Prentice Hall Connected Mathematics 2, 7th Grade Units 2009

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O Oregon Mathematics Content Standards Grade 7

Introduction The Correlation of Connected Mathematics 2 (CMP2), 7 th Grade Units 2009 to the Oregon Mathematics Content Standards for Grade 7, demonstrates the alignment of content between CMP2 and the Oregon Mathematics Content Standards. This document contains references from the Teacher Guides (TG) and Student Editions (SE) to the relevant standards in Grade 7. Additional Topics that will be available on Pearson SuccessNet were added to this correlation to further enhance the alignment of CMP2 to the Oregon Mathematics Content Standards. As part of the CMP2 program, teachers also have these resources to draw from for professional development, support for parents and students, assessment, and practice. Additional CMP2 Teacher Resources include: Implementing and Teaching Guide, Strategies for English Language Learners, Parent Guide, Special Needs Handbook, Teaching Transparencies, Grade 7 Additional Practice and Skills Workbook, Grade 7 Assessment Resources, Additional CMP2Technology Resources include: StudentEXPRESS CD-ROM, ExamView 6.0 Test Bank CD-ROM, TeacherSTATION (includes Teacher Express, MindPoint QuizShow and Presentation Resources), Teaching Middle Grades with TI Technology, Success Tracker, and pearsonschool.com The National Science Foundation funded Connected Mathematics Project between 1991 and 1997 to develop a middle school mathematics program. That program, Connected Mathematics, was a complete mathematics curriculum to help students develop understanding of important concepts, skills, procedures, and ways of thinking and reasoning in number, geometry, measurement, algebra, probability, and statistics. The National Science Foundation funded a revision of Connected Mathematics in 2000. This revision, CMP2 took advantage of lessons learned in the six years that the first edition was used in classrooms. With the introduction of CMP2, it is important to note that for more than five years, the authors worked to build on the solid foundation already established by the first CMP and the research supporting the program. Research has been the central, guiding force in the product development process. Authors and product developers relied on the efficacy data for making improvements in design and content, resulting in an even more effective program. Fifteen sites, with varying characteristics that are representative of schools across the nation, participated in three rounds of revisions for each grade level. Input from more than 15,000 students and 300 teachers was integrated into CMP2. CMP2 has already proven to support student learning, helps students to develop and maintain their skills, and enhances their mathematical thinking and reasoning. Connected Mathematics 2 provides 24 Student Units (8 per grade level). Every unit develops a big mathematical idea, important clusters of related concepts, skills, procedures, and ways of thinking. Students develop understanding of algorithms and strategies for computing and estimating in a variety of ways. They learn to recognize when an algorithm or strategy applies to a new context and when they can build on the skills and strategies they know in order to develop new strategies. In these processes, students practice skills as an ongoing activity throughout the curriculum. In addition, Connected Mathematics 2 helps students develop algebraic reasoning. The program aims to expand student views of algebra beyond symbolic manipulation and offers opportunities for students to apply algebraic reasoning to problems in many different contexts throughout the course of the curriculum. 1

Grade 7 It is essential that these standards be addressed in contexts that promote problem solving, reasoning, communication, making connections, and designing and analyzing representations. 7.1 Number and Operations and Algebra: Develop an understanding of operations on all rational numbers and solving linear equations. 7.1.1 Develop, analyze, and apply models (including everyday contexts), strategies, and procedures to compute with integers, with an emphasis on negative integers. 7.1.2 Extend knowledge of integers and positive rational numbers to solve problems involving negative rational numbers. 7.1.3 Develop and use strategies to estimate the result of rational number computations and justify the reasonableness of results. SE: Accentuate the Negative Investigation 1: Extending the Number System (10 15), Investigation 2: Adding and Subtracting Integers (22 29), Investigation 3: Multiplying and Dividing Integers (44 45, 47 48, 53, 57), Investigation 4: Properties of Operations (60 63, 66 67, 71 73); What Do You Expect? Investigation 4: Binomial Outcomes (58) TE: Accentuate the Negative (4 5), Investigation 1: Extending the Number System (21 32), Investigation 2: Adding and Subtracting Integers (37 48), Investigation 3: Multiplying and Dividing Integers (63 68, 73 76, 82, 84), Investigation 4: Properties of Operations (87 90, 95 98, 100 101); What Do You Expect? Investigation 4: Binomial Outcomes (93) SE: Accentuate the Negative Investigation 1: Extending the Number System (5 15, 19-20), Investigation 2: Adding and Subtracting Integers (22 30), Investigation 3: Multiplying and Dividing Integers (44 45, 47 48, 55 57), Investigation 4: Properties of Operations (71) TE: Accentuate the Negative Investigation 1: Extending the Number System (15 32, 34 35), Investigation 2: Adding and Subtracting Integers (37 52), Investigation 3: Multiplying and Dividing Integers (63 68, 73 76, 83 84), Investigation 4: Properties of Operations (100) SE: Filling and Wrapping Investigation 2: Designing Rectangular Boxes (22 23); What Do You Expect? Investigation 1: Evaluating Games of Chance (7 8), Investigation 4: Binomial Outcomes (50 51); Data Distributions Investigation 2: Making Sense of Measures of Central (29 35) 2

TE: Filling and Wrapping Investigation 2: Designing Rectangular Boxes (47 50); What Do You Expect? Investigation 1: Evaluating Games of Chance (23 26), Investigation 4: Binomial Outcomes (79 82); Data Distributions Investigation 2: Making Sense of Measures of Central (46 54) 7.1.4 Apply properties of rational numbers and algebra to write and solve linear equations in one variable. SE: Variables and Patterns Investigation 3: Rules and Equations (50 51); Comparing and Scaling Investigation 3: Comparing and Scaling Rates (33 34), Investigation 4: Making Sense of Proportions (49 51, 53 54); Accentuate the Negative Investigation 2: Adding and Subtracting Integers (37); Moving Straight Ahead Investigation 1: Walking Rates (8 11), Investigation 2: Exploring Linear Functions With Graphs and Tables (27 29), Investigation 3: Solving Equations (46 48, 50 54) TE: Variables and Patterns Investigation 3: Rules and Equations (69 72); Comparing and Scaling Investigation 3: Comparing and Scaling Rates (52 56), Investigation 4: Making Sense of Proportions (74 78, 83 88); Accentuate the Negative (6), Investigation 2: Adding and Subtracting Integers (59); Moving Straight Ahead (6 7), Investigation 1: Walking Rates (25 34), Investigation 2: Exploring Linear Functions With Graphs and Tables (51 54), Investigation 3: Solving Equations (67 70, 77 84) 7.2 Number and Operations, Algebra and Geometry: Develop an understanding of and apply proportionality, including similarity. 7.2.1 Represent proportional relationships with coordinate graphs and tables, and identify unit rate as the slope of the related line. SE: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (31-32); Comparing and Scaling Investigation 3: Comparing and Scaling Rates (33 39); Moving Straight Ahead Investigation 1: Walking Rates (8 9), Investigation 2: Exploring Linear Functions With Graphs and Tables (39), Investigation 4: Exploring Slope (70 75) 3

TE: Variables and Patterns (4 7), Investigation 2: Analyzing Graphs and Tables (45 54); Comparing and Scaling Investigation 3: Comparing and Scaling Rates (52 68); Moving Straight Ahead (4 6), Investigation 1: Walking Rates (25 30), Investigation 2: Exploring Linear Functions With Graphs and Tables (63), Investigation 4: Exploring Slope (96 110) 7.2.2 Apply ratio and proportionality to solve problems, including percent and simple probability. 7.2.3 Use coordinate graphs, tables, and equations to distinguish proportional relationships from other relationships, including inverse proportionality. SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (24); Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (10-11, 15 16), Investigation 4: Similarity and Ratios (59 65), Investigation 5: Using Similar Triangles and Rectangles (82 83); Comparing and Scaling Investigation 2: Comparing Ratios, Percents, and Fractions (21 23), Investigation 4: Making Sense of Proportions (49 54); What Do You Expect? Investigation 3: Expected Value (40 41) TE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (40 41); Stretching and Shrinking (6 7), Investigation 1: Enlarging and Reducing Shapes (25 28, 30), Investigation 4: Similarity and Ratios (75 86), Investigation 5: Using Similar Triangles and Rectangles (99 102); Comparing and Scaling (5 7), Investigation 2: Comparing Ratios, Percents, and Fractions (43 46), Investigation 4: Making Sense of Proportions (74 88); What Do You Expect? Expected Value (65 68) SE: Variables and Patterns Investigation 1: Variables, Tables, and Coordinate Graphs (7 11), Investigation 2: Analyzing Graphs and Tables (33 34), Investigation 3: Rules and Equations (50 53, 60); Moving Straight Ahead Investigation 1: Walking Rates (10 11), Investigation 2: Exploring Linear Functions With Graphs and Tables (25 30), Investigation 3: Solving Equations (46 48) 4

7.2.4 Develop and use scale factors and proportional relationships to solve problems, including similarity and congruence. TE: Variables and Patterns (4 7), Investigation 1: Variables, Tables, and Coordinate Graphs (21 28), Investigation 2: Analyzing Graphs and Tables (55 58), Investigation 3: Rules and Equations (69 76, 84); Moving Straight Ahead (4 6), Investigation 1: Walking Rates (31 34), Investigation 2: Exploring Linear Functions With Graphs and Tables (47 60), Investigation 3: Solving Equations (67 70) SE: Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (7 11), Investigation 2: Similar Figures (22 23, 25 27, 33 34), Investigation 3: Similar Polygons (40 43), Investigation 5: Using Similar Triangles and Rectangles (78 83); Filling and Wrapping Investigation 5: Scaling Boxes (64 65) 7.2.5 Convert among different units of measurement to solve problems, including rates. 7.2.6 Apply scale factor to analyze how the change in one measure (e.g., length, area, volume) affects another. TE: Stretching and Shrinking (4 6) Investigation 1: Enlarging and Reducing Shapes (19 28), Investigation 2: Similar Figures (33 38, 43 48, 52), Investigation 3: Similar Polygons (61 68), Investigation 5: Using Similar Triangles and Rectangles (91 102); Comparing and Scaling (6 7); Filling and Wrapping Investigation 5: Scaling Boxes (101 104) SE: Comparing and Scaling Investigation 3: Comparing and Scaling Rates (35, 45); Moving Straight Ahead Investigation 1: Walking Rates (5 7), Investigation 3: Solving Equations (66), Investigation 4: Exploring Slope (76 77); Filling and Wrapping Investigation 5: Scaling Boxes (70) TE: Comparing and Scaling Investigation 3: Comparing and Scaling Rates (57 60, 71); Moving Straight Ahead Investigation 1: Walking Rates (16 18), Investigation 3: Solving Equations (93), Investigation 4: Exploring Slope (111 114); Filling and Wrapping Investigation 5: Scaling Boxes (111) SE: Stretching and Shrinking Investigation 2: Similar Figures (24 27), Investigation 3: Similar Polygons (38 43), Investigation 5: Using Similar Triangles and Rectangles (78 81); Comparing and Scaling Investigation 4: Making Sense of Proportions (52 53); Filling and Wrapping Investigation 5: Scaling Boxes (63, 66) 5

TE: Stretching and Shrinking (5), Investigation 2: Similar Figures (39 48), Investigation 3: Similar Polygons (55 68), Investigation 5: Using Similar Triangles and Rectangles (91 98); Comparing and Scaling Investigation 4: Making Sense of Proportions (79 82); Filling and Wrapping Investigation 5: Scaling Boxes (96 100, 105 108) 7.3 Measurement and Geometry: Develop an understanding of and use formulas to determine surface area and volume. 7.3.1 Use models to explain the reasonableness of formulas for the circumference and area of circles. SE: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (43); Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (15 16, 18); Filling and (34 36, 43) TE: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (64); Stretching and Shrinking Investigation 1: Enlarging and Reducing Shapes (29 30); Filling and (61 68, 75) 7.3.2 Know common estimates of π and use these values to estimate and calculate the circumference and area of a circle. 7.3.3 Solve problems involving areas and circumferences of circles. 7.3.4 Use models to explain the reasonableness of formulas for the surface area of pyramids and cylinders, and volume of pyramids, cylinders, and cones. SE: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (43); Filling and (43), Investigation 4: Cones, Spheres, and Pyramids (51 52) TE: Variables and Patterns Investigation 2: Analyzing Graphs and Tables (64); Filling and (75), Investigation 4: Cones, Spheres, and Pyramids (83 86) SE: Variables and Patterns Investigation 3: Rules and Equations (59), Investigation 4: Calculator Tables and Graphs (77); Filling and (34 37), Investigation 4: Cones, Spheres, and Pyramids (48 50, 52 53) TE: Variables and Patterns Investigation 3: Rules and Equations (83 84), Investigation 4: Calculator Tables and Graphs (101); Filling and (61 72), Investigation 4: Cones, Spheres, and Pyramids (79 82, 87 90) SE: Filling and Wrapping Investigation 3: Prisms and Cylinders (34 36, 39), Investigation 4: Cones, Spheres, and Pyramids (48 53), Investigation 5: Scaling Boxes (63 65) 6

7.3.5 Find and justify relationships among the formulas for the areas of different polygons when determining surface area. 7.3.6 Solve problems involving surface areas of pyramids and cylinders and volumes of pyramids, cylinders, and cones. 7.3.7 Estimate and compute the area and volume of complex or irregular shapes by dividing them into basic shapes. TE: Filling and Wrapping (5 6), Investigation 3: Prisms and Cylinders (61 68, 73), Investigation 4: Cones, Spheres, and Pyramids (79 90), Investigation 5: Scaling Boxes (96 104) SE: Filling and Wrapping Investigation 3: Prisms and Cylinders (34-37, 42) TE: Filling and Wrapping Investigation 3: Prisms and Cylinders (61 72, 74) SE: Filling and Wrapping Investigation 3: Prisms and Cylinders (37), Investigation 4: Cones, Spheres, and Pyramids (51 53, 55 58), Investigation 5: Scaling Boxes (63) TE: Filling and Wrapping Investigation 3: Prisms and Cylinders (69 72), Investigation 4: Cones, Spheres, and Pyramids (83 90, 92 93), Investigation 5: Scaling Boxes (96 100) SE: Stretching and Shrinking Investigation 4: Similarity and Ratios (71); Filling and (46), Investigation 4: Cones, Spheres, and Pyramids (59) TE: Stretching and Shrinking Investigation 4: Similarity and Ratios (88); Filling and (76), Investigation 4: Cones, Spheres, and Pyramids (93) 7