A Correlation of

to the

Common Core State Standards for Mathematics Grade 3

A Correlation of enVisionmath2.0, ©2016 to the Common Core State Standards for Mathematics Introduction enVisionmath2.0 is a comprehensive K-6 mathematics curriculum that provides the focus, coherence, and rigor required by the CCSSM. enVisionmath2.0 offers a balanced instructional model with an emphasis on conceptual understanding, fluency, and application through rigorous problem solving. PearsonRealize online learning management system offers the flexibility and data teachers need to customize content and monitor student progress so that all students demonstrate proficiency in the CCSSM. The new enVisionmath2.0 is organized to promote Focus, Coherence, and Rigor. • Focus on Common Core Clusters • Develop Coherence across and within grades • Conceptual Understanding lays the foundation for Rigor Problem-based learning and visual learning personalize learning of rigorous mathematics! The new enVisionmath2.0 program engages learners with: 

Interactive learning aids and video tutorials

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Personalized practice and immediate feedback

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Built-in RtI activities in multiple modalities

The new enVisionmath2.0 program lets you customize content, auto-assign differentiation, and use assessment data quickly and easily to adjust instruction for your learners. 

Upload district content and other favorite resources

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Customize topics and lessons

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Assess in the format of the new high-stakes assessments

enVisionmath2.0 is the next evolution of a proven program that supports the latest interpretation of the CCSSM and the Next Generation assessment objectives.

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A Correlation of enVisionmath2.0, ©2016 to the Common Core State Standards for Mathematics Common Core State Standards for Mathematics Grade 3

Operations and Algebraic Thinking

enVisionmath2.0, ©2016 Grade 3

3.OA

Represent and solve problems involving multiplication and division. 3.0A.A.1 Interpret products of whole numbers, SE: Topic 1: 7–12, 13–18, 19–24, 43–48, 51– e.g., interpret 5 × 7 as the total number of 52; Topic 2: 61–66, 67–72, 73–78, 79–84, objects in 5 groups of 7 objects each. For 85–90, 99–100 example, describe a context in which a total number of objects can be expressed as 5 × 7. TE: Topic 1: 7A–12, 13A–18, 19A–24, 43A– 48, 51–52; Topic 2: 61A–66, 67A–72, 73A– 78, 79A–84, 85A–90, 99–100 3.0A.A.2 Interpret whole-number quotients of SE: Topic 1: 31–36, 37–42, 43–48, 52 whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or TE: Topic 1: 31A–36, 37A–42, 43A–48, 52 as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.0A.A.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.1

SE: Topic 1: 7–12, 13–18, 19–24, 25–30, 31– 36, 37–42, 43–48, 51–52; Topic 2: 61–66; 67–72, 73–78, 79–84, 85–90, 91–96, 99–100, Topic 3: 115–120, 121–126, 127–132, 133– 138, 139–144, 145–150, 159–160; Topic 4: 169–174, 175–180, 181–186, 187–192, 193– 198, 199–204, 205–210, 211–216, 217–222, 225–228; Topic 5: 255–260, 261–266, 267– 272, 273–278, 288–290; Topic 7: 359–364, 365–370, 371–376, 377–382, 383–388, 391– 394 TE: Topic 1: 7A–12, 13A–18, 19A–24, 25A– 30, 31A–36, 37A–42, 43A–48, 51–52; Topic 2: 61A–66, 67A–72, 73A–78, 79A–84, 85A–90, 91A–96, 99–100; Topic 3: 115A–120, 121A– 126, 127A–132, 133A–138, 139A–144, 145A– 150, 159–160; Topic 4: 169A–174, 175A–180, 181A–186, 187A–192, 193A–198, 199A–204, 205A–210, 211A–216, 217A–222, 225–228; Topic 5: 255A–260, 261A–266, 267A–272, 273A–278, 288–290; Topic 7: 359A–364, 365A–370, 371A–376, 377A–382, 383A–388, 91–394

2 SE = Student Edition

TE = Teacher’s Edition

A Correlation of enVisionmath2.0, ©2016 to the Common Core State Standards for Mathematics Common Core State Standards for Mathematics Grade 3 3.0A.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.

enVisionmath2.0, ©2016 Grade 3 SE: Topic 4: 205–210, 211–216, 227–228 TE: Topic 4: 205A–210, 211A–216, 227–228

Understand properties of multiplication and the relationship between multiplication and division. 3.0A.B.5 Apply properties of operations as SE: Topic 1: 25–30, 52, 73–78, 99; Topic 3: strategies to multiply and divide.2 Examples: If 109–114, 115–120, 121–126, 127–132, 133– 6 × 4 = 24 is known, then 4 × 6 = 24 is also 138, 139–144, 145–150, 151–156, 159–160; known. (Commutative property of Topic 4: 199–204, 227 multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, TE: Topic 1: 25A–30, 52, 73A–78, 99; then 3 × 10 = 30. (Associative property of Topic 3: 109A–114, 115A–120, 121A–126, multiplication.) Knowing that 8 × 5 = 40 and 8 127A–132, 133A–138, 139A–144, 145A–150, × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = 151A–156, 159–160; Topic 4: 199A–204, 227 (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) 3.0A.B.6 Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Multiply and divide within 100. 3.0A.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

SE: Topic 4: 169–174, 175–180, 181–186, 187–192, 199–204, 205–210, 225–227 TE: Topic 4: 169A–174, 175A–180, 181A– 186, 187A–192, 199A–204, 205A–210, 225– 227

SE: Topic 5: 237–242, 243–248, 249–254, 255–260, 261–266, 267–272, 273–278, 279– 284, 287–290 TE: Topic 5: 237A–242, 243A–248, 249A– 254, 255A–260, 261A–266, 267A–272, 273A– 278, 279A–284, 287–290

Solve problems involving the four operations, and identify and explain patterns in arithmetic. 3.0A.D.8 Solve two-step word problems using SE: Topic 4: 217–222, 228; Topic 7: 377– the four operations. Represent these problems 382, 393; Topic 11: 573–578, 579–584, 585– using equations with a letter standing for the 590, 591–596, 599–600 unknown quantity. Assess the reasonableness of answers using mental computation and TE: Topic 4: 217A–222, 228; Topic 7: 377A– estimation strategies including rounding. 382, 393; Topic 11: 573A–578, 579A–584, 585A–590, 591A–596, 599–600

3 SE = Student Edition

TE = Teacher’s Edition

A Correlation of enVisionmath2.0, ©2016 to the Common Core State Standards for Mathematics Common Core State Standards for Mathematics Grade 3 3.0A.D.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Number and Operations in Base Ten

enVisionmath2.0, ©2016 Grade 3 SE: Topic 2: 61–66, 67–72, 73–78, 79–84, 85–90, 99–100; Topic 3: 115–120, 121–126, 127–132, 133–138, 159–160; Topic 4: 193– 198, 227; Topic 5: 237–242, 287; Topic 8: 411–416, 461 TE: Topic 2: 61A–66, 67A–72, 73A–78, 79A– 84, 85A–90, 99–100; Topic 3: 115A–120, 121A–126, 127A–132, 133A–138, 159–160; Topic 4: 193A–198, 227; Topic 5: 237A–242, 287; Topic 8: 411A–416, 461

3.NBT

Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.A.1 Use place value understanding to SE: Topic 8: 417–422, 462 round whole numbers to the nearest 10 or 100. TE: Topic 8: 417A–422, 462 3.NBT.A.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

SE: Topic 8: 405–410, 423–428, 429–434, 435–440, 441–446, 447–452, 453–458, 461– 464; Topic 9: 475–480, 481–486, 487–492, 493–498, 499–504, 505–510, 511–516, 517– 522, 525–528 TE: Topic 8: 405A–410, 423A–428, 429A– 434, 435A–440, 441A–446, 447A–452, 453A– 458, 461–464; Topic 9: 475A–480, 481A–486, 487A–492, 493A–498, 499A–504, 505A–510, 511A–516, 517A–522, 525–528

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

Number and Operations—Fractions

SE: Topic 10: 539–544, 545–550, 551–556, 557–562, 565–566 TE: Topic 10: 539A–544, 545A–550, 551A– 556, 557A–562, 565–566

3.NF

Develop understanding of fractions as numbers. 3.NF.A.1 Understand a fraction 1/b as the SE: Topic 12: 609–614, 615–620, 621–626, quantity formed by 1 part when a whole is 651–656, 659–662 partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts TE: Topic 12: 609A–614, 615A–620, 621A– of size 1/b. 626, 651A–656, 659–662

4 SE = Student Edition

TE = Teacher’s Edition

A Correlation of enVisionmath2.0, ©2016 to the Common Core State Standards for Mathematics Common Core State Standards for Mathematics Grade 3 3.NF.A.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

enVisionmath2.0, ©2016 Grade 3 SE: Topic 12: 627-632, 633-638 TE: Topic 12: 627A-632, 633A-638

3.NF.A.2.A Represent a fraction 1/b on a SE: Topic 12: 627–632, 633–638, 660–661 number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into TE: Topic 12: 627A–632, 633A–638, 660–661 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. 3.NF.A.2.B Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

SE: Topic 12: 627–632, 633–638, 660–661

3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

SE: Topic 12: 621-626, Topic 13: 673-678, 679-684, 685-690, 691-696, 697-702, 703708

TE: Topic 12: 627A–632, 633A–638, 660–661

TE: Topic 12: 621A-626, Topic 13: 673A678, 679A-684, 685A-690, 691A-696, 697A702, 703A-708 3.NF.A.3.A Understand two fractions as SE: Topic 13: 673–678, 679–684, 709–714, equivalent (equal) if they are the same size, or 723–726 the same point on a number line. TE: Topic 13: 673A–678, 679A–684, 709A– 714, 723–726 3.NF.A.3.B Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

SE: Topic 13: 673–678, 679–684, 715–720, 723–726

3.NF.A.3.C Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

SE: Topic 12: 621-626, 660; Topic 13: 709– 714, 726

TE: Topic 13: 673A–678, 679A–684, 715A– 720, 723–726

TE: Topic 12: 621A-626, 660; Topic 13: 709A–714, 726

5 SE = Student Edition

TE = Teacher’s Edition

A Correlation of enVisionmath2.0, ©2016 to the Common Core State Standards for Mathematics Common Core State Standards for Mathematics Grade 3 3.NF.A.3.D Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or