, 457, 460, 461, 464, 465, 469, 472, 485


In most Teacher Edition lessons. Some examples are: 123, 130, 289A, 290, 291, 293, 295, 303, 305A, 369, 379, 403

In most Student Edition lessons. Some examples are: 97, 100, 101, 104, 105, 108, 109, 112, 117, 129, 132, 369, 372, 373, 376, 377, 380

Correlations

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Grade 1

Correlations



Represent and solve problems involving addition and subtraction.

CC.1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

13A–13B, 13–16, 17A–17B, 17–20, 21A–21B, 21–24, 25A–25B, 25–27, 37A–37B, 37–40, 53A–53B, 53–56, 57A–57B, 57–60, 61A–61B, 61–64, 65A–65B, 65–68, 73A–73B, 73–75, 81A–81B, 81–84, 173A–173B, 173–176, 185A–185B, 185–188, 209A–209B, 209–212

CC.1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

141A–141B, 141–144

See Also: 140

Understand and apply properties of operations and the relationship between addition and subtraction.

CC.1.OA.3 Apply properties of operations as strategies to add and subtract. Examples: If 8 1 3 5 11 is known, then 3 1 8 5 11 is also known. (Commutative property of addition.) To add 2 1 6 1 4, the second two numbers can be added to make a ten, so 2 1 6 1 4 5 2 1 10 5 12. (Associative property of addition.)

29A–29B, 29–32, 33A–33B, 33–36, 97A–97B, 97–100, 133A–133B, 133–136, 137A–137B, 137–140

CC.1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 2 8 by finding the number that makes 10 when added to 8.

157A–157B, 157–160, 161A–161B, 161–163


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Grade 1


Domain: Operations and Algebraic Thinking (continued) Teacher Edition and Student Edition Pages

Add and subtract within 20.

CC.1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

101A–101B, 101–104, 153A–153B, 153–156

CC.1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 1 6 5 8 1 2 1 4 5 10 1 4 5 14); decomposing a number leading to a ten (e.g., 13 2 4 5 13 2 3 2 1 5 10 2 1 5 9); using the relationship between addition and subtraction (e.g., knowing that 8 1 4 5 12, one knows 12 2 8 5 4); and creating equivalent but easier or known sums (e.g., adding 6 1 7 by creating the known equivalent 6 1 6 1 1 5 12 1 1 5 13).

41A–41B, 41–44, 85A–85B, 85–88, 105A–105B, 105–108, 109A–109B, 109–112, 113A–113B, 113–116, 117A–117B, 117–119, 121A–121B, 121–124, 125A–125B, 125–128, 129A–129B, 129–132, 165A–165B, 165–168, 169A–169B, 169–172, 189A–189B, 189–192, 193A–193B, 193–196, 197A–197B, 197–199, 213A–213B, 213–216, 221A–221B, 221–224, 317A–317B, 317–320

See Also: 101A–101B, 101–104, 133A–133B, 133–136, 137A–137B, 137–140, 141A–141B, 141–144, 153A–153B, 153–156, 133A–133B, 133–136, 137A–137B, 137–140, 141A–141B, 141–144, 153A–153B, 153–156, 201A–201B, 201–204, 205A–205B, 205–208, 209A–209B, 209–212, 217A–217B, 217–220, 349A–349B, 349–352

Work with addition and subtraction equations.

CC.1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 5 6, 7 5 8 2 1, 5 1 2 5 2 1 5, 4 1 1 5 5 1 2.

217A–217B, 217–220

See Also: 17A–17B, 17–20, 297A–297B, 297–299

CC.1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 1 ? 5 11, 5 5 u 2 3, 6 1 6 5 u .

69A–69B, 69–72, 77A–77B, 77–80, 201A–201B, 201–204, 205A–205B, 205–208

See Also: 73A–73B, 73–75, 101A–101B, 101–104, 105A–105B, 105–108, 109A–109B, 109–112, 113A–113B, 113–116, 117A–117B, 117–119, 121A–121B, 121–124, 125A–125B, 125–128, 129A–129B, 129–132, 153A–153B, 153–156, 157A–157B, 157–160, 161A–161B, 161–163, 165A–165B, 165–168, 169A–169B, 169–172, 189A–189B, 189–192, 193A–193B, 193–196, 197A–197B, 197–199


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14

Grade 1

Correlations



Extend the counting sequence.

CC.1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

241A–241B, 241–244, 245A–245B, 245–248, 273A–273B, 273–276, 277A–277B, 277–280

Understand place value.

CC.1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

261A–261B, 261–264, 265A–265B, 265–268

a. 10 can be thought of as a bundle of ten ones — called a “ten.” 257A–257B, 257–259, 269A–269B, 269–272

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

249A–249B, 249–252, 253A–253B, 253–256

c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

257A–257B, 257–259

CC.1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols ., 5, and ,.

269A–269B, 269–272, 289A–289B, 289–292, 293A–293B, 293–296, 297A–297B, 297–299, 301A–301B, 301–304

Use place value understanding and properties of operations to add and subtract.

CC.1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

321A–321B, 321–324, 329A–329B, 329–332, 333A–333B, 333–336, 337A–337B, 337–340, 341A–341B, 341–344, 345A–345B, 345–348, 349A–349B, 349–352

CC.1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

305A–305B, 305–308

CC.1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

325A–325B, 325–327, 349A–349B, 349–352


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15

Grade 1



Measure lengths indirectly and by iterating length units.

CC.1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.

369A–369B, 369–372, 373A–373B, 373–376

CC.1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

377A–377B, 377–380, 381A–381B, 381–384, 385A–385B, 385–387

Tell and write time.

CC.1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.

389A–389B, 389–392, 393A–393B, 393–396, 397A–397B, 397–400, 401A–401B, 401–404

Represent and interpret data.

CC.1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

413A–413B, 413–416, 417A–417B, 417–420, 421A–421B, 421–424, 425A–425B, 425–427, 429A–429B, 429–432, 433A–433B, 433–436, 437A–437B, 437–440


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16

Grade 1

Correlations




Reason with shapes and their attributes.

CC.1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

457A–457B, 457–460, 473A–473B, 473–476, 485A–485B, 485–488, 489A–489B, 489–492

CC.1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

461A–461B, 461–464, 465A–465B, 465–467, 469A–469B, 469–472, 493A–493B, 493–496, 497A–497B, 497–500, 501A–501B, 501–503, 505A–505B, 505–508, 509A–509B, 509–512

CC.1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

513A–513B, 513–516, 517A–517B, 517–520, 521A–521B, 521–524


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17

Grade 2





In most Teacher Edition lessons. Some examples are: 159, 191, 205, 211, 263, 303, 347, 349A, 355, 385E, 487, 527

In most Student Edition lessons. Some examples are: 88, 176, 188, 256, 264, 268, 270–272, 292, 308, 316, 380, 524

CC.K–12.MP.2 Reason abstractly and quantitatively. In most Teacher Edition lessons. Some examples are: 9E, 153A, 169E, 187, 197, 205, 207, 211, 239, 263, 317, 445

In most Student Edition lessons. Some examples are: 149–151, 153–156, 157–160, 176, 184, 192, 261–263, 265–267, 270–272, 292, 445–447, 458–460


In most Teacher Edition lessons. Some examples are: 27, 127, 137, 139, 175, 179, 199, 203, 235, 271, 295, 333E


CC.K–12.MP.4 Model with mathematics. In most Teacher Edition lessons. Some examples are: 159, 197, 206, 211, 225E, 263, 303, 305, 395, 445A, 483, 545A

In most Student Edition lessons. Some examples are: 97–100, 137, 141, 149–151, 197, 205–207, 210–212, 282–283, 348, 360, 405–407, 545–548

CC.K–12.MP.5 Use appropriate tools strategically. In most Teacher Edition lessons. Some examples are: 35, 97, 197, 243, 289A, 298, 309, 393, 402, 417A, 419, 505E

In most Student Edition lessons. Some examples are: 97–99, 149–151, 189–191, 197, 282–283, 293, 301–303, 305, 350–352, 361–363, 402–404, 418–419

CC.K–12.MP.6 Attend to precision. In most Teacher Edition lessons. Some examples are: 19, 71, 117E, 195, 203, 217A, 255, 257A, 267, 277E, 423, 489A

In most Student Edition lessons. Some examples are: 20, 66–68, 102–104, 134–136, 196, 214–216, 340, 354–355, 422–424, 442–444, 486–488, 509

CC.K–12.MP.7 Look for and make use of structure. In most Teacher Edition lessons. Some examples are: 37, 45A, 53E, 59, 87, 94, 135, 215, 295, 339, 411, 451

In most Student Edition lessons. Some examples are: 18–20, 33–36, 37–40, 41–44, 45–48, 69–72, 88, 93–96, 129, 138–139, 231, 370–371


In most Teacher Edition lessons. Some examples are: 86, 101A, 103, 198, 247, 290, 307, 315, 351, 375, 429E, 465C

In most Student Edition lessons. Some examples are: 13–15, 58–59, 97–99, 102–104, 130–131, 174–176, 178–180, 230–231, 314–315, 338–340, 358–359, 449–452

Correlations

Untitled-4971 126 5/30/2011 3:25:48 AM

18

Grade 2

Correlations



Represent and solve problems involving addition and subtraction.

CC.2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

149A–149B, 149–152, 153A–153B, 153–156, 205A–205B, 205–208, 209A–209B, 209–212, 261A–261B, 261–264, 265A–265B, 265–268, 269A–269B, 269–272

Add and subtract within 20.

CC.2.OA.2 Fluently add and subtract within 20 using mental strategies.By end of Grade 2, know from memory all sums of two one-digit numbers.

121A–121B, 121–124, 125A–125B, 125–128, 129A–129B, 129–132, 133A–133B, 133–136, 137A–137B, 137–140, 141A–141B, 141–143, 145A–145B, 145–148

Work with equal groups of objects to gain foundations for multiplication.

CC.2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

13A–13B, 13–16, 17A–17B, 17–20

CC.2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

157A–157B, 157–160, 161A–161B, 161–164

See Also: 529A–529B, 529–531


Untitled-4971 127 5/30/2011 3:25:50 AM

19

Grade 2



Understand place value.

CC.2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

a. 100 can be thought of as a bundle of ten tens — called a “hundred.”

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–72, 73A–73B, 73–76

57A–57B, 57–60

57A–57B, 57–60

CC.2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s. 41A–41B, 41–44, 45A–45B, 45–48

See Also: 93A–93B, 93–96

CC.2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.


See Also: 69A–69B, 69–72

CC.2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using ., 5, and , symbols to record the results of comparisons.

97A–97B, 97–100, 101A–101B, 101–104


Untitled-4971 128 5/30/2011 3:25:51 AM

20

Grade 2

Correlations


Domain: Number and Operations in Base Ten (continued) Teacher Edition and Student Edition Pages

Use place value understanding and properties of operations to add and subtract.

CC.2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

193A–193B, 193–196, 197A–197B, 197–199, 201A–201B, 201–204, 229A–229B, 229–232, 233A–233B, 233–236, 237A–237B, 237–240, 241A–241B, 241–244, 245A–245B, 245–248, 249A–249B, 249–251, 253A–253B, 253–256, 257A–257B, 257–260

See Also: 133A–133B, 133–136, 173A–173B, 173–176, 177A–177B, 177–180, 181A–181B, 181–184, 205A–205B, 205–208, 209A–209B, 209–212, 261A–261B, 261–264, 265A–265B, 265–268, 269A–269B, 269–272

CC.2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

173A–173B, 173–176, 177A–177B, 177–180, 181A–181B, 181–184, 185A–185B, 185–188, 189A–189B, 189–192, 213A–213B, 213–216, 217A–217B, 217–220

See Also: 193A–193B, 193–196, 201A–201B, 201–204

CC.2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

281A–281B, 281–284, 285A–285B, 285–288, 289A–289B, 289–292, 293A–293B, 293–296, 297A–297B, 297–299, 301A–301B, 301–304, 305A–305B, 305–308, 309A–309B, 309–312, 313A–313B, 313–316, 317A–317B, 317–320

See Also: 197A–197B, 197–199

CC.2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

89A–89B, 89–92, 93A–93B, 93–96

CC.2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.

185A–185B, 185–188, 237A–237B, 237–240

See Also: 189A–189B, 189–192, 193A–193B, 193–196, 241A–241B, 241–244, 245A–245B, 245–248


Untitled-4971 129 5/30/2011 3:25:53 AM

21

Grade 2



Measure and estimate lengths in standard units.

CC.2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

389A–389B, 389–392, 393A–393B, 393–396, 401A–401B, 401–404, 417A–417B, 417–420, 433A–433B, 433–436, 441A–441B, 441–444

CC.2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

409A–409B, 409–412, 449A–449B, 449–452

CC.2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

397A–397B, 397–400, 413A–413B, 413–416, 437A–437B, 437–440, 453A–453B, 453–456

CC.2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

457A–457B, 457–460

Relate addition and subtraction to length.

CC.2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

405A–405B, 405–407, 445A–445B, 445–447

CC.2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, . . . , and represent whole-number sums and differences within 100 on a number line diagram.

405A–405B, 405–407, 445A–445B, 445–447

See Also: 145A–145B, 145–148

Work with time and money.

CC.2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

365A–365B, 365–368, 369A–369B, 369–372, 373A–373B, 373–376, 377A–377B, 377–380

CC.2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

337A–337B, 337–340, 341A–341B, 341–344, 345A–345B, 345–348, 349A–349B, 349–352, 353A–353B, 353–355, 357A–357B, 357–360, 361A–361B, 361–364


CC.2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

421A–421B, 421–424

CC.2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

469A–469B, 469–472, 473A–473B, 473–476, 477A–477B, 477–479, 481A–481B, 481–484, 485A–485B, 485–488, 489A–489B, 489–492


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22

Grade 2

Correlations





CC.2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

509A–509B, 509–512, 513A–513B, 513–516, 517A–517B, 517–520, 521A–521B, 521–524, 525A–525B, 525–528

CC.2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

529A–529B, 529–531

CC.2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

533A–533B, 533–536, 537A–537B, 537–540, 541A–541B, 541–544, 545A–545B, 545–548


Untitled-4971 131 5/30/2011 3:25:56 AM

23

Grade 3


COMMON CORE STATE STANDARDS FOR MATHEMATICSCorrelations

Standards for Mathematical Practices Student Edition and Teacher Edition Pages


In most Student Edition lessons. Some examples are: 26, 163, 171, 210, 235, 254, 291, 296, 330, 359–362, 423, 441–442, 455, 464

In most Teacher Edition lessons. Some examples are: 3E, 11, 71, 77, 83A, 83, 135, 165, 171, 193, 207E, 313, 319, 323, 333, 340, 343, 459A, 512, 517A

CC.K–12.MP.2 Reason abstractly and quantitatively. In most Student Edition lessons. Some examples are: 80, 90, 123, 152, 165, 185, 225, 243–244, 253, 311, 459–461

In most Teacher Edition lessons. Some examples are: 15, 21, 25, 31, 47, 49, 107, 111A, 122, 124, 213, 221A, 235, 242, 251E, 329A, 363A, 387E, 441A


In most Student Edition lessons. Some examples are: 6, 8, 78, 87, 148, 159, 162, 164, 217, 231, 276, 340, 358, 436, 449, 509, 518

In most Teacher Edition lessons. Some examples are: 30, 35, 104, 147, 161, 295A, 309, 321, 326, 337, 356, 365, 431E, 451, 479E, 506, 507

CC.K–12.MP.4 Model with mathematics. In most Student Edition lessons. Some examples are: 51, 79–82, 101–104, 141, 185, 222, 235–236, 279, 291, 326, 337–340, 412, 424, 441–442, 453

In most Teacher Edition lessons. Some examples are: 51, 59E, 69–70, 81, 111–112, 135–136, 143, 147, 201, 245, 281, 293, 325, 379, 397A, 412, 422, 425

CC.K–12.MP.5 Use appropriate tools strategically. In most Student Edition lessons. Some examples are: 39, 47, 61, 143, 147, 195, 226, 262, 363–366, 397–398, 406, 411, 413, 419–422, 441–444, 454

In most Teacher Edition lessons. Some examples are: 15, 37, 43, 62, 71, 101, 138, 199A, 232, 398, 411A, 418, 439

CC.K–12.MP.6 Attend to precision. In most Student Edition lessons. Some examples are: 21–24, 191, 222, 240, 270, 284, 323–326, 445–448, 450, 483, 491–492, 501–504, 505–508, 515–518

In most Teacher Edition lessons. Some examples are: 23, 65, 75, 179E, 192, 289, 305E, 309, 413, 445, 509, 515, 518

CC.K–12.MP.7 Look for and make use of structure. In most Student Edition lessons. Some examples are: 5–8, 25–28, 47–50, 155, 160, 167–170, 199, 232, 239–240, 438, 453, 464–465, 492, 497–498, 501–504, 510, 513–515

In most Teacher Edition lessons. Some examples are: 5, 39A, 117, 131E, 133, 149A, 160, 219, 237, 257A, 309, 331, 349E, 353, 448, 463A


In most Student Edition lessons. Some examples are: 25–28, 47–50, 133, 145, 149–152, 191, 257, 453, 459–461, 463–466, 468, 472–473, 491, 505–508, 515–518

In most Teacher Edition lessons. Some examples are: 25, 49, 95E, 102, 103, 164, 172, 174, 183, 184, 193, 212, 213, 260, 369, 442, 455

Untitled-352 128 6/1/2011 7:44:08 AM

24

Grade 3

Correlations


Domain: Operations and Algebraic Thinking Student Edition and Teacher Edition Pages

Represent and solve problems involving multiplication and division.

CC.3.OA.1 Interpret products of whole numbers, e.g., interpret 5 3 7 as the total number of objects in 5 groups of 7 objects each.

97A–97B, 97–100, 101A–101B, 101–104See Also: 105A–105B, 105–108, 111A–111B, 111–114, 115A–115B, 115–118, 119A–119B, 119–122, 123A–123B, 123–126, 133A–133B, 133–136, 137A–137B, 137–140, 141A–141B, 141–144, 145A–145B, 145–148, 149A–149B, 149–152, 155A–155B, 155–158, 163A–163B, 163–166, 167A–167B, 167–170, 185A–185B, 185–188, 295A–295B, 295–298

CC.3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 4 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.

213A–213B, 213–216, 217A–217B, 217–220, 221A–221B, 221–224 See Also: 209A–209B, 209–212, 225A–225B, 225–228, 231A–231B, 231–234, 235A–235B, 235–238, 239A–239B, 239–242, 243A–243B, 243–246, 253A–253B, 253–256, 257A–257B, 257–260, 261A–261B, 261–264, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 279A–279B, 279–282, 283A–283B, 283–286, 287A–287B, 287–290, 291A–291B, 291–294, 295A–295B, 295–298

CC.3.OA.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.

105A–105B, 105–108, 115A–115B, 115–118, 133A–133B, 133–136, 137A–137B, 137–140, 141A–141B, 141–144, 209A–209B, 209–212, 225A–225B, 225–228, 231A–231B, 231–234, 253A–253B, 253–256, 261A–261B, 261–264 See Also: 97A–97B, 97–100, 101A–101B, 101–104, 111A–111B, 111–114, 119A–119B, 119–122, 123A–123B, 123–126, 145A–145B, 145–148, 149A–149B, 149–152, 155A–155B, 155–158, 163A–163B, 163–166, 167A–167B, 167–170, 171A–171B, 171–174, 181A–181B, 181–184, 185A–185B, 185–188, 191A–191B, 191–194, 195A–195B, 195–198, 199A–199B, 199–202, 213A–213B, 213–216, 217A–217B, 217–220, 221A–221B, 221–224, 235A–235B, 235–238, 239A–239B, 239–242, 243A–243B, 243–246, 257A–257B, 257–260, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 279A–279B, 279–282, 283A–283B, 283–286, 287A–287B, 287–290, 291A–291B, 291–294, 295A–295B, 295–298, 453A–453B, 453–456, 459A–459B, 459–462, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

CC.3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

185A–185B, 185–188, 283A–283B, 283–286, See Also: 145A–145B, 145–148, 149A–149B, 149–152, 155A–155B, 155–158, 163A–163B, 163–166, 167A–167B, 167–170, 235A–235B, 235–238, 257A–257B, 257–260, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 279A–279B, 279–282, 287A–287B, 287–290


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Domain: Operations and Algebraic Thinking (continued) Student Edition and Teacher Edition Pages

Understand properties of multiplication and the relationship between multiplication and division.

CC.3.OA.5 Apply properties of operations as strategies to multiply and divide. Examples: If 6 3 4 5 24 is known, then 4 3 6 5 24 is also known (Commutative property of multiplication.) 3 3 5 3 2 can be found by 3 3 5 5 15, then 15 3 2 5 30, or by 5 3 2 5 10, then 3 3 10 5 30. (Associative property of multiplication.) Knowing that 8 3 5 5 40 and 8 3 2 5 16, one can find 8 3 7 as 8 3 (5 1 2) 5 (8 3 5) 1 (8 3 2) 5 40 1 16 5 56. (Distributive property.)

119A–119B, 119–122, 123A–123B, 123–126, 145A–145B, 145–148, 155A–155B, 155–158, 243A–243B, 243–246 See Also: 149A–149B, 149–152, 159A–159B, 159–162, 163A–163B, 163–166, 167A–167B, 167–170, 191A–191B, 191–194, 195A–195B, 195–198, 269A–269B, 269–272, 273A–273B, 273–276, 287A–287B, 287–290, 463A–463B, 463–466

CC.3.OA.6 Understand division as an unknown-factor problem. 235A–235B, 235–238 See Also: 257A–257B, 257–260, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 279A–279B, 279–282, 283A–283B, 283–286, 287A–287B, 287–290

Multiply and divide with 100.

CC.3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 3 5 5 40, one knows 40 4 5 5 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

149A–149B, 149–152, 163A–163B, 163–166, 167A–167B, 167–170, 239A–239B, 239–242, 257A–257B, 257–260, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 279A–279B, 279–282, 287A–287B, 287–290See Also: 101A–101B, 101–104, 119A–119B, 119–122, 123A–123B, 123–126, 133A–133B, 133–136, 137A–137B, 137–140, 141A–141B, 141–144, 145A–145B, 145–148, 155A–155B, 155–158, 171A–171B, 171–174, 181A–181B, 181–184, 185A–185B, 185–188, 191A–191B, 191–194, 195A–195B, 195–198, 199A–199B, 199–202, 225A–225B, 225–228, 235A–235B, 235–238, 243A–243B, 243–246, 253A–253B, 253–256, 261A–261B, 261–264, 283A–283B, 283–286, 291A–291B, 291–294, 295A–295B, 295–298, 423A–423B, 423–426, 459A–459B, 459–462, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

CC.3.OA.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.

51A–51B, 51–54, 111A–111B, 111–114, 171A–171B, 171–174, 291A–291B, 291–294, 295A–295B, 295–298 See Also: 25A–25B, 25–28, 29A–29B, 29–32, 47A–47B, 47–50, 83A–83B, 83–86, 192, 342, 405A–405B, 405–408

CC.3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

5A–5B, 5–8, 159A–159B, 159–162, 181A–181B, 181–184 See Also: 141A–141B, 141–144, 163A–163B, 163–166, 167A–167B, 167–170, 171A–171B, 171–174, 459A–459B, 459–462

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Correlations


Domain: Number and Operations in Base Ten Student Edition and Teacher Edition Pages


CC.3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

9A–9B, 9–12, 13A–13B, 13–16, 35A–35B, 35–38 See Also: 25A–25B, 25–28, 29A–29B, 29–32, 43A–43B, 43–46, 47A–47B, 47–50

CC.3.NBT.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.

17A–17B, 17–20, 21A–21B, 21–24, 25A–25B, 25–28, 29A–29B, 29–32, 39A–39B, 39–42, 43A–43B, 43–46, 47A–47B, 47–50 See Also: 13A–13B, 13–16, 35A–35B, 35–38, 51A–51B, 51–54, 61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–72, 75A–75B, 75–78, 79A–79B, 79–82, 83A–83B, 83–86, 87A–87B, 87–90, 101A–101B, 101–104, 401A–401B, 401–404, 405A–405B, 405–408, 423A–423B, 423–426, 437A–437B, 437–440, 441A–441B, 441–444, 453A–453B, 453–456, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

CC.3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 3 80, 5 3 60) using strategies based on place value and properties of operations.

191A–191B, 191–194, 195A–195B, 195–198, 199A–199B, 199–202

Domain: Number and Operations—Fractions Student Edition and Teacher Edition Pages


CC.3.NF.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.

307A–307B, 307–310, 311A–311B, 311–314, 315A–315B, 315–318, 319A–319B, 319–322, 333A–333B, 333–336, 337A–337B, 337–340, 341A–341B, 341–344 See Also: 351A–351B, 351–354, 355A–355B, 355–358, 359A–359B, 359–362, 363A–363B, 363–366, 369A–369B, 369–372, 373A–373B, 373–376, 377A–377B, 377–380, 517A–517B, 517–520

CC.3.NF.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.

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.

323A–323B, 323–326, 329A–329B, 329–332

323A–323B, 323–326 See Also: 329A–329B, 329–332, 373A–373B, 373–376

323A–323B, 323–326 See Also: 329A–329B, 329–332, 355A–355B, 355–358, 371, 373A–373B, 373–376


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Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices as Council of Chief State School Officers. All rights reserved. This product is not sponsored or endorsed by the Common Core State Standards Initiative of the National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Domain: Measurement and Data Student Edition and Teacher Edition Pages

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

CC.3.MD.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.

389A–389B, 389–392, 393A–393B, 393–396, 397A–397B, 397–400, 401A–401B, 401–404, 405A–405B, 405–408

CC.3.MD.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.

415A–415B, 415–418, 419A–419B, 419–422, 423A–423B, 423–426


CC.3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.

61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–72, 75A–75B, 75–78, 79A–79B, 79–82, 83A–83B, 83–86

CC.3.MD.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.

87A–87B, 87–90, 411A–411B, 411–414See Also: 437A–437B, 437–440

Domain: Number and Operations—Fractions (continued) Student Edition and Teacher Edition Pages


CC.3.NF.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.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 5 2/4, 4/6 5 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. Examples: Express 3 in the form 3 5 3/1; recognize that 6/1 5 6; locate 4/4 and 1 at the same point of a number line diagram.

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 ., 5, or ,, and justify the conclusions, e.g., by using a visual fraction model.

363A–363B, 363–366, 373A–373B, 373–376, 377A–377B, 377–380

373A–373B, 373–376, 377A–377B, 377–380

373A–373B, 373–376, 377A–377B, 377–380

329A–329B, 329–332, 373A–373B, 373–376

351A–351B, 351–354, 355A–355B, 355–358, 359A–359B, 359–362, 363A–363B, 363–366, 369A–369B, 369–372 See Also: 517A–517B, 517–520

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Correlations


Domain: Measurement and Data (continued) Student Edition and Teacher Edition Pages

Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

CC.3.MD.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.

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.

445A–445B, 445–448 See Also: 449A–449B, 449–452, 453A–453B, 453–456, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474, 517A–517B, 517–520

445A–445B, 445–448 See Also: 449A–449B, 449–452, 453A–453B, 453–456, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

449A–449B, 449–452 See Also: 445A–445B, 445–448, 453A–453B, 453–456, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

CC.3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

445A–445B, 445–448, 449A–449B, 449–452See also 453A–453B, 453–456

CC.3.MD.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.

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 whole-number 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 1 c is the sum of a 3 b and a 3 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.

453A–453B, 453–456

449A–449B, 449–452, 453A–453B, 453–456

459A–459B, 459–462 See Also: 453A–453B,453–456, 463A–463B, 463–466, 467A–467B, 467–470, 471A–471B, 471–474

191A–191B, 191–194, 463A–463B, 463–466 See Also: 121, 233

463A–463B, 463–466

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

CC.3.MD.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.

433A–433B, 433–436, 437A–437B, 437–440, 441A–441B, 441–444, 467A–467B, 467–470, 471A–471B, 471–474 See Also: 445A–445B, 445–448

Domain: Geometry Student Edition and Teacher Edition Pages


CC.3.G.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.


CC.3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

517A–517B, 517–520 See Also: 307A–307B, 307–310, 311A–311B, 311–314, 315A–315B, 315–318, 319A–319B, 319–322, 329A–329B, 329–332, 373A–373B, 373–376, 377A–377B, 377–380

Pages only in Teacher Edition are shown in italics.

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In most Student Edition lessons. Some examples are: 50–51, 58–59, 76–77, 123–126, 145–148, 202, 207, 235–236, 351–353, 359–360, 369–370, 425, 480, 505, 515–518

In most Teacher Edition lessons. Some examples are: 31A, 47, 51, 53A, 87A, 253A, 261, 291, 295, 301, 391, 423, 515A, 516

CC.K–12.MP.2 Reason abstractly and quantitatively. In most Student Edition lessons. Some examples are: 23–26, 29, 45–49, 61–64, 75, 119, 235, 301–304, 355–358, 368, 423, 432, 475–478, 487–490

In most Teacher Edition lessons. Some examples are: 5A, 8, 77, 85, 179A, 231A, 267A, 271A, 304, 319A, 467A, 487A, 490


In most Student Edition lessons. Some examples are: 94, 110, 112, 146, 174, 192, 213, 254, 270, 286, 318, 368, 389, 397, 490, 498

In most Teacher Edition lessons. Some examples are: 15, 25, 43H, 84, 142, 174, 230, 241, 243, 318, 393, 402, 489, 497A

CC.K–12.MP.4 Model with mathematics. In most Student Edition lessons. Some examples are: 35–38, 45–51, 91–93, 127–130, 231–234, 257–258, 267–269, 271–274, 278, 435–436, 461–464, 514, 515–518

In most Teacher Edition lessons. Some examples are: 35A, 45A, 49, 111, 147, 235A, 243A, 270, 305A, 450–451, 497A, 501A, 505A, 511A

CC.K–12.MP.5 Use appropriate tools strategically. In most Student Edition lessons. Some examples are: 5–6, 17, 141–144, 171–174, 227–229, 241, 249–250, 319–322, 425–428, 433, 449, 452, 467

In most Teacher Edition lessons. Some examples are: 141A, 163A, 171, 193, 207A–207B, 227A, 249, 291, 325, 425A, 447, 470, 479

CC.K–12.MP.6 Attend to precision. In most Student Edition lessons. Some examples are: 14, 85, 110, 115, 181, 198, 211–212, 228, 231, 293, 389–392, 421–423, 433–434, 449–452, 483–485

In most Teacher Edition lessons. Some examples are: 33, 80, 148, 199, 209, 381A, 393, 399, 407A, 421A, 481, 483A

CC.K–12.MP.7 Look for and make use of structure. In most Student Edition lessons. Some examples are: 54–56, 61–63, 65–66, 109–111, 149–152, 157–159, 215–217, 320–321, 385–386, 394–395, 407–410, 457

In most Teacher Edition lessons. Some examples are: 13A, 65, 151, 149A, 215A, 233, 325A, 329A, 330–331, 347A, 351A, 395, 407, 461A, 507


In most Student Edition lessons. Some examples are: 54, 66, 101–102, 120, 163–166, 179, 237, 315, 316–318, 325, 403, 497, 499

In most Teacher Edition lessons. Some examples are: 19, 79, 103, 112–113, 119A, 172, 214, 303, 315A, 371, 325B, 327


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Correlations



Use the four operations with whole numbers to solve problems

CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 5 5 3 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

45A–45B, 45–48

CC.4.OA.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.

49A–49B, 49–52

CC.4.OA.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.

79A–79B, 79–82, 91A–91B, 91–94, 127A–127B, 127–130, 145A–145B, 145–148, 183A–183B, 183–186See Also: 27A–28A, 27–30, 31A–31B, 31–34

Gain familiarity with factors and multiples.

CC.4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

193A–193B, 193–196, 197A–197B, 197–200, 201A–201B, 201–204, 207A–207B, 207–210, 211A–211B, 211–214

Generate and analyze patterns.

CC.4.OA.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.

215A–215B, 215–218, 407A–407B, 407–410


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Generalize place value understanding for multi-digit whole numbers.

CC.4.NBT.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.

5A–5B, 5–8See Also: 23A–23B, 23–26, 53A–53B, 53–56, 101A–101B, 101–104, 149A–149B, 149–152

CC.4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons.

9A–9B, 9–12, 13A–13B, 13–16See Also: 23A–23B, 23–26,

CC.4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

17A–17B, 17–20See Also: 27A–28A, 27–30, 31A–31B, 31–34, 56A–56B, 57–60, 105A–105B, 105–108


CC.4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

27A–28A, 27–30, 31A–31B, 31–34, 35A–35B, 35–38

CC.4.NBT.5 Multiply a whole number of up to four digits by a one-digit 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.

53A–53B, 53–56, 57A–57B, 57–60, 61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–72, 75A–75B, 75–78, 83A–83B, 83–86, 83–86, 87A–87B, 87–90, 101A–101B, 101–104, 105A–105B, 105–108, 109A–109B, 109–112, 113A–113B, 113–116, 119A–119B, 119–122, 123A–123B, 123–126 See Also: 79A–79B, 79–82, 127A–127B, 127–130

CC.4.NBT.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.

137A–137B, 137–140, 141A–141B, 141–144, 149A–149B, 149–152, 153A–153B, 153–156, 157A–157B, 157–160, 163A–163B, 163–166, 167A–167B, 167–170, 171A–171B, 171–174, 175A–175B, 175–178, 179A–179B, 179–182 See Also: 145A–145B, 145–148, 183A–183B, 183–186

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Correlations



Extend understanding of fraction equivalence and ordering.

CC.4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n 3 a)/(n 3 b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

227A–227B, 227–230, 231A–231B, 231–234, 235A–235B, 235–238, 239A–239B, 239–242, 243A–243B, 243–246

CC.4.NF.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 ., 5, or ,, and justify the conclusions, e.g., by using a visual fraction model.

249A–249B, 249–252, 253A–253B, 253–256, 257A–257B, 257–260

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

CC.4.NF.3 Understand a fraction a/b with a . 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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. Examples: 3/8 5 1/8 1 1/8 1 1/8; 3/8 5 1/8 1 2/8; 2 1/8 5 1 1 1 1 1/8 5 8/8 1 8/8 1 1/8.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

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.

267A–267B, 267–270

271A–271B, 271–274, 289A–289B, 289–292

293A–293B, 293–296, 297A–297B, 297–300, 301A–301B, 301–304

275A–275B, 275–278, 279A–279B, 279–282, 283A–283B, 283–286, 305A–305B, 305–308

CC.4.NF.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.

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.

315A–315B, 315–318

319A–319B, 319–322, 325A–325B, 325–328

319–322, 329A–329B, 329–332, 333A–333B, 333–336See Also: 319A–319B, 325A–325B, 325–328


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Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

CC.4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; 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-column table.

445A–445B, 445–448, 449A–449B, 449–452, 453A–453B, 453–456, 457A–458B, 457–460, 467A–467B, 467–470, 471A–471B, 471–474, 475A–475B, 475–478, 487A–487B, 487–490See Also: 479A–479B, 479–482, 483A–483B, 483–486

CC.4.MD.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.

359A–359B, 359–362, 471A–471B, 471–474, 479A–479B, 479–482, 483A–483B, 483–486See Also: 449A–449B, 449–452, 453A–453B, 453–456, 457A–458B, 457–460, 461A–461B, 461–464, 475A–475B, 475–478

CC.4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

497A–497B, 497–500, 501A–501B, 501–504, 505A–505B, 505–508, 511A–511B, 511–514, 515A–515B, 515–518


CC.4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

461A–461B, 461–464



Understand decimal notation for fractions, and compare decimal fractions.

CC.4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

351A–351B, 351–354, 365A–365B, 365–368

CC.4.NF.6 Use decimal notation for fractions with denominators 10 or 100. 343A–343B, 343–346, 347A–347B, 347–350, 355A–355B, 355–358See Also: 351A–351B, 351–354

CC.4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols ., 5, or ,, and justify the conclusions, e.g., by using a visual model.

369A–369B, 369–372

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Grade 4

Correlations



Domain: Measurement and Data (continued) Student Edition and Teacher Edition Pages

Geometric measurement: understand concepts of angle and measure angles.

CC.4.MD.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 “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

417A–417B, 417–420, 421A–421B, 421–424

421A–421B, 421–424

CC.4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

425A–425B, 425–428

CC.4.MD.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.

431A–431B, 431–434, 435A–435B, 435–438


Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

CC.4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

381A–381B, 381–384, 389A–389B, 389–392See Also: 385A–385B, 385–388

CC.4.G.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.

385A–385B, 385–388, 393A–393B, 393–396

CC.4.G.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.

399A–399B, 399–402, 403A–403B, 403–406


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Grade 5





In most Student Edition lessons. Some examples are: 20, 87, 95–98, 233, 255–258, 279, 329–332, 347–350, 369–372, 417–420, 483–486, 487–490

In most Teacher Edition lessons. Some examples are: 33, 39A, 59E, 79, 87A, 169–170, 199E, 269A, 411, 417A, 427–430, 483–486

CC.K–12.MP.2 Reason abstractly and quantitatively. In most Student Edition lessons. Some examples are: 35–38, 43–46, 121, 169–172, 231, 321, 353–354, 388, 395–398, 475

In most Teacher Edition lessons. Some examples are: 37, 40, 51, 96, 110, 141, 201E, 243–246, 259A, 275, 269A, 359


In most Student Edition lessons. Some examples are: 8, 12, 30, 124, 134, 164, 208, 209–212, 304, 306, 347–350, 380, 452

In most Teacher Edition lessons. Some examples are: 7, 85, 123, 133, 171, 246, 277A, 329A, 380, 398, 439E, 455

CC.K–12.MP.4 Model with mathematics. In most Student Edition lessons. Some examples are: 35–38, 69–71, 95–97, 165–168, 173, 247–250, 291–294, 343–345, 357–358, 405, 409, 467

In most Teacher Edition lessons. Some examples are: 35A, 37, 97, 185, 233, 243A, 249, 343A, 367E, 375, 395A, 427A, 471A

CC.K–12.MP.5 Use appropriate tools strategically. In most Student Edition lessons. Some examples are: 121–124, 132, 151–154, 227–230, 291–294, 381–384, 405–408, 453–456, 463, 467–470

In most Teacher Edition lessons. Some examples are: 159E, 289E, 291–294, 295–298, 303–306, 309, 323, 453–456, 469, 471–474

CC.K–12.MP.6 Attend to precision. In most Student Edition lessons. Some examples are: 67, 87–90, 105–108, 186, 208, 306, 340, 395–398, 417–420, 449–452

In most Teacher Edition lessons. Some examples are: 7, 44, 87–90, 105–108, 135–138, 139, 382, 403E, 415, 449–452

CC.K–12.MP.7 Look for and make use of structure. In most Student Edition lessons. Some examples are: 9–12, 21–25, 35–38, 109–112, 227–230, 298, 321–324, 353–356, 387–390, 471–474

In most Teacher Edition lessons. Some examples are: 3E, 31, 69A, 103E, 166, 173A, 227A, 273E, 326, 337C


In most Student Edition lessons. Some examples are: 17–20, 73–76, 161–164, 201–204, 223–226, 273–276, 391–394, 423–426, 441, 475–478

In most Teacher Edition lessons. Some examples are: 17–20, 85, 143A, 189, 273–276, 305, 317–320, 389, 423–426, 475–478

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Grade 5


Correlations


Write and interpret numerical expressions.

CC.5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

47A–47B, 47–50, 51A–51B, 51–54See Also: 9, 13A–13B, 13–16, 21B, 21–22, 36–37, 39A–39B, 39–41, 43B, 44–45, 369A–369B, 369–372

CC.5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them

43A–43B, 43–46See Also: 51B, 51–54, 307–310, 321–324

Analyze patterns and relationships.

CC.5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

387A–387B, 387–390, 391A–391B, 391–394, 395A–395B, 395–398


Understand the place value system.

CC.5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5A–5B, 5–8, 9A–9B, 9–12, 105A–105B, 105–108See Also: 109A–109B, 109–112, 169A–169B, 170, 174, 187B, 187, 191A–191B, 191, 193, 201A–201B, 201–204, 209–212, 223A–223B, 223–226, 227A–227B, 228–230, 423A–423B, 423–426, 428, 430

CC.5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

17A–17B, 17–20, 21A–21B, 21–24, 161A–161B, 161–164, 169A–169B, 169–172, 173A–173B, 173–176, 187A–187B, 187–190, 191A–191B, 191–194, 201A–201B, 201–204, 213A–213B, 213–216, 223A–223B, 223–226See Also: 5–8, 9–12

CC.5.NBT.3 Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 5 3 3 100 1 4 3 10 1 7 3 1 1 3 3 (1/10) 1 9 3 (1/100) 1 2 3 (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each place, using ., 5, and , symbols to record the results of comparisons.

109A–109B, 109–112See Also: 105A–105B, 105–108

113A–113B, 113–116See Also: 423A

CC.5.NBT.4 Use place value understanding to round decimals to any place. 117A–117B, 117–120See Also: 131A–131B, 131, 133–134, 136–137, 140–141, 169, 188, 209–212, 214, 224


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Use equivalent fractions as a strategy to add and subtract fractions.

CC.5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

255A–255B, 255–258, 259A–259B, 259–262, 265A–265B, 265–268, 269A–269B, 269–272, 273A–273B, 273–276, 281A–281B, 281–284See Also: 243A–243B, 243–246, 247A–247B, 247–250, 277A–277B, 277–280, 291A, 295A, 299A, 303A, 343A, 357A, 369A–369B, 387A

CC.5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.

243A–243B, 243–246, 247A–247B, 247–250, 251A–251B, 251–254, 277A–277B, 277–280See Also: 259A–259B, 259–262, 265A–265B, 265–268, 269A–269B, 269–272, 291A, 295A, 299A


Domain: Number and Operations in Base Ten (continued) Student Edition and Teacher Edition Pages

Perform operations with multi-digit whole numbers and with decimals to hundredths.

CC.5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

27A–27B, 27–30, 31A–31B, 31–34 See Also: 47–48, 50, 66–67, 73–76, 83–86, 87–90, 91–94, 95–98, 165–168, 169–172, 173A–173B, 173–176, 177–180, 187A–187B, 187–190, 191A, 191–194, 213A, 214–216, 223–226, 227–230, 231–234, 317A, 387A, 391–394, 395A, 406–408, 411, 413–416, 417A, 417–420, 433, 475–478, 479–482, 483–484, 486, 487–490

CC.5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.

13A–13B, 13–16, 35A–35B, 35–38, 39A–39B, 39–42, 61A–61B, 61–64, 65A–65B, 65–68, 69A–69B, 69–72, 73A–73B, 73–76, 79A–79B, 79–82, 83A–83B, 83–86, 91A–91B, 91–94, 95A–95B, 95–98See Also: 87A–87B, 87–90, 213–216, 224–226, 227–230, 243A, 339A, 391A, 395A, 397A, 406–408, 411, 415

CC.5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

121A–121B, 121–124, 125A–125B, 125–128, 131A–131B, 131–134, 135A–135B, 135–138, 139A–139B, 139–142, 143A–143B, 143–146, 147A–147B, 147–150, 151A–151B, 151–154, 165A–165B, 165–168, 169A–169B, 169–172, 173A–173B, 173–176, 177A–177B, 177–180, 183A–183B, 183–186, 187A–187B, 187–190, 191A–191B, 191–194, 205A–205B, 205–208, 209A–209B, 209–212, 213A–213B, 213–216, 219A–219B, 219–222, 223A–223B, 223–226, 227A–227B, 227–230, 231A–231B, 231–234See Also: 161A–161B, 161–164, 243A, 247A, 307A, 311A, 321A

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Grade 5


Correlations


Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

CC.5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a 4 b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

87A–87B, 87–90, 347A–347B, 347–350See Also: 227A–227B, 227–230, 408

CC.5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (a/b) 3 q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a 3 q 4 b.

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

291A–291B, 291–294, 295A–295B, 295–298, 299A–299B, 299–302, 311A–311B, 311–314See Also: 317A

303A–303B, 303–306, 317A–317B, 317–320

CC.5.NF.5 Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b 5 (n 3 a)/(n 3 b) to the effect of multiplying a/b by 1.

307A–307B, 307–310, 321A–321B, 321–324 See Also: 311A–311B, 311–314

307A–307B, 307–310, 321A–321B, 321–324, 329A–329B, 329–332See Also: 311A–311B, 311–314

CC.5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

325A–325B, 325–328, See Also: 329A–329B, 329–332

CC.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.

339A–339B, 339–342See Also: 353A–353B, 353–356, 357A–357B, 357–360, 369A–369B, 369–372

339A–339B, 339–342, 343A–343B, 343–346 See Also: 353A–353B, 353–356, 357A–357B, 357–360

353A–353B, 353–356, 357A–357B, 357–360See Also: 339A–339B, 339–342


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Grade 5



Convert like measurement units within a given measurement system.

CC.5.MD.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

405A–405B, 405–408, 409A–409B, 409–412, 413A–413B, 413–416, 417A–417B, 417–420, 423A–423B, 423–426, 427A–427B, 427–430, 431A–431B, 431–434


CC.5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

369A–369B, 369–372

Geometric measurement: understand concepts of volume and relate volume to multiplication and addition.

CC.5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

457A–457B, 457–460

463A–463B, 463–466

467A–467B, 467–470See Also: 471A–471B, 471–474

CC.5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

467A–467B, 467–470, 471A–471B, 471–474

CC.5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

b. Apply the formulas V 5 l 3 w 3 h and V 5 b 3 h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

475A–475B, 475–478

479A–479B, 479–482, 483A–483B, 483–486

487A–487B, 487–490

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Grade 5



Correlations


Graph points on the coordinate plane to solve real-world and mathematical problems.

CC.5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

373A–373B, 373–376

CC.5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

377A–377B, 377–380, 381A–381B, 381–384See Also: 395A–395B, 395–398

Classify two-dimensional figures into categories based on their properties.

CC.5.G.3 Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category.

441A–441B, 441–444, 445A–445B, 445–448, 453A–453B, 453–456

CC.5.G.4 Classify two-dimensional figures in a hierarchy based on properties.

445A–445B, 445–448, 449A–449B, 449–452See Also: 457A–457B, 457–460


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Grade 6




CC.K-12.MP.1 Make sense of problems and persevere in solving them.

In most Student Edition lessons. Some examples are: 8, 21, 74, 97, 107, 112, 196, 212, 222, 229, 255, 273, 296, 297, 334, 357, 378, 379, 420, 430, 454, 476, 496, 502

In most Teacher Edition lessons. Some examples are: 9, 34, 50, 74, 97, 109, 149, 223, 227, 257, 273, 295, 296, 349A, 371, 418, 425, 453, 477, 483

CC.K-12.MP.2 Reason abstractly and quantitatively. In most Student Edition lessons. Some examples are: 20, 28, 78, 85, 110, 158, 175, 176, 249, 251, 256, 286, 305, 316, 331, 358, 397, 408, 420, 424, 436, 458, 478, 506

In most Teacher Edition lessons. Some examples are: 6, 57, 73, 104, 119A, 164, 172, 233A, 254, 261, 264, 315, 323, 361, 371, 381, 444, 473, 495, 506

CC.K-12.MP.3 Construct viable arguments and critique the reasoning of others.

In most Student Edition lessons. Some examples are: 12, 32, 74, 108, 112, 194, 222, 224, 262, 280, 282, 300, 341, 358, 372, 374, 389, 418, 452, 479, 480, 503

In most Teacher Edition lessons. Some examples are: 13, 49, 51, 99, 103, 125, 171, 188, 222, 281, 285, 293, 302, 331, 375A, 385, 404, 434, 466, 521

CC.K-12.MP.4 Model with mathematics. In most Student Edition lessons. Some examples are: 13, 68, 70, 82, 99, 147, 176, 190, 225, 257, 264, 282, 300, 309, 332, 334, 376, 378, 417, 418, 452, 455, 493, 502

In most Teacher Edition lessons. Some examples are: 11, 77, 86, 100, 111, 163A, 163, 193, 205, 209A, 223, 237, 276, 387, 435, 475, 497

CC.K-12.MP.5 Use appropriate tools strategically. In most Student Edition lessons. Some examples are: 67, 79, 147, 187, 301, 309, 375, 383, 433, 469, 499

In most Teacher Edition lessons. Some examples are: 39A, 67, 69, 97, 115, 223, 254, 297, 301, 387, 433, 437, 469, 499, 503

CC.K-12.MP.6 Attend to precision. In most Student Edition lessons. Some examples are: 10, 35, 74, 109, 134, 178, 192, 250, 268, 286, 303, 316, 330, 334, 372, 406, 420, 458, 476, 496

In most Teacher Edition lessons. Some examples are: 6, 11, 37, 131, 149, 151, 163, 188, 203, 239, 249, 328A, 356, 359, 420, 428, 460, 463A, 493, 496

CC.K-12.MP.7 Look for and make use of structure. In most Student Edition lessons. Some examples are: 9, 14, 187, 279, 283, 349, 359, 375, 383, 491

In most Teacher Edition lessons. Some examples are: 9, 17, 19, 49, 51, 97, 177, 189, 192, 236, 237, 258, 261A, 347, 372, 378, 417, 419, 420, 458

CC.K-12.MP.8 Look for and express regularity in repeated reasoning.

In most Student Edition lessons. Some examples are: 9, 14, 75, 80, 152, 194, 220, 256, 267, 273, 312, 328, 333, 358, 372, 390, 424, 438, 451, 464, 500, 506

In most Teacher Edition lessons. Some examples are: 49A, 75, 152, 155, 177, 179, 180, 229, 250, 253, 306, 344, 348, 349, 376, 383, 403, 420, 479, 494

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Grade 6

Correlations


Domain: Ratios and Proportional Relationships Student Edition and Teacher Edition Pages

Understand ratio concepts and use ratio reasoning to solve problems.

CC.6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”


CC.6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b fi 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

151A–151B, 151–154, 169A–169B, 169–172, 173A–173B, 173–176, 177A–177B, 177–180; also 237–240

CC.6.RP.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.

b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

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.

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

155A–155B, 155–158, 159A–159B, 159–162, 163A–163B, 163–166, 173A–173B, 173–176, 177A–177B, 177–180, 187A–187B, 187–190, 191A–191B, 191–194, 195A–195B, 195–198, 201A–201B, 201–204, 205A–205B, 205–208, 209A–209B, 209–212, 219A–219B, 219–222, 223A–223B, 223–226, 227A–227B, 227–230, 233A–233B, 233–236, 237A–237B, 237–240

Domain: The Number System Student Edition and Teacher Edition Pages

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

CC.6.NS.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. For example, create a story context for (2/3) 4 (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) 4 (3/4) 5 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) 4 (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lbof chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

67A–67B, 67–70, 71A–71B, 71–74, 75A–75B, 75–78, 79A–79B, 79–82, 83A–83B, 83–86, 87A–87B, 87–90

Pages only in Teacher Edition are italics Domain continued on next page c

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Grade 6


Domain: The Number System (continued) Student Edition and Teacher Edition Pages

Compute fluently with multi-digit numbers and find common factors and multiples.

CC.6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. 5A–5B, 5–8, 35A–35B, 35–38, 39A–39B, 39–42; also 50–52, 83A, 169A

CC.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

27A–27B, 27–30, 31A–31B, 31–34, 35A–35B, 35–38, 39A–39B, 39–42, 61A, 159A, 169A; also 307–308, 394, 396, 475

CC.6.NS.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. For example, express 36 1 8 as 4 (9 1 2).

9A–9B, 9–12, 13A–13B, 13–16, 17A–17B, 17–20, 21A–21B, 21–24, 57A–57B, 57–60

Apply and extend previous understandings of numbers to the system of rational numbers.

CC.6.NS.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.

97A–97B, 97–100

CC.6.NS.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., 2(–3) 5 3, and that 0 is its own opposite.

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.

49A–49B, 49–52, 53A–53B, 53–56, 61A–61B, 61–64, 97A–97B, 97–100, 105A–105B, 105–108, 123A–123B, 123–126, 127A–127B, 127–130

CC.6.NS.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. For example, interpret –3 . –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C . –7°C to express the fact that –3°C is warmer than –7°C.

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. For example, for an account balance of –30 dollars, write | –30| 5 30 to describe the size of the debt in dollars.

101A–101B, 101–104, 109A–109B, 109–112, 115A–115B, 115–118, 119A–119B, 119–122

Domain continued on next page c

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Domain: The Number System (continued) Student Edition and Teacher Edition Pages

CC.6.NS.7(continued)

d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.

101A–101B, 101–104, 109A–109B, 109–112, 115A–1157B, 115–118, 119A–119B, 119–122

CC.6.NS.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.

131A–131B, 131–134, 135A–135B, 135–138; also 405–407


Domain: Expressions and Equations Student Edition and Teacher Edition Pages

Apply and extend previous understandings of arithmetic to algebraic expressions.

CC.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

249A–249B, 249–252, 253A–253B, 253–256

CC.6.EE.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. For example, express the calculation “Subtract y from 5” as 5 2 y.

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. For example, describe the expression 2 (8 1 7) as a product of two factors; view (8 1 7) as both a single entity and a sum of two terms.

c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world 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). For example, use the formulas V 5 s³ and A 5 6s² to find the volume and surface area of a cube with sides of length s 5 1/2.

257A–257B, 257–260, 261A–261B, 261–264, 265A–265B, 265–268, 371A–371B, 371–374, 379A–379B, 379–382, 387A–387B, 387–390, 393A–393B, 393–396, 397A–397B, 397–400, 423A–423B, 423–426, 437A–437B, 437–440

CC.6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 1 x) to produce the equivalent expression 6 1 3x; apply the distributive property to the expression 24x 1 18y to produce the equivalent expression 6 (4x 1 3y ); apply properties of operations to y 1 y 1 y to produce the equivalent expression 3y.

275A–275B, 275–278, 279A–279B, 279–282

CC.6.EE.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). For example, the expressions y 1 y 1 y and 3y are equivalent because they name the same number regardless of which number y stands for.

283A–283B, 283–286


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Solve real-world and mathematical problems involving area, surface area, and volume.

CC.6.G.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.

371A–371B, 371–374, 375A–375B, 375–378, 379A–379B, 379–382, 383A–383B, 383–386, 387A–387B, 387–390, 393A–393B, 393–396, 397A–397B, 397–400, 401A–401B, 401–404, 441A–441B, 441–444

CC.6.G.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 5 lwh and V 5 bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

423A–423B, 423–426, 427A–427B, 427–430, 433A–433B, 433–436, 437A–437B, 437–440, 441A–441B, 441–444

Domain: Expressions and Equations (continued) Student Edition and Teacher Edition Pages

Reason about and solve one-variable equations and inequalities.

CC.6.EE.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 specified set makes an equation or inequality true.

293A–293B, 293–296, 323A–323B, 323–326

CC.6.EE.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.

271A–271B, 271–274

CC.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x 1 p 5 q and px 5 q for cases in which p, q and x are all nonnegative rational numbers.

297A–297B, 297–300, 301A–301B, 301–304, 305A–305B, 305–308, 309A–309B, 309–312, 313A–313B, 313–316, 317A–317B, 317–320, 371A–371B, 371–374

CC.6.EE.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.

327A–327B, 327–330, 331A–331B, 331–334

Represent and analyze quantitative relationships between dependent and independent variables.

CC.6.EE.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 graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d 5 65t to represent the relationship between distance and time.

341A–341B, 341–344, 345A–345B, 345–348, 349A–349B, 349–352, 355A–355B, 355–358, 359A–359B, 359–362


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Domain: Statistics and Probability Student Edition and Teacher Edition Pages

Develop understanding of statistical variability.

CC.6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.

451A–451B, 451–454, 456, 517A–517B, 517–520

CC.6.SP.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.

455A–455B, 455–458, 473A–473B, 473–476, 491A–491B, 491–494, 503A–503B, 503–506, 513A–513B, 513–516, 517A–517B, 517–520, 521A–521B, 521–524

CC.6.SP.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.

473A–473B, 473–476, 503A–503B, 503–506, 513A–513B, 513–516

Summarize and describe distributions.

CC.6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

459A–459B, 459–462, 463A–463B, 463–466, 481A–481B, 481–484, 495A–495B, 495–498

CC.6.SP.5 Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations.

b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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.

469A–469B, 469–472, 473A–473B, 473–476, 477A–477B, 477–480, 491A–491B, 491–494, 499A–499B, 499–502, 503A–503B, 503–506, 509A–509B, 509–512


Domain: Geometry (continued) Student Edition and Teacher Edition Pages

CC.6.G.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.

405A–405B, 405–408

CC.6.G.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.

415A–415B, 415–418, 419A–419B, 419–422, 423A–423B, 423–426, 427A–427B, 427–430, 441A–441B, 441–444

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