Correlation to the Common Core State Standards. Math in Focus


 Darrell Fletcher
 2 years ago
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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 crossreference 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 TEA Teacher s Edition A TEB 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 gradelevel 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 gradelevel 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 highperforming 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 gradeappropriate 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 baseten 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, K5, 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 6070% 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/TEA: 7, 26, 37, 5758, 61, 9091, 127, 135, , 189, , 247 Workbook A: 19A, 26A, 37A, 61A, 91A, 135A, 135B, 159A, 189A, 215A, 247A SE/TEB: 23, 3940, 4142, 49, 7677, 100, , 129, 148, 170, 201, 237, 239, , 255, Workbook B: 48A, 77A, 129, 148A, 170A, 237A, 255A, 291A, 291B Reason abstractly and quantitatively. SE/TEA: 2223, 25, 27, 36, 37, 46, 4852, 55, 5758, 5961, 63, 9091, 135, , , 188, 189, , , , 247 Workbook A: 19A, 25A, 26A, 37A, 38C, 52A, 56A, 61A, 91A, 135A, 135B, 188A, 189A, 191A, 215A, 230A, 247A SE/TEB: 912, 23, 26, 3940, 4142, 49, 54, 7071, 7374, 7677, 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/TEA: 10, 35, 36, 90, 108, 109, 119, 156, 182, 214, the reasoning of others. SE/TEB: 121, 122, 140, 146, 200, 245, 253, 288 Model with mathematics. SE/TEA: 4345, 5763, 68, 70, 73, 7781, 8284, 8587, 8990, 93, 103, 112, , 126, , 137, , , , 217 Workbook A: 63A, 73A, 76A, 81A, 93A, 93C 4 SE/TEB: 84, 8693, 9498, 100, , , 115, 117, 119, , 205, , , 219, , Workbook B: 93A 5 6 Use appropriate tools strategically. SE/TEA: 46, 10, 1617, 2021, 2226, 30, 3233, 35, 38, 44, 51, 103, 118, 120, 130, 160, 169, , , , 232, , 238, , Workbook A: 38B, 38C, 47A, 93C, 174A SE/TEB: 8, 11, 15, 19, 20, 5861, 6365, 69, 7677, 9495, , , 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/TEA: 11, 46, 71, 90, 108, 109, 119, 149, 156, 169, 182, 207, 214, 224 SE/TEB: 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/TEA: , 191 Workbook A: 159A, 188A, 191A SE/TEB: 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/TEA: 2325, 27, 3133, 35, 37, 38, 4247, 4852, 5356, 5761, 63, 6773, 7476, 7781, 8291, 9293, , , , , , , , 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/TEB: 8493, , , , , , , , , 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/TEA: 4850, 52, 5761, 6263, 67, 70, 7476, 8285, 8789, 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/TEB: , 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/TEA: 214 Workbook A: 215A SE/TEB: , 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/TEA: 36, 4852, 63 strategies to add and subtract. Examples: Workbook A: 52A, 63A, 93C, 215A If = 11 is known, then = SE/TEB: 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 unknownaddend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. SE/TEA: 6773, 7476, 7781, 8291, 9293, , , 217 Workbook A: 73A, 76A, 81A, 91A, 93A, 93C, 208A, 215A, 217A, 249E, 249F, 249G SE/TEB: , , , 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/TEA: 4347, 62, Workbook A: 47A, 63A, 73A, 93A SE/TEB: 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/TEA: 4247, 4852, 5356, 5761, 6263, 6773, 7476, 7781, 8291, 9293, , , , , , 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/TEB: , , 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/TEA: 4247, 4852, 5356, 5761, 6263, 6773, 7476, 7781, 8291, 9293, , , , , , 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/TEB: 8493, , , , , , , , , 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/TEA: 43, 5859, 8283, , 203, 205 SE/TEB: 8485, 8792, 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 BaseTen 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/TEA: 412, 19, 22, 27, 7273, 92, , , 184, 188, 190 Workbook A: 12A, 25A, 26A, 27A, 33A, 33B, 33C, 38A, 38B, 38C, 73A, 93A, 170A, 170B, 191A, 249E, 249F SE/TEB: 5762, 6365, 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 twodigit 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/TEA: , 170, , , Workbook A: 170A, 170B, 174A SE/TEB: 5861, 6365, 6769, 72, 78, 84, 8692, 9698, 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/TEA: , 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 twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Workbook A: 174A SE/TEB: 58, 59, 65, 8788, 104, 105, , , 192, 202, 211, 224, 225 Workbook B: 62A SE/TEA: , 188, 189, 191 Workbook A: 188A, 191A, 249F SE/TEB: 6970, 7273, 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 twodigit number and a onedigit number, and adding a twodigit number and a SE/TEA: 68, 7273, 7476, 78, 8384, 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 twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. SE/TEB: 8486, 93, 9697, 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 twodigit 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/TEB: 138, 140, 140A, 144, 147, 149, 149A, 171C Workbook B: 140A, 149A, 171C SE/TEB: 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/TEA: , 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 samesize 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/TEA: , , , 246, 249 Workbook A: 239A, 249A, 249D, 249E SE/TEB: , , 170, 171 Workbook B: 165A, 165B, 169A, 170A, 171A, 171C, 293F SE/TEB: 3135, 3641, 4248, 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 threesided) versus nondefining attributes 1 (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 2 3 Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quartercircles) or threedimensional 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/TEA: , , 136 Workbook A: 105A, 120A, 135A, 137A, 249E SE/TEA: , , , 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/TEA: , Workbook A: 120A SE/TEB: Workbook B: 250A 250B, 255A See Grade 2: SE/TEA: 73, 75 82, 87, SE/TEB: 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/TEA: 2628, 2930, 31, 32, 54, 59, 8889, 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/TEB: 8, 1015, 3839, 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/TEA: 2628, 2930, 31, 32, 3537, 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/TEB: , 155, 156, 157, , , , , , 267, , 296, , , 305 Workbook B: 156A, 231A, 302A SE/TEA: 29, 30, 120, 131, 147, 172, 183 SE/TEB: 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/TEA: 612, 1721, 23, 33, 3840, 6163, 6768, 7274, 7880, 8485, 9697, 9899, , , , , , , , , 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/TEB: 67, 1718, 2025, 6668, 72, 79, 8386, 8889, 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/TEA: 610, 1112, 17, 1821, 23, 33, 3840, 42, 44, 4647, 4950, 6163, 6768, 7274, 76, 7880, 8485, 92, 9699, 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/TEB: 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/TEA: 29, 30, 100, 101, 105, 112, 120, 131, 139, 147, 172, 183, 194, 198, 205, 213, 230, 247, 249, 255, 267, 270 SE/TEB: 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/TEA: 2426, 30, 33, 89, 237, 239, 245, 250, 260, Workbook A: 31A, 33A, 54B, 123C, 252A, 258A, 261A, 272A, 277A, 283E SE/TEB: 8486, 89, 99 Workbook B: 99A This standard is covered throughout the program; the following are examples. SE/TEA: 2630, 31, 32, 8889, , , , Workbook A: 31A, 32A, 33A, 123C, 123D, 167A, 178A, 188A, 188C SE/TEB: , , 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/TEA: 9699, , 106, , , to solve oneand twostep word problems Workbook A: 102A, 108A, 114A, 121A, 121B, 123A, 123C, 123D, 283D, 283F involving situations of adding to, taking SE/TEB: 67, 1719, 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 onedigit numbers. SE/TEB: 815, 16, 2026, 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/TEA: , 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/TEA: , 168, 171, , Workbook A: 161A, 172A, 178A, 188A, 188D SE/TEB: , 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 BaseTen Understand place value. Understand that the three digits of a threedigit 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; skipcount by 5s, 10s, and 100s. SE/TEA: 610, 1112, 17, 1821, 23, 33, 3840, 42, 44, 46, 47, 4950, 6163, 6768, 7274, 76, 7880, Workbook A: 10A, 17A, 33A, 283E SE/TEA: 9, 1113, 1617, 33 Workbook A: 17A, 17B, 33A SE/TEA: 610, 2630, 31, 33, , , , Workbook A: 10A, 31A, 32A, 33A, 123C, 167A, 178A, 188A, 188C, 283E 3 4 Read and write numbers to 1000 using baseten numerals, number names, and expanded form. Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. SE/TEA: 610, 1117, 33, 4041, 4345, 4748, 4953, 55, 6165, 6769, 71, 7275, 77, 77A, 7882, 8488, Workbook A: 10A, 17A, 17B, 33A, 41A, 45A, 48A, 54A, 55A, 66A, 71A, 77A, 83A, 91A, 283E SE/TEA: 1821, 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/TEA: 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/TEB: 68, 13, 15, 1619, 20, 26, 27, 3435, 37, 3940, , 129 Workbook B: 15A, 19A, 26A, 126A, 305D 6 Add up to four twodigit numbers using strategies based on place value and properties of operations. SE/TEA: 3841, 4245, 4648, 4954, 55, 6166, 6771, 7277, 7883, 8491, , , , , , , 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/TEB: 615, 1619, 2026, 27, 3435, 37, 3941, , 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 threedigit 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/TEA: 3840, 42, 44, 4647, 4950, 52, 6163, 6768, 7274, 76, 7880, 8485, 89, , , , , , , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123C, 123D, 281A, 281B, 283A, 283D, 283F SE/TEB: 68, 1014, 1719, 2025, , 129 Workbook B: 15A, 19A, 26A, 126A, 127A, 129A SE/TEB: 815, 17, 2326, 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/TEA: 3841, 4245, 4648, 4954, 55, 6166, 6771, 7277, 7883, 8491, , , , , 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/TEB: 615, 1619, 2026, 27, 3435, 37, 3941, , 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/TEA: , , 210, , Workbook A: 195A, 210A, 215A, 223A SE/TEB: , 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/TEA: 243 Workbook A: 249D See Grade 1: SE/TEA: 243, 247, 249 Workbook A: 246, 249A, 249D SE/TEA: , 204 Workbook A: 195A, 223A SE/TEB: 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 wholenumber sums and differences within 100 on a number line diagram. SE/TEA: , , 222 Workbook A: 215A, 221A, 223A, 283C SE/TEB: , , 128 Workbook B: 110A, 121A, 127A, 129A, 158C, 305D SE/TEA: 9699, 100, , , , , , , 223, , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123D, 220A, 281A, 283A, 283D, 283F SE/TEB: , 127, 129, 198, 200, , , Workbook B: 126A, 127A, 129A, 200A, 200B, 205, 205A, 216A, 216B, 219A, 305F SE/TEA: 26, 27, 89, 9699, 100, , , , , , , 223, , 283 Workbook A: 102A, 108A, 114A, 121A, 121B, 121C, 123A, 123D, 220A, 281A, 283A, 283D, 283F SE/TEB: 2833, 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 wholenumber units. Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. 10 Solve simple puttogether, takeapart, and compare problems using information presented in a bar graph. SE/TEB: , , 142, 149, , Workbook B: 136A, 141A, 149A, 156A, 158A, 158C, 158D, 305D, 305E SE/TEB: 49, 51, 62, 6670, Workbook B: 70A, 72A, 99D, 99E, 305D, 305F This standard is also covered to mastery in Grade 1. See Grade 1: SE/TEB: , , , 293 Workbook B: 289A, 289B, 289C, 291A, 291B, 293A, 293D, 293E This standard is addressed in depth in Grade 3. See Grade 3: SE/TEB: , 106, Workbook B: 104A, 104B, 104C, 105A, 218D SE/TEB: , , 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 samesize 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/TEB: 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/TEB: , , 338, Workbook B: 318A, 318B SE/TEB: 75, 78, 79, 82, 8388, 9194, 96, Workbook B: 82A, 82B, 89, 96A, 97, 99A, 99D, 305E SE/TEB: 7779, 8182, 8389, 9094, 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/TEA: 511, 2729, 3132, 4152, 5862, 63, 6569, 7273, 7980, 8289, 91, , , , , 151, , , , , , 189, , 223, , , Workbook A: 11A, 29A, 52A, 63A, 73A, 78A, 89A, 150A, 226A, 253A SE/TEB: 27, 56, 75, 8490, 9196, , 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/TEA: 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/TEB: 23, 41, 56, 75, 105, 156, 211, 241, 259, , 337, 381 Workbook B: 27A, 56A, 75A, 105A, 156A, 211A, 259A, 293A, 337A, 381A SE/TEA: 30, 82, 125, 140 SE/TEB: 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/TEA: 511, 1214, 17, 2023, 5357, 63, 77, 79, 8486, 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/TEB: 45, 12, 1516, 21, 2426, 27, 4245, 47, 4853, 55, 56, 57, 6368, 6974, 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/TEA: 512, 14, 1617, 2023, 4344, 47, 51, 5758, 77, 79, 81, 8486, 94, , , 106, , 140, 156, 166, 174, , 197, , , 207, 210, 215, 222, , Workbook A: 19B SE/TEB: 13, 3234, 4247, 64, 81, 83, 8596, 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/TEA: 26, 30, 57, 60, 63, 69, 82, 96, 125, 140, 179, 197 SE/TEB: 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/TEA: 25, 2729, 31, 33, 35 7 SE/TEB: 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/TEA: 4144, 4548, 4952, 5363, 69, 70, 72, 7987, 8889, 9091, 9497, , , , 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/TEB: 414, 1523, 2426, 27, 2830, , 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/TEA: 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 wholenumber 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/TEA: 176, See Grade 2: SE/TEA: , 185 Workbook A: 185A, 185B, 186A, 188A, 188C, 188D SE/TEA: 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: 6668, 6974, 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/TEA: , , , , , , , 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: 6668, 6974, Workbook B: 68A, 74A, 78C, 387G Understand properties of multiplication and the relationship between multiplication and division. Apply properties of operations as SE/TEA: , , , , , , , 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/TEB: 6668, 6974, Workbook B: 68A, 74A, 78C, 387G 42
45 Great Source Education Math in Focus, Grade Grade 3 Understand division as an unknownfactor problem. SE/TEA: , , 183, 186, , , 226A, , , 235, , , , 258, 259, Workbook A: 177A, 230A, 234A, 253A, 258A, 258B, 263B, 263C, 263D, 263F, 263G SE/TEB: 6768, 7273, 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 onedigit numbers. Workbook B: 74A, 78C, 387G SE/TEA: , , , , , , , 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/TEB: 6668, 6974, 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 twostep 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/TEA: 6063, , 127, , , , 258, 259, 261, 263 Workbook A: 63A, 73B, 126A, 126B, 126C, 127A, 131B, 249A, 249B, 258A, 258B, 263C, 263F, 263G SE/TEA: 511, 2729, , , 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 BaseTen Use place value understanding and properties of operations to perform multidigit arithmetic. 1 Use place value understanding to round whole numbers to the nearest 10 or 100. SE/TEA: 5359, 6163, 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 onedigit 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/TEA: 4144, 4548, 4952, 5863, 6568, 69, 7073, 7778, 7987, 8889, 9091, 9497, , , , 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/TEB: 414, 1523, 2426, 27, 2830, 6366, 68, 6974, 7678, 371, , 381 Workbook B: 14A, 23A, 26A, 26B, 27A, 68A, 74A, 75A, 78C, 380A, 380B, 387E, 387G SE/TEA: 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/TEB: , 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/TEB: , 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/TEB: , , , 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/TEB: , , , 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
1) Make Sense and Persevere in Solving Problems.
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