Correlation to the Common Core State Standards. Math in Focus

Transcription

1 Correlation to the Common Core State Standards Math in Focus

2 Correlation to the Common Core State Standards Table of Contents Explanation of Correlation Grade Grade Grade Grade Grade

3 Explanation of Correlation The following document is a correlation of Great Source Education, Math in Focus to the Common Core State Standards for Mathematics. The format of this correlation follows the same basic format established by the State Standards for Mathematics, modified to accommodate the addition of page references. The correlation provides a cross-reference between the skills in the State Standards for Mathematics and representative page numbers where those skills are taught or assessed. The references contained in this correlation reflect Great Source Education s interpretation of the Mathematics objectives outlined in the Common Core State Standards for Mathematics. Key to References SE Student s Edition TE-A Teacher s Edition A TE-B Teacher s Edition B Math in Focus is published by Marshall Cavendish International (Singapore) and exclusively distributed by Houghton Mifflin Harcourt. Common Core State Standards for Mathematics Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Correlation prepared August

4 Correlation of Math in Focus to the Common Core State Standards Attached are grade-level correlations showing how closely Math In Focus covers the skills and concepts outlined in the Common Core State Standards. It is also important to recognize the parallel assumptions behind the Common Core State Standards and Math In Focus. The Common Core State Standards for Mathematics is an initiative towards more focused grade-level standards. The research base used to guide the Common Core State Standards noted conclusions from TIMSS, where Singapore has been a top scoring nation for 15 years. Apparent in the TIMSS and other studies of high-performing countries is a more coherent and focused curriculum. The Singapore math framework was one of the 15 national curriculums examined by the committee and had a particularly important impact on the Common Core writers and contributors. What follows is a guide that identifies the parallel assumptions behind Math in Focus the U.S. Edition of Singapore s most widely used program and the Common Core State Standards. Curriculum must be focused and coherent Common Core State Standards: For over a decade, research studies of mathematics education in high performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. (Common Core State Standards for Mathematics, 3) Math in Focus is organized to teach fewer topics in each grade, but to teach them thoroughly. When a concept appears in a subsequent grade level, it is always at a higher level. For instance, Math in Focus teaches fractions in a way that builds from grade to grade, where mastery of grade-appropriate concepts eliminates the need for repetition year after year. Fractions are not taught in first grade, to allow students the time they need to master the whole number concepts that form the basis of fractions. Fractions are introduced in second grade, which covers what a fraction is. In third grade, students cover equivalent fractions and fractions of a set. Fourth grade deals with mixed fractions and addition of simple fractions. Finally, fifth grade moves on to addition, subtraction, and multiplication of fractions, as well as division of fractions by whole numbers. Each grade level addresses an increasingly complex facet of fractions, and draws on the mastery of concepts that has been developed in previous years. This is the coherence and focus that the Common Core State Standards call for. 2

5 Teach to mastery Common Core State Standards: In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes. (Common Core State Standards for Mathematics, 17) In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication and division and strategies for multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions; (3) developing understanding of the structure of rectangular arrays and of area; and (4) describing and analyzing two dimensional shapes. (Common Core State Standards for Mathematics, 21) Math in Focus is structured for mastery learning. Rather than repeating topics, students master them in a grade level, and subsequent grades develop them to more advanced levels. Moving from addition and subtraction in second grade to multiplication and division in third grade is such an example. Students continue to practice all the operations with whole numbers in every grade in the context of problem solving and deep applications. The Skills Trace, appearing before each chapter, shows how concepts build and connect as students move through the grade levels. 3

6 Focus on number, geometry, and measurement in elementary grades Common Core State Standards: Mathematics experiences in early childhood settings should concentrate on (1) number (which includes whole number, operations, and relations) and (2) geometry, spatial relations, and measurement, with more mathematics learning time devoted to number than to other topics. (Common Core State Standards for Mathematics, 3) Math in Focus emphasizes number and operations in every grade, K-5, just as recommended in the Common Core State Standards. The textbook is divided into two books, roughly a semester each. Approximately 75% of Book A is devoted to number and operations and 60-70% of Book B to geometry and measurement where the number concepts are practiced, connected, and applied. The key number topics are in the beginning of the school year so students have a whole year to master them. 4

7 Organize content by big ideas, such as place value Common Core State Standards: These Standards endeavor to follow such a design, not only by stressing conceptual understanding of key ideas, but also by continually returning to organizing principles such as place value or the properties of operations to structure those ideas. (Common Core State Standards for Mathematics, 4) Math in Focus is organized around place value and the properties of operations. The first chapter of each grade level from second to fifth begins with place value. In first grade, students learn the teen numbers and math facts through place value. In all the grades, operations are taught with place value materials so students understand how the standard algorithms work. Even the mental math that is taught uses understanding of place value to model how mental arithmetic can be understood and done. This example, from Grade 1, shows how visual place value charts are used to reinforce concepts early on to ensure that students understand both the how and the why. These visual representations are carried throughout the program to reinforce the underlying principle of place value. Here, a more complex place value chart is used as fifth grade students learn to divide by tens. 5

8 Curriculum must include both conceptual understanding and procedural fluency Common Core State Standards: The Standards for Mathematical Content are a balanced combination of procedure and understanding. (Common Core State Standards for Mathematics, 8) Math in Focus is built around the Singapore Ministry of Education s famous pentagon that emphasizes conceptual understanding, skill development, strategies for solving problems, attitudes towards math, and metacognition that enables students to become excellent problem solvers. The highly visual nature of the text and the consistent concrete to visual to abstract approach enables all students to both understand how procedures work and to fluently apply them to solve problems. Singapore s Mathematics Framework Appreciation Interest Confidence Perseverance Estimation and Approximation Mental calculation Communication Use of mathematical Tools Algebraic manipulation data analysis Skills Attitudes Concepts Metacognition Mathematical Problem Solving Processes Monitoring one s own thinking Thinking skills Heuristics Strategies Math in Focus follows the Singapore Mathematics Framework pentagon. Students are encouraged to consider how they think, how they communicate, and how they solve problems so they can apply their skills to subsequent problems. Numerical Geometrical Algebraic Statistical 6

9 Mathematics is about reasoning Common Core State Standards: One hallmark of mathematical understanding is the ability to justify in a way appropriate to the student s mathematical maturity. (Common Core State Standards for Mathematics, 4) Math in Focus is famous for its model drawing that enables students to solve problems, as well as justify their solutions. In addition to journal questions and other explicit opportunities to explain their thinking, students are systematically taught to use visual diagrams to represent mathematical relationships in such a way as to not only accurately solve problems, but also to explain their thinking. Put On Your Thinking Cap requires students to put their problem solving skills to use and work through challenging concepts. Students can use the model drawing strategies they have learned to both solve the problems and justify their answers. Works Cited: Common Core State Standards for Mathematics: corestandards.org National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 7

10 Correlation to the Common Core State Standards Grade 1 8

11 Great Source Education Math in Focus, Grade Grade 1 Standards for Mathematical Practice Make sense of problems and persevere in solving them. 1 2 SE/TE-A: 7, 26, 37, 57-58, 61, 90-91, 127, 135, , 189, , 247 Workbook A: 19A, 26A, 37A, 61A, 91A, 135A, 135B, 159A, 189A, 215A, 247A SE/TE-B: 23, 39-40, 41-42, 49, 76-77, 100, , 129, 148, 170, 201, 237, 239, , 255, Workbook B: 48A, 77A, 129, 148A, 170A, 237A, 255A, 291A, 291B Reason abstractly and quantitatively. SE/TE-A: 22-23, 25, 27, 36, 37, 46, 48-52, 55, 57-58, 59-61, 63, 90-91, 135, , , 188, 189, , , , 247 Workbook A: 19A, 25A, 26A, 37A, 38C, 52A, 56A, 61A, 91A, 135A, 135B, 188A, 189A, 191A, 215A, 230A, 247A SE/TE-B: 9-12, 23, 26, 39-40, 41-42, 49, 54, 70-71, 73-74, 76-77, 79, , 120, 127, 129, 148, 170, 178, 183, 191, 200, 201, 203, 237, 239, , 255, Workbook B: 12A, 12B, 26A, 77A, 135A, 201A, 237A, 255A 9

12 Great Source Education Math in Focus, Grade Grade 1 Standards for Mathematical Practice Construct viable arguments and critique SE/TE-A: 10, 35, 36, 90, 108, 109, 119, 156, 182, 214, the reasoning of others. SE/TE-B: 121, 122, 140, 146, 200, 245, 253, 288 Model with mathematics. SE/TE-A: 43-45, 57-63, 68, 70, 73, 77-81, 82-84, 85-87, 89-90, 93, 103, 112, , 126, , 137, , , , 217 Workbook A: 63A, 73A, 76A, 81A, 93A, 93C 4 SE/TE-B: 84, 86-93, 94-98, 100, , , 115, 117, 119, , 205, , , 219, , Workbook B: 93A 5 6 Use appropriate tools strategically. SE/TE-A: 4-6, 10, 16-17, 20-21, 22-26, 30, 32-33, 35, 38, 44, 51, 103, 118, 120, 130, 160, 169, , , , 232, , 238, , Workbook A: 38B, 38C, 47A, 93C, 174A SE/TE-B: 8, 11, 15, 19, 20, 58-61, 63-65, 69, 76-77, 94-95, , , 126, 137, 139, 145, 173, 179, , 189, 191, 200, 201, 202, 244, , , 248, 281 Workbook B: 12B, 62A, 79A, 186A, 201A Attend to precision. SE/TE-A: 11, 46, 71, 90, 108, 109, 119, 149, 156, 169, 182, 207, 214, 224 SE/TE-B: 94, 111, 121, 122, 140, 145, 146, 194, 200, 234, 235, 245, 253, 281,

13 Great Source Education Math in Focus, Grade Grade Look for and make use of structure. SE/TE-A: , 191 Workbook A: 159A, 188A, 191A SE/TE-B: 21, 23, 66, 70, 79, , 187, , 199, 203 Workbook B: 22A, 23A, 26A, 73A, 77A, 79A, 131B, 131C, 170A, 199A, 239D, 293F Look for and express regularity in repeated reasoning. SE/TE-A: 23-25, 27, 31-33, 35, 37, 38, 42-47, 48-52, 53-56, 57-61, 63, 67-73, 74-76, 77-81, 82-91, 92-93, , , , , , , , Workbook A: 25A, 27A, 33A, 33B, 37A, 38A, 38C, 47A, 52A, 56A, 61A, 63A, 73A, 76A, 81A, 91, 93A, 93C, 170A, 170B, 188A, 189A, 197A, 199A, 202A, 208A, 208B, 215A, 217A, 249C, 249D, 249E, 249F, 249G, , , 293 SE/TE-B: 84-93, , , , , , , , , 149, , , , , 237, , , 256 Workbook B: 93A, 100A, 110A, 118A, 122A, 129A, 129B, 131A, 131C, 131D, 140A, 148A, 149A, 171C, 171D, 215A, 221A, 221B, 229A, 236A, 236B, 237A, 239A, 239D, 246A, 246B, 257A, 289A, 289B, 289C, 291B, 293A, 293C, 293D, 293E 11

14 Great Source Education Math in Focus, Grade Grade 1 1.OA Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Use addition and subtraction within 20 SE/TE-A: 48-50, 52, 57-61, 62-63, 67, 70, 74-76, 82-85, 87-89, 93, 195, 198, to solve word problems involving situations of adding to, taking from, putting 203, 205, , 217 together, taking apart, and comparing, Workbook A: 61A, 63A, 93A, 93C, 215A, 217A, 249D, 249G 1 with unknowns in all positions, e.g., by using objects, drawings, and equations SE/TE-B: , with a symbol for the unknown number to represent the problem. Workbook B: 129A, 131D, 140A, 148A, 149A 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. SE/TE-A: 214 Workbook A: 215A SE/TE-B: , 129, 130 Workbook B: 122A, 129B, 131C, 148A Assessments: 36, 82, 109, 125, 167 Enrichment B: 33 Reteach B: Extra Practice B:

15 Great Source Education Math in Focus, Grade Grade 1 Understand and apply properties of operations and the relationship between addition and subtraction. Apply properties of operations as SE/TE-A: 36, 48-52, 63 strategies to add and subtract. Examples: Workbook A: 52A, 63A, 93C, 215A If = 11 is known, then = SE/TE-B: 120, 130, , 140, 146, is also known. (Commutative pro Workbook B: 140A, 148A 3 perty of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) 4 Understand subtraction as an unknown-addend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. SE/TE-A: 67-73, 74-76, 77-81, 82-91, 92-93, , , 217 Workbook A: 73A, 76A, 81A, 91A, 93A, 93C, 208A, 215A, 217A, 249E, 249F, 249G SE/TE-B: , , , 131, , , 239 Workbook B: 110A, 118A, 129A, 129B, 131A, 131C, 131D, 229A, 236A, 236B, 239A, 239D, 239E 13

16 Great Source Education Math in Focus, Grade Grade 1 Add and subtract within 20 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). 5 SE/TE-A: 43-47, 62, Workbook A: 47A, 63A, 73A, 93A SE/TE-B: 57, 61, 84, 176, 187, Workbook B: 62A, 93A, 201A, 215A, 239D 6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = =14); decomposing a number leading to a ten (e.g., 13 4 = =10 1 =9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). SE/TE-A: 42-47, 48-52, 53-56, 57-61, 62-63, 67-73, 74-76, 77-81, 82-91, 92-93, , , , , , Workbook A: 47A, 52A, 56A, 61A, 63A, 73A, 76A, 81A, 91A, 93A, 93C, 197A, 199A, 202A, 208A, 208B, 215A, 217A, 249C, 249D, 249E, 249F, 249G SE/TE-B: , , 130, , , , , 149 Workbook B: 122A, 129A, 129B, 131A, 131C, 140A, 148A, 149A 14

17 Great Source Education Math in Focus, Grade Grade 1 Work with addition and subtraction equations. 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 7 are false? 6 = 6, 7 = 8 1, = 2 + 5, = Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 =? 3, =? SE/TE-A: 42-47, 48-52, 53-56, 57-61, 62-63, 67-73, 74-76, 77-81, 82-91, 92-93, , , , , , 215A, , Workbook A: 47A, 52A, 56A, 61A, 63A, 73A, 76A, 81A, 91A, 93A, 197A, 199A, 202A, 208A, 208B, 215A, 217A, 249C, 249D, 249E, 249F, 249G SE/TE-B: 84-93, , , , , , , , , 149, , , , , 237, 237A, , , 290, 293 Workbook B: 93A, 100A, 110A, 118A, 122A, 129A, 129B, 131A, 131C, 131D, 140A, 148A, 149A, 215A, 221A, 221B, 229A, 236A, 236B, 239A, 239C, 239D, 289A, 289B, 289C, 291A, 291B, 293A, 293C, 293D, 293E, 293F SE/TE-A: 43, 58-59, 82-83, , 203, 205 SE/TE-B: 84-85, 87-92, 96, 98, , , , 119, 121, , , 140, , 149, , 214, 216, 219, , ,

18 Great Source Education Math in Focus, Grade Grade 1 1.NBT Number and Operations in Base-Ten Extend the counting sequence. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number 1 of objects with a written numeral. SE/TE-A: 4-12, 19, 22, 27, 72-73, 92, , , 184, 188, 190 Workbook A: 12A, 25A, 26A, 27A, 33A, 33B, 33C, 38A, 38B, 38C, 73A, 93A, 170A, 170B, 191A, 249E, 249F SE/TE-B: 57-62, 63-65, 66, 78, , , 188, 202 Workbook B: 62A, 79A, 110A, 183A, 186A, 186B, 201A, 203A, 229A, 239D, 293F Understand place value. Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as 2 special cases: a 10 can be thought of as a bundle of ten ones called a ten. SE/TE-A: , 170, , , Workbook A: 170A, 170B, 174A SE/TE-B: 58-61, 63-65, 67-69, 72, 78, 84, 86-92, 96-98, 101, , 113, 115, , 182, , , 198, 202, , 214, , 219, 222, , Workbook B: 62A, 73A, 79A, 93A, 131C, 183A, 186A, 186B, 239C, 293E, 293F 16

19 Great Source Education Math in Focus, Grade Grade 1 b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. SE/TE-A: , 170, , , , 189, Workbook A: 170A, 170B, 174A, 181, 181A, 182, 188A, 189A, 191A c 3 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). Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Workbook A: 174A SE/TE-B: 58, 59, 65, 87-88, 104, 105, , , 192, 202, 211, 224, 225 Workbook B: 62A SE/TE-A: , 188, 189, 191 Workbook A: 188A, 191A, 249F SE/TE-B: 69-70, 72-73, 74, 77A, 79, , , , 203 Workbook B: 73A, 73B, 77A, 79A, 199A, 201A, 203A, 293F 17

20 Great Source Education Math in Focus, Grade Grade 1 Use place value understanding and properties of operations to add and subtract. Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a SE/TE-A: 68, 72-73, 74-76, 78, 83-84, 89, 92, 195, , , , Workbook A: 52A, 73A, 76A, 81A, 93A, 199A, 202A, 208A, 208B, 215A, 217A, multiple of 10, using concrete models or 249C, 249D, 249E, 249F 4 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. SE/TE-B: 84-86, 93, 96-97, 100, , 110, , , , 126, 129, , , 140, , , 209, 210, 215, , 221, , 229, , 236, Workbook B: 93A, 100A, 110A, 118A, 129A, 129B, 131A, 131C, 131D, 140A, 149A, 171C, 215A, 221A, 221B, 229A, 236A, 236B, 239A, 239C, 239D 5 6 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Subtract multiples of 10 in the range from multiples of 10 in the range (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. SE/TE-B: 138, 140, 140A, 144, 147, 149, 149A, 171C Workbook B: 140A, 149A, 171C SE/TE-B: 104, 110, , 229 Workbook B: 110A, 229A, 236B, 239A 18

21 Great Source Education Math in Focus, Grade Grade 1 1.MD Measurement and Data Measure lengths indirectly and by iterating length units. 1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. SE/TE-A: , 247, 248 Workbook A: 230A, 247A, 249A, 249C, 249D 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 2 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. Tell and write time. Tell and write time in hours and halfhours using analog and digital 3 clocks. Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total 4 number of data points, how many in each category, and how many more or less are in one category than in another. SE/TE-A: , , , 246, 249 Workbook A: 239A, 249A, 249D, 249E SE/TE-B: , , 170, 171 Workbook B: 165A, 165B, 169A, 170A, 171A, 171C, 293F SE/TE-B: 31-35, 36-41, 42-48, 49, Workbook B: 35A, 41A, 41B, 48A, 49A, 51A, 131B, 293G 19

22 Great Source Education Math in Focus, Grade Grade 1 1.G Geometry Reason with shapes and their attributes. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes 1 (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 2 3 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. 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. SE/TE-A: , , 136 Workbook A: 105A, 120A, 135A, 137A, 249E SE/TE-A: , , , 137 Workbook A: 120A, 135A, 135B, 137A The skills and concepts presented on these pages prepare students to address the state standard in more depth at Grade 2. SE/TE-A: , Workbook A: 120A SE/TE-B: Workbook B: 250A 250B, 255A See Grade 2: SE/TE-A: 73, 75 82, 87, SE/TE-B: 73A, 82A, 82B 20

23 Correlation to the Common Core State Standards Grade 2 21

24 Great Source Education Math in Focus, Grade Grade 2 Standards for Mathematical Practice Make sense of problems and persevere in solving them. 1 This standard is covered throughout the program; the following are examples. SE/TE-A: 26-28, 29-30, 31, 32, 54, 59, 88-89, 121, 137, 147, 155, , 173, 186, 194, 204, 221, 230, 247, 259, 281 Workbook A: 31A, 32A, 33A, 54B, 121C, 123C, 123D, 147A, 167A, 178A, 186A, 186C, 195A, 221A, 223A, 259A, 281B SE/TE-B: 8, 10-15, 38-39, 70, 97, 127, 128, 157, , 190, 193, 217, , , 240, 243, 245, 265, 266, , 296, , , 303, 305 Workbook B: 15A, 19A, 26A, 70A, 97A, 127A, 190A, 217A, 231A, 237A, 237B, 247A, 302A 22

25 Great Source Education Math in Focus, Grade Grade 2 Reason abstractly and quantitatively. This standard is covered throughout the program; the following are examples. 2 3 Construct viable arguments and critique the reasoning of others. SE/TE-A: 26-28, 29-30, 31, 32, 35-37, 89, 147, 155, , , , , 181, 183, 186, 187, 188, , , , 249, , Workbook A: 31A, 32A, 33A, 54B, 123C, 123D, 147A, 161A, 172A, 174A, 178A, 183A, 186A, 188A, 188C, 188D, 259A, 272A, 283F SE/TE-B: , 155, 156, 157, , , , , , 267, , 296, , , 305 Workbook B: 156A, 231A, 302A SE/TE-A: 29, 30, 120, 131, 147, 172, 183 SE/TE-B: 16, 27, 33, 51, 53, 173,

26 Great Source Education Math in Focus, Grade Grade 2 Model with mathematics. This standard is covered throughout the program; the following are examples. 4 SE/TE-A: 6-12, 17-21, 23, 33, 38-40, 61-63, 67-68, 72-74, 78-80, 84-85, 96-97, 98-99, , , , , , , , , 129, 146, , 220A, , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123C, 123D, 133A, 141A, 146A, 220A, 223B, 258A, 261A, 261B, 281A, 283D, 283F, 283G SE/TE-B: 6-7, 17-18, 20-25, 66-68, 72, 79, 83-86, 88-89, 93, 96, 99, , , Workbook B: 19A 24

27 Great Source Education Math in Focus, Grade Grade 2 Use appropriate tools strategically. This standard is covered throughout the program; the following are examples. 5 6 Attend to precision. SE/TE-A: 6-10, 11-12, 17, 18-21, 23, 33, 38-40, 42, 44, 46-47, 49-50, 61-63, 67-68, 72-74, 76, 78-80, 84-85, 92, 96-99, 139, , 163, 168, 171, , , , , , , , , , 235, , 239, , , 244, 245, 248, , , , 277, 283 Workbook A: 10A, 17A, 33A, 161A, 172A, 188A, 188C, 188D, 195A, 210A, 215A, 223A, 234A, 239A, 244A, 252A, 258A, 259A, 261A, 277A, 281B, 283A, 283D, 283E, 283F SE/TE-B: 9, , , 126, , 164, , 174, , 183, , 193 Workbook B: 99C, 99D, 110A, 121A, 174A, 183A This standard is covered throughout the program; the following are examples. SE/TE-A: 29, 30, 100, 101, 105, 112, 120, 131, 139, 147, 172, 183, 194, 198, 205, 213, 230, 247, 249, 255, 267, 270 SE/TE-B: 16, 27, 33, 51, 53, 59, 77, 80, 87, 105, 109, 120, 135, 154, 168, 173, 180, 185, 187, 199, 203, 204, 235, 236, 254, 256, 262, 263, 273, 275, 278, 280, 290,

28 Great Source Education Math in Focus, Grade Grade 2 Look for and make use of structure. This standard is covered throughout the program; the following are examples. 7 8 Look for and express regularity in repeated reasoning. SE/TE-A: 24-26, 30, 33, 89, 237, 239, 245, 250, 260, Workbook A: 31A, 33A, 54B, 123C, 252A, 258A, 261A, 272A, 277A, 283E SE/TE-B: 84-86, 89, 99 Workbook B: 99A This standard is covered throughout the program; the following are examples. SE/TE-A: 26-30, 31, 32, 88-89, , , , Workbook A: 31A, 32A, 33A, 123C, 123D, 167A, 178A, 188A, 188C SE/TE-B: , , 178, 191, 193, , , , 305 Workbook B: 169A, 178A, 302A, 305A, 305C, 305E 26

29 Great Source Education Math in Focus, Grade Grade 2 2.OA Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 SE/TE-A: 96-99, , 106, , , to solve oneand two-step word problems Workbook A: 102A, 108A, 114A, 121A, 121B, 123A, 123C, 123D, 283D, 283F involving situations of adding to, taking SE/TE-B: 6-7, 17-19, 40, , 129 from, putting together, taking apart, and Workbook B: 19A, 126A, 129A, 305F 1 comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Add and subtract within Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. SE/TE-B: 8-15, 16, 20-26, 27, 40 Workbook B: 15A, 26A, 41A, 99C Work with equal groups of objects to gain foundations for multiplication. Determine whether a group of objects This standard is addressed in depth in Grade 3. (up to 20) has an odd or even number of members, e.g., by pairing objects See Grade 3: 3 or counting them by 2s; write an SE/TE-A: , 236 equation to express an even number as Workbook A: 226A, 263E a sum of two equal addends. 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. SE/TE-A: , 168, 171, , Workbook A: 161A, 172A, 178A, 188A, 188D SE/TE-B: , 179, , Workbook B: 174, 174A, 183, 183A, 193, 247C 27

30 Great Source Education Math in Focus, Grade Grade 2 2.NBT Number and Operations in Base-Ten Understand place value. Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 1 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a b can be thought of as a bundle of ten tens called a hundred. 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). Count within 1000; skip-count by 5s, 10s, and 100s. SE/TE-A: 6-10, 11-12, 17, 18-21, 23, 33, 38-40, 42, 44, 46, 47, 49-50, 61-63, 67-68, 72-74, 76, 78-80, Workbook A: 10A, 17A, 33A, 283E SE/TE-A: 9, 11-13, 16-17, 33 Workbook A: 17A, 17B, 33A SE/TE-A: 6-10, 26-30, 31, 33, , , , Workbook A: 10A, 31A, 32A, 33A, 123C, 167A, 178A, 188A, 188C, 283E 3 4 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. SE/TE-A: 6-10, 11-17, 33, 40-41, 43-45, 47-48, 49-53, 55, 61-65, 67-69, 71, 72-75, 77, 77A, 78-82, 84-88, Workbook A: 10A, 17A, 17B, 33A, 41A, 45A, 48A, 54A, 55A, 66A, 71A, 77A, 83A, 91A, 283E SE/TE-A: 18-21, 23, 33 Workbook A: 23A, 33A, 123C 28

31 Great Source Education Math in Focus, Grade Grade 2 Use place value understanding and properties of operations to add and subtract. Fluently add and subtract within 100 SE/TE-A: 41, 65, , 106, 106, 108, 110, , 115, 117, 122, 278- using strategies based on place value, 281, 283 properties of operations, and/or the Workbook A: 102A, 108A, 114A, 121C, 123A, 123D, 281A, 281B, 283A, 283E, 5 relationship between addition and 283G subtraction. SE/TE-B: 6-8, 13, 15, 16-19, 20, 26, 27, 34-35, 37, 39-40, , 129 Workbook B: 15A, 19A, 26A, 126A, 305D 6 Add up to four two-digit numbers using strategies based on place value and properties of operations. SE/TE-A: 38-41, 42-45, 46-48, 49-54, 55, 61-66, 67-71, 72-77, 78-83, 84-91, , , , , , , 283 Workbook A: 41A, 41B, 45A, 48A, 54A, 54B, 55A, 66A, 71A, 77A, 83A, 91A, 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123C, 123D, 281A, 281B, 283A, 283E, 283F, 283G SE/TE-B: 6-15, 16-19, 20-26, 27, 34-35, 37, 39-41, , 129 Workbook B: 15A, 19A, 26A, 41A, 126A, 129A, 305D, 305E 29

32 Great Source Education Math in Focus, Grade Grade 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. Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a given number SE/TE-A: 38-40, 42, 44, 46-47, 49-50, 52, 61-63, 67-68, 72-74, 76, 78-80, 84-85, 89, , , , , , , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123C, 123D, 281A, 281B, 283A, 283D, 283F SE/TE-B: 6-8, 10-14, 17-19, 20-25, , 129 Workbook B: 15A, 19A, 26A, 126A, 127A, 129A SE/TE-B: 8-15, 17, 23-26, 27, 40 Workbook B: 15A, 19A, 26A, 41A, 99C 9 Explain why addition and subtraction strategies work, using place value and the properties of operations. SE/TE-A: 38-41, 42-45, 46-48, 49-54, 55, 61-66, 67-71, 72-77, 78-83, 84-91, , , , , Workbook A: 41A, 41B, 45A, 48A, 54A, 54B, 55A, 66A, 71A, 77A, 83A, 91A, 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123C, 123D, 283E, 283F, 283G SE/TE-B: 6-15, 16-19, 20-26, 27, 34-35, 37, 39-41, , 129 Workbook B: 15A, 19A, 26A, 41A, 126A, 129A, 305D, 305E 30

33 Great Source Education Math in Focus, Grade Grade 2 2.MD Measurement and Data Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools 1 such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe 2 how the two measurements relate to the size of the unit chosen. 3 Estimate lengths using units of inches, feet, centimeters, and meters. SE/TE-A: , , 210, , Workbook A: 195A, 210A, 215A, 223A SE/TE-B: , 109, , , 128 Workbook B: 106A, 117A, 121A, 129A This standard is covered to mastery in Grade 1; opportunities to review can be found on pages: SE/TE-A: 243 Workbook A: 249D See Grade 1: SE/TE-A: 243, 247, 249 Workbook A: 246, 249A, 249D SE/TE-A: , 204 Workbook A: 195A, 223A SE/TE-B: 104, , 114 Workbook B: 106A, 129A 31

34 Great Source Education Math in Focus, Grade Grade 2 Measure to determine how much longer one object is than another, expressing 4 the length difference in terms of a standard length unit. Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by 5 using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 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 6 whole-number sums and differences within 100 on a number line diagram. SE/TE-A: , , 222 Workbook A: 215A, 221A, 223A, 283C SE/TE-B: , , 128 Workbook B: 110A, 121A, 127A, 129A, 158C, 305D SE/TE-A: 96-99, 100, , , , , , , 223, , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123D, 220A, 281A, 283A, 283D, 283F SE/TE-B: , 127, 129, 198, 200, , , Workbook B: 126A, 127A, 129A, 200A, 200B, 205, 205A, 216A, 216B, 219A, 305F SE/TE-A: 26, 27, 89, 96-99, 100, , , , , , , 223, , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123D, 220A, 281A, 283A, 283D, 283F SE/TE-B: 28-33, 36, , 127, 129, 198, 200, , , Workbook B: 36A, 126A, 127A, 129A, 200A, 200B, 205, 205A, 216A, 216B, 219A, 305F 32

35 Great Source Education Math in Focus, Grade Grade 2 Work with time and money. Tell and write time from analog and 7 digital clocks to the nearest five minutes, using a.m. and p.m. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. 8 Example: If you have 2 dimes and 3 pennies, how many cents do you have? Represent and interpret data. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated 9 measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. 10 Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. SE/TE-B: , , 142, 149, , Workbook B: 136A, 141A, 149A, 156A, 158A, 158C, 158D, 305D, 305E SE/TE-B: 49, 51, 62, 66-70, Workbook B: 70A, 72A, 99D, 99E, 305D, 305F This standard is also covered to mastery in Grade 1. See Grade 1: SE/TE-B: , , , 293 Workbook B: 289A, 289B, 289C, 291A, 291B, 293A, 293D, 293E This standard is addressed in depth in Grade 3. See Grade 3: SE/TE-B: , 106, Workbook B: 104A, 104B, 104C, 105A, 218D SE/TE-B: , , 237, , 243, Workbook B: 231A, 237A, 237B, 242B, 247A, 247C, 247D, 305F 33

36 Great Source Education Math in Focus, Grade Grade 2 2.G Geometry Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of 1 equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2 3 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 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. SE/TE-B: 262, 264, , 287, , 303, Workbook B: 264A, 286A, 286B, 286C, 305A, 305E Pentagons and quadrilaterals are fully covered in Grade 3. See Grade 3: SE/TE-B: , , 338, Workbook B: 318A, 318B SE/TE-B: 75, 78, 79, 82, 83-88, 91-94, 96, Workbook B: 82A, 82B, 89, 96A, 97, 99A, 99D, 305E SE/TE-B: 77-79, 81-82, 83-89, 90-94, 96, 98 Workbook B: 82A, 82B, 96A, 99A, 99D, 305E 34

37 Correlation to the Common Core State Standards Grade 3 35

38 Great Source Education Math in Focus, Grade Grade 3 Standards for Mathematical Practice Make sense of problems and persevere in solving them. 1 This standard is covered throughout the program; the following are examples. SE/TE-A: 5-11, 27-29, 31-32, 41-52, 58-62, 63, 65-69, 72-73, 79-80, 82-89, 91, , , , , 151, , , , , , 189, , 223, , , Workbook A: 11A, 29A, 52A, 63A, 73A, 78A, 89A, 150A, 226A, 253A SE/TE-B: 27, 56, 75, 84-90, 91-96, , 105, , 156, 211, , 337, 381 Workbook B: 27A, 56A, 75A, 90A, 90B, 96A, 96B, 104A, 104B, 104C, 105A, 156A, 211A, 218B, 218D, 259A, 293A, 337A, 381A, 387F 36

39 Great Source Education Math in Focus, Grade Grade 3 Reason abstractly and quantitatively. This standard is covered throughout the program; the following are examples. 2 3 Construct viable arguments and critique the reasoning of others. SE/TE-A: 32, 69, 89, 89A, 114, 127, 157, 181, 209, 210, 210A, 213, 218, 223, 235, 259 Workbook A: 114A, 126B, 126C, 127A, 131B, 150A, 157A, 162A, 167A, 175A, 177A, 193A, 198A, 198B, 209A, 209B, 209C, 210A, 213A, 226A, 230A, 234A, 245A, 249A, 249B, 253A, 258A, 258B SE/TE-B: 23, 41, 56, 75, 105, 156, 211, 241, 259, , 337, 381 Workbook B: 27A, 56A, 75A, 105A, 156A, 211A, 259A, 293A, 337A, 381A SE/TE-A: 30, 82, 125, 140 SE/TE-B: 94, 145, 146, 272, 305, 352, 369, 370,

40 Great Source Education Math in Focus, Grade Grade 3 Model with mathematics. This standard is covered throughout the program; the following are examples. SE/TE-A: 5-11, 12-14, 17, 20-23, 53-57, 63, 77, 79, 84-86, 94, , , , , , , 127, , , , , , , , 180, , , , 202, , , , , , , , , Workbook A: 11A, 19B, 63A, 126A, 126B, 126C, 131B, 150A, 175A, 213B, 226A, 245A, 249A, 249B, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TE-B: 4-5, 12, 15-16, 21, 24-26, 27, 42-45, 47, 48-53, 55, 56, 57, 63-68, 69-74, 75, 77, , , , , , , 156, , , , , 211, , , , , 254, 257, Workbook B: 23A, 26A, 26B, 27A, 47A, 55A, 56A, 68A, 74A, 75A, 78B, 78C, 120A, 125A, 129A, 145A, 150A, 150B, 155A, 156A, 185A, 185B, 2011A, 210A, 211A, 218B, 218C, 227A, 247A, 250A, 259A, 387E, 387G 38

41 Great Source Education Math in Focus, Grade Grade 3 Use appropriate tools strategically. This standard is covered throughout the program; the following are examples. SE/TE-A: 5-12, 14, 16-17, 20-23, 43-44, 47, 51, 57-58, 77, 79, 81, 84-86, 94, , , 106, , 140, 156, 166, 174, , 197, , , 207, 210, 215, 222, , Workbook A: 19B SE/TE-B: 13, 32-34, 42-47, 64, 81, 83, 85-96, 105, 107, 109, , , 146, 166, , 186, , , 194, , 207, , 270, 272, 274, 278, 281, 289, 293, 297, 300, 302, 312, 315, 325, 337, 344, 346, 355, , , Attend to precision. Workbook B: 96A, 96B, 105A, 201A, 218C, 318B, 337A, 352A, 361A, 374A, 374B, 381A, 387E This standard is covered throughout the program; the following are examples. 6 SE/TE-A: 26, 30, 57, 60, 63, 69, 82, 96, 125, 140, 179, 197 SE/TE-B: 13, 89, 94, 102, , 132, 140, , 178, 181, 190, 197, 208, 246, 271, 272, 276, 277, 283, 290, 305, , 312, , 325, 332, , 352, 359, 367, , 373, 374,

42 Great Source Education Math in Focus, Grade Grade 3 Look for and make use of structure. SE/TE-A: 25, 27-29, 31, 33, 35 7 SE/TE-B: 114, 116, 135, , 145, 147, 159, 161 Workbook B: 156A, 218B, 387D 8 Look for and express regularity in repeated reasoning. This standard is covered throughout the program; the following are examples. SE/TE-A: 41-44, 45-48, 49-52, 53-63, 69, 70, 72, 79-87, 88-89, 90-91, 94-97, , , , 114, , , 127, , , , , , , 177, , , 189, , , , , , , , , , , , 262 Workbook A: 44A, 48A, 52A, 63A, 73A, 73B, 87A, 89A, 97A, 101A, 106A, 113A, 114A, 126A, 126B, 126C, 127A, 131B, 150A, 157A, 162A, 167A, 175A, 177A, 193A, 198A, 209A, 209B, 209C, 213B, 213C, 230A, 234A, 245A, 249A, 249B, 263B, 263C, 263D, 263F SE/TE-B: 4-14, 15-23, 24-26, 27, 28-30, , 381, 387 Workbook B: 14A, 23A, 26A, 26B, 27A, 380A, 380B, 387D, 387E, 387G 40

43 Great Source Education Math in Focus, Grade Grade 3 3.OA Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Interpret products of whole numbers, SE/TE-A: 157, , 162, 167 e.g., interpret 5 7 as the total Workbook A: 175A, 213B, 263D 1 number of objects in 5 groups of 7 objects each. 2 3 Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. 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. This standard is covered to mastery in Grade 2; opportunities to review can be found on pages: SE/TE-A: 176, See Grade 2: SE/TE-A: , 185 Workbook A: 185A, 185B, 186A, 188A, 188C, 188D SE/TE-A: 152, , , 168, 172, 177, , 183, 186, 213, , , 230, , 239, , , , , Workbook A: 157A, 162A, 167A, 177A, 198A, 198B, 209B, 209C, 213C, 245A, 249A, 249B, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TE B: 66-68, 69-74, Workbook B: 68A, 74A, 78C, 387G 41

44 Great Source Education Math in Focus, Grade Grade 3 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. SE/TE-A: , , , , , , , 191, 194, 198, 201, , , , , , 235, , , , , , 258, 259, Workbook A: 150A, 157A, 162A, 167A, 175A, 177A, 193A, 213B, 226A, 230A, 234A, 245A, 249A, 249B, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TE B: 66-68, 69-74, Workbook B: 68A, 74A, 78C, 387G Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as SE/TE-A: , , , , , , , strategies to multiply and divide. 191, 194, 198, 201, , , , , , 235, , , , , , 258, 259, Workbook A: 150A, 157A, 162A, 167A, 175A, 177A, 193A, 213B, 226A, 230A, 234A, 245A, 249A, 249B, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TE-B: 66-68, 69-74, Workbook B: 68A, 74A, 78C, 387G 42

45 Great Source Education Math in Focus, Grade Grade 3 Understand division as an unknown-factor problem. SE/TE-A: , , 183, 186, , , 226A, , , 235, , , , 258, 259, Workbook A: 177A, 230A, 234A, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TE-B: 67-68, 72-73, Multiply and divide within 100. 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 7 operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Workbook B: 74A, 78C, 387G SE/TE-A: , , , , , , , 191, 194, 198, 201, , , , , , 235, , , , , , 258, 259, Workbook A: 150A, 157A, 162A, 167A, 175A, 177A, 193A, 213B, 226A, 230A, 234A, 245A, 249A, 249B, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TE-B: 66-68, 69-74, Workbook B: 68A, 74A, 78C, 387G 43

46 Great Source Education Math in Focus, Grade Grade 3 Solve problems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word problems using the four operations. Represent these problems using equations with a letter 8 standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. SE/TE-A: 60-63, , 127, , , , 258, 259, 261, 263 Workbook A: 63A, 73B, 126A, 126B, 126C, 127A, 131B, 249A, 249B, 258A, 258B, 263C, 263F, 263G SE/TE-A: 5-11, 27-29, , , 151, , , , , 189, , Workbook A: 11A, 29A, 73A, 150A, 226A 44

47 Great Source Education Math in Focus, Grade Grade 3 3.NBT Number and Operations in Base-Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. 1 Use place value understanding to round whole numbers to the nearest 10 or 100. SE/TE-A: 53-59, 61-63, 71, 73 Workbook A: 63A, 69, 69A, 73B 2 3 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. Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 80, 5 60) using strategies based on place value and properties of operations. Se/TE-A: 41-44, 45-48, 49-52, 58-63, 65-68, 69, 70-73, 77-78, 79-87, 88-89, 90-91, 94-97, , , , 114, , , 127, Workbook A: 44A, 48A, 52A, 63A, 68A, 69A, 73B, 78A, 87A, 89A, 97A, 101A, 106A, 113A, 114A, 126A, 126B, 126C, 127A, 131B, 263D, 263E, 263F SE/TE-B: 4-14, 15-23, 24-26, 27, 28-30, 63-66, 68, 69-74, 76-78, 371, , 381 Workbook B: 14A, 23A, 26A, 26B, 27A, 68A, 74A, 75A, 78C, 380A, 380B, 387E, 387G SE/TE-A: 152, , 157, , 167, , 175, 186, , 201, , 261 Workbook A: 150A, 157A, 162A, 175A, 193A, 213B, 249A, 249B, 263E 45

48 Great Source Education Math in Focus, Grade Grade 3 3.NF Number and Operations - Fractions Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity SE/TE B: , , 125, , 129, 156, 157, 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. Workbook B: 120A, 125A, 129A, 218B 2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line SE/TE-B: , 131, , 144, 146, 157, 159 diagram by defining the interval from 0 to 1 as the whole and partitioning it into b Workbook B: 125A, 146A, 147, 156A, 218B a 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. Represent a fraction a/b on a number SE/TE-B: , 131, , 144, 146, 157, 159 b 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. Workbook B: 125A, 146A, 147, 156A, 218B 3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. Understand two fractions as equivalent SE/TE-B: , , , 143, 147, , a (equal) if they are the same size, or the same point on a number line. Workbook B: 125A, 129A, 387E Recognize and generate simple SE/TE-B: , , , 143, 147, , b 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. Workbook B: 125A, 129A, 387E 46

49 Great Source Education Math in Focus, Grade Grade 3 c d Express whole numbers as fractions and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. This standard is covered to mastery in Grade 2; opportunities to review can be found on pages: SE/TE-B: 113, 117, 159 Workbook B: 120A See Grade 2: SE/TE-B: 76, 79, 87, 90, 95 SE/TE-B: , , 147, Workbook B: 146A, 147, 156A, 218B 47

50 Great Source Education Math in Focus, Grade Grade 3 3.MD Number and Operations - Fractions Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and SE/TE-B: , , , , , , measure time intervals in minutes. Solve word , 258, 259, 260, problems involving addition and subtraction of time intervals in minutes, e.g., by representing the Workbook B: 227A, 232A, 236A, 247A, 240A, 258A, 258B, 259A, 387F, problem on a number line diagram. 387G 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 2 word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Represent and interpret data. Draw a scaled picture graph and a scaled bar graph to represent a data set with several 3 categories. Solve one and two-step how many more and how many less problems using information presented in scaled bar graphs. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a 4 line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. SE/TE-B: 42-47, 48-55, 56, 57-58, 64, 66-68, 71-74, 75, Workbook B: 47A, 55A, 56A, 68A, 74A, 75A, 78B, 78C, 387E, 387G SE/TE-B: 84-87, 90, 91-96, 105, 107, 109 Workbook B: 90A, 90B, 96A, 96B, 105A, 218B, 218D, 387F SE/TE-B: , , , 143, 147, , Workbook B: 125A, 129A, 387E 48

51 Great Source Education Math in Focus, Grade Grade 3 3.MD Measurement and Data Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Tell and write time to the nearest minute and measure time intervals in minutes. Solve SE/TE-B: , , , , , , , 258, 259, 260, word problems involving addition and subtraction of time intervals in minutes, e.g., Workbook B: 227A, 232A, 236A, 247A, 240A, 258A, 258B, 259A, 387F, by representing the problem on a number 387G line diagram. Measure and estimate liquid volumes and SE/TE-B: 42-47, 48-55, 56, 57-58, 64, 66-68, 71-74, 75, masses of objects using standard units of grams(g), kilograms(kg), and liters(l). Add, Workbook B: 47A, 55A, 56A, 68A, 74A, 75A, 78B, 78C, 387E, 387G 2 subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Represent and interpret data. Draw a scaled picture graph and a scaled bar SE/TE-B: 84-87, 90, 91-96, 105, 107, graph to represent a data set with several categories. Solve oneand two-step how many more and how many less problems using information presented in scaled bar graphs. Workbook B: 90A, 90B, 96A, 96B, 105A, 218B, 218D, 387F Generate measurement data by measuring lengths using rulers marked with halves and SE/TE-B: , , 237, , 243, fourths of an inch. Show the data by making Workbook B: 231A, 237A, 237B, 242B, 247A, 247C, 247D, 305F a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. 49

52 Great Source Education Math in Focus, Grade Grade 3 Geometric Measurement: understand concepts of area and relate area to multiplication and to addition. 5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area. SE/TE-B: , , , , 366, , , Workbook B: 352A, 361A, 370A, 374A, 374B, 387C, 387F b A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. SE/TE-B: , , , 366, , , Workbook B: 352A, 361A, 370A, 374A, 374B, 381A, 387F 6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). SE/TE-B: , , , 366, , , Workbook B: 352A, 361A, 370A, 374A, 374B, 381A, 387F 7 Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-number SE/TE-B: , , 167, , 180, 183, 185 a side lengths by tiling it, and show that the area is the same as would be found by Workbook B: 162, 175A multiplying the side lengths. Multiply side lengths to find areas of rectangles SE/TE-B: , , 172 with whole-number side lengths in the context b of solving real world and mathematical problems, and represent whole number products as rectangular areas in mathematical reasoning. Use tiling to show in a concrete case that the SE/TE-B: , , 167, c area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning. Workbook B: 175A 50

53 Great Source Education Math in Focus, Grade Grade 3 Recognize area as additive. Find areas of SE/TE-B: 355, , 361, 364, , , d 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. Workbook B: 361A, 370A, 374A, 374B, 387C, 387F Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. Solve real-world and mathematical problems involving SE/TE-B: , , perimeters of polygons, including finding 8 the perimeter given the side lengths, finding an Workbook B: 374A, 374B, 380A, 380B, 381A, 387C, 387D unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. 3.G Geometry Reason with shapes and their attributes. 1 2 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. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. SE/TE-B: 272, 274, , , , 319, 337, 338, Workbook B: 274A, 318A, 318B, 387B SE/TE-B: , , 125, , 129, , 139, , , , 156, Workbook B: 120A, 125A, 129A, 146A, 150A, 150B, 155A, 156A, 218B 51

54 Correlation to the Common Core State Standards Grade 4 52

55 Great Source Education Math in Focus, Grade Grade 4 Standards for Mathematical Practice Make sense of problems and persevere in solving them. 1 This standard is covered throughout the program; the following are examples. SE/TE-A: 17, 19,22, 43, 62-63, 76, , 116, , 131, , , 150, 151, 158, 169, 173, , , 215, Workbook A: 9A, 20A, 20B, 22A, 43B, 63A, 79C, 115A, 117, 139A, A, 151, 158D, 173B, 203A, C, 215A, B, 269A SE/TE-B: 26-30, 34, 48-49, 52, 76, 101, 121, 144, 148, , 208, , 217, 235 Workbook B: 34A, 50, 76, 76A, 79B, 102, 121A, 121-B, 144A, 187A-187B, 189A-189B, 214, 235A 53

56 Great Source Education Math in Focus, Grade Grade 4 Reason abstractly and quantitatively. This standard is covered throughout the program; the following are examples. SE/TE-A: 32-43, 92-95, , 109, , , , , , , , 2 Workbook A: 20B, 43A, 43B, 63A, 95A, 108A, 258A, 267A, 267B, 273, 273D, 273E SE/TE-B: 47, 50, 93, 94-97, , , , , 157, 162, 176, , 187, 190 Construct viable arguments and critique the reasoning of others. Workbook B: 71B, 93A, 162A, 169A, 169B This standard is covered throughout the program; the following are examples. SE/TE-A: 9, 17, 51, 84, 93, 131, 138, 145, 166, 170, 176, 190, 196, 202, 231, Workbook A: 20B, 115B, 267B SE/TE-B: 33, 39, 87, 91, 96, 99, 113, 117, 133, , 142, 156, 160, 174, 184, 199, 201, , 211, 225, 229, 233 Workbook B: 162A, 267A 54

57 Great Source Education Math in Focus, Grade Grade 4 Model with mathematics. This standard is covered throughout the program; the following are examples. 4 5 Use appropriate tools strategically. SE/TE-A: 45, 78-82, 85, 86-88, 94, , 115, , , , , , , 166, 176, , , , , 207, 214, , , , , , , , , , Workbook A: 85A, 95A, 115A, 116A, 133A, 150A, 158C, 158D, 158E, 186A, 186B, 214B, A, 242A, 258A, 267B, 269A, 273C, 273D SE/TE-B: 6-9, 11-12, 14-18, 21-22, 25, 32, 35-41, 42-45, 56-59, 61-62, 65-66, 69, 73-75, Workbook B: 12A-12A, 23A, 37, 41 This standard is covered throughout the program; the following are examples. SE/TE-A: 5-7, 9, 10, 71 75, 77-79, 86, 96-99, 131, 138, 196 Workbook A: 22A SE/TE-B: 88-93, 94-97, 99, 102, 104, 106, , , 124, 113, , 156, 168 Workbook B: 93A, 97A, 114A, 118A 55

58 Great Source Education Math in Focus, Grade Grade 4 Attend to precision. This standard is covered throughout the program; the following are examples. 6 SE/TE-A: 9, 17, 40, 51, 52, 84, 93, 107, 114, 131, 138, 145, 166, 170, 171, 176, 177, 180, 190, 195, 196, 200, 202, 231, 240 Look for and make use of structure. SE/TE-B: 31, 32, 39, 40, 87, 91, 96, 99, 113, 117, 133, , 142, 156, 160, 168, 174, 184, 185, 199, 201, , 211, 225, 226, 229, 233 This standard is covered throughout the program; the following are examples. SE/TE-A: 5-9, 10-13, 14-18, 21, 23-24, 70-75, 77-79, 86, 96-99, , , 142, 145, , 152, , , 177, 183, Workbook A: 9A, 13A, 20A, 20B, 85B, 100A, 133A, 139A, 158B, 158C, 173A- 173B, 186A, 273D, 273E SE/TE-B: 24-29, 34, 35-41, 56-64, 65-67, 69-71, 11, , 138, 142, , 167, 168, 170, 173, , 184, 186, 193, , 217 Workbook B: 34A, 61, 64A, 71A-71B, 139A, 150, A, 187A, 189A, 189B, 239B, 239G 56

59 Great Source Education Math in Focus, Grade Grade 4 8 Look for and express regularity in repeated reasoning. This standard is covered throughout the program; the following are examples. 4.OA Operations and Algebraic Thinking Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as SE/TE-A: 77-85, 86-88, 115, 116, 117 a comparison, e.g., interpret 35= 5 Workbook A: 85A, 115A, 115B 7 as a statement that 35 is 5 times as 1 many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 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. SE/TE-A: 77-85, 86-95, , , , Workbook A: 85A, 95A, 100A, 100B, 108A, 115A, 115B, 158B, 158D, 273B, 273D, 273F, 273G SE/TE-B: 56-64, 65-71, 72-76, 77-79, , 161, , , , , , , Workbook B: 64A, 64B, 71A, 71B, 76A, 79B, 162, 162A, 1165A, 169A, 169B, 175A, 187A, 189A, 189B, 239B, 239C, 239D, 239F, 239G SE/TE-A: 80-81, 86, 90, , Workbook A: 115A-115B, 267A 57

60 Great Source Education Math in Focus, Grade Grade 4 Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be 3 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. Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given onedigit number. Determine whether a given whole number in the range is prime or composite. Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit 5 in the rule itself. SE/TE-A: 41-43, 62-63, , 119, , Workbook A: 43B, 63A, 115A-115B, 117, 119A, C, 267A SE/TE-B: 72-75, , Workbook B: 76, 143A-143B, 187A SE/TE-A: 50-51, 53-54, 55, 65, 67-68, 44, Workbook A: 54A, 61A, 68B, 68C, 273D SE/TE-A: 6, 8, 14-17, 19, 26 Workbook A: 9A, 20A, 20B, 63A, 63B SE/TE-B: 26-30, 34, 52, 208, , 217, , Workbook B: 34A, 50, A, 235A-235C 58

61 Great Source Education Math in Focus, Grade Grade 4 4.NBT Number and Operations in Base-Ten Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, SE/TE-A: 5-9, 10-13, 14-20, 21-22, 22A, 23-26, 32-34, 62, 77-79, 81-82, a digit in one place represents ten times 86, what it represents in the place to its right. Workbook A: 13A, 20A, 20B, 22A, 68B, 273D 1 SE/TE-B: 6-9, 11-12, 14-19, 22-23, 28-29, 32, 34, 54-57, 59, 61-62, 65-66, Read and write multi-digit whole numbers using baseten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Use place value understanding to round multi-digitwhole numbers to any place. Workbook B: 12A, 23A, 34A SE/TE-A: 5-9, 10-13, 14-20, 21-22, 23-26, 32-34, 62, 77-79, 81-82, 86, Workbook A: 9A, 13A, 20A, 20B, 22A, 68B, 273D SE/TE-B: 6-9, 11-12, 14-19, 22-23, 28-29, 32, 34, 54-57, 59, 61-62, 65-66, 69 Workbook B: 12A, 23A, 34A SE/TE-A: 32-33, 35-36, 43, 63, 64, 66-67, 93, 95, 116 Workbook A: 43A, 63A, 68B, 95A, 273F 59

62 Great Source Education Math in Focus, Grade Grade 4 Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole SE/TE-A: 32-35, 41-43, 64, 66-67, 68, numbers using the standard algorithm. 4 Workbook A: 43A, 43B, 68B, 95A, 100A-100B, 273D, 273F 5 6 Multiply a whole number of up to four digits by a onedigit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. SE/TE-B: 56-64, 64A-64B, 65-71, 71A-71B, , 175A SE/TE-A: 78-85, 87-89, 91-95, 109, Workbook A: 85A, 95A, 115A, 115B, 158B, 158D, 273B, 273C, 273G SE/TE-B: SE/TE-A: , , , 115, Workbook A: 100A, 100B, 108A, 115A, 115B, 158B, 158D, 273D, 273F, 273G 60

63 Great Source Education Math in Focus, Grade Grade 4 4.NF Number and Operations - Fractions Extend understanding of fraction equivalence and ordering. 1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n 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. SE/TE-A: 199, , , , 236, , , , 273 Workbook A: 203A, 214C, 249A, 267, 267A, 267B, 273B, 273C SE/TE-B: 42-44, 47 Workbook B: 47, 239D 2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. This standard covered to mastery in Grade 3. See Grade 3: SE/TE-B: Workbook B: 146A, 147, 156A, 218B 61

64 Great Source Education Math in Focus, Grade Grade 4 Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. SE/TE-A: , 230, 232, , , 269 Workbook A: 236, 236A, 242A, 269A SE/TE-B: b c d 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. 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. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. SE/TE-A: , , 270 Workbook A: 242A, 249A The skills and concepts presented on these pages prepare students to address the state standard in more depth at Grade 5: SE/TE-A: , , , 156, 159, Workbook A: 144A, 149A, 153B, 153C, 153D, 155A, 203C, 203D, 315F, 315G SE/TE-A: Workbook A: 267, 267A, 273D 62

65 Great Source Education Math in Focus, Grade Grade 4 4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b. SE/TE-A: , , 270 a Workbook A: 242A, 249A Understand a multiple of a/b as a multiple of SE/TE-A: , , 271, 273 b 1/b, and use this understanding to multiply a Workbook A: 258A, 267A, 267B, 269A 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. 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. Use decimal notation for fractions with denominators 10 or 100. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. SE/TE-A: 255, , 271, 273 Workbook A: 267A, 267B SE/TE-B: 13 19, 62 SE/TE-B: 4-9, 11, 12, 13-19, 22-23, 42-45, 47, Workbook B: 12A, 23A, 79A, 239D SE/TE-B: 14-19, 25-26, 28-29, 32, 34, 50, 52 Workbook B: 34A, 79B 63

66 Great Source Education Math in Focus, Grade Grade 4 4.MD Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. 1 Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; 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. SE/TE-A: 235, , 264, 267, 270 Workbook A: 236A, 267A, 269A, 273C, 273F SE/TE-B: 9, 35, 37, 41, 76, 79, , 134, 137, , 144, 145, 147, , , , , 175, , , Workbook B: 12A, 138A, 143B, 144A, 147B, 162A, 165A, 169A, 169B, 175A, 187A, 189A, 189B, 239B, 239C, 239D, 239E, 239G 2 3 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. Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. SE/TE-A: , 264, 267, 270 Workbook A: 267A, 269A, 273C, 273F SE/TE-B: 76, 78-79, , 134, 137, , 144, 145, 147, , , , , 175, , , Workbook B: 12A, 76A, 79B, 138A, 143B, 144A, 147B, 162A, 165A, 169A, 169B, 175A, 187A, 189A, 189B, 239B, 239C, 239D, 239E, 239G SE/TE-B: , , , , , 176, , 189, Workbook B: 162A, 165A, 169A, 169B, 175A, 187A, 188, 189A, 189B, 239B, 239C, 239E, 239G 64

67 Great Source Education Math in Focus, Grade Grade 4 Represent and interpret data. Make a line plot to display a data set of measurements This standard is covered to mastery in Grade 3: in fractions of a unit (1/2, 1/4, 1/8). Solve problems See Grade 3: 4 involving addition and subtraction of fractions by SE/TE-B: , 106, 110, 111 using information presented in line plots. Workbook B: 104A, 104B, 104C, 105A, 387F Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of 5 angle measurement: An angle is measured with reference to a circle with SE/TE-B: 88, 98, 100, 102, 104 its center at the common endpoint of the rays, by considering the fraction of the circular arc between a the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a onedegree angle, and can be used to measure angles. An angle that turns through n one-degree angles is SE/TE-B: , 104 b said to have an angle measure of n degrees. Workbook B: 147B 6 7 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 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. SE/TE-B: 88-93, 94-97, 99, 102, 104 Workbook B: 93A, 97A SE/TE-B: 97, 98, , 147 Workbook B: 97A, 143A-143B, A 65

68 Great Source Education Math in Focus, Grade Grade 4 4.G Geometry Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, SE/TE-B: 87-93, 94-97, , 104, , , 121, 122, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify Workbook B: 93A, 97A, 114A, 118A, 121A, 121B, 147A, 147B, 239D, these in two-dimensional figures. 239E, 239F Classify two-dimensional figures based on SE/TE-B: 114, 116, , , the presence or absence of parallel or 2 perpendicular lines, or the presence or Workbook B: 121B, 138A, 143B absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Recognize a line of symmetry for a twodimensional SE/TE-B: , 209, , 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. Workbook B: 202A, 239B 66

69 Correlation to the Common Core State Standards Grade 5 67

70 Great Source Education Math in Focus, Grade Grade 5 Standards for Mathematical Practice Make sense of problems and persevere in solving them. 1 This standard is covered throughout the program; the following are examples. SE/TE-A: 3-4, 14, 15, 27-32, 34-35, 44, 46, 81, 94-95, , , 109, 110, 113, , 125, 129, 143, , , 159, 162, , , 179, , , , 199, 216, 230, , 237, , 241, 245, 262, , , 291, , , 311, 312, 315 Workbook A: 35B, 35C, 35D, 102A, 102B, 109A, 154C, 155A, 199A, 241A, 262A, 262B, 311B, 315G SE/TE-B: 25, 35, 51-52, 66, 68-77, 81, 82-83, 115, 149, 153, , 179, 203, 223, , 251, 261, 273, 296 Workbook B: 25A, 74A, 81A, 95A, 115B, 153A, 179A, 223B, 297C 68

71 Great Source Education Math in Focus, Grade Grade 5 Reason abstractly and quantitatively. This standard is covered throughout the program; the following are examples. 2 3 Construct viable arguments and critique the reasoning of others. SE/TE-A: 35, 65, 67-69, 98, 109, 112, 122, 127, , 158, 199, , , , 262 Workbook A: 69A, 69B, 136A, 235A, 262A SE/TE-B: 59, 69-74, 82-83, 125, , , , , , , , 179, , 184, , , 223, 251 Workbook B: 74A, 168A, 168B, 173A, 178A, 178B, 179A, 194A, 204A, 204B, 223B, 228B, 228C, 228D, 297C SE/TE-A: 14, 15, 81, 94, 95, 125, 129, 143, 168, 179, 216, 262, 291, 311 SE/TE-B: 66, 149, 203, 243, 244, 261,

72 Great Source Education Math in Focus, Grade Grade 5 Model with mathematics. This standard is covered throughout the program; the following are examples. 4 5 Use appropriate tools strategically. SE/TE-A: 47-50, 52, 55, 57, 60, 71, 73, 75, 78, , 102, 104, 108, 113, , 167, 188, 216, , 254, 257, 259, 281, 300 Workbook A: 50A, 63B, 102A, 102B, 108A, 262B SE/TE-B: 36-39, 43-44, 46-47, 51, 53-55, 60-61, 63-64, 128, 136, 142, 167, 172, 175, 206, 212, 241, , , Workbook B: 50A, 67A This standard is covered throughout the program; the following are examples. SE/TE-A: 47, 48-50, 55, 60, 73, 78, , 102, 104, 108, 113 Workbook A: 50A, 63B, 102A, 102B, 108A, 262B SE/TE-B: 159, , 167, 170, 172,

73 Great Source Education Math in Focus, Grade Grade 5 Attend to precision. This standard is covered throughout the program; the following are examples Look for and make use of structure. Look for and express regularity in repeated reasoning. SE/TE-A: 11, 14, 15, 47, 49, 50, 53, 55, 58, 60, 72, 73, 76, 78, 80, 81, 94-95, 123, 125, 128, 129, 133, 135, 143, 167, 168, 179, 188, 216, , , 262, 281, 291, 300, 311 SE/TE-B: 14, 44, 46, 49, 61, 64, 66, 79, 99, 105, 113, 128, 136, 142, 148, 149, 167, 172, 175, 196, 203, 206, , 220, 241, 243, 244, 249, 261, 273, 282 This standard is covered throughout the program; the following are examples. SE/TE-A: 90-95, , , 109, 113, 153, 184, , 198, 222 Workbook A: 95A, 95B, 102A, 102B, 108A, 108B, 109A, 113D, 113E, 153A, 153C, 153D, 184A, 315E, 315F, 315H SE/TE-B: Workbook B: 80A, 80B SE/TE-A: 35, 52-53, 57-58, 71-72, 75-76, 81, 109, 199,

74 Great Source Education Math in Focus, Grade Grade 5 5.OA Operations and Algebraic Thinking Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate 1 expressions with these symbols. Write simple expressions that record calculations with numbers, and interpret 2 numerical expressions without evaluating them. Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered 3 pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. SE/TE-A: 55, 60-63, 64-66, 68, 73-74, 77-80, 92-95, 109, 113, , , 230, 235, , 242, 245 Workbook A: 63A, 81A, 81B, 95B, 108A, 108B, 109A, 113D, 225A, 240A, 241A, 315B, 315C, 315F, 315H SE/TE-A: 90-93, 95, , 111, 113, Workbook A: 95A, 95B, 218A, 315E SE/TE-A: 51-54, 56-59, 70-72, 74-77, 81 SE/TE-B: , 136, 138, 156 Workbook B: 138A, 153A 72

75 Great Source Education Math in Focus, Grade Grade 5 5.NBT Number and Operations in Base-Ten Understand the place value system. 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 1 of what it represents in the place to its left. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the 2 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 Read, write, and compare decimals to thousandths. a b Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. SE/TE-A: 5-8, 9-10, 12-13, 16, 18, 20-21, 36, 38-39, 52-53, 57-58, 71-72, 75-76, 81 Workbook A: 15A, 15B, 19A, 24A SE/TE-B: 7-14, 16-17, 18-19, 20-22, 23, 27-29, 36-39, 42, 43-44, 46-47, 51, 53-58, 60-61, Workbook B: 17A, 22A, 42A, 50A, 59A, 59B, 67A SE/TE-A: 51-54, 56-59, 70-72, 74-77, 81 SE/TE-B: 43-48, 50A, 60-65, 67A, 82-83, 118C Workbook B: 50A, 67A, 118C SE/TE-B: 7-17, 17A, 23-25, Workbook B: 17A, 25A, 25B, 118B SE/TE-B: 18-22, 27 Workbook B: 22A, 118B 73

76 Great Source Education Math in Focus, Grade Grade 5 Use place value understanding to round SE/TE-B: 20-22, 27, 29, 56-58, 68-74, 75-80, decimals to any place. Workbook B: 22A, 25B, 74A, 80A, 118B, 118C Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers SE/TE-A: 49, 51-63, 64-69, 91-95, , , 108, 109, 110, using the standard algorithm Workbook A: 50A, 63A, 63B, 69A, 69B, 95A, 95B, 102A, 102B, 108A, 5 108B, 109A, 113C, 113D, 113E SE/TE-B: , 272, 274, , 299, , Workbook B: 247A, 297, 297A, 297B, 297C, 302B, 302C, 302D, 302E, 302G 6 7 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. 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. SE/TE-A: 50, 70, 72-74, 77-81, 82-89, 92-94, 96-97, 100, 102, , 108, Workbook A: 50A, 81A, 81B, 89A, 95A, 95B, 102A, 108B, 113C, 113E, 315E, 315G SE/TE-B: 13, 17, 26, 36-42, 43-50, 51-59, 60-67, 68-74, 75-80, 81, Workbook B: 17A, 25B, 42A, 50A, 59A, 59B, 67A, 74A, 80A, 80B, 81A, 118B, 118C, 302G 74

77 Great Source Education Math in Focus, Grade Grade 5 5.NF Number and Operations - Fractions Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike SE/TE-A: , , , , , 154, 156, denominators (including mixed numbers) by replacing given fractions with equivalent Workbook A: 126A, 126B, 130A, 144A, 149A, 153A, 153B, 153C, 153D, 1 fractions in such a way as to produce an 155A, 203B, 203C, 203D, 315E, 315F, 315G equivalent sum or difference of fractions with like denominators. 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. SE/TE-A: 122, 127, 129, , , 139, , , , , 159 Workbook A: 130A, 139A, 153A, 153B, 153C, 153D, 155A, 203D, 315F, 315G Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve Workbook A: 136A, 139A, 153A, 153B, 203B SE/TE-A: , 138, 150, 157, 159 word problems involving division of whole 3 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. 75

78 Great Source Education Math in Focus, Grade Grade 5 4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) q as a part of SE/TE-A: , , , , , 191, a partition of q into b equal parts; equivalently, , 196, 198, a as the result of a sequence of operations Workbook A: 168A, 174A, 176A, 180A, 184A, 198A, 199A, 203C, 203D, a q b. 203E, 315E, 315F 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. SE/TE-A: 165, 175, 203 Workbook A: 168A, 176A Perform operations with multi-digit whole numbers and with decimals to hundredths. 5 Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size SE/TE-A: 168, , 299, 301, 304, 313 of one factor on the basis of the size of the Workbook A: 282, 301A a 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 = (n a)/(n b) to the effect of multiplying a/b by 1. SE/TE-A: , , Workbook A: 168A, 176A SE/TE-B: Workbook B: 42A, 50A 76

79 Great Source Education Math in Focus, Grade Grade a b c Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. SE/TE-A: 165, 167, , 177, , , 203 Workbook A: 174A, 184A, 199A, 203D, 203E Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a unit fraction by a SE/TE-A: , , 201, 203 non-zero whole number, and compute such Workbook A: 189A, 199A, 203C, 203D, 203E, 315E quotients. Interpret division of a whole number by a This standard will be met in Grade 6. unit fraction, and compute such quotients. 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. Measurement and Data 5.MD Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement 1 system (e.g., convert 5cm to 0.05 m), and use these conversions in solving multistep, real-world problems. SE/TE-A: , , 203 Workbook A: 189A, 199A, 203D, 203E SE/TE-B: 134, , 299, Workbook B: 153A, 228B, 228D, 297A, 297B, 297C, 302C, 302D, 302E Represent and interpret data. Make a line plot to display a data set of Line Plots are covered to mastery in Grades 3 and 4; opportunity to review can measurements in fractions of a unit (1/2, be found on page: 2 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information SE/TE-B: 153 presented in line plots. 77

80 Great Source Education Math in Focus, Grade Grade 5 Geometric measurement: understand concepts of volume and relate volume to multiplication and addition. 3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a unit SE/TE-A: , , 201, 203 a cube, is said to have one cubic unit of volume, and can be used to measure volume. Workbook A: 189A, 199A, 203C, 203D, 203E, 315E A solid figure which can be packed without This standard will be met in Grade 6. b gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, SE/TE-A: , , using cubic cm, cubic in, cubic ft, and improvised units. Workbook A: 189A, 199A, 203D, 203E 5 Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. Find the volume of a right rectangular prism SE/TE-B: 277, 279, , 285, , 299 with wholenumber side lengths by packing it with unit cubes, and show that the volume is Workbook B: 285A, 302C the same as would be found by multiplying a 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. Apply the formulas V = l w h and V = b SE/TE-B: , 297A, 297B, 297C, 299, b 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. Workbook B: 297A, 297B, 297C, 302C, 302D, 302G 78

81 Great Source Education Math in Focus, Grade Grade 5 Recognize volume as additive. Find volumes SE/TE-B: 278, 279, 281, 282, 284 of solid figures composed of two non-overlapping right rectangular prisms by c adding the volumes of the nonoverlapping parts, applying this technique to solve real-world problems. 5.G Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. 1 2 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). 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. SE/TE-B: , 156 Workbook B: 138A, 153A, 228B, 228D, 302E SE/TE-B: , 156 Workbook B: 138A, 153A, 228B, 228D, 302E 79

82 Great Source Education Math in Focus, Grade Grade 5 Classify two-dimensional figures into categories based on their properties. 3 Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. SE/TE-A: 257 SE/TE-B: , , , , , Workbook B: 190A, 204A, 204B, 223A, 223B, 228C, 228D, 302F 4 Classify two-dimensional figures in a hierarchy based on properties. SE/TE-A: 257 SE/TE-B: , , , , , Workbook B: 190A, 204A, 204B, 223A, 223B, 228C, 228D, 302F 80

83 Let s Connect Today! TM For more information, contact your local Account Manager at , Option 6 Explore the complete program online with the Math in Focus virtual sample. hmheducation.com/mathinfocus Houghton Mifflin Harcourt Publishing Company. All rights reserved. Printed in the U.S.A. 10/10 ADV-7615 Math in Focus is a trademark of Times Publishing Limited. Math in Focus is published by Marshall Cavendish International (Singapore) and exclusively distributed by Houghton Mifflin Harcourt. Common Core State Standards for Mathematics Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 81